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Do not deface books by marks and writing. l^lt Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924003873480 "^ RIVER DISCHARGE PREPARED FOR THE USE OF ENGINEERS AND STUDENTS JOHN CLAYTON HOYT M. Am. Soc. C. E. Hydraulic Engineer in charge Division of Surf ace Waters United States Geological Siirvey NATHAN CLIFFORD GROVER M. Am. Soc. C. E. Chief Hydraulic Engineer United States Geological Survey THIRD KDITIOS KEVI8KD AND ENLARGED FOURTH THOUSAND NEW YORK JOHN WILEY & SONS, Inc. London : CHAPiMAN & HALL, Limited 1914. 5 -44rM- Copyright, 1907, 1912, 1914. BY JOHN C. HOYT AND NATHAN C. GROVER. The MoQuefn Press, WAaniNGTON. D. C. j^ PREFACE TO THIRD EDITION. Developments in the application of water to power, irrigation, and other engineering works during the last ten years have been accompanied by such progress in the development of methods for collecting and using data concerning the flow of streams that the art of river-discharge meas- urement has attained a recognized position as a branch of hydraulics. The subject is now included in the regular courses of engineering schools and is admittedly essential to the work of the practicing engineer. The first edition of River Discharge correlated the methods of col- lecting, analyzing, and using stream-flow records as developed at that time; the second edition was revised and expanded to include progress in the art; this new edition has been further expanded to present the latest information on the subject. In the preparation of the book clearness and conciseness have been sought, and lengthy theoretical and mathematical discussions have been avoided in order to adapt the book to the use of both student and engineer. J. C. H. N. C. G. Washington, D. C, August, 1914. PREFACE TO FIRST EDITION. With the rapid increase in the development of the water resources of the United States there has arisen among capitalists and engineers throughout the country a great demand for information in regard to the flow of streams. Although much has been written on the methods of measuring stream flow and the interpretation of the data, such infor- mation is widely scattered through periodicals and Government reports, maiiy of which are out of print and therefore not easily accessible for use by either the student or the engineer. The short descriptions of stream gaging in text-books are indefinite in character, stating only general methods and giving but little information in regard to the details of field work or the conditions requisite for reliable records of river dis- charge. Experience with the graduates of many of the best engineering schools in the country indicates that these men have generally had but little instruction in hydraulic field work or methods, and are practically help- less in attempting to carry on even the simplest hydrologic investigation. Correspondence with engineers in all sections of the country shows that they are not getting the maximum benefit from the available stream- gaging data, apparently on account of lack of understanding of the records. In the preparation of this book there has been brought together from all available sources information in regard to the best practice in this work. Much new matter is also presented, especially the descriptions of the conditions necessary for good gaging stations at which measure- ments of discharge may be made either by weir, current meters, floats, or slope; the routine of the selection, establishment, and maintenance of gaging stations; the details of the field work of discharge measurements, and the office methods of computing the regimen of flow. The authors hope and believe that the information here presented will be valuable both to the student and the engineer. Acknowledgments are here made to the United States Geological Survey, the United States Weather Bureau, and the American Society of Civil Engineers, for use of cuts and other material; also to Messrs. J. C. Stevens, R. H. Bolster, G. M. Wood, F. W. Hanna, and E. C. Murphy for assistance and suggestions. John C. Hoyt. Nathan C. Grover. Washington, D. C, May, 1907. v CONTENTS. Page. Chapter I. — Introduction . . 1 Historical sketch . ... .... 1 Scope of discussion .... ..... '2 Outline of methods o Chapter II. — Instruments and equipment . 5 Instruments for determining velocity . . 5 Floats . . 5 Surface floats . . .5 Subsurface floats ... . . 5 Tube or rod floats . . 6 Current meters . . 6 General features of current meters H Description of the small Price current meter and equipment 9 The head .... 9 The tail . . . 11 The hanger and weights . 12 The recording or indicating device . . .12 The suspending device . . 13 Care of the current meter ... 16 Rating the current meter . . .20 Sounding appliances .... 22 Gages . . 23 Non-recording gages . . . .24 Direct gages . .... 24 Vertical staff' gages . .... . . 24 Inclined staff gages ... ... 25 Indirect gages .... . . 25 Hook gages . . 25 Weight gages . 26 Float gages . . ... 28 Establishment and maintenance of non-recor?'ing gages 28 Installation of gage . ... 28 Checking gage datum 28 Stilling box .... . . 30 Recording gages ... . 30 Continuous record gages . .31 Intermittent record gages . 33 Installation of recording gages 35 Structures for making discharge measurements . . . ... 36 Structure from which measurements are made 36 Bridges ... . 37 VII VIII ■CONTENTS. Chapter II. — Structure from which measurements are made — Continued. Cables The cable Supports ... Anchorage Turnbucltle Car Boats . . . , Stay line cables Lines for indicating measuring points Artificial controls , Instruments for determining climatological data Chapter III. — ^Velocity-area stations . . Selection of site Requisite conditions Conditions pertaining to measurements of flow and stage . Conditions pertaining to computation of flow Conditions pertaining to cost of records Reconnaissance . . ... Establishment and maintenance of stations ... Gages . . . ... Structures for making measurements Controls Description of station Measurement of discharge .... Area of cross-section Soundings Standard cross-sections , Velocity Laws governing velocity . Vertical velocity-curves , Distribution of velocity in the vertical . . Methods of determining mean velocity in a vertical Vertical velocity-curve method Six-tenth-depth method Surface method Two-point method . . . . Three-point method ... Integration method Current meter measurements Procedure Computations Low-water and wading measurements High-water measurements . . Measurements of ice-covered streams Measurements in artificial channels Float measurements Slope measurements Observations of stage Page. 37 37 38 39 39 39 41 42 42 42 43 44 44 44 44 45 46 46 48 48 . 48 49 49 49 50 50 51 51 53 54 55 65 59 60 60 61 61 61 61 64 65 68 69 76 76 77 80 CONTENTS. IX Page. Chapter IV. — Weir stations 82 Sliarp-crested weirs 82 Broad-crested weirs 84 Weir formulas 86 Fundamental formulas 86 Rectangular weirs ... 87 Trapezoidal weirs . . 88 Broad-crested weirs .... . . 89 Computations .... . . 80 Chapter V. — Discussion and use of data . . . . ... 91 Computations of daily flow . . . . 91 Gaging stations with permanent control 91 Area curve . . . .... 92 Mean velocity curve 95 Station rating curve 97 Ordinary cross-section paper with discharge and gage height as coordinates ... 97 Ordinary cross-section paper with discharge and A-^'d as coordinates ... . 101 Logarithmic cross-section paper 103 Eating or discharge table . . . . 104 Application of rating table to gage heights . .... 104 Gaging stations with changeable beds . 109 Periodically changing beds .... . . ... 109 Constantly changing beds . . 109 Stout method . ... 109 Bolster method .... . . 110 Ice-covered streams ... . 113 First method . . . . . 114 Second method . . ... 1J4 Third method 115 Eye method 115 Graphic method ........ 116 Application of graphic method . 118 Computation of other values of discharge and runoff . 120 Units of discharge . . . .... 121 The second-foot 121 Gallons per minute ... , . . 121 Miner's inch 121 Second-feet per square mile 121 Units of runoflf 121 Runoflf in inches 121 Acre-feet . 121 Accuracy of stream-gaging data 122 Determination of duration of flow and horsepower 122 Suggestions for estimating discharge 125 Hydrographs 125 Measurement of drainage areas from maps 125 X CONTENTS. Chaiter V. — Discussion and use of data — Continued. Page. Logaritliraic plotting . . • 129 Where stream-gaging data can be found ... 137 Reports of tiie United States Geological Survey . . 138 Reports of the United States Census . . ... l^S Reports of the United States Weather Bureau . . 138 Reports of the Chief Engineer, United States Army 139 Reports of State officials ... 139 Reports of special commissions 139 Reports of city officials . . ... 139 How to obtain Government publications . ... 1.39 Chapter VI. — Conditions affecting stream flow . 141 Precipitation . . .... . . . 141 Evaporation . . . 150 Temperature . . 152 Geology . . . 153 Topography ... 154 Vegetation .... ... 155 Artificial control . . 156 Tables .... 157 Index .... 179 ILLUSTRATIONS. Page. Plate I. A, Various forms of the Price meter; B, Types of meters experi- mented with by tiie United States Geological Survey . 6 11. A, United States Geological Survey current-meter rating station, Chevy Chase, Md. ; B, Typical gaging station for bridge measurement . 22 III. Recording gagea. A, Stevens; B, Gurley; C, Friez 30 IV. A, Box shelter for recording gage; B, Cable tower and car ... 34 V. A, Typical cable station with automatic gage; B, Typical gaging station for wading measurement . .... . 36 VI. A, Natural control section; B, Artificial control section . 42 VII. Diagram for the Kutter fornmla . . . 80 VIII. A, Precipitation and evaporation station, MadLson, "Wis. ; B, Snow observation station, White Mountains, N. H. 142 IX. Map of United States showing mean annual precipitation . . . 144 X. Map of United States showing mean annual run-ofi' . 150 Fig. 1. Subsurface float . ... . . 6 2. Price current-meter and attachments . ... 10 3. Arrangement of circuit in single wire suspension ... . 16 4. Testing meter circuit . 19 5. Testing meter circuit .... 19 6. Testing meter circuit . . . . . . 19 7. Bating curve for small Price meter . . 21 8. Typical current meter rating curves . ... . 23 9. Simple form of hook gage 26 10. United States Geological Survey weight gage . 27 11. Typical continuous-record gage sheet .32 12. Typical intermittent-record gage sheet . . 34 13. Details of hangers for cable car . 40 14. Distribution of velocity in open channel, Zumbro River at Zumbro Falls, Minn 52 15. Groups of vertical velocity-curves, Chenango River at Binghamton, N. Y 53 16. Typical vertical velocity-curve . 58 17. Cross-section of stream to illustrate discharge measurement compu- tation . . . 65 18. Distribution of velocity under ice cover. Cannon River at Welch, Minn . . . 72 19. Diagram showing factors used in making discharge measurements under ice and form for notes . 75 20. Cippoletti weir with water register in place . . . 83 21. Typical area curves illustrating their form 93 22. Typical area curves illustrating their construction 94 23. Typical rating curve showing low water extension . . . 96 XII ILLUSTRATIONS. 24. Discharge, mean velocity, and area curves, Potomac River at Point of Rocks, Md • ■ ^^ 25. Discharge, mean velocity, and area curves, Ohio River at Wheeling, W. Va 100 26. Rating curve showing discharge as a function of J i/d 27. Typical curves illustrating the Stout and the Bolster methods of computing the daily flow .111 28. Gage height, backwater temperature and precipitation curves. Rainy River, International Falls, Minn • • • ^^' 29. Computation sheet, winter records . .- 11" 30. Hydrograph and curve of duration of flow for 1904, Potomac River at Point of Rocks, Md 123 31. Logarithmic plotting 1-^' 32. Logarithmic plotting l™ .33. Logarithmic plotting 133 34. Logarithmic plotting 134 35. Logarithmic plotting . . 135 36. Logarithmic plotting . ... • • 136 37. Rain gage and support 142 38. Types of weirs referred to in Tables 5, 6, and 7 ] 70 RIVER DISCHARGE. By John C. Hoyt and Nathan C. Ghover CHAPTER I. INTRODUCTION. HISTORICAL SKETCH. Practical acquaintance with and useful application of the general laws of flowing water date from the first century. In A. D. 98 Rome wa^ supplied with water by nine aqueducts having an aggregate length of 250 miles and discharging 27,000,000 cubic feet a day. Yet hydrau- lics was not regarded as a science until about the fourteenth century, and there was little advancement until the seventeenth century, when, , owing to the influence of Galileo, more rapid progress was made. The principal investigations during the seventeenth and the first half of the eighteenth century were made by CastelH (1628), Torricelli (1643), Guglielmini (1700), Pitot (1730), and Bernouilli (1738), and the work done was mainly theoretical. Active experimental hydraulic investigations were begun by Pro- fessor Michelotti in 1764, and from this time the modern school of hydraulics dates. Writings and investigations made prior to 1764 are now of comparatively little importance to the practicing engineer. "^ In 1775 M. Chezy, the celebrated French engineer, developed the formula now known by his name, F = ci/i2s, in which F—. velocity and c = a coefficient combining the effects of roughness of the bed and all other conditions affecting velocity except the slope (s) and hydraulic radius {R) , which equals the area of the cross-section of water divided by the wetted perimeter. This was the first algebraic expression of the law of moving water and has served as the basis of all subsequent slope formulas. »A detailed review of early hydraulic studies is given in " Physics and Hydraulics of the Missis- «ippi," by Humphreys and Abbot. Z KIVEK J)ISC;HARGE. In the United States attention was first given to the flow of water in open channels between 1840 and 1850, in work on the Mississippi River and its tributaries. In 1850 Humphreys and Abbot started their extensive investigations on that river, and in about the same year Charles Ellet used gage heights and a rating curve based on discharge measurements to determine the daily discharge of Ohio River at Wheeling.* In 1855 Francis published the results of his investigations made at Lowell, Mass., in which he developed his formula for flow over weirs. In 1870 Ellis, in his work on the Connecticut River, added much valuable data. It was not until 1888, when the United States Geological Survey began to collect data in regard to the water supply of the country at large, that the general applicability of hydraulic laws was investigated and methods were developed for determining the regimen or the distribution of flow. In starting the hydrographic work of the Survey, Major J. W. Powell, then Director, stated:'' It will be necessary to gage a certain number of representative streams at all seasons of the year, so as to ascertain their total discharge and its seasonal distri- bution, and also to gage a greater number of streams at certain seasons determined to be critical. Starting with this object, the Survey developed methods for um"- versal stream gaging and collected data in regard to the flow of streams in all sections of the United States, which are now extensively used by engineers in enterprises involving the use of water. In all this work the Survey has contended that, inasmuch as the flow of a stream is constantly changing, data of reasonable accuracy showing the dis- tribution of flow over several consecutive years are of more importance than very accurate measurements covering short periods of time. SCOPE OF DISCUSSION. The hydraulic engineer is interested in water from the time it reaches the earth in the form of rain or snow until it returns again to the atmos- phere in the form of an invisible vapor. Of the water which falls upon the earth, a portion immediately returns to the atmosphere; a portion soaks into the earth, reappearing in vegetation or as surface water, or remaining below in small amount as permanent ground water; and another portion stays for a time on the surface of the earth, in streams ponds, lakes, or oceans. A knowledge of the phenomena that pertain to these changes in conditions and of the physical and chemical prop- '*' The Mississippi andOliio rivers, Lippenoott, Urambo & Co.. 1853. b Tenth Ann. Report, U. 8. Qeol. Survey, 1890, p. 8. INTRODUCTION. .3 erties of the water itself constitutes the science of hydrology. Every feature of this great science is of direct value in the economic devel- opment of the country, but probably none is of greater importance than a knowledge of the discharge of surface streams and of the con- ditions that affect its magnitude and variations — knowledge that is prerequisite for preliminary as well as final plans for the construction and successful operation of works utilizing the water in surface streams. Among the hydrologic data necessary either for the design or operation of such works records of daily discharge are the most important. Iso- lated observations of stage or discharge are of little value unless made at stages that are known to be extreme, and even then the record of the duration is equal in importance to that of the magnitude of the flow. This discussion of surface flow is arranged under the following heads : Instruments and equipment. Velocity-area stations. Weir stations. Discussion and use of data. Conditions affecting stream flow. OUTLINE OF METHODS. The discharge of a stream is the quantity of water flowing past a given section in a unit of time and is expressed in various units, among which the second-foot is the most common. This term is an abbrevia- tion for cubic foot per second, which is equivalent to the quantity of water flowing in a stream 1 foot wide, 1 foot deep, at a velocity of 1 foot per second. The determination of the discharge is termed "discharge measurement." The discharge may be obtained as the product of two factors — (1) the area of cross-section, which depends on the shape and dimensions of the bed and banks and on the stage; (2) the velocity, which depends on the surface slope, the roughness of the bed and banks, the hydraulic radius, and the conditions along the channel of the stream. In general these factors are controlled by the stage. Therefore the dis- charge may be considered as a function of the stage. By means of this general law it is possible, from discharge measure- ments covering the range of stage, to construct a rating curve and table from which, the main daily stage of the stream being known, the daily discharge can be taken. Points at which discharge measurements are made and records of the daily fluctuations of stage are kept for deter- mining the daily flow are termed "gaging stations." These stations may be grouped in two classes, one comprising those where measure- 4 RIVER DISCHARGE. ments are made by the velocity-area method, which consists in measuring the velocity of the current and the area of the cross-section ; the other comprising those where measurements are made by the weir method, in which the discharge is obtained by measuring the head on a weir and using a weir formula. The selection of a gaging station, the equipment, and the method to be used in determining the discharge depend on many factors and are accomplished in various ways. Among the principal factors are the use for which the records are to be collected, the funds available, the period of time over which the observations are to be extended, and the condi- tions of the stream to be measured, as explained in the following pages. CHAPTER II. INSTRUMENTS AND EQUIPMENT. The establishment and maintenance of gaging stations for obtaining records of discharge of rivers and other hydrologic data require the use of certain instruments and equipment. These may consist of: 1. Instruments for determining the velocity and other factors of the discharge measurement. 2. Gages and bench marks for determining stage relative to a fixed datum. 3. Structures from which discharge measurements are made and the appurtenances thereto. 4. Structures to produce artificial control and regulate the relation between stage and discharge. 5. Instruments for determining climatological data. INSTRUMENTS FOR DETERMINING VELOCITY. Two principal types of instruments are used for measuring the velocity of flowing water — floats, which measure the velocity directly, and cur- rent meters, by which the velocity is obtained indirectly from observa- tions of the number of revolutions of the wheel. Another instrument sometimes used for measuring velocity is the Pitot tube, but it is not practicable to use this tube for the work discussed in this book. FLOATS. Floats are utilized for the direct measurement of the velocity of streams. Those in common use are surface, subsurface, and tube or rod floats. Surface floats. — A corked bottle with a flag in the top and a weight in the bottom makes a very satisfactory surface float, as it is but little affected by the wind. In flood measurements good results can be obtained by observing the velocity of debris or of floating cakes of ice. In all surface-float measurements coefficients must be used to reduce observed velocities to the mean velocity. Subsurface floats.— The subsurface float (Fig. 1) is designed to measure velocities below the surface and may be made to float at any depth. By 5 6 RIVER DISCHARGE. arranging the submerged float at the depth of mean velocity it may be utilized in observing mean velocity directly. Allowance must be made, however, for the accelerating effect of the attached line and surface float. Tube or rod floats. — The tube or rod float is designed also to measure directly the mean velocity in a ver- tical. It is generally a cylinder of tin, about 2| inches in diameter, weighted at its lower end and plugged with wood or cork at its top. Small extra weight to make it float at the exact depth desired may readily be added by admitting water or by putting in shot. The tube should be graduated, and alternate feet painted black and red in order that the depth of flotation may be readily observed. A number of tubes of different lengths are necessary for measuring the velocity at different depths in an ordinary cross-section. A float of this type is consequently best adapted for use in artificial channels, in which the depth is nearly uniform, as natural charmels are generally too rough and too variable to permit its satisfactory use. Although designed to measure directly the mean velocity in a vertical, the tube can not be made to float in contact with the bed of the stream, and consequently it does not receive the effect of the slowest moving water. The rougher the bed the greater the error in this respect. A factor less than unity is therefore necessary to reduce the observed velocity to the mean. Fig. 1.— Subsurface Float. CURRENT METERS. A current meter for measuring the velocity of flowing water comprises two essential parts: (a) a wheel arranged so that when suspended in flow- ing water the pressure of the water against it causes it to revolve; (6) a device for recording or indicating the number of revolutions of this wheel. The relation between the velocity of the moving water and the revolu- tions of the wheel is determined by rating each meter. The earliest type of meter was the float wheel, which was used by Borda "Tranaactioiis American Society of Civil Engineers. Paper No. 1138. Vol. LXVI, page 70 (1910). Plate I. A. VARIOUS FORMS OF THE PRICE METER. B. TYPES OF METERS EXPERIMENTED WITH BY UNITED STATES GEOLOGICAL SURVEY. INSTEUMENTS AND EQUIPMENT. 7 and Dupuit in the latter part of the eighteenth century, and was prac- ticable only for measuring velocities at the surface. About 1790, Woltmann modified this wheel so that it could be used beneath the sur- face, the number of revolutions being recorded by a gear mechanism, which was started and stopped at the beginning and end of a run by a catch operated by a cord. It was necessary, however, to lift the meter out of the water in order to read it. LaPointe arranged the recording apparatus above the surface by connecting the axle with a vertical rod and beveled gear. Baumgarten, Saxton, Brewster, Laignel, and others made various modifications of the instrument. Prior to the invention of an electric device for recording or indicating the number of revolutions of the wheel, the meter was of limited use because of its lack of adapta- bility to varying conditions and because of difficulties with the operation of the recording mechanism. In America current meters were earliest used in connection with the investigations of the Mississippi, started in 1850 by Humphreys and Abbot," in which the ship's log and the Saxton meter were used to a small extent and with little success. About 1860, the late D. Farrand Henry, M. Am. Soc. C. E., Assistant, United States Lake Survey, invented for use with the current meter an electrical recorder," which eliminated the serious difficulties peculiar to the mechanical recorder, and made feasible the further development of the meter. The first extended and successful series of measurements with the current meter in the United States was made on Connecticut River by the late T. G. Ellis, M. Am. Soc. C. E., in connection with studies begun in 1871.° General Ellis started his work with the Woltmann meter, equipped with an electrical recording device, but later used an electrical recording meter devised by himself. The results obtained by these measurements have had an important effect on the development of stream-gaging instruments. The earliest American patents for current meters were taken out in 1851. There are now on file in the Patent Office, classified under ship's logs, more than fifty patents for devices for measuring the velocity of water. Many unpatented devices haVe also been constructed. The only meters which have had much general use, however, are those devised by Price, Haskell, Fteley, and Ellis or modifications of these types (PI. I, B, Nos. 3-2-4 and 1). Each of the various meters has first been developed to meet the require- * Report upon the Physics and Hydraulics of the Mississippi River, 1861. ''Journal of the rranklin Institute. Vol. XCII, 1S71. 'Report, Chief of Engineers, D. S. Army, 1878, Part I. 8 RIVER DISCHARGE. ments of some special condition, and, until recently, the use of all has been confined to special hydrologic investigations in connection with some public work, municipal. State, or Federal. The present widespread interest in the value and use of water has created such a demand for records of the discharge of streams that the current meter is now in general use, and has become an essential part of the equipment of every engineer engaged in hydraulic work. In 1888 the United States Geological Survey began the gaging of streams of all sizes and in all sections of the country. These streams pre- sented an infinite variety in combination of range in depth, width, and velocity. No adequate meter or methods had been developed for work of this varied nature. Furthermore, elaborate equipment and methods were out of question on account of the limited funds. It was necessary to devise or adapt a current meter which could be readily carried in the field and operated by one man, either from a bridge, boat, cable and car, or by wading. After experimenting with various types (PL I, B) the engineers of the Survey developed a meter combining certain essential features of the Price acoustic and the large Price electric meter" (PI. I, A, Nos. 1 and 2.) This is known as the small Price meter, and has since been in general use in the Survey work. Modifications in its construction have been made from time to time until now it represents the ideas of many engineers, resulting from the experience of more than twenty years in stream gaging. The methods developed by the Survey engineers are also believed to represent the best practice in this line of work. The Survey's data are now used extensively in all hydraulic development in the United States. Its methods have been accepted as standard in this country and have been adopted in similar work by many engineers in all parts of the world. GENERAL PEATtJHES OF CURRENT METERS. Current meters may be divided into two general classes: direct action and differential action, the division depending on whether the water, in revolving the wheel, does or does not exert a force which tends to retard the motion of the wheel. The wheel of the direct-action meter consists of flat or warped-surface vanes set on a horizontal axis, which are caused to revolve by the direct pressure of the water against them. Each vane receives the water pres- sure in the same way as all of the others. The principal types of direct- action meters are the Haskell and Fteley (PI. I, B, Nos. 2 and 4). The wheel of the differential meter consists of a vertical axis carrying a series of cups which are revolved by the water pressure on the concave * Manufactured and sold by W. & L. E. Ourloy, Troy, N. Y, INSTRUMENTS AND EQUIPMENT. 9 side of the cups and are retarded by the lesser pressure on the convex side. The principal types of differential meters are the Price and the Ellis (PI. I, B, Nos. 3 and 1). The essentials for a good current meter are : (a) simplicity and lightness of construction, with no delicate parts which easily get out of order ; (b) sim- phcity in operation, including its preparation for use under any conditions, and its dismantling, cleaning, and boxing after use; (c) a small area of resistance to the action of the water; (d) a simple and effective device for indicating the number of revolutions of the wheel; and (e) adaptability for use under all conditions. The small Price meter is the only one fully described herein. The dis- cussion on the care and use of current meters is, however, generally applicable to any type. DESCRIPTION OF THE SMALL PRICE CURRENT METER AND EQUIPMENT. The small Price current meter and equipment consists of five principal parts: (1) the head; (2) the tail; (3) the hanger and weights; (4) the recording or indicating device ; and (5) the suspending device. In the fol- lowing descriptions the numbers in parentheses refer to figure 2. The Head. — The head consists of a 3-shaped yoke (1) carrying a wheel made of six conical cups (2) , brazed to a horizontal frame (3) . This wheel, referred to as the cups, turns in a counter clockwise direction on a vertical axis known as the cup shaft, which rests and revolves on a cone point bearing at the lower end and engages the recording mechanism at the upper end. The cup shaft consists of two parts (4, 5), screwed together from either side of the cup frame, thus fastening the cups rigidly to the cup shaft. At the lower part of the cup shaft there is a cone bearing which receives the cone point (6) on which the cups revolve. The cone point is screwed through a metal bushing (7) known as the cone plug, and is firmly held by a lock-nut (8). The cone plug fits into the lower arm of the yoke by a sliding connection, and is clamped in posi- tion by a set-screw. By means of a sleeve-nut (9) on the lower part of the shaft, the cups can be lifted from the cone point when the meter is not in use. This sleeve-nut has a left-handed thread, so that it will not tighten when the cups revolve. The upper part of the cup shaft is fitted with either a worm gear or a,n eccentric which passes into a cylindrical chamber (10), known as the con- tact chamber, as it contains the mechanism for making the contact which indicates the revolutions of the cups. The construction and arrange- ment of both the contact chamber and the mechanism contained in it 10 RIVER DISCHARGE. Kii.. '.'.— Frieo I'lirront Motor and Attachments. INSTRUMENTS AND EQUIPMENT. 11 depend on whether the indicating device is penta-count electric, single- count electric or acoustic. When the penta-count electric indicating device is used, the contact chamber (10) which is closed by a screw cap (11) provided with a leather gasket for keeping out the water, fits by a sliding connection into the upper end of the yoke, and is clamped into position by a set-screw. In the contact chamber there is fitted a cylindrical plug (12) which is held in position by a screw and carries a gear-wheel (13) which engages the worm gear on the upper end of the cup shaft, the gearing being arranged so that the wheel makes one revolution for every twenty revolutions of the cups. On the side of the wheel there are four platinum pins, equally spaced and set so that they will strike the contact spring (14) at each fifth revolution of the cups, thus closing the electric circuit to the indicating device, as explained later. These contact parts are known as the contact wheel, the contact pins, and the contact spring. The contact spring is of platinum, and is carried by the contact plug (15) which is screwed into the contact chamber through a hard-rubber bushing (16), thus insulating the contact spring from the meter when it is not touching one of the pins on the contact wheel. In the end of the contact plug there is a hole and a set-screw for connecting with a wire from the indicating device. When the single-count electric indicating device is used, the contact chamber (10a) and appurtenances are the same as described for the penta-count contact chamber with the exception that the gear wheel (13) is omitted and the worm gear on the upper part of the shaft (4) is replaced by the eccentric (4a) which strikes the contact spring (14a) at each revolution, thus closing the electric circuit to the indicating device. The penta- and single-count contact chambers are interchangeable. When the acoustic indicating device is used, the contact chamber (10b) is closed with a cap (lib) fitted with a metal drum (49), and, in place of the platinum contact spring (14) and plug (16), there is a small hammer (50) which is caused by the pins on the side of the gear-wheel (13a) to strike the drum at each fifth revolution of the cups. In order to keep the water from deadening the sound by rising into the contact chamber (10b), it is raised about four inches above the yoke (la) by inserting the tube (59) and lengthening the upper part of the shaft (4a). When the electric indicating device is used, the yoke is equipped with a stem which contains a slot and a screw hole (22) for attaching the meter hanger (23), and a socket into which the tail of the meter (17) is fastened. When the acoustic indicating device is used, this stem is omitted and the meter is supported on a rod (51) attached to the con- tact chamber. The Tail. — The tail is used when the meter is suspended by a cable, or 12 RIVER DISCHARGE. on a sliding hanger rod. It provides for balancing the head, and also keeps the axis of the meter parallel to the direction of the current. It consists of a stem (17) which fits by a sliding connection into a socket in the stem of the yoke where it is clamped by a set-screw. On this stem there are two vanes (18 and 19) set at right angles. One of the vanes is rigidly atuached to the stem; the other fits into it by grooves, so that it can readily be pulled out when the key (20) which holds it in place is turned. On one of the vanes there is a slot carrying a weight (21) which can be so adjusted as to balance the meter. The Hanger and Weights. — When suspended by a cable, the meter is hung by a screw-bolt (22) on a steel stem (23) which passes through a slot in the stem of the yoke. The slot in the stem of the yoke is wide enough to allow the meter to swing freely in a vertical plane, and the bolt passes through the frame a little above the center of gravity of the meter, so that the latter will readily adjust itself to a horizontal position. In the upper end of the hanger there is a hole for attaching the suspending cable, and at intervals along the stem there are other holes by which the meter and lead weights may be hung. The weights (24) are of torpedo shape — this design offering the least resistance to the current — and are made in two sizes, weighing, respectively, 10 and 15 pounds. They are attached to the stem by a screw bolt. The manner of arrangement of the weights and meter on the stem depends on the conditions under which the measurements are to be made. When the meter is used on a rod, the hanger, weights, and usually the tail are dispensed with. The set-screws for clamping the various sliding connections are all of the same size and are of standard make. Beveled grooves are provided in each of these connections so that when the set-screws engage them the parts are drawn into place. All parts of the meter are standard, and can readily be replaced in the field. The Recording or Indicating Device. — A recording or indicating device is necessary for determining the number of revolutions of the meter wheel, and the successful use of the meter depends largely on this part of the apparatus. Various devices, operated either on the meclianical, electric, or acoustic principle, have been used for this purpose. These include the teloKraph ticker, automalio recorder, electric buzzer, telephone receiver, drums, etc. Of these, however, tlie telephone attachment and the acous- tic indicator have been found to be most satisfactory in general practice. The telephone attachment consists of a telephone receiver (25) and small battery (26) placed in a partial circuit which terminates in a con- INSTRUMENTS AND EQUIPMENT. 13 necting plug (27) by means of which the apparatus can be readily con- nected in circuit with the meter. The magnets of the telephone receiver are wound for'10-ohm resistance so as to secure a loud click. Either a dry-cell or a wet-cell battery may be used. The most satis- factory dry cell (26) which has been tested is the No. 409, "Ever Ready" cell, which is 1 inch in diameter and 3 inches long. This cell is equipped with two screw connecting posts (28), both at the same end. The wet cell in common use consists of an outer casing of hard rubber (29), about 1| inches square, containing a carbon compartment (30) into which a zinc pole (31) having a rubber stopper (32) is inserted. The cur- rent is generated by means of a solution of bisulphate of mercury and water. Contact is made with the cell through a platinum plug (33) extending into the carbon at the bottom and through the screw (34) in the zinc pole which extends through the rubber stopper. The cell is encased in a leather box (35), and connection is made with it through two screw connecting posts (36), each of which terminates in a separate spring plate (37) against which the poles of the battery bear. In use, the telephone receiver is pinned to the shoulder (PI. II, B) and the battery cell is placed in the side coat pocket. The connecting plug (27) will then hang a httle below the shoulder and is easily accessible for attaching and detaching the meter. In the acoustic indicator, the striking of the hammer (50) on the drum (49) in the contact chamber (10b) indicates each fifth or tenth revolu- tion of the meter, as already explained. The sound is transmitted through the rods (51) and a rubber tube to the ear of the operator. The rubber tube and ear-piece are not necessary unless there is considerable noise. Automatic recorders have been used to some extent, but for general work have not been found to be satisfactory, because they are likely to get out of order. They frequently require an assistant to operate them and make the outfit more cumbersome. Furthermore, a sounding device which requires the operator to count the revolutions of the meter is always safer and more satisfactory than either a mechanical or electric self-counting device or recorder, because the operator will at once detect any irregularities caused by trouble with the meter, battery, electric cir- cuit, or other part of the equipment. A stop-watch is essential to the proper observation of time. The Suspending Device. — The suspending device, which consists of a rod or of some form of cable, must make provision for lowering the meter and weight into the water and also for completing an electric circuit between the contact chamber of the meter and the recording device. 14 RIVER DISCHARGE. The rod in common use in connection with the electric recorder con- sists of a §-inch tube (55) graduated to feet and tenths. For convenience in carrying, it is made in 1.0 or 1.5-foot sections fitted with screw threads. Two methods of hanging the meter on the rod are in use. By the first the head and tail of the meter are attached to a sliding hanger (54), which can be moved up and down the rod or clamped in any position. On the bottom of the rod there is a flat foot (53) which keeps it from sinking into the bed of the stream, and at the top there is a plug (56) for connecting one of the wires from the recording device. The circuit between the meter wheel and the recording device is made by attaching one of the wires from the recording device to the plug in the top of the rod. The other wire follows down the rod and is attached to the contact plug of the meter. In the second method the rod (58) is connected by the screw socket (57) in the yoke. The rods (51) for use with the acoustic indicator are of |-inch tubing ^aduated to feet and tenths, and, for convenience in carrying, are made in l.Oor 1.5-foot sections which screw together. The bottom rod connects with the contact chamber (49) by a screw, and is cut so that the distance from the center of the cups to the end of the rod is just 1.0 foot. On the upper end of the top rod there is a flat plate (52), in the center of which there is a hole through which the sound from the drum can be heard. The soundings are made with this end of the rod, and the plate keeps the end from sinking into the bed of the stream. The best form of cable in use is a combination of No. 16, "old code, double-insulated, show-window cord" (38) and No. 12 or 14 galvanized wire (39) about which is wound a small insulated wire (40). The show- window cord is used for the upper part of the cable. It is large enough to be manipulated easily with bare hands, and, being made of two insulated wires, provides for making a circuit between the meter and the recording device. In its use, the two wires of which it is made must be separated at either end (41, 42, 43, 44) in order to make the attachment with the con- necting plug (27) of the indicating device at the upper end and with the galvanized wire (39) and small wire (40) which lead to the meter at the lower end. A ring or snap (45), into which the galvanized wire is looped, is fasten(;d, either by a loop (46) or a knot (47) to the lower end of the show-window cord. In fastening the meter cable to the snap or ring with a knot (47), a strip of adhesive tape is wound around the cable two or three times, about 1 foot from the end, leaving about 6 inches of the tape at the beginning and end of the winding. The cable is then inserted through the snap or ring so that the snap bears on the adhesive tape, and a knot is tied in the INSTRUMENTS AND EQUIPMENT. 15 cable about the snap (45) and drawn down as tight as possible. The ends of the adhesive tape (48) are then wound around the cable, one above and the other below the knot, to keep it from sliding. The outside covering of the end of the cable can then be taken off to within 3 or 4 inches of the knot, exposing the ends of the two insulated wires (41, 42) which may then be fastened to the wires (39, 40) leading to the contact plug and to the hanger. If the snap is held in a loop (46), a length of about 12 or 14 inches of the outside insulation is removed so that the wires can be doubled back and connected with those leading to the contact plug and hanger. The loop is first tied with string and then wound with adhesive tape, the tape being placed also around the cable where the ring bears on it. The galvanized and small wires (39 and 40), which make up the lower end of the cable, should be long enough to reach from the surface to the bottom at the deepest point in the stream. Their use is advantageous because they offer small resistance to the moving water and thus reduce the distance that the meter is carried down stream. The galvanized wire (39) provides both for carrying the weight of the meter and for one side of the circuit between the meter and the recording device. It is attached by ordinary loop connections to the snap in the lower end of the show-window cord and to the meter hanger (23). The circuit is made through it by the direct connection with the meter stem and by its connection at the upper end with one of the insulated wires (41) from the show-window cord. The small wire (40), which provides for the other side of the circuit between the meter and the recording device, should be wound loosely around the galvanized wire in order to prevent annoying motion and wear, and may, if the water is swift, be held more securely if fastened with tire tape. At the upper end it is connected with one of the insulated wires (42) from the show-window cord, and at the lower end with the contact plug (15) of the meter. In order to aid in preserving the insulation between the galvanized and small wires they may be shellacked. If the velocities or depths are not so great as to carry the meter down stream, the galvanized and small wires may be dispensed with. The snap (45) at the lower end of the show-window cord would then be attached directly to the meter stem and the circuit completed by attach- ing the insulated wires (41, 42) to the contact plug at one end and to the screw of the meter hanger at the other. The meter may also be suspended by a single uninsulated galvanized wire, the circuit being completed through the water and ground (Fig. 3). In using the single wire the connection is from the water to the meter w 16 RIVER DISCHARGE. through the contact point to the Hne, then to the battery and through the telephone to the bridge or cable, then to the ground and back to the water. It makes no difference on which side of B ^^ the battery the telephone is placed in ' ''' ^r ^ the line. ~"\ When using a single wire, a clean Thisconncouonmuat i metallic coutact must be made be- be insulated. .' r — ■ — \ y tween it and the bridge or cable from ^^''' which the observations are taken. A --''' little paint, rust, or other coating will Fig. 8.— Arrangement of Circuit in Single J. . . Wire Suspension. prevent eihcient work. In measuring high velocities and deep streams, stay-lines or guy-lines are used in addition to the sus- pending cable to keep the meter in place. CARE OF THE CURRENT METER. The equipped current meter consists of : (a) Meter itself. (6) Telephone or other indicating device. (c) Battery. (d) Connecting wires. (e) Connecting plug. (/) Cable for supporting the meter. {g) Insulated wires for completing the circuit. (/i) Weights. (i) Hangers. (j) Hanger screws. (A;) Stop-watch. (Z) Rods for wading measurement. (m) Rods or lines for sounding. Aside from this equipment, the engineer, when on a field trip, should always be supplied with the following articles which are frequently neces- sary or desirable for making repairs to the station equipment and for the ordinary operation and care of the current meter. (a) Small screw-driver. (6) Parallel pliers with wire cutter. (c) Spanner wrench for dismantling meter. (d) Can of oil. (e) Roll of adhesive tire tape. (/) 25-foot metallic tape. INSTRUMENTS AND EQUIPMENT. 17 (g) 50-foot steel tape. (h) Extra cone point. (i) Extra set of screws. (j) Small hatchet. (k) Extra battery. (l) Insulated wire. (m) Assortment of nails. For carrying the meter and equipment two types of cases are in general use. One is a box SJ by 6| by 5 inches, arranged with a shoulder strap and just large enough to carry the meter and tail when taken apart, the weights, cable, and other equipment being carried in a separate case. The other is a box 17 by 12 by 6 inches, with a lower and upper compart- ment, the lower being designed to carry the weights, cable, and heavier tools, and the upper to carry the meter and more delicate parts of the equipment. A partition in the upper compartment provides a space into which the head is fitted and carefully packed so as to avoid injury. This case is shaped like a small suitcase and arranged with a carrying strap. When an additional case is needed for the equipment, the canvas hand- bag, used by masons for carrying tools, is most convenient. In taking the meter apart, remove, the tail vanes and the hanger stem; then loosen the set-screw to the contact chamber, and pull the chamber out by a slight twisting motion. Care must be taken to let the cups be free to turn, so that the worm gear on the upper end of the shaft can dis- engage from the teeth of the contact wheel. In handling the contact chamber, it is well to take off the cap, so that the gear-wheel can be seen during the operation. The cone point can then be taken out and the cups released by loosening the upper part of the shaft with a spanner wrench. This wrench is so arranged that it can be used for loosening all parts of the meter. In putting the meter together, first attach the cups to the cup shaft. In doing this, the upper part of the shaft should be inserted through the upper hole of the yoke before it is screwed to the lower part. Care must be taken to place the cups so that they will move counter-clockwise. After the cups have been fastened to the shaft, insert the cone point and clamp it in place, and then insert the contact chamber. In replacing the contact chamber, the cups should be left free to move on the cone point and care should be taken not to allow the cogs on the worm gear to catch on the teeth of the contact wheel. Before inserting the cone plug, the cone point should be adjusted and firmly secured with a lock-nut. The adjustment should allow a slight vertical motion of the cups. Although the current meter is substantially made and will stand con- 18 RIVER DISCHARGE. siderable hard usage, it needs special attention and care to insure its proper working. In this connection the following instructions should be carefully observed : 1. Be sure that the set-screws are all tightened before putting the meter in the water; otherwise one of the parts may be lost. 2. Loosen the sleeve-nut and see that the meter runs freely before beginning a measurement; and spin the meter cups occasionally during a measurement to see that they are running freely, that is, that they will continue to move for a considerable time at a slow velocity. 3. See that the weights play freely on the stem, so as to take the direc- tion of the current and thus avoid an unnecessary drag on the line. 4. If any apparent inconsistency in the results of an observation throws doubt on its accuracy, investigate the cause at once. Grass may be wound around the cup shaft; the cups may be tilted by tension on the contact- wire; the channel may be obstructed immediately above the meter; the meter may be in a hole; or the cups may be bent so as to come in conta;ct with the yoke. 5. After a measurement, clean and oil the bearings (in order to pre- vent rust) and inspect the cone point. 6. In packing the meter, turn the sleeve-nut to lift the cups from the cone point. 7. Always see that the lock-nut on the cone point is screwed firmly against the cone plug. 8. If the cone point is dulled, it can be sharpened with an oilstone. 9. In measuring low velocities, be sure that the meter is in a horizontal position. If it has a tendency to tip, the balance weight on the tail should be adjusted or the meter be held rigidly by inserting a plug in the slot against the stem. 10. Avoid taking measurements in velocities of less than 0.5 foot per second, because the accuracy of the meter diminishes as zero velocity is approached. 11. For velocities of less than 1 foot per second the bearing point should be the same as at the time of rating. As the velocity increases, the condition of the point is less important, because the friction factor decreases. 12. In taking measurements at high velocities, sufficient weight, and a stay-line, should be used to hold the meter in the vertical. 13. In very shallow streams the meter should be suspended from the lower hole on the stem, and the weight should be placed above. 14. If the cups of a small Price meter are bent, they may be easily put in shape by pressing them with a piece of wood or metal with a round, smooth end. INSTRUMENTS AND EQUIPMENT. 19 15. The telephone receiver is very sensitive to electric currents, and can be used to locate any break in the circuit. First try the telephone and battery together (Fig. 4) in a circuit having a make-and-break point, as at a. This may be done by using a knife blade or a screw-driver, mak- ing connection where the wires enter the plug. If there is no cUck in the telephone, then the battery or the telephone does not make a circuit. If there is a click, insert the. meter in the line and test for a contact in the meter head (Fig. 5) by revolving the meter wheel. If the meter is all right, put the meter cord in the circuit and test both sides by making double connection and touching alternate sides of the line, a (Fig. 6). 16. When the meter is not in use, discormect the meter line from the battery, so that it will not become exhausted. 17. When a wet cell is used, the solution may be left in it for a time, if the zinc pole and stopper are replaced by a cork. 18. Never let the bisulphate dry, however, in the cell, as it forms a hard cake and polarizes the battery. 19. Do not let any bisulphate of mercury remain loose in the meter box; if it gets into the meter bear- ings it will corrode them. ^ ^ 20. The zinc pole in the bisul- ^ — 1 1 '- phate cell sometimes gets pushed down so that it touches the bot- ^^ -X- tom of the cell, in which case the ^°- *• cell is short-circuited and becomes useless. To test this, lift the plug a little way out of the bat- tery and see if there is a flow of current. 21. Keep the points clean where the battery makes contact with the metal plates. Fia. 5. 22. The amount of current necessary to work a telephone receiver is very small, and a bat- tery may be serviceable even though nearly exhausted. 23. If care is taken, it is very improbable that the telephone re- ceiver will get out of order. 24. Do not strike the tele- Testing Meter circuit. phone receiver, as a heavy jar will to a greater or less extent damagnetize the pole pieces, and to that extent will injure the receiver. .« ^ Fig. 6. 20 RIVER DISCHARGE. 25. Care must be taken not to short-circuit the dry battery when the meter is not in use, as in that way the cell becomes exhausted in a short time, the energy being used in heating the cell. To avoid this, the poles may be wound with adhesive tape. 26. If a dry cell which has been long in stock fails to work well, punch two nail holes in the wax on top of the cell and put it in water over night, when it may absorb enough moisture to renew it. The holes should then be coated over by heating the wax with a match and pressing it into place, or by pouring in melted paraffin. A cell which has been exhausted by use is not benefited much by this treatment. The life of a cell depends largely on the amount of leakage in the line during use. BATING THE CURRENT METER. The relation between the revolutions of the meter wheel and the velocity of the water must be determined by rating each meter before it is used. Theoretically, the rating for all meters of the same make should be the same, but, as a result of slight variations in construction, and in the bearing of the wheel on the axis at different velocities, the ratings differ. Observations for rativg meter No. S15, made February 19, 191£, at Chery Chase Lake, Maryland, by W. McC. and M. I. W. Method of suspension. Cable ; meter last rated at Chevy Chase Lake, May W, 1909 ; present condition good, in repair. No. Observations for length of run. Time in No. of revolu- Revolu- Velocity seconds. run. Start. End. Distance. tions. second. second. Feet. Fed. Feet. 1 30.3 54.0 23.7 42 10 .238 .502 2 60.5 26.5 24.0 43 10 .233 .558 3 28.4 51.7 23.3 27 10 .371 .S(B 4 43.8 20.0 23.2 2(1 10 .385 .892 •5 24.5 70.8 4(1.3 34 20 ..588 1.3,57 6 (13,9 18.1 45.8 30 20 .007 1.527 7 20.3 (1(1.2 45.9 20 20 1.000 2.295 8 ()L'.4 10.9 45.5 20 20 1.000 2.275 9 2I.G 112.9 91.3 24 40 1.67 3.80 i:i 117. !» 27.5 90.4 23 40 1.74 3.93 11 21.(1 1 13.0 91.4 25 40 1.00 3.66 12 119.1 29.1 90.0 27 40 1.48 3.33 13 22.5 113.5 91.0 17.4 40 2.30 5.23 .1 I 119.2 28.7 90.5 17.0 40 2.35 5.32 1.5 23.7 114.7 91.0 14.0 40 2.74 6.23 10 125.3 35.0 90.3 15.0 40 2.07 6.02 Note. — The runs are in pairs, the odd nuinbora being across the track and the even numbers in the return to the startln)? intint. INSTRUMENTS AND EQUIPMENT. 21 Revolutions per second Revolutions per second 22 EIVER DISCHARGE. A meter is rated by conducting it through still water with uniform speed (PL II, A) and noting the time, the number of revolutions, and the distance. The revolutions per second and the velocity in feet per second are afterward computed from these data. Many runs are made, as shown in the preceding table, the speeds varying from the least which will cause the wheel to revolve to several feet per second. The results of these runs, when plotted (Fig. 7) with revolutions per second and velocity in feet per second as co-ordinates, locate the points which define the meter rating curve, in general a straight line from which the rating table is prepared. In making the run for the rating the time and distance corresponding to a given number of complete revolutions are recorded automatically by electric devices which are operated by the closing of the circuit in the contact head of the meter. Theoretically, the wheel of a differential-action meter, when carried through still water, should revolve as a wheel revolves in passing over the ground. That is, in going a given distance it should make practi- cally the same number of revolutions, regardless of speed. The rating of a great many small Price electric meters shows this number to be from 42 to 44 revolutions in going 100 ft. Standard current meter rating tables are usually furnished by the makers of meters and when the meters are used under the same condi- tions under which ratings were made, the tables will usually give results within 1 or 2 per cent of the individual rating table for the meter in ques- tion. Special ratings for individual meters can be obtained, for a nom- inal fee, from the United States Bureau of Standards, which maintains a fully equipped rating station at Washington, D. C. The relative ratings of various types of current meters are shown in Fig. 8. SOUNDING APPLIANCES. The most common sounding appliances in general use are rods and weight and line. Rods are limited in use to depths of less than 15 feet. If over 5 feet long, they should be round in order to be easily handled and may be made either of gas-pipe or of wood. Rods under 5 feet in length should be made of flat strips of wood 3 inches by J inch with one face cut to a knife edge, against which the water will not rise in swift velocities. The grad- uations should be as close as the desired accuracy of soundings and so marked as to be easily road. In order to avoid sinking into the bed of the stream, the bottom of the rod should be protected by a shoe 3 inches or more in diameter. Plate M. A. UNITED STATES GEOLOGICAL SURVEY CURRENT-METER RATING STATION, CHEVY CHASE, MD. B. TYPICAL GAGING STATION FOR BRIDGE MEASUREMENT. INSTRUMENTS AND EQUIPMENT. 23 Weights and lines of many forms are in use and are manipulated either directly by hand or by means of a sounding-reel in case of very deep soundings. The line should be of some material which does not shrink or stretch on wetting. For reels piano or sash-weight wire is generally used. The best form of hand line for use at bridges is a combination of the show- window cord used for supporting the meter, which can be easily grasped with the hands, for the upper part, and No. 12 or 14 galvanized wire, which offers but little resistance to the current, for the lower part. 9A as Oa 7.S 7.0 &5 6,0 5.5 5.0 4.5 4.0 3.5 3.0 Z.S Z.0 1.5 1.0 Votocity in fe&t per second FiG. 8. — Typical Current Meter Rating Curves. The shajpe of the weight should be such as to offer small resistance to the water, and the amount of weight required will depend on the depth and velocity of the current. The Una with meter and weight attached frequently is used in making soundings. GAGES. The gage is the instrument, graduated scale or other device, whereby the stage and changes in stage are observed or recorded. This fluctua- tion is measured with reference to a fixed datum which must be referred 24 KIVER DISCHARGE. to one Ol more permanent bench marks, and to which the position of the gage must maintain a constant relation. The accuracy of all records of discharge is absolutely dependent on the maintenance of this relation. In coimection with all gage height records, special care should be taken to keep a full history of each and every condition which may affect the gage records or their interpretation. These should include full notes of all matters which pertain to the gage and its installation, such as repairs and changes in datum or location, and also a history of all conditions which may affect the gage readings, such as changes in the channel or the construction of dams or other works in the vicinity. The value of most series of gage height records increases with their length, and many long-time records have been rendered practically value- less on account of insufficient data to make possible their proper inter- pretation. The many styles of gages in use all belong to two classes, non-recording and recording. NON-RECORDING GAGES. The various forms of non-recording gages may be grouped into (1) direct gages, consisting of fixed, graduated staffs or scale boards on which the water rises and the stage is observed directly, and (2) indirect gages, consisting of graduated scale boards located above the water surface, to which the index of the stage of the water is transferred b3'' means of a movable chain or rod of known length operated either automatically by means of a float and counterweight or by the observer whenever a record is desired. DIRECT GAGES. Direct gages consist of Gxed staffs which may be either vertical or inclined. If a gage of this type can be established and properly main- tained, it is doubtless the most satisfactory non-recording gage that can be used. The requirements for a satisfactory gage of this class are (1) that the graduations be both clear and permanent; (2) that the gage be easily accessible to read; and (3) that it be stable. It has the advantage of certainty in datum so long as the gage is undisturbed, small first cost, and simplicity in reading, but the disadvantage of being liable to dis- turbance or destruction by frost action or by floating ice, logs, or drift. Vertical staff gages. — The vortical staff is better than the inclined, when there is available, either in or over the water, an artificial or natural object having a vertical face to which the gage may be attached. Such object may be a bridge abutment or pier, a wharf, a tree, or a rock. The best form of vertical gage consists of a base of rough 2-inch by 4- INSTRUMENTS AND EQUIPMENT. 25 inch or 2-inch by 6-inch planlc, to which a lighter plank having the gradu- ated face may be easily fitted and nailed, with the zero at the desired elevation. The graduated plank will be found satisfactory if made in about 5-foot sections of |-inch by 5-inch pine, painted white, with gradu- ations cut as V-shaped notches painted black. This facing and gradua- tion is cheaply made, the graduations are reasonably permanent, the sections are convenient to carry and are easily installed. Inclined staff gages. — The inclined staff is useful where there is no existing object to which a vertical staff may be attached. It should be made of 4-inch by 4-inch timber, or larger, supported at short intervals on posts or concrete piers firmly set in the ground, and should be gradu- ated by level after being placed in position so as to give the readings directly. Such gages are especially liable to change of datum and should be frequently checked in elevation at several points. Plate V, A, shows a hook gage in the well and an inclined gage on the bank. INDIEECT GAGES. Indirect gages in common use are of three types, the hook, the weight, and the float. The essential requirements for gages of this type are : (1) a constant length of the intermediate part used for transferring the index of stage to the scale board, and (2) a permanent scale board so graduated and placed that it may be easily and accurately read. They are adapted for use where a fixed staff gage would be in danger of disturbance or can not be easily read. Hook gages. — The hook gage invented by Boyden about 1840 is the most precise instrument known for the measurement of stage and will be f oimd of value wherever determinations of stage to a hundredth of a foot or closer are desirable. By careful adjustment such a gage can be made to read to a thousandth of a foot. The value of such accuracy of reading is, however, dependent upon the same accuracy in the determination of the other factors affecting discharge. This gage consists of a vertical inversely graduated rod, carrying a hook at the bottom. The rod slides in fixed supports provided with a vernier for reading. The hook is sub- merged and by means of a tangent screw is gradually raised until the point just breaks the surface of the water so as to show the pimple resulting from capillary action. A simple form of hook gage (Fig. 9) can be arranged by using a mov- able staff inversely graduated to feet only, with a hook on the bottom, sliding against a fixed scale 1 foot in length carefully graduated to frac- tions of a foot. In reading the stage the feet are indicated by the foot- 26 RIVER DISCHARGE. r.2 2:-o mark on the staff which is opposite the fixed foot scale from which the tenths and hundredths are read. Hook gages arranged with verniers are applicable for use only in con- nection with experimental hydraulic work or with carefully adjusted sharp-crested weirs. The simple type of hook gage has a wider range of use and will be found advantageous in conjunction with automatic gages, in canals, and other chan- nels connected with diversion works and, during low water periods, at many gaging stations where small changes in stage correspond to large per- centage changes in discharge. Weight gages. — The simplest form of the weight gage consists of a graduated rod or tape, which the observer uses to measure vertically down to the surface of the water from a reference mark on a bridge, vertical ledge, or overhanging tree. The record of stage obtained by this means must be adjusted to read directly from the datmn. The weight gage used by the United States Geological Survey (Fig. 10) is believed to be the most practical gage of this class. It consists of a graduated scale board, 10 feet or more in length, usually either extending from or contained in a box supporting a pulley wheel, over which runs a heavy sash chain, to which is attached at one end a weight and, near the other end, a marker. This, as a whole, is fastened in a horizontal position to a bridge or other structure, so that the weight when lowered will come in contact with moving water, as the exact point of contact of the weight and water can not easily be determined by the observer above if the water is still. Generally the scale board is graduated only for a length of 10 feet. If the range of stage is greater than that amount, provision must be made formeasuring it. This is accomplished by a second and, inextreme cases, a third marker, spaced at intervals of 10 feet from the first marker. The most satisfactory chain so far used for this form of gage is "Morton's champion metal window sash chain, No. 1 regular. " Of the substitutes which have been used the best is probably some form of steel or bronze tape, which will change little if any in length but which has Pio. 9.— Simple Form of Hook Gage. INSTRUMENTS AND EQUIPMENT. 27 been found to be liable to break, expensive to mend, and if exposed to the wind to offer considerable resistance, making it difficult to take accurate observations. Woven wire sash cord and various forms of wire are not so satisfactory as they are liable both to kink and to stretch and are not easily adjusted in length. To read the chain gage the observer releases the chain and allows the Fig. 10.— United States Geological Survey weight gage. A shows the complete boxed chain gage with the " marker " or " index " shown at a. B, b b' shows the part of the chain that is measured to detect elongation, and d shows the threaded pin and lock nut, by means of which the length of the chain is adjusted. If the zero marker reads above the 10-foot mark at high stages, a second marker is attached to the chain 10 feet below the first and the reading of the second marker is increased by 10 feet. (7 shows the chain and scale with a projecting nail at c, over which a link of tlae chain is hooked when the weight is drawn up into the down-spout. D and E show cross-sections of the box through the hasp and lock. weight to lower until it just touches the surface of the water, in which position the stage is read on the graduated scale opposite the marker. This gage has the advantage of stability in position, as it is above all danger from ice and drift. It has the disadvantage of possible uncer- tainties in the datum, on account of change in length of chain, due to wear- ing caused by the moving of many parts upon one another, and by changes in elevation of the structure to which it is attached. To avoid error the chain length, that is, the length from the end of the weight to the marker, must be frequently measured and adjusted to the standard length. This adjustment is made either by cutting out a link or by the adjusting device with which the chain is attached to the weight. 28 RIVER DISCHARGE. Float gages. — A non-recording float gage consists of a float arranged to rise and fall with the stage. The float carries either a staff or a chain passing over a pulley and kept taut by a counterweight. A marker attached to the staff or chain at a fixed distance from the float moves along a fixed graduated scale board and thus indicates the stage reading. If a staff is used on the float it may be graduated inversely and the stage observed opposite a fixed marker, or it may be arranged to read as explained for the simple form of hook gage. This type of gage is best adapted for use in pump houses and per- manent buildings erected over the water surface as, under these condi- tions, the float and all parts of the gage will be fully protected. When the float carries a chain, the same requirements should be observed as described for the chain on the weight gage. ESTABLISHMENT AND MAINTENANCE OF NON-RECORDING GAGES. In addition to the points already discussed relative to the establish- ment and maintenance of the various types of non-recording gages, the following conditions are generally applicable. In this connection too great emphasis can not be placed on the importance of conditions affect- ing the gage and its reading as the accuracy of all discharge records depends largely upon them. Installation of gage. — The gage should be so located that it may be easily read and be without the influence of disturbing effects, such as boils, backwater, and crosscurrents. It should be graduated to read directly the elevation above the datum or zero which should be placed well below the lowest water in order to avoid negative stage readings. In order to accomplish this it is generally advisable to put the zero at the approximate elevation of the bed of the river at the lowest point in the section. The construction and installation should be accomplished in a thor- ough and workmanlike manner, thus assuring the permanence of the gage and the accuracy of the results obtained by it. The scale board should be clearly graduated in accordance with the degree of accuracy expected in the observations, and each foot and tenth mark should be numbered, thereby eliminating many errors in readings. The reading of the gage should receive special consideration. Checking gage datum. — The permanent maintenance of the datum of every gage is absolutely necessary. To accomplish this it must be referred to at least two permanent bench-marks from which it can be readily checked by means of a level. INSTRUMENTS AND EQUIPMENT. 29 It will be convenient if one of the bench-marks is fixed on an easily accessible part of the bridge or on an overhanging tree or rock from which the stage of the river may be directly determined by measurements made from it to the surface of the water by a staff or steel tape. Such a mark, generally known as the reference point, should be as permanent as pos- sible and not generally any part of the gage or gage box. The other bench-marks should be placed on objects apart from the structure to which the gage is attached, out of reach of possible damage or interference and so located, if possible, that the gage can be checked with one set up of a level. The elevation of the bench-marks should always be determirfed and expressed above the datum of the gage without reference to an inter- mediate datum. In order that the gage heights may be readily used in flood studies and in determining slopes along the river, the datum of the gage should be, whenever possible, connected with sea level or with any city or railroad datum available. In making the original reference and in future comparisons of the gage with its bench-marks, the level, if practicable to do so, should first be so set as to obtain directly the height of the instrument above the datum of the gage. In the case of a staff this can be accomplished by reading directly from the gage, or by setting the bottom of the level rod at some definite point on the gage. For the standard weight gage the instrument should be set below the elevation of the pulley and the gage weight low- ered until its bottom is on a level with the horizontal cross-hair. The reading of the gage in this position gives directly the height of instrument. The height of instrument should not be measured from a water surface, because the elevation of the surface of the river may vary materially within its width or within short distances up and down the stream. In cormection with the checking of indirect gages the first operation is to check and adjust, if necessary, the length of the intermediate part for transferring the index of the gage to the scale board. This having been accomplished, the datum of the gage should be compared with the bench-marks by means of a level. If the standard chain is used, the length of the chain from the end of the weight to the marker should be measured carefully under about a 12- pound pull. In order that this measurement may be made easily the marker should be placed a few feet from the end of the chain. Nails properly spaced in the floor of the bridge will facilitate this measurement and will be serviceable in future checkings of the chain length, which should be made at each subsequent visit of the engineer to the station. 30 RIVER DISCHARGE. The engineer should paint or mark plainly on the inside of the cover of the gage box the length of the chain and the elevation of the reference point from which stage can be determined. STILLING BOX. A stilling box for eliminating wave action is desirable, and ofttimes necessary, in connection with all types of gages, especially where precise records of stage are desired, as, for example, in canals, at weirs, and at current meter stations during low water periods. In general such a stilling box may consist of a wooden box or a metal pipe erected in the stream around the gage and extending to the bed of the stream, into which the water is admitted through small holes, or a well connected with the stream by a pipe as described for recording gages. The level of the water in the stream and in the stilling box must be fre- quently compared in order to eliminate errors due to the clogging of the openings to the box. For u> e on staff gages, whether vertical or inclined, a special adjustable box is necessary on account of the great range of stage for which pro- vision must be made. A wooden box that has openings through the bottom and made to slide up and down on the gage may be set at the sur- face of the water by the observer at the time of each observation. Fre- quently a tin can or pail may be utilized in a similar maimer with good results. These adjustable boxes must be varied and arranged to suit particular gages. BECORDING GAGES. Recording gages make a record of stage either continuously by a curve, the coordinates of which indicate the time and the stage, or at stated intervals of time by a printing device. The essential parts of the record- ing gage are: (a) a float which rises and falls with the surface of the water, (6) a device for transferring this motion of the float to the record, either directly or through a reducing mechanism, (c) the recording device, and (d) the clock. These gages should be used where the diurnal fluctuation of stage is so great and irregular that it is impossible to determine even approximately the mean daily gage height from a limited number of staff gage readings daily, as on streams artificially regulated for power or other purposes, or on those fed by melting snow or ice or subject to short and violent storms. Their use is also frequently necessary in connection with the division Plate II!. iM-A^ INSTRUMENTS AND EQl'Il'MENT. 31 of water both in streams and canals, as well as on streams where daily observations of stage on a staff gage would be sufficient, but where ob- servers are not available. They are also being used increasingly and with great benefit in the operation of power plants. With each recording gage a staff or some other form of non-record- ing gage is necessary in order that the accuracy of the stage record may be easily and frequently checked. CONTINVOCe'-KECOKD GAGES. Various automatic gages have been built to record stage by means of a graph. These are generally similar in having a drum for carrying the record sheet, a movable arm for carrying the pencil or pen, a clock which propels either the pencil or the drum and determines the time ordinate, and a float with counterweight which propels either the drum or the pencil and determines the stage ordinate. Of the many gages of this type that have been devised the Friez,"* Gurley, and Stevens^ (PI. Ill, A and C) have been found well adapted for general use. The Friez and Gurley gages are similar in that they are operated by 8-day clocks, and the record sheets are de- signed to carry one- week records. The time ordinate is parallel to the axis of the drum, which carries the record sheet, and the stage ordinate is perpendicular to this axis. The Stevens gage is operated by a weight-driven clock which can be arranged to run from 30 to 90 days by providing sufficient fall for the weight. The record sheet is furnished through a supply roll over a main drum to a receiving roll. The supply roll is arranged to carry sufficient paper for a year's record. The graph for any period of time can be removed as desired. In this gage the stage ordinate is parallel with the axis of the drum and the time ordinate perpendicular to this axis. The drum is operated by the clock, and the pencil carriage, operated by the float, is so arranged that when it reaches either limit of the gage sheet it reverses, thus recording any stage. It is essential that continuous-record gages be arranged so that the graph will not extend beyond the limits of the record sheet. This is accomplished on the Friez and Gurley gages by having the stage ordi- nate pass around the drum and on the Stevens gage by the reversal of the pencil carriage. * Manufactured and sold by Julien P. Friez. Baltimore, Md. ^ Manufactured and sold by Leupold & Voelpel, Portland, Ore. 32 rivp:r discharge. The scales of the record sheet will depend upon the range of stage to be recorded. The usual vertical scale for large streams is 1 to 10 and for smaller streams 1 to 6. A time ordinate of an inch to a day is usually satisfactory. The possible accuracy of a continuous-record gage is determined by the reliability of the clock and the amount of lost motion in other parts of the gage, which may introduce errors in the curve. In the operation of the continuous-record gage, visits at regular intervals are necessary in order to wind the clock and change or remove the record sheet (Fig. 11). In changing the sheet, the exact time and Sun. Men. 1 Tues. Wed. Thurs. 1 Fri. 1 Sat 1 Sun. 1 ;io.5 Noon No'or Noon Noon lllo'on Noor .^Noon flNooh 1 9.10 a. m.' May 24, 1910-U Staff gage height, 10.26 feet - -p\ ' , 1 '\ 1 \\ V i-L- W" Clock 10 minutes slo\ if, 1 \ \ V y n \ \ - 10.0 \ 1 \] !\ \ \ \ \ J \ i\ ]\ l\ i\ j 1 1 \ \ / \| 1 l\ / 1 \ 1\ \ \ 1 J \ \ / \ 1 1 \ ]\ \ / 1 1 \ \ 9 5 \ 1 \ \ \\ 1 \ \ \ kJ 1 ^ \ \ 1 ^ ms 1 V ' \ 1 1 .12.45 p.m. Mav22. 1910 1 1 u '6.30 p. m. May 29, 1910_L_|_1_ Staff gage heigF t, 9.84 feet 1 - 1 i Staff gage height. 9.70 feet Qn c ■ _1 10 _j :kcc 1 rr ec 1 mil 1 _L.. 1 OL k 1 Jn 1 in (It 1 es slo 1 "[I Fin. II.— Typical Continuous-rpcoril Gagf Sheet. stage as observed on the staff gage, should be noted on the face of both the old and the new record sheets. The clock should be set, if neces- sary, and the amount of error in time also recorded on the old record sheet. In placing the new sheet care must be taken to start the pencil at the proper time and stage ordinates. In addition to these regular visits, intermediate visits should be made as frequently as possible in order to insure the accuracy and continuity of the record. The exact time of such visits, together with the stage as determined by the staff gage and other pertinent notes, should be made on the face of the record sheet or in a special note book and referred to the curve by an arrow pointing to the location of the pencil point at the time of the visit. When a note book is used each entry should be numbered and dated both in the book and on the record sheet. The continuity of a record obtained by this type of instrument does INSTRUMENTS AND EQUIPMENT. 33 not necessarily indicate that the record is accurate. The above pre- cautions are therefore of importance. Full notes of all conditions which may in any way affect the record or its interpretation should be inade on the record sheet or in a special note book at each and every visit of the observer. The following sources of error are inherent in continuous-record gages of the float type: 1. Difference between elevation of water in the float well and the river. 2. Inaccurate starting of pencil on the record sheet. 3. Lag in the mechanism which prevents the recording pencil from responding promptly to changes in stage. 4. Errors in the clock. 5. Insufficient scale of both time and stage to enable accurate inter- pretation of the record. 6. Imperfect printing of the record sheet. 7. Expansion and contraction of the recoi'd sheet due to moisture. This can be partly eliminated by placing cubes of camphor or other absorbents in the gage box. The mean daily gage height may be determined from the continuous record sheet in three ways : 1. By taking the average of readings at regular intervals of time, depending upon the variation in fluctuation of stage; 2. B.y means of an ordinary planimeter, in which case the area bounded by the curve and its base line is divided by the length of the base; 3. By the Fuller integrator, which gives the mean height directly by tracing the line. In certain studies it may be desired to plot on the record sheet the curve of corresponding discharge or run-off, from which the mean daily discharge will be taken. IXTEKMITTENT-RECORD GAGES. The only successful automatic gage so far constructed which prints the stage and the time at regular intervals of time is the Gurley gage (PI. Ill, B) which has been designed and built along lines suggested by the engineers of the Water Resources Branch of the United States Geo- logical Survey. This gage is free from lost motion and the time and stage are printed (Fig. 12) to the nearest hundredth of a foot each 15 minutes. The gage is operated by a weight-driven clock and, with sufficient fall for the weight, will run 60 or even 90 days without wind- 34 RIVER DISCHARGE. 1 2--.07 -.08 4-30- .] 2- -.04 -05 4-45— .12--01 =.i8 1 1-J 99 ing. It is compact, small and comparatively simple in construction, and is adapted to work where the highest degree of accuracy is desired. The mechanism of the gage sets on an iron base 14 inches square and is covered with a tight metal cover about 21 inches high which protects it from both dust and moisture. The recording mechanism consists of three parallel type wheels (behind the clock), on the face of which are raised figures and divisions. On the first of these wheels the periods of time from 1 to 12 hours are indicated at intervals of 15 minutes, for- recording time. The height is recorded by the other two wheels, one of which carries the feet-numbers to 36 feet and the other the tenths and hundredths of a foot. The time-type wheel is controlled by a weight- driven clock, which is so constioicted as to endure changes in temperature without variation in its regular operation. The two wheels which indicate the stage of the river are actuated by a float which with its counter- weight is supported by a metal band perforated at intervals to fit over the pins in the periphery of the pulley wheel attached to the height wheel over which it run p. The record is made by the striking of a mechan- ically actuated cushioned hammer, every 15 minutes, against a strip of paper which is backed with a carbon strip and passed over the face of the type wheels. The record paper and carbon paper are unwound from separate spools and taken up on two other spools, after they p)ass over the type wheels. Maintenance of this gage, in addition to general inspection, requires attention in regard to the following: Check the relation of water in and outside the float well. See that the stage-type wheel is recording correctly. Check the clock. If desired, remove the record printed since the last visit. A history of each visit, of changes, and of work done should be made in a special note book and referred to by date and number both on the record sheet and in the book. 5-00- 5-15- 5-30- 5-45- 6-00- 1 1--9^ 1 1— .94 1 1--.91 1 1— .89 6-15--11-l|f -:88 6-30— -1 1— .84 6-45-. 11.-81 7-00-.11-4S -r 1 c ~77 _7-1 5 - ^1 1 --^ Fig. 12,— Typical Intermit- tent-record Gage Sheet. 1. 2. 3. 4. 5. Plate IV. INSTRUMENTS AND EQUIPMENT. 35 INSTALLATION OF RECORDING GAGES. A large element in the satisfactory operation of any automatic gage is its proper installation, which will determine the accuracy of any record- ing gage record. Improper installation will deteriorate the results from the best of gages, while with an adequate installation the accuracy of the results is only limited by the construction of the gage. If the expense of an automatic gage is to be incurred, approximate results are not satis- factory and it is, therefore, essential that the installation be so thorough as to eliminate any question of the accuracy of the results. Special care and thoroughness in installation are necessary if the records are to extend over winter months and times of freshet, in order that freezing and dis- turbance from floating ice and debris may be eliminated. In installing an automatic gage (PL V, A) it is necessary to provide a well , connected with the river, for the float ; a house to shelter the gage ; and staff gages with bench-marks for checking the record and maintain- ing its datum. Local conditions will usually determine the method and details of the installation. (PI. IV, A.) In the ideal installation the well and the house should be located far enough back from the river to be out of danger from floating ice or drift and to provide sufficient protection for the well and pipes to prevent freezing. The bottom of the well must be below the lowest stage and not less than 3^ feet square. It should be provided with a permanent ladder, extending to the bottom, so that the float and intake pipe can be readily inspected, and if the gage is to be maintained for a long period of time it should be lined with concrete. Otherwise a heavy plank lining can be substituted. The float pipe should be not less than 4 inches in diameter and the intake must be well below the lowest stage of the river and pro- vided with a screen for keeping out silt, etc. It should also be provided with a check gate as it enters the well, so that the flow can be reduced to eliminate wave action. The best material for the intake pipe is spiral- welded steel with flange unions. The shelter for the gage should have inside dimensions of at least 5 feet square and 6 feet high, in order to provide sufficient room for the observer to conveniently look after the gage. The house should have a window and the door should be closed when the cover is removed from the gage, to keep out dust. The floor should have a trap door for entering the well and a ventilating pipe should be provided both for the house and the well, in order to eliminate the dampness. The stand for the gage should be high enough to provide for its easy inspection. The most satisfactory material for the house is concrete with metal 36 RIVER DISCHARGE. covering on the roof and door which will insure the gage against destruc- tion by fire or from being otherwise disturbed. Many automatic gages in out-of-way places have been destroyed by being used as targets for rifle shooting. Two staff gages, referred to permanent bench-marks, should be installed with each automatic gage in order to check the readings with the stage of the river. One (preferably a hook gage) should be located in the float well to determine whether the water in the well is at the same elevation as in the river, and the other should be placed in the river and of a type best suited to the locality. The river gage should be in the same cross- section of the river as the intake pipe. It may, however, be dispensed with by the use of a reference point so located that the elevation of the water surface can be easily determined from it. When the well is properly constructed and located back from the river, there should be no danger from frost, even in temperatures as low as 30 degrees below zero. In case there is danger from freezing, it can be pre- vented by arranging a floating lamp in the well, or by hanging an electric light bulb near the surface of the water. Where the float is in a tube of small diameter, freezing can be prevented to some extent by pouring oil in the well. The best type of lamp is a floating iron kettle suspended by a counter- weight. In the kettle a tight cover, carrying a burner, should be soldered a few inches from the top. Such an arrangement will provide for two or three quarts of oil, which, with an ordinary lamp burner, will burn several days. STRUCTURES FOR MAKING DISCHARGE MEASUREMENTS. In addition to gages, as already described, regular gaging stations must be provided with — 1. A structure to support the engineer while observing the velocity and depth, when the stream is too large to permit making measurements by wading. 2. A cable and stay line to hold the meter in the vertical when the soundings and velocity observations are made. 3. A graduated line for indicating the distances between the points of measurement. STRUCTURE FROM WHICH MEASURKMENTS ARE MADE. Discharge measurements will be made either (1) from an existing or specially constructed bridge (PI. II, B), (2) from a cable carrying a car (Pis. IV, B, and V, A), or (3) from a boat held in position by a cable or guy line. Plate v. A. TYPICAL CABLE STATION WITH AUTOMATIC GAGE. B. TYPICAL GAGING STATION FOR WADING MEASUREMENT. INSTRUMENTS AND EQUIPMENT. 37 When existing bridges are available in localities where the conditions of channel and current are suitable for the collection of a good discharge record, a gaging station may properly be located at such structure, and when so located it can generally be installed at a minimum cost. Ideal conditions for measurements are not usually found at existing bridges, and stations so located generally involve the sacrifice of accuracy to save expense. The selection of a gaging section without reference to existing structures makes possible the securing of better conditions of measure- ment. A material saving will be made thereby in maintenance if the station is to be continued through a considerable period of time, even though the first cost of the station is large, because fewer discharge meas- urements will be necessary for determining the station rating curve. If the stream is not too large, a special cheap wooden or suspension bridge may often be constructed advantageously. In the absence of a bridge as a support for the engineer in making observations of velocity and depth, a cable for carrying a car may be stretched across the stream. The equipment and appurtenances for such a cable station (PI. IV, B) consist of the cable, supports and anchorages for sustaining it, turnbuckles for regulating the sag, and a car for car- rying the observer. The cable. — Iron or steel cable of sufficient tensile strength to sustain the car and two men, in addition to the weight of the cable itself, should be used. The stress in the cable due to a vertical load will increase as the sag decreases. Consequently the cable is least safe when the sag is a minimum. In the following table the diameter is computed for a five load of 450 pounds on the cable at the center of span and an initial ten- sion corresponding to the sag given in the table. With an ultimate strength of 80,000 pounds per square inch the factor of safety for these dimensions is about 5. The sag given in the table is the least allowable; if it is increased, the factor of safety is increased. In making connections the cable should not be bent to a shorter radius than three diameters and the turnbuckle and connections should have a safe working strength of an amount given in the last column of the table. Galvanized cable, pulley, etc., should be used, in order to delay corrosion. "Engineering News, May 6, 1909. " Tlie Design of Cable Stations for River Measurements," by J. C.Stevens. 38 Proper diameter and RIVER DISCHARGE. of galvanized steel cable, with live load of 450 pounds for spans of 100 to 800 feet. Span. Diameter. Sag. Stress. Feet. Inches. Feet. Feet. 100 i 4 2,(«8 200 9 6 4,167 300 5 8 5,061 400 1 10 6,300 500 -_ 12 7,813 600 i 12 10,125 700 1 14 12,626 800 H 15 16,660 Supports. — The nature of the supports for the cable will depend on the physical characteristics of the location. It may be supported either by some natural object, as a tree or cliff, or by some form of artificial tower. Frequently trees are properly located to serve as supports, and when so located may be cheaply and satisfactorily used. The only objection to them arises from their swaying in the wind. Protection in the form of wooden blocks must be provided for the limbs which support the cable to insure that the motion of the tree shall not speedily cause the destruc- tion of the support. A better way, when possible, is to pass the cable through a pulley block, which, in turn, is attached to the support. Large rocks, when available at sufficient elevation above the stream bed, make excellent cable supports, as the cable can be connected directly to the anchorage. In case artificial supports are required the form will depend somewhat on the height necessary. For low support and a short span, a single post, 10 to 14 inches in diameter, set firmly in the ground, is sufficient. When, however, heights greater than 12 or 15 feet are necessary, "shear legs" (PI. IV, B) are generally used. In their construction two posts (8 inches by 10 inches or their equivalent in round logs) should be set in the ground 10 to 15 feet apart at the base, inclined toward each other so that they will be 2 to 5 feet apart at the top, and connected by at least three strong pieces secured to them by bolts fitted with washers and nuts or by "drift bolts" of suitable lengths; or these posts may be set so that they will cross near their ends, and should then be fastened to each other by two or more bolts with nuts. The cable may rest on the top cross-bar in the first instance or in the crotch in the second instance, but in either case should preferably be passed through a pulley block at the end having the turnbuckle. All towers should be well guyed INSTKUMENTS AND EQUIPMENT. 39 SO they can not move toward the stream. In crossing the shear legs the cable should make equal angles with the legs on both sides. Anchorage. — The form of anchorage will vary with different conditions. If solid rock is available, an eye-bolt split at the lower end and driven against a wedge may be set in a drill hole, which should then be com- pletely filled with sulphur, lead, or Portland cement grout. If no solid rock is at hand, a "deadman, " made of a log 8 to 12 inches in diameter, may be buried in the ground below the limits of frost and at least 4 feet deep, the length of the log and depth in the ground depending somewhat on the span of the cable. The anchorages should be so arranged by means of long eye-bolts embedded in concrete, or auxiliary cables attached to the "deadman," that the main cable and its connections will be exposed for inspection. The cable should be attached at each end to two independent anchor- ages or supports. In case posts are used for supports the cable should be attached to them by means of a short piece of cable with clips. A support which is not set in the ground should be guyed to anchors of some kind, both forward and backward, and the cable attached to it. In still other cases it is advisable to make a second independent anchorage in the ground. Turnbuckle. — ^A turnbuckle for use in taking up sag, having a capacity of 2 to 6 feet, should be inserted in the cable on the side of the river from which the engineer approaches the station. This should have right-and- left screws and not a screw at one end and a swivel at the other. An arrangement can easily be made whereby one man alone can tighten the cable, even if a greater length than the capacity of the turnbuckle must be taken up. This is accomplished by means of an auxiliary cable, which spans the turnbuckle and is clipped to both the main cable and the anchorage. The turnbuckle having been unscrewed and in that condition clipped to the main cable, the auxiliary cable is released and the turnbuckle drawn up. If the capacity of the turnbuckle does not remove a sufficient amount of sag, the auxiliary cable must again be clipped to the main cable and the turnbuckle released, unscrewed, and slipped along the main cable to a new position and the operation repeated. Car. — The car should be made about 5 feet by 3 feet and about 1 foot deep and attached at each end to a pulley on the cable by means of iron or steel straps or by light cable, or by wooden standards, never by manila or cotton rope. If wooden standards are used, they should be so securely attached to the car that in case of accident they will not be wrenched loose. Plate IV, B, shows an excellent type of car. The details of the iron work for this car are shown in figure 13. The car in operation is 40 RIVER DISCHARGF. shown on Plate V, A, and a full bill of materials necessary for its con- struction is given in the following table. Fig. 13.— Details of Hangers for Cable Car. For safety and ease in propelling the car, a puller as shown on Plate III, B, should be provided. Ordinary cable stations for spans up to 100 feet can be installed and equipped at a cost of from $50 to $100. Bill of materials for large standard gaging car. No. of pieces WOODWORK (straight GRAINED). 2 If" X 2f " X 5' 4" sides of bed frame. 2 If X 2f " X 1' 6§" ends of bed frame. INSTEUKENTS AND EQUIPMENT. 41 2 f " X 9i" X 5' 5^' sides of bed. 2 f " X 9i" X 1' 10" ends of bed. 4 f'X 71" XI' 91" seats. 1 If" X 3|" X 2' 2" foot rest. 1 If" X 2 " X 5' 6" top spacing bar. 2 If " X 2 " X 4" spacing blocks. 2 2 " X 2 " X 4" split diagonally, corners. IRONWORK. Sheaves. 2 8" roller bushed sheaves, spoked. 2 4" X f " X f " loft sheaves. Hangers, as shown on drawing. 2 If" X t\" X 11' 10" steel hangers, bent. 2 li" X A" X 3' 0" steel hangers, bent and twisted. Machine bolts, with two washers each. 2 2f " X f " bolts with cotter pins for 8" sheaves. 7 2f " X J" bolts for spacing blocks. 5 1|" X I" bolts for main hangers. 5 4|" X f " bolts for main hangers. 5 3|" X I" bolts for foot-rest hangers. 2 2|" X f " bolts for foot rest. 2 4 " X f " bolts for small sheaves. 2 6" galvanized line cleats with screws. Boat stations as ordinarily equipped are unsatisfactory on account of the difficulty in holding the boat in position, in making soundings and in operating the meter. Ferry boats operated from cables can often be advantageously used. In the measurement of large rivers, as in the work of the Corps of Engineers, United States Army, on the Niagara, St. Lawrence, and other large rivers, specially constructed catamarans" with special equipment for their control and operation, have been used with great success. Such equipment is expensive and is generally applicable only for special investigations on large streams. "See reports ol tl. S. Lake Surrey. , 42 RIVER DISCHARGE. STAY LINE CABLEg. In order to hold the meter in the vertical when making measurements, all stations should be equipped with cables and stay lines (PI. V, A), The cable need not exceed one-fourth inch in diameter and for ordinary stations a cable of No. 10 or No. 12 galvanized wire will be ample. It should be located from 30 to 100 feet above the measuring section, depend- ing on the width and depth of the stream, and should carry a ring about 3 inches in diameter, through which a small rope is run, one end of which is connected to the upper end of the meter stem and the other end is held by the man operating the meter. In operation, the ring moves freely on the cable and the rope shdes through the ring, thus enabling the observer to hold the meter in any desired position in the stream. A cable and stay line are easily installed and manipulated and are indispensable for obtaining accurate measurements when the velocities and depths are considerable. LINES FOR INDICATING MEASURING POINTS. In order that the measuring points at a gaging station may be easily located at the time of making measurements, and that the distance between the measuring points may be readily determined, they should be referred to a fixed initial point, and the section should be divided into regular intervals by permanent marks placed on the bridge rail or floor, in case of a bridge station; on the main cable or on a secondary tagged cable, in case of a cable station; and on a tape or tagged line stretched across the stream for measurements made from a boat or by wading. In the latter case, if it is not practicable to leave the line in place, the initial point should be so located and marked that the line can be stretched for each discharge measurement in the same position as for previous meas- urements. ARTIFICIAL CONTROLS. Streams, whose beds are changing or which offer no satisfactory section for making discharge measurements, or for collecting records of stage from which discharge may be computed, may require the building of artificial controls for maintaining a constant relation between gage height and discharge and also for improving the channel conditions so that satis- factory measurements can be made (PI. VI). In the construction of artificial controls care should be taken to main- tain the natural conditions as nearly as possible*; that is, they should con- Plate VI. A. NATURAL CONTROL. B. ARTIFICIAL CONTROL. INSTRUMENTS AND EQUIPMENT. 43 form closely to the natural bed of the stream and should not project into the channel, as such projection will greatly reduce the sensitiveness of the station at low stages and thus reduce the accuracy of the record. Where a reef or bar or gravel or boulders is available it may be possible to pre- vent scouring and change of channel by grouting with cement. In case of shifting channels in sand or silt, sheet piling can be driven across the section nearly flush with the bottom, which will tend to prevent scour, and over which the natural current may reduce the probability of silting. The effectiveness of artificial controls or of channel improve- ments will depend upon local conditions, and such changes should only be attempted after a careful consideration of local conditions. Any modifications of a cross section or alignment of a stream which will change the conditions of equilibrium already established by nature may be expen- sive to maintain and should always be carefully considered and closely watched. INSTRUMENTS FOR DETERMINING CLIMATOLOGICAL DATA. In the study of the hydrology of a given area the engineer will often need to consider the cHmatological conditions which affect the quantity and distribution of the water supply. In such studies it may be neces- sary to collect data in regard to: 1. Precipitation in the form of rain. 2. Precipitation in the form of snow. 3. Evaporation. 4. Temperature. 5. Relative humidity. 6. Wind movements. The methods and instruments of the United States Weather Bureau, representing the best practice for the collection of all climatological data, have been fully described in special bulletins of that bureau, from which they may be obtained upon application. CHAPTER III. VELOCITY- ARE A STATIONS. Velocity -area gaging stations are divided, according to the method by which the velocities are measured, into current-meter, float, and slope stations. Current-meter stations are further divided, with respect to the facilities for making the observations, into bridge, cable, boat, and wading stations. The data necessary for continuous records of stream-flow at velocity- area stations are, first, results of measurements of discharge, and, second, records of mean daily stage. The collection of such data requires four distinct procedures: 1. Selection of a site for the gaging stations, 2. Establishment and maintenance of the station, 3. Measurement of discharge, and 4. Observation of stage. SELECTION OF SITE. REQUISITE CONDITIONS. Conditions that determine the desirability of a site for a velocity-area station comprise, first, conditions that insure good measurements of discharge and stage, second, those that affect the computation of flow at times when measurements of discharge are not made, and, third, those that affect the cost of obtaining the records. Conditions pertaining to measurements of flow and stage. — The measure- ment of discharge by current meter requires a fairly smooth bed and a measurable and uniform velocity of current. The velocity of the current should be uniformly distributed throughout the section, which should show no marked eddies, cross currents, or boils, and its mean should not be less than 0.5 foot per second at low stages. Measurements to be made by floats or by determinations of slope require also a straight stretch of channel, 200 to 1,000 feet long, through which the cross-section and velocity are reasonably uniform. The site should be so selected that the gages for measuring stage may be economically installed and may be readily accessible for reading. 44 VELOCITY-AREA STATIONS. 45 Conditions pertaining to computation of flow. — The essential conditions affecting the computation of flow are permanency of the relation of stage to discharge and the sensitiveness of this relation. The elevation of the water surface of a stream flowing in an open channel is regulated from point to point by certain features that may conveniently be referred to as control sections. A control section may be a dam or weir, the crest of rapids or abrupt falls, a bar extending across the river, or, where the slope is uniform throughout, a long stretch of the river bed itself. The slope of the water surface above each control section is determined by the height of water at the control section. Computations of daily discharge are based on the assumption that the discharge of a stream for any given stage is unchanged so long as the character of the river at the control section remains unchanged, and that it varies with the stage according to some law. This relation between stage and discharge makes practicable the construction of a rating curve from a few measurements of discharge made at times which cover the range of stage. This rating curve is, therefore, the graphic representa- tion of the formula for computing the discharge over or past the control section , and by its use the flow can be computed from records of stage at times when discharge measurements are not made. Any change in conditions at the control section will modify the relation between stage and discharge and make necessary the construction of a new rating curve; if, however, the conditions are permanent, measurements made in dif- ferent years will define a curve that may be applied to a record of gage height extending over an indefinite time to obtain estimates of discharge. A permanent control is, therefore, of prime importance for a gaging station maintained for the determination of daily discharge, as otherwise it is necessary to construct new rating curves after each shift, and if shifting is continuous, as in many streams in the Southwest, one or more discharge measurements a week may be required. Attention is particularly called to the fact that permanence of flow past the gage is the essential condition, because the records of gage heights and the rating table pertain to the section at the gage and not necessarily to the section in which discharge measurements are made. This involves the requirement that the bed and banks at the control section shall be permanent. The shifting of a bar of sand or gravel in the channel below the gage may make a decided change in the relation between discharge and gage height, even though the cross-section at the point of the measurement remains unchanged. On the other hand, a permanent reef or ledge extending across the stream a short distance below the gage will control the relation between gage height and discharge, even though 46 RIVER DISCHARGE. the bed at the measuring section or at the gage may change. Stations established under such conditions of control give excellent records. The relation between stage and discharge may be disturbed by various modifying conditions even when the natural control is permanent, and care should be taken in the selection of a site for a station to avoid those conditions, which may occur in the backwater from a dam as a result of intermittent diversions, or result from the choking of the river with flood water discharged from a tributary below, or from the temporary accumulation of ice, logs, or other drift. For a given stream the shape and size of the control will govern the magnitude of change in stage resulting from a change in discharge. This relation is referred to as the sensitiveness of the station, and the station should be selected so as to give as large a change in stage as is possible for a given change in discharge. Estimates of flow at non- sensitive stations which have relatively small fluctuations in stage, are liable to large errors on account of lack of refinement in the determina- tion of mean daily stage. Conditions pertaining to cost of records. — Three principal factors enter into the cost of obtaining stream-flow records — the character of the records, the position and character of the gaging station, and the instru- ments and equipment to be used. 1 . The character of the records will depend on the use for which the data are needed and the length of time that the observations are to be continued . 2. The position and character of the gaging station will depend on the characteristics of the regimen of the stream, the accessibility of the station, the availability of gage readers, and the permanency of the con- trol, which determines the number of discharge measurements necessary for computing daily discharge. 3. The instruments and equipment for collecting the data will depend on the necessity for a recording gage, the availability of structures or equipment by means of which velocity and depth may be measured, and, in the absence of a suitably located bridge, conditions of bank favorable to anchorages and support for a cable. keconnaissanck. A gaging station should be established only after a thorough recon- naissance has been made of the section of the river in which the station is to be placed. As the object of this reconnaissance is to find the best site to furnish the desired results, it should be made, if possible, during a low stage of the river and, if feasible, should be supplemented by VELOCITY-AREA. STATIONS. 47 an inspection at a high stage. At low stages the bed can be carefully examined, and the minimum velocity can be determined, and a fair estimate of conditions.at high stages can also be made. At medium and high stages it is generally impossible to examine the bed or to make any estimate of velocity at low stages. Careful notes and sketches should describe the conditions at the localities examined, as the position of the station can not be finally chosen until all possible sections of the stream have been inspected. The notes should be complete in all details and should include negative as well as positive information. In making the reconnaissance consideration should be given to the three requisite conditions that have been described, and the recorded information should include the following subdivisions of these topics: 1. Conditions pertaining to measurements of flow and stage, including (a) the type, dimensions, and location of the gage or gages ; (b) the velocity and distribution of the current of water; (c) the bed — whether rough or smooth, permanent or shifting, and (d) the section of river available for determinations of slope when measurements of discharge are to be made by the slope method, estimated length, curvature, slope, obstructions, facilities for measurements of cross-sections, etc. 2. Conditions pertaining to computations of flow, including (a) the location and character of the control section ; (b) the proximity of dams or tributaries above or below the section and their probable effects at the station and (c) the banks — shifting or permanent, wooded or clear, high or low, etc. 3. Conditions pertaining to cost of records, including (a) the accessi- bility of the site; (b) the availability of gage readers and their qualifi- cations; (c) the estimated cost of establishment of the station ; (d) the estimated annual cost of maintenance, and (e) the structures available for supporting the engineer in making measurements, or, in the absence of such structures, the span, supports, and anchorages necessary for a cable, with a statement whether or not all flood water passes under the structure or cable. The selection must be determined largely by the facilities afforded for obtaining an accui-ate record of stage and for measuring precisely the area of cross-section and the velocity of the current. In general it has been found economical, in the end, to establish a gaging station where conditions are good, even though the cost of instal- lation may be relatively great, as the cost of operation and maintenance will probably be less and the records will be more satisfactory than at stations where conditions are poorer. 48 RIVER DISCHARGE. ESTABLISHMENT AND MAINTENANCE OF STATIONS. The site for the gaging station having been selected, the routine of establishment and maintenance will depend on the equipment necessary, that is, on (1) gages, (2) structures for making measurements, and (3) controls. The character of the equipment and the manner of its installation will in large measure determine the accuracy and cost of the records. Money expended in the initial installation will generally materially reduce the cost of operation and maintenance, and thus reduce Ihe cost of the records. Gages. — The type of gage to be used will depend on the physical conditions at the site, the availability of a gage reader, the importance of the station, and the number of readings necessary for the proper determination of the mean daily stage. In general the gage or gages, with the necessary bench marks, will be first installed in the manner described on pages 23 to 36. The determining factor in the "use of a staff gage will be the availability of a reliable gage reader, lack of which will render the use of a recording gage necessary, even though other conditions may be favorable for a non-recording gage. The accuracy of the records of stage will depend largely on the ease with which the observations can be made; therefore the gage should be so placed as to be readily accessible, and the convenience and even the comfort of the person reading and caring for the gage should be insured by facilities provided in the vicinity of the gage. If the gage is not located in the section in which meter measurements are made, an auxiliary gage or, preferably, a reference point should be placed in the measuring section, in order that a standard cross-section may be used for determining the area factor of the discharge. It should be borne in mind that the rating curve of discharge applies to the cross-section of the river in which the gage is located. Therefore the location of the gage, once decided upon, should not be changed without good reason, as relocation will require the development of a new rating curve. If it is considered necessary or desirable to replace a gage, the new one if installed in the same section should be made to read from the same datum as the old one, unless there is some excellent reason to the contrary. Furthermore, secondary gages should be avoided except where necessary for determining slopes or the areas of cross sections at the measuring section. This precautioi^ is necessary because, for a given change in discharge, the stage will vary differently at different cross-sec- tions because of differences in condition of channel. Structures for making meanurements. — General discussion of structures VELOCITY-AREA STATIONS. 49 for making measurements appears on pages 36 to 41, but two important considerations, the safety of the equipment and the ease with which it can be used, are here mentioned. As the lives of the men who are to make the measurements will depend on the strength of these structures, liberal factors of safety should be employed and the materials used should be durable. Controls. — As stated on page 45, a permanent control section is one of the fundamental requisites for a satisfactory gaging station. If the site to be used lacks a permanent natural control, an artificial control rany be provided by grouting the bed or by building a low weir as described on pages 42 and 43. Description of station. — A complete description of the gaging station is necessary, covering the following topics: 1. The location referred to the nearest post office, railway station, dwelling, and tributary streams above and below, and if in a public-land State, to the smallest legal subdivision. 2. Date of establishment. 3. Name of person who established the station. 4. Name, post office address, and rate of compensation of observer. 5. Gage or gages and their bench marks. 6. Equipment from which measurements are made. 7. The control section. 8. Channel and other conditions which may affect rrieasurements of discharge or stage. 9. Conditions which may affect estimates. The description of each station should be accompanied by a general sketch showing the situation of the station with reference to topographic features, the observer's house, roads, towns, tributary streams, dams, and diversions. A detail sketch showing conditions at the gaging section may often be desirable. THE MEASUREMENT OF DISCHARGE. The discharge at velocity-area stations is obtained by measuring the area of the cross-section, and the velocity of the moving water. The area of the cross-section is determined by soundings. The velocity of the moving water is measured either directly — by observing the time of passage of a float over a measured course — or indirectly — by noting the revolutions of the wheel of a current meter or by measuring slope and using slope formulas. Discharge measurements are classed in accord- ance with these three methods of measuring velocity. r>0 i{i\;er discharge. In.Riakingthe meaeurement by means of a current meter or floats the area of the gaging section (Pi. II B) that is perpendicular to the thread of the current of the stream is divided into partial areas, for each of which the discharge is determined independently by multiplying its mean velocity by its area. The total discharge is the sum of the partial discharges. This computation of partial discharges eliminates the application of results obtained for conditions existing in one part of the channel to parts in which they do not apply. AREA or CROSS-SECTION. The area of cross-section of a stream, the first factor in measuring discharge, depends on the contour of the bed, which is determined by soundings, and on the stage of the river, which is observed on the gage. The methods used in its determination will be the same regardless of the methods used for measuring the velocity. For current-meter stations the area of only the measuring section is required. For float and slope stations the average area throughout the jwrtion of the river used for the observations must be obtained. Soundings. — Soundings are made either by a graduated rod or by weight and line. Sounding rods are limited in use to depths of less than 15 feet and are best adapted for use at wading and boat stations, where the depths and velocities are relatively small, but may occasionally be used at bridge stations where the bridge is not high above the water. The weight and line are used in making soundings in water of greater depth than 15 feet, and from bridges or cables which are high above the water. Soundings from a bridge or cable with weight and line are most readily taken as follows : Lower the weight and line until the weight rests on the bed of the river directly underneath the measuring IX)int. With the line taut, mark a point on it opposite a fixed ix)int on the bridge or car; then raise the weight until it just touches the surface of the water and measure the length of the sounding line that passes the fixed point mentioned above. The depth is most readily measured by placing the end of a linen or metallic tape opposite the fixed starting point on the sounding line, grasping both the line and the tape in the hands, and drawing up the line and tape without permitting them to slip on each other until the weight rests on the surface of the water. The length of line thus drawn up, representing the depth of the water, can th(:n be read directly from the tape. This measurement may usually be made by one person even when the depth is 10 to 12 feet. Where meter measurements are made from a bridge or cable, the meter VELOCITY-AREA STATIONS. 51 cable, with meter and lead attached, is generally used for sounding if the depths and velocities are small but care must be taken that the meter is not damaged. The greatest and most common errors in measurements of discharge are caused by erroneous soundings. Errors in soundings by weight and line are due to the weight being carried downstream, so that it does not fall immediately below a point perpendicularly beneath the meas- uring xx)int, or, sometimes, to the bowing of the line. Both these causes make the soundings too great. Errors in soundings with rods are due to the rod not being perpendicular, to the water rising on the rod, and to the rod sinking in the bed. ~ Standard cross-section. — For gaging stations on streams whose beds are permanent or nearly so, a standard cross-section should be constructed from careful soundings. This cross-section should be referred to the zero of the gage, so that the depths for any stage can be found by adding the gage height to the depth below the zero of the gage. Standard cross- sections have three uses: (1) They serve as checks on future soundings; (2) they indicate changes which may occur in the bed of the stream ; and (3) they may be used in determining the area for measurements taken at times when it is impossible to make soundings on account of high water or other conditions. VELOCITY. Velocity of flowing water, indicated by V, is generally expressed in feet per second, and depends principally upon (1) surface slope of the stream, (2) roughness of the bed, and (3) hydraulic radius. The surface slope is the fall divided by the distance in which that fall takes place, and is represented by s. It depends on the slope of the bed, the channel conditions, and the stage. It is greater for a rising than for a falling stage. The coefficient of roughness of the bed varies for different streams and stages of the water and is expressed by n. The hydraulic radius or hydraulic mean depth is the area of the cross-section divided by the wetted perimeter. It is usually represented by R, and can be determined for all stages from a single complete measurement of permanent cross- section. The mean velocity of a stream is the average rate of motion of all the filaments of water in the cross-section. It is not a directly measurable quantity, being usually found by dividing the total discharge by the area of the cross-section at a given stage. Its use is generally limited to purposes of comparison. 52 RIVER DISCHARGE. LAWS CtOVEnNINO VKI-OCITY. A systematic study of the flow of streams shows that mean velodty is in general a function of the stage and that the distribution of velocity through the cross-section follows well-defined laws which pertain to all streams flowing in open channels and which are in the main independent Distances 60 70 80 CURVES OF EQUAL VELOCITY' s o 'j:3 VERTICAL VELOCITY CURVES Note: Numbers at top of curves indicate measuring points Numbers at bottom of curves indicate mean velocity in the vertical 30 -^O 50 60 70 80 90 100 110 120 130 1-»0 Horizontal divisions represent one foot per second velocity Vifi. 14.— DUtribution of VidoclLy In Open Channel. Kumbro River, Zumbro Full:*, Minn. of the stage (figs. 14, 16, 16). These laws make possible the deter- mination of the velocity factor of the discharge measurement by com- paratively few properly distributed observations of velocity. Upon them also depend the methods for determining the regimen of the stream. These laws have been studied both mathematically and graphically VELOC[TY-A l!EA STATIONS. 53 by means of vertical velocity-curves (figs. 15 and 16) which show graphically the distribution in a vertical line of the horizontal veloci- ties of the filaments of water from the surface to the bottom of the stream. Vertical velocity-curve. — A vertical velocity-curve is determined by a series of velocity observations taken at regular intervals in a vertical Velocity in feet. 1231234123 Fig. 15. — Groups of Vertical Velocity-Curves. Chenango River at Binghamton, N. Y. from the surface to the bottom of the stream, usually from 0.5 to 1 foot apart. The results of these observations, when plotted with the veloc- ities as abscissas and the depths as ordinates, define the curve. Studies by Humphreys and Abbot" on the Mississippi, by General Ellis* on the Connecticut, and by the United States Geological Survey" on many streams under various conditions of depth, velocity, and "Piiysics and Hydraulics of the Mississippi, 1851, p. 234. 'Report of the Chief of Engineers, V. S. Army, 1878. Part I, p. 259. "Water-Supply and Irrigation Papers Nos. 95, 109, 187i and others. r.4 RIVER DISCHARGE. roughness of bed, show that these vertical velocity-curves have approx- imately the form of the parabola whose axis, coinciding with the filament of maximum velocity, is parallel with the surface and is in general situated between the surface and one-third of the depth of the water. From the maximum the velocity decreases gradually upward to the surface and downward nearly to the bottom, where it changes more rapidly on account of the friction on the bed. As the depth and velocity increase, the curve approaches a vertical line as its limiting position. Distribution of velocity in the vertical. — If, as stated above, the veloci- ties in a vertical line vary as the ordinates of a parabola, it may be shown mathematically that (1) a filament of water which has the same velocity as the mean of the velocities in that vertical occurs at a point between .5 and .7 of the depth measured from the surface of the stream, and (2) that the mean velocity equals the mean of the ^•eloci- ties occurring at .2114 and .7886 of the depth. The demonstration" of the location of the filament of mean velocity is based on the theory of mean values, using the fundamental equation, y = ad +d 1' J (o"-!- 6'), in which d equals the total depth of water; a, the depth of maximum velocity below the surface; b, the unitary complement of a; y, the depth of the thread of mean velocity. By assigning values to a between and J d and substituting them with simultaneous values of b in the above equation, there results the following table, showing the depth of the mean ordinate for parabolic curves with various positions of depth to the maximum ordinates. Depth of Depth of maximum ordinate. mean ordinate. When a = y = 0.58d a =0.10d y = 0.59d a = 0.15d y = 0.60d a = 0.20d y = 0.62d a = 0.25d y = 0.63d a = 0.30d y = 0.65d a = 0.33d y ^ 0.67d The maximum ordinate in streams that are neither very shallow nor very deep usually lies at or above one-third depth (see table, pp. 56, 67). * Englneerlner News, Vol. LV, p. 47. VELOCITY-AREA STATIONS. ^'> U it lies above one-fourth depth, the ordinate at 0.6 depth is very closely the mean ordinate. If the stream is very deep the maximum thread lies generally at a greater proportional depth, and the thread of mean velocity therefore lies at a greater depth. If a stream is shallow and has in addition a rough bed, the frictional effect on the flow is so large that the vertical velocity-curve is no longer parabolic near the bottom and the thread of mean velocity may be near mid-depth. A study of vertical velocity-curves shows that the mean velocity in the vertical equals from 85 to 95 per cent of the surface velocity, and it also equals one-fourth the sum of the velocity near the surface plus twice the velocity at mid-depth plus the velocity near the bottom. That these properties generally hold in nature has been proved by huhdreds of vertical velocity-curves made on a large number of streams having a wide range in conditions of depth, character of beds, and magnitude of velocity. Fig. 14 shows the form of a number of typical vertical velocity-curves and the table on pages 66-57 gives a summary of results of a large number of vertical velocity-curves. A study of these measurements, together with many others which are not available for publication, shows the general applicability in nature of the foregoing laws upon which depend the common methods of measur- ing discharge by floats and current meters. METHODS OF DETERMINING MEAN VELOCITY IN A VERTICAL. In the application of the laws of the distribution of velocity there have besn developed the following methods of determining mean velocity in the vertical: (1) Vertical velocity-curves; (2) .6 depth; (3) surface; (4) .2— .8 depth; (5) three-point; (6) integration. Measurements of velocity are therefore generally made by one of the above-mentioned methods, each of which has its special advantages and limitations. Their essential use is to determine the mean horizontal velocity in a vertical line and not features of measurement or compu- tation that involve other factors. As a discharge measurement contains a large number of velocity determinations the error introduced in the result by an individual erroneous measurement of velocity is generally inappreciable. The application of the methods and the relative accuracy obtained by each, as determined by a comparative study of all available vertical velocity-curves, are discussed in the following paragraphs: Vertical velocUy-curve method. — By the vertical velocity-curve method measurements of horizontal, velocity are usually made just under the m EIVER DISCHARGE. S + H Z+J, S2J oojoo)OOoco>ONOowO'-iooo--ioioiooooJOsoo>o ■t~a>a> o a> o,o»a> c oooooooooooooooaiooooioosoio 'Oio>o» ooa.< J3d uiiC:»ioojaA ranui -ixBui p-eamj n5d3Q ■^dap ivify^ JO (^uaO J3d Ul /C)IDO|3A n'Baca pBdiq') i|;)d30 d o S^ V 01 ^ -^ ,-( rH r- -tt- i-H CO "^ rH ^H i-( 1-1 ^Hi-t -H X U3 0> t* lO O (M lO ■* « »H N O ^ eq N U3 U3 Tj< 00 CO CD eO •-< m t^ O (^ !>■ O OS O "-^ •-' «30NM«N.H'^«^CO^oasoooooososoJOoo)oio>o|oooi cocoioocic OCOJ ^ ^WW^^^^^ ^,H^ rt^^^rt^ ^,H .-(U,-. rt,_(rtrt^^ "-' 010COOCCO-* l^CCO -'cooicpW'^WNWrHcocpcgiMeocoN P (M M i-H CO l^ OOO'-'Tt^ o o. oo 2 S'2a55«-S as S S O 03^ Q O CTS O O .oco 03 flS-2 H to o3 ^o I s 5 c 5 HpqOOZCQh Oj » CQ C9 sees s s s a £cq SW> < 3'§-§-gB=iSS„"sS|S.2S.Ss : ???g^gs4.| &§••« g gj c=i tgE I i s si's •SrnrnrS orT Q Q El da £ tri cd r/^ f-. & e 0 RIVER DISCHARGE. shows that such a point lies approximately at .6 depth of the stream. The preceding table shows that the thread of mean velocity lies between 56 per cent and 73 per cent of the depth, with an average of 61 per cent. The error resulting from the use of .6 depth is very small, ranging from — 6 per cent to + 4 per cent, with a mean of per cent. Therefore, in the . 6 depth method it is assumed that the velocity at .6 depth is the mean velocity in the vertical and the meter is held at that point in this method. Although this method is intended to be used without coefficients it may be found by vertical velocity-curve measurements that a coef- ficient is necessary in some instances to reduce the observed velocities to the mean. The method is applicable over a wide range of condi- tions, is easy of execution, and is reasonably accurate for normal flow in the straight reaches of all streams except very deep and very shallow ones. The surface method. — The surface method is used in the measurement of velocities of swift streams, especially at times of freshet, when it is impracticable to sink the meter much below the surface. Therefore the observation of velocity is made at a point near the surface, but far enough below to eliminate- any disturbance from wind or waves. The point of observation in this method should be from .5 foot to 1 foot below the surface, its location depending on the depth of the stream. The measured velocity must, however, be multiplied by a coefficient to reduce it to the mean. This coefficient, as shown in the preceding table, varies between 78 and 98 per cent, depending upon the depth of the stream and the magnitude of the velocity. For average streams a coefficient of about 90 per cent will generally give fairly accurate results. The two-point method. — The two-point method is used on streams in which the location of the point of mean velocity is uncertain, or when greater accuracy is desired than can be obtained by the . 6 depth method. As noted in the foregoing theory, the mean of the velocities at .2 and .8 depth gives nearly the mean velocity in the vertical. The preceding table shows that this theory holds very closely in nature. Therefore in this method the meter is held at . 2 and . 8 depth of each vertical. Observations of velocity near the surface and near the bottom of the stream have in the past been used in the two-point method. Both the theory and the tables show that .2 and .8 depth should be used. This iiH'tliod is recommended for general stream-gaging. VELOCITY-AREA STATIONS. 61 The three-point method. — The three-point method approaches more nearly the vertical velocity-curve and is used for obtaining greater accuracy than is possible by the one- and two-point methods. In this method the meter should be held at .2, .6, and .8 depth. The mean velocity is then obtained by dividing by 4 the sum of the velocities measured at .2 and .8 depth plus 2 times that at .6 depth. In this method the observations have in the past been frequently taken at top, bottom, and mid-depth, but both theory and experience show that .2, .6, and .8 depth are the proper points for such obser- vations. The integration method. — The integration method is used • both for obtaining the mean velocity in the vertical and also the mean velocity in the entire cross-section of the stream. In determining the mean velocity in the vertical the meter is moved at a uniform speed from the surface of the water to the bed of the stream and return, and the revolutions and time are observed. The meter thus passe? successively through all velocities in that vertical and tlie result- ing observations determine the mean in that vertical. The method is valuable for checking other methods, but generally requires the service of at least one more man to observe time, as the engineer must be occupied with the movements of the meter. It is consequently not so commonly used as the point methods. The Price meter is not suited to observations by this method, as the vertical motion of the meter causes the wheel tu I'evolve. The Haskell and Fteley meters, on the other hand, may be moved vertically with little or no effect on the wheel. In determining the mean for the entire section the meter is moved with uniform speed throughout the section, usually in a zigzag path extending from surface to bottom and from side to side of the section . CURRENT-METER MEASUREMENTS. PROCEDURE. In making a current-meter measurement the cross-section (PI. II, B) is divided into partial areas, varying in width from 2 to 20 feet, depend- ing on the size of the stream. These partial areas are bounded by perpendiculars terminating at points in the surface known as measuring points, because they indicate where the observations of depth and velocity are taken. They should be so spaced as to show any irregulari- ties either in the cross-section or the velocity. When measurements are made at bridge or cable stations, the measuring points should be permanently marked on the bridge rail or floor, or on the cable, and used for successive measurements of discharge. When measurements 62 KIVEK DIS(5HAT!fiE. are made at boat and wading stations the points will be indicated by the graduations on a tape or tagged line, which is generally stretched at the time of each measurement. The procedure in the measurement will vary somewhat, depending on the sounding appliance. If the meter and cord are used for sounding, observations of depth and velocity will be made at each measuring iwint successively across the stream. If other sounding apparatus is used, soundings will be made at all measuring points prior to taking the velocities. In making velocity observations, one of the methods described on pages 55-61 should be used, the method chosen depending upon the conditions at the station . Care must be taken to place the center of the meter wheel at the points called for by the method. This is best accom- plished by measuring the required depth on the meter line with the wheel in the surface of the water, and then lowering the meter into i)osition. Special attention is called to the requirement, both in sounding and in placing the meter in position for observing velocity, that a tagged line should not be used for measuring depth. Such distances should be determined by means of a tape line, as indicated on page 50. In making the observations a stop-watch is desirable but not indispensable. In general, time should be noted at the click of the receiver, or at the Start or finish of the buzz. The time is then observed for a given num- ber of revolutions. The number will depend on the velocity and should be sufficient to make the time interval at least 30 seconds, as shown on the sheet of current meter notes given on pages 66 and 67. This method is preferable to observing the number of revolutions for a given time as it eliminates the error due to fractional revolutions. With a stop-watch time can be observed to half or fifth seconds. If the velocity of the current makes other than a right angle with the measuring section the deviation from the right angle must be observed and a coefficient applied to reduce the velocity to the normal. This coefficient can usually be applied to the final completed discharge. If, however, the angle varies throughout the cross-section, it is necessary to apply appropriate coefficients to the various observed velocities. The angle can readily be determined by holding the meter just below the surface of the water and placing the notebook perpendicular to the ci'oss- section of the stream and drawing a line parallel to the meter. This line should be divided into ten arbitrary divisions and projected upon a line normal to the gaging section. The length of this projection will be the coefficient to be used. If the current-meter measurement of discharge is made at a regular VELOCITY-AREA STATIONS. 63 gaging station established for obtaining a record of discharge, a certain routine should be followed, consisting of the steps indicated below in consecutive order. 1 . Check gage datum if facilities are available. 2. Set up meter, using precautions described on page 18. 3. Read the gage. 4. Make the observations necessary for the measurement of discharge by one of the methods described on preceding pages. 5. Read the gage. (If the stream is fluctuating notably the gage should be read frequently and at regular intervals during the measurement.) 6. Check the notes to make certain that all records have been made. 7. Dismantle and pack meter, using precautions described on page 18. 8. Be careful to note under " remarks " changes in stage, backwater, wind, and other conditions knowledge of which may be of future value. 9. If possible, see the gage reader and his record, and call his atten- tion to any lack of interest or apparent discrepancies in his work. Each of the above observations is essential to the reliability of the record at a station. On each visit of the engineer the stage of the river should also be determined by observing the distance to the surface of the water from a reference point, as a check on the gage record. Either temporary or permanent changes in channel conditions which affect the rating of the station should be noted and recorded in as great detail as possible. Such conditions include changes in channel in the vicinity of the station, the building of dams below, the formation of jams of logs or drift, and the extent, character, and thickness of ice. Gage readers should receive written instructions in regard to reports to be made concerning such conditions; otherwise they may make no record of the time or extent of such changes. If the engineer can reach a gaging station in time of flood, he should as a rule remain and make measurements of discharge at each foot of stage as the river rises or falls. Observation of a single freshet may thus enable him, with a minimum expenditure, to rate the station for practically all except low stages. In addition to the general procedure described above, special pre- cautions and methods are necessary in connection with low water and wading measurements, high-water measurements, measurements of ice- covered streams, and measurements in artificial channels, as described on pages 69 to 75. 64 RIVER DISCHARGE. COMPUTATIONS. The computations of current-meter measurements are usually made to determine: (a) the total area of cross-section; (6) the mean velocity, and ((■) the total discharge of the stream. The observed data from which these computations are made consist of (a) soundings at known intervals across the stream, (6) the velocity determinations in the vertical at each sounding point, and (c) the distance between the points of measurement (see table, pp. 66 and 67). The mean velocity, area, and discharge are computed independently for each partial area included between perpendiculars drawn from suc- cessive measuring points. The total discharge is the sum of the partial discharges thus computed. The computation of the partial discharges eliminates errors which would arise from the distribution of conditions existing in one part of thie cross-section to parts in which they do not apply. The mean velocity is determined by dividing the total discharge by the total ai-ea of the cross-section. The formulas used in connection with computations of discharge may, in general, be classed as rectilinear and curvilinear^depending on the assumption that the bed of the stream and the horizontal velocity - curve are made up of straight lines or of curves between the measuring points. A comparison of the computation of discharge measurements by various formulas has been prepared by J. C. Stevens, Member Am. Soc. C. E.* In this discussion it is shown that the following rectilinear formula gives the most accurate results and is readily used : '"(^-^) C--^^0 In this formula, do, di, d2 d^ and Vo, Vi, v^ »„ are the depths and velocities at the respective measuring points, a^, Oi, aj .... .«„, which are spaced at the distances ^i, Zj, l^ l^ (fig. 17). The area, between the perpendiculars drawn from any two suc- sessive measuring points is equal to the mean of the depths at such points multiplied by the distance between them. Similarly, the mean velocity for the area between the two perpendiculars is equal to the mean of the velocities observed at the two perpendiculars. The product of this area by its mean velocity gives the discharge for the partial area included between the two perpendiculars. The sum of these partial areas and discharges gives the total area and total discharge. The tables on * Englneorlng News, Jiino 25, 190S. VELOCITY-AREA STATIONS. 65 pages 66 and 67 show the field notes and computations for a typical cu rren t- m eter measuremen t . The velocities at the respective observation points, as shown in column 6, are determined from the current meter rating table, and the mean velocity in the verticals is the mean of the velocities taken at the respec- tive measuring points. In computing the measurement, it is not usually warranted to carry the velocity computations to more than two decimal places and the partial areas and discharges to more than one decimal llace. Fig. 17. — Cross-section of Stream to Illustrate Discharge Measurement (Computation. LOW-WATEli AND WADING MEASURK.MENTS. At low stages of a river when the velocity is small it is advisable to find a section near by in which conditions of channel are suitable for a discharge measurement and a meter measurement may be made by wading (PL V, B). Low'-water measurements should preferably be made by the .2-. 8 depth method, except where the depth is less than 2 feet, when the .6 depth method should be used. Meters hung on rods are best adapted for use in measurements by wading. In making the measurements a graduated line is stretched across the stream to mark the points of measurement. For this purpose a steel or metallic tape may be used. If, however, the stream is wide, an oil- silk fish line or Barbours Irish flax salmon thread, conveniently grad- uated, is more satisfactory as it offers less resistance to wind. When the steel tape is not used special care must be taken to check graduations to eliminate the possibility of errors due to stretching or shrinking of the line. The engineer making velocity observations should stand below the graduated line and preferably to one side of the meter, in order not to disturb the current of the water flowing past the meter. Three-eighths- 66 EIVER DISCHAEGE. Typical .current meter notes Boise River, DowUng, Idaho. March ^8, I914. Date. M<5rC/^ 5. .BoisQ : River a.t..DQ!W//n^ , State ol /dBh.Q,.j Width B£.0. Area j5*/?Z ...Mean Ve\. \3-s3/ Cor. M. G. H ^-SG Party A. B.jPartO/?. Disch._^_Z£^___ Staff gage, checked with level and to}xi\A..A/.0../eV£:/...Cl.. _ , ,....-. Area from soundings (date)..../^^^^/^. Method of suspension ../^/i'S Stay wire../tfo Approx. dist. toW. S..-^ -. Arrangement of weights and meter; top hole..— :r:. ; middle hol&4K?&7 bottom holei^l2. Gage inspected, found... .0.shou/a( he^od.. Sheet No 1 of 2... ..sheets. If inouffioicnt opaet, usi. bauk vit alitct . VKLOCITY-A RE A STATIONS. 67 Typical current meter noten Boise River, Bowling, Idaho. March 28, 1914 (continiierl). Dlst Depth, of ot>- serys^t Time in sec- onds Rev- olu- tions VKWJCITY Area Mean Depth Width from inilill point Depth At point Mean in ver- tical Mean in sec- tion Discharffc — — — /.35 /5 /.25 /2 20.2 4-5 2.5 5 49.0 -70 3.18 2.70 20 500 50 2.23 296 43.5 2.9 /5 /28. a 60 3.3 65 49.8 90 403 3.23 2.65 55.0 60 243 3.38 5/8 345 /5 /76 / 75 3.6 7 528 /GO 4.22 3.53 2.8 470 60 284 358 53.2 3.55 /s I9G5 90 3.6 .7 52.6 /GO 4.23 3.62 2.9 52.0 7G 3.00 3.66 53.2 3.55 /5 /94.7 /OS 3.6 .7 S/.4 /OO 4.33 3.70 2.9 50.8 70 3.07 3.72 £5 5 37 /s 206.5 /ZO 3.8 .75 54:5 /GG 4.06 3.74 3.0S 52.2 8G 3.4/ 364 56.2 3.76 /6 204.6 /35 3.7 .75 552 /GO 4.04 3.Sf 2.95 S/.4 70 3.04 3.5& 54 3 3.65 /5 /96.2 _ " " 240 3.2 .65 660 /CO 3.38 2.86 ) 2.55 476 50 2.3S 274 4S.O 3.0 /s 723.3 Z55 28 .65 56.8 80 3.13 2.62 225 530 50 2.// 236 36.0 2.4 /5 85. 270 2. a /.a 530 SO 2.// 2// /06 73.0' /.o 73 73.3 283 O — — — — q_ Totals 826.8 2,738.9 No 2 ol 2. Sheets. Cotnp. by A . B. P. Chk. by £, H, /i. 68 KIVEK DISCHARGE. inch iron rods, 3 or 4 feet long and having a slit in the top, are con- venient for supporting the tape. If tlie water is shallow or accurate determinations of small flows are desired, it may be necessary to instal sharp-crested weirs to confine the flow to a small channel in which depth and velocity will be measurable. When convenient tlie soundings across the stream may be made before the observations of velocity. In making the soundings a thin, flat, graduated wooden rod should be used on which the water will not pile up, as in low-water measurements sounding errors may be rela- tively large. The round rods on the meter are not generally adapted to soundings. Measurements can not be made by wading if the product of depth times velocity is greater than 8. The stage of zero flow should be determined if possible for each gaging station. This stage will be the elevation of the lowest ptoint of the con- trol section and should generally be determined by a level . Its great value arises in determining the position of the lower end of the station rating curve for use in estimating discharges for stages below the lowest current-meter measurement of discharge. HIGH-WATEE MEASUREMENTS. Measurements made at high stages generally consist of observations of surface velocity only. Areas must be computed from a standard section or from soundings made at a lower stage. Under these condi- tions extra precautions must be taken to secure data from which a reliable estimate of the flow can be made. The great velocity and the presence of drift or of cakes of ice may render good meter measurement practically impossible. Meter observations 10 to 30 seconds long may, however, frequently be obtained when there is considerable drift, but great care must be exercised that the meter is not damaged . If a weight of more than 30 pounds is required to submerge the meter, a secondary line must be used in conjunction with the insulated cable for supporting the meter, and a stay line will often greatly assist in holding the meter in position. When there is much drift it is generally advisable to use the float method, the drift serving as floats. Or it may be practicable to determine the slope of the river for a considerable distance and compute the discharge by means of the slope formula. If a level is not at hand marks may be made by which the slope may be determined at some future visit. When possible two of these methods may be used and a check thus obtained on the work . When it is impossible to obtain flood measurements the discharge VELOCITY-AREA STATIONS. 69 may be computed as the product of the area and mean velocity, determined by extensions of the area and mean velocity curves. In such computations the area above the level of the flood plain, if any, should include only the section above the ordinary channel or channels of the stream, as the mean velocity curve usually applies only to this channel and not to the overflow channel. The discharge on the flood plain will generally be a comparatively small part of the total flow and may usually be estimated with such accuracy that the error introduced by it into the total discharge will not be great. MEASUREHrENTS OF ICE-COVERED STREAMS.* The general parabolic law of the distribution of velocity in a cross section of a stream with open channel holds also for a stream under ice. The table on pages 70 and 71, giving a summary of the results of many vertical velocity-curves, shows that there are two points, in which the thread of mean velocity occurs under ice. These points are at about .1 and .71 depth below the bottom of the ice, varying between and .22 for the upper and .63 and .79 for the lower. It is thus seen that they lie very nearly at .2 and .8 of the depth. As seen in the table the .2 and .8 depth method gives the mean velocity within a small percentage of error, and in making measurements under ice this method should be used. If it is desired to make measurements having a high degree of accuracy, or for the purpose of checking results made by the two-point method, the whole measurement may be made by vertical velocity-curves (fig. 18). When it is necessary to make observations at mid-depth a coefficient should be determined for reducing the velocity to the mean. If the river is not deep enough to get vertical velocity-curves a coefficient may be obtained at a number of stations by comparing the average of the velocity at the .2 and .8 depth with that observed at the mid-depth. See tables, pages 70 and 71, giving coefficients to reduce mid-depth velocity to mean. In measuring an ice-covered stream the procedure is in general the same as for a stream with open channel, except that provision must be made to eliminate interference due to ice and frost. The equipment necessary for making the measurement includes the ordinary current- meter outfit, ice chisel, axe, and shovel for cutting away and removing the ice, and an ice measuring stick for determining the thickness of the ice. The meter should be operated on a rod if the depth will permit. If, "■See Water-Supply Papers Nos. 187 and 337, U. S. Geol. Survey. 70 RIVEK DISCHARGE. -I ■5 I •a £■§ irtdap 8-0+5'0 ■indap £ o f5 u -t H o I W H ■^ O O ■| ^ 'k> I 05 md3p 8-0+50 •qjdap fi-0 n 06 0000 ■uinuiixBpi ■umuipcBi'I ■UBam jaAvoi ■UBetu iwidn. •ji^poTaA U-BBJ^ '6B9ID[am) 901 •301 jepon qjdao; •aoBjjns *89Ajno }0 jgqmn^ SS2g58 .00 to m> =1 .sl w o o ocoSSSoo cSoOTOoSci 00^00 oD^^wa^mo^w HCCOOO H M^5^ CO Oa 00 00 to iOOt-"*CQ t* t^ 1-1 V.'S .-( OS ^ to ST Wm 5.P » IH C3 gto •S?" i;^3 "■o 300C lo^cdoo ot-e measured and the depths at which the meter is to be placed computed before the meter is assembled. The meter should be so held in the hole that the head is as far upstream as possible to avoid the effect of the vertical pulsations. If a rod is used, the meter can be kept in position by hold- ing the rod against the upstream side of the hole; if a cable, the meter can be held at one posi- tion more easily by standing on the cable than ))y hold- ing it in the hand. The number of rev- olutions and the time are recorded as in open-water meas- urements. After the complete data for each observation have been recorded while the meter is still in the water, the meter can be carried quickly to the next hole and the observations continued. In this' way, if no frazil is present, the entire measurement ma.y be completed without having the meter in the air long enough for the water on it to congeal. The section for winter measurements should preferably be chosen during the open season to insure favorable conditions. If the presence of frazil or of floating anchor ice at a section affects more than 10 per cent of the total cross-section, the measurements should, if possible, be made at another section where such conditions do not exist. Sections OBSERVATIONS Distance from initial point Thici^ness of ice Total depth of water Depth of meter from water surface Time in seconds Revolutions Water surface to bottom of ice Effective waterdepth 1,0 a ^ c c-h (c-b)x.2+b (c-b)x.5+b (c-b^K-S+b 15 -Diagram showing factors usea 1 dis :A*-n^ • mti suret rs/7fy ■^ ^- ~-- — ""' 1<^ ^ '9°t f^ 1' • ' ^ y ^3 1 rW-i 1 50 8^ ( > s IC K) 1! lO 2 DO L 3< )0 3 50 4 00 4 ts 5 DO S M «< e so 71 90 T Ana in square fict Fig. ifi.— Typical Area Curves, Illustrating Their Comtruotioii. apparent (fig. 22). The abscissas between the plotted points and the curve show the error resulting from the combination of errors in compu- tation and soundings, and from changes in channel. At stations where the banlcs of the stream are practically permanent, changes in section, if any, take place usually below the low-water line. If th( area of such a section changes, the part of the curve above low water, which has been accurately constructed, may be shifted a proper distance horizontally to the right or left and be made to show accurately the urcNiH of the new cross-section (fig. 21). The constant abscissa length between the old and new position of the curve is the algebraic sum of the changes in the area of the section, -|- for gain in area by DISCUSSION AND USE OF DATA. 95 scour and — for loss in area by fill. A single determination of area at any gage height above low water therefore determines the new position ■of the curve, c (fig. 21). MEAN VELOCITV CURVE. As stated in Chapter III, the mean velocity of the stream is the aver- age rate of motion of all the filaments of water of the cross-section and depends principally upon (1) the surface slope of the stream, (2) the roughness of the bed, and (3) thehydrauhc radius, and has been expressed in the Chezy formula as F = c |/ Rs, in which the coefficient c has been expressed by Kutter in terms of s, R, and n. Since slope is the most important factor affecting velocity, when the rate of change in the slope is rapid the velocity tends to follow such change. When the slope becomes constant, changes in the velocity are controlled by the other two factors, the hydraulic radius and the coeffi- cient of roughness. The curve of mean velocity shows the relation between the gage height and the mean velocity of the current in the measured section. It is located by means of points which are determined by plotting the gage heights and corresponding mean velocities as coordinates. If sufficient measurements have been made to define the curve throughout the range of stage, no further investigation of its properties will be necessary. It frequently happens, however, that the curve must be constructed from limited or discordant values of velocity. To do this intelligently and satisfactorily a knowledge of the properties of the curve under various conditions of flow is essential, and in such cases it is advisable to develop the curves of R and s. For usual conditions of natural flow in which the stage of no flow is the lowest point in the measured section, the mean velocity curve has approximately the form of a parabola with axis vertical and origin at or below the bed. It approaches a straight line, however, for the higher stages. When the gaging section is in a stretch of the stream where zero flow occurs with ponded water at the section of the gage, the mean velocity curve will reverse at low stages and approach zero convex to the gage axis. The degree of curvature and the point at which the curve re- verses are apparently governed chiefly by the amount of ponded water at the gage, the roughness of the bed, the form of the controlling bar, and ■other channel conditions. If the stream is small and shallow the change in direction is more abrupt. This peculiar reversal is probably 96 RIVER DISCHARGE. due to the rapid rate of change of the slope at extreme low flow. At zero flow the slope is of course zero. The least flow causes a slope of the surface and this slope increases with the stage, up to a certain point. Three i5tiethods of extending the mean velocity curve from medium stages to high water have been employed: (1) Extend the curve as a tangent from the last observed value; (2) extend the curve as a hyperbola, i. e., approaching the straight line as its asymptote; (3) assume the slope constant or increasing slightly over the intermediate stages and compute the value of the velocity from the formula V = c ] Rs, using the most probable value of the coefficient of roughness. To! roS Boil 900 1000 iiw izbo liw hoo imo hoo itm ib» Otse^rgt in stcomf-fief FiQ. 23.— Typical Ratinsr Curve, Showing Low- Water Extension. The curve should be extended into low water with the greatest care. A slight variation from the true direction of the curve means a large percentage of error in the resulting estimate of minimum discharge. All conditions at the station should be studied. The curve must always be drawn to intersect the Y axis at the gage height of zero flow. If the point of zero flow is not known its true position will lie between the gage height of the bottom of the channel and the point where the tan- gent to the discharge curve at its lowest known value cuts the Y axis, as between a and h, fig. 23). If the mean velocity curve intersects the axis above the gage height of the bed of the stream — that is to say, if DISCUSSION AND USE OF DATA. 97 o ^ Cl « Gage hei'jght in feet u o >a e • o : N U -Ik t 5 5 S %% 1 '1 a ; 10 a> i\) ^ 3 3 C5 N ,5 \ g \ g \ S \ ; g > a 8 \ \, * ^ \ -> § \ 55 \ vo ^ > c as -* ? \ c. 6' \ ^" ^B \ \ \ 3' 5j g ,t

\ "■ a 4 V ^ ^^"^ •K ^ °l ^ ^^< ^ \ c ?, ^- ^% s \ i fe £ t ^ — = y V ^ \, c ii '^ \ \ i s ^ ^-^ \ 8 "^ \ ^ c °s V. \ 8 -A \ N I ^ H V 1 ? \ N ^ X j^ 98 RIVER DISCHARGE. there is ponded water — the curve will, be convex to the Faxis; if it cuts the axis at the gage height of the bed of the stream the curve will be concave to the Faxis (fig. 23). When measurements are not made at the gage — for example, when low-water measurements are made by wading — the discharge should be divided by the area of the section at the gage and the resulting velocity plotted on the velocity-curve. Points so found are useful in extending the velocity-curve into low water. When the current is diagonal to the measured section the observed velocities should be reduced to velocities at right angles to the meas- ured section, but the area should not be reduced. The area is a measured quantity, while the angle of the current is usually estimated and often varies with the stage. STATION RATING CURVE. Station rating curves which show graphically the discharge corre- sponding to any stage of the stream may be plotted either on ordinary or logarithmic cross-section paper. When ordinary cross-section paper is used the measurements of discharge are plotted either with discharge and gage heights as coordinates or with discharge and A i/d as coordi- nates, in which A is the area and d is the mean depth of the cross-section. When logarithmic cross-section paper is used, discharges and gage heights are the coordinates. Ordinary cross-section paper with discharge and gage height as coordv- Tiates. — ^The usual method of constructing a rating curve for a gaging station is to plot the results of the discharge measurements on ordinary cross-section paper with gage heights and corresponding discharges as coordinates (fig. 24). The points so located define the position of a curve which is drawn among them. The horizontal and vertical scales will be so chosen that the curve may be used within the limits of accu- racy for the work, and in its critical portions will make, as nearly as may be,, angles of 45° with each axis. The discharge curve under natural special conditions, due to change in control, it may reverse at high stages and become concave to the gage axis. If a sufficient number of accurate discharge measurements are avail- able and are distributed throughout the range of stage, the discharge curve may be readily and accurately constructed. When such meas- urements are not available curves of reasonable accuracy may frequently be constructed by use of area and mean velocity curves or by one of the other methods of plotting. DISCUSSION AND USE OF DATA. 99 Gage height in feei 100 RIVER DISCHARGE. In order to determine the accuracy of the individual measurements used in locating the station rating curve it is necessary to plot, as a function of the gage height, not only the discharge but also the mean velocity and area for each measurement. In this plotting the same gage-height scale should be used. The true area curve and approximate curves of discharge and mean velocity are then drawn through the points. The relation of the plotted points of discharge to the rating curve will show any discordant measurements. Whether the discord is due to erroneous area or velocity determinations will be shown by the relation of these respective points to the area and velocity curves, and the cause of any discrepancies in either factor can then be investi- gated. Such discrepancies may arise from error of observation or of computation. The relative accuracy of the various plotted discharges having been determined, the rating curve can then ]ye drawn, due weight being given to the various measurements. Points for portions of the curve not defined by actual discharge measurements can be determined by multiplying the area by the mean velocity as measured from the curves of area and velocity. For extending the rating curve either above or below the limits of the measurements the mean velocity and area curves may be constructed, as previously described, to the stages for which the discharge curve is desired, and the discharge curve found by taking the product of the two curves. Whatever the method adopted in drawing the rating curve it should always be checked by computing the curve of mean velocity from the curves of area and discharge. If the curve of mean velocity so deter- mined is not consistent with conditions at and near the station the discharge curve should be revised. The discharge at a given stage of a rapidly rising stream is larger than for a falling or stationary stream at the same stage, as the surface slope, and hence the velocity, is greater for the first condition. This effect is but little noticed except during periods of extreme high water. At such times the water passes down the stream in a flood wave, and after the crest is passed a retarding effect may be caused which may reduce the slope practically to zero. The curves shown in fig. 25 illustrate this. Tliey are based upon the table of measurements on page 101. Thoreforo, in studying the plotted measurements, the fact whether the stream is rising, falling, or station- ary should be considered. Inasmuch as rising stages are of much shorter duration than falling or stationary stages, more weight should DISCUSSION AND USE OF DATA. 101 be giv en to measurements made on falling or stationary than on rising stages . Discharge measvremmts of Ohio River at Wheeling, W. Va. Made in 1905 by E. C. Murphy. No. Date. Area of section. Mean velocity. Gage height. Change of stage." Discharge. Sq. ft. Ft. per sec. Feet. Feet. Sec.-fi. 5 March 20 38,890 5.89 28.2 + .68 229,200 6 " 20 42,750 6.13 30.8 + .60 261,900 7 " 21 54,780 6.23 38.9 + .37 341,100 8 " 21 57,360 6.18 40.7 + .20 354,400 9 " 22 59,580 6.07 42.05 + .05 361,600 10 " 22 60,510 6.05 42.5 + .05 366,700 H " 23 58,830 5.73 41.6 -.20 336,900 12 " 23 56,790 5.60 40.3 -.27 318,100 13 " 24 49,250 5.20 35.2 -.35 255,800 14 " 24 45,550 4.99 32.7 -.40 227,300 15 " 25 37,560 4.95 27.2 -.23 186,100 16 " 25 35,050 4 80 25.5 -.14 168,100 17 " 27 30,830 4.83 22.44 -.05 149,100 «Rate of rise or fall per hour; rising +; falUng — . As the mean velocity and area curves, which are factorial curves in making the station rating curve, do not under ordinary conditions follow any mathematical law, the discharge curve will not generally be a mathematical curve. For ordinary streams it is made up of a series of parabolas. For many streams it approaches very nearly the form of a single parabola. Some engineers construct the rating curve by mathematical treatment, by use of least squares. In ordinary practice, however, this is not considered practicable, as the graphic method can be used with greater ease and speed and gives results as close as the data will justify. If the engineer is familiar with the conditions in the channel at and near the station, a few careful measurements, well distributed, may serve to define the curve of mean velocity. If slope observations are taken and the point of zero flow is determined, a very good approxi- mate rating can be made from two or three measurements. Ordinary cross -section paper, with discharge and A i/ das coordinates. — In the construction of a rating curve based on a limited number of measurements, it is evident that it is much safer to extend a straight line than a curve. Investigations have consequently been made of the component parts of the discharge curve for a quantity which is readily measurable, and to which the discharge is approximately proportional, for use in conjunction with the discharge as a coordinate for plotting the discharge curve. The area times the square root of the mean depth of the stream, Ai/d, has been found by J. C Stevens to be such a quantity. 102 RIVER DISCHARdK. From Kutter's formula Q = Ac]'^Rs may be written Q = {A\' R) (cr i). If (ci s)is constant or approximately so, then Q varies directly as (Ai/fl),and consequently when these two quantities are plotted as coordinates the result is a straight line, c is a function of s,i2,and n. R increases with the stage. It is also a matter of observation that s in general increases with the stage, the relative change being small for high stages. For comparatively large slopes the effect of s on c is insig- nificant, or, to quote Trautwine, "for slopes greater than .01 the coeffi- cient c is the same as for that slope," For flat slopes s has an appre- ciable effect on c. For a value of R greater than 3.28 feet or 1 meter, c Diatanee from in/fiat pe/nt 20 40 60 80 100 200 14000 16000 1000 2000 3000 4000 5000 GOOD 7000 6000 9000 10000 12000 Discharge in second feet Fig. 26. — Rating Curve showing Discharge as a Function of .1 i Z. and s vary inversely, while c is of itself a decreasing function of s and an increasing function of R. Hence the product of r i s may remain prac- tically constant for a given set of conditions, but for values of R less than 3.28 feet, c is an increasing function of both s and fi,and hence the product of rr s is not a constant. The vuhie of this method lies chiefly in making estimates for the higher stages and is not so generally appli- cable to shallow streams. Based on the above conditions and assumptions, discharge curves may be plotted with Q and A \/R as coordinates. It has been found, however, that d, the mean depth of cross-section, can be substituted DISCUSSION AND USE OF DATA. 103 for R and give practically the same results in plotting. It is also easier to determine d than R. In the application of this method (fig. 26) plot the elevation of the bed of the stream above gage datum and thereby obtain a cross-section. From the cross-section prepare a table giving widths, areas, mean depths and values of A] d for each foot or half-foot of gage heights. Widths may be scaled directly from the cross-section. The table of areas is quickly prepared by first computing the area for one gage height about midway of the range of stage. For increasing gage heights add success- ively the areas of trapezoids formed by the widths and gage-heights interval. For decreasing gage heights subtract these successive areas. After the table of areas has been prepared the quantities A]/ d I or A^ — ) , where w =width, can be read directly with aslide rule. On cross-section paper draw the curve oi A] ^d, using gage heights as ab- scissas, as shown in the diagram. After this curve is drawn the values oi A] d are no longer required. Lay off a scale of discharge as abscissas To plot a discharge measurement project from the horizontal scale of gage heights to the .curve of A\ d, thence horizontally to intersect the given discharge as indicated by dotted line. Points so plotted will generally conform to a straight line. The illustration (fig. 26) also shows the station rating curve, in which the same scale of discharges is used with gage heights as ordinates, shown on the left. The straight line marked "discharge as a function of ^ y d" does not pass through the origin for reasons elsewhere stated as to the effect on the coefficient c of the rapidly changing slope at this stage. There- fore, when but a single measurement is at hand the line should be drawn to intersect the scale of A \/d at some point above the origin. This point has been found to correspond approximately to the gage height at which the mean depth of flowing water is between 1 and 2 feet. In the case, frequently encountered, where there is ponded water at the gage height of zero discharge, the corresponding value of Ay d should be subtracted from the tabular values of this quantity before plotting. The gage height for which the discharge is zero can be determined by a careful examination, with levels or soundings, of the bed below the gaging section. Even in this case the straight line dis- charge curve will pass above the origin and should be treated as above outlined for conditions where ponded or dead water does not exist. Logarithmic cross-section paper. — Cross-section paper graduated log- arithmically may also be used in plotting the rating curve. On this 104 RIVER DISCHARGE. paper discharges and gage heights are plotted as coordinates. The curve resulting from the points so plotted is practically a straight line and has a corresponding advantage for extension. Logarithmic paper may give reliable results in the hands of an experienced operator, but if it is not properly and intelligently used large errors may arise. It is best used for channels with uniform conditions of cross-section and flow. The use of logarithmic cross-section paper is fully discussed on pages 129 to 137. RATING OR DISCHARGE TABLE. After the station rating curve has been constructed the next step in the computation of daily discharge is to prepare the station rating table, which gives the discharge of the stream at any stage. This table (see page 108) will be constructed either for tenths, half-tenths, or hundredths of gage height, according to the readings of the gage to which it is to be applied. The table is made by first taking the discharges for various gage heights directly from the station rating curve. These discharges are then so adjusted that the differences for successive stages shall be either constant or gradually increasing, but never decreasing unless the control of the station has changed. The station rating table so obtained is applied to the gage heights to obtain the corresponding discharges. APPLICATION OF EATING TABLE TO GAGE HEIGHTS, The first step in using records of daily gage readings in connection with a rating table to compute the flow of a stream, is to ascertain the degree of refinement necessary to give a sufficiently accurate determina- tion of discharge. In general the refinement will vary inversely with the stage and is determined by a study of the discharge rating table. Gages are usually read to hundredths, quarter tenths, half tenths, or tenths. The resulting absolute error of observation in individual read- ings are shown by the following table: Absolute errors for iwiividval gage readings. Maxinuini orror. A vornge error. Readlnas to hundrodtlis Readinsa to quarter-tenths Readings to half-tenths Readings to tontns Foot. 0.005 .0V> .026 .05 Fool. 0.0025 .006 .012 ,025 Fmatlnnai parts of Tenths of a foot. t i DISCUSSION AND USE OF DATA. 105 For staff and chain gages 2 per cent has been selected, more or less arbitrarily, as the limit of allowable average error in a daily discharge due to errors in the mean daily gage height. Th5^ table indicates that the maximum error for any one day is twice the average error, so that the maximum error for any one day may be 4 per cent. According to the principles of least squares, for fluctuating stages the average error in the monthly mean discharge resulting from a 2 per cent average error in mean daily discharge is about one-third of 1 per cent. The refinement to which the mean daily gage-height records must be used — whether to hundredths, half tenths, or tenths — in order to obtain this limit of accuracy of discharge at any given stage, will depend on the percentage of difference in discharge for such least differences in gage readings at that stage, as shown by the rating table. In determining this refinement proceed as follows and enter the results in a table of the form given below, in which the Potomac at Point of Rocks, which is read twice daily to tenths, is used as an example. Limits of accuracy in the use of gage readings. Present Readings Mini- mum Gage Heiglit Mini- mum dis- cliarge Error in discliarge due to error of .10 ft. in the gage at minimum discharge Use gage heights to— station Hun- dredths below Half tenths between Tenths above Per day To No. Foot Feet Sec. ft. Per cent Feet Feet Feet Potomac River, Point of Rocks, Md. 1 0.1 0.60 900 21. 1.0 1.0-2.0 2.0 Enter in column 1, the name of station; in column 2, the number of readings per day ; in column 3, smallest subdivision used in reading gage; in column 4, the minimum known gage height; in column 5, minimum discharge as taken from the discharge rating table or curve ; and in column 6, the percentage of error in the minimum discharge due to an error of .10 of a foot in gage height. The discharge rating table (p. 108) shows that the minimum discharge is 900 second-feet and occurs at gage height .50 foot. The difference per tenth between gage heights .50 and .60 is 190 second feet, or 21 . 1 per cent of the minimum discharge. 106 RIVER DISCHARGE. The limits of stage between which it is necessary to use mean daily gage heights to hundredths, half-tenths, and tenths, respectively, in order not to introduce an average error of over 2 per cent in the daily dis- charge are shown in columns 7, 8 and 9 and are determined by trial by testing values from the discharge rating table (p. 108) at selected half -foot intervals as follows: (a) Testing at the 2-foot gage height for gage records to tenths. The difference between the discharges at 2.00 feet and 2.10 feet is 360 second-feet. The average error of a mean daily record to tenths is one- fourth tenth (see table, p. 104). Therefore at gage height 2.00 feet the average error for such record, expressed in second-feet, is -^=90 second-feet, which is 1.8 per cent of 5,020 second-feet, the discharge at the 2-foot stage. Therefore, it is not necessary to use gage-height records closer than .10 foot above the 2-foot stage, as above this stage the average error is less than 2 per cent, which is the allowable error. (b) Testing at the 1.5-foot gage height for gage recoi-ds to tenths. The difference at this stage is 300 second-feet per tenth, -f^ = 75 second-feet, which is 2.2 per cent of 3,400 second-feet, the discharge at the 1.5-foot stage. Therefore all gage-height records below 2.00 feet should be used closer than tenths. (c) Testing at the 1.5-foot gage height for gage records to half-tenths. The difference at this stage is 300 second-feet per tenth . The average error of a mean daily record to half-tenths is -j~ = 38 second-feet, which is 1.1 per cent of 3,400 second-feet, the discharge at 1.5 foot stage. Therefore all gage-height records between 1.5 and 2.00 feet should be used to half-tenths. A continuation of this analysis shows that in order to keep the dis- charge error resulting from lack of refinement in gage readings, below 2 per cent, the gage at Point of Rocks should have been read to hun- dredths at all stages and used to hundredths below the 1-foot stage, to. half-tenths between 1.0 feet and 2.0 feet, and to tenths above 2.0 feet, instead of to tenths for all stages, as shown in the table of daily gage heights, page 108. An analysis of the gage readings for each station, as thus outlined, is essential if accurate and consistent results are to be obtained. It will show, not only the limits of accuracy to which gage records should be used, but also the refinement to which gage heights should be observed. In order to avoid confusion in reading, a'll observations should be made to the greatest refinement required for any stage, and in the computa- tions the hundredths should be discarded as described above. DISCUSSION AND USE OF DATA. 107 For automatic gage records the same procedure is followed except that the allowable error should be 1 per cent. For stations with shifting channels the methods of analysis above described can be used only in a general way. In practice the limits of use of gage heights can be readily determined by the following rules: Find the stage at which the difference in discharge per tenth is 8 per cent of the discharge at that stage. Gage heights above this stage should be used to tenths. Find the stage at which the difference in discharge per tenth is 16 per cent of the discharge at that stage. Gage heights below this stage should be used to hundredths. Gage heights between the first and second stages should be used to half-tenths. The following tables and figs. 24 and 26 illustrate the method of determining daily discharge of streams with permanent beds: Discharge measurements of Potomac River at Point of Rocks, Md., in 1902-7. Date. 1902 June 22 Sept. 2 1903 Mar. 12 Apr. 17 Apr. 17 Apr. 18 Sept. 14 Nov. 9 1904 July 11 1905 Mar. 13 June 20 Oct. 30 Nov. 9 Nov. 9 1906 May 30 Dec. 7 1907 Uar. 15 Hydrographer. Newell and Paul E. G. Paul E. C. Murphy Hoyt and Paul Hoyt and Stokes Hoyt and Stokes Paul and Sawyer W. C. Sawyer Hoyt and Grover Tillinghast and Comstock Grover and Lyman G. F. Harley G. F. Harley Harley and Stewart R. FoUansbee R. H. Bolster R. H. Bolster Area of section. Sq. ft. 2,897 2,356 6,600 17,250 16,500 12,180 2,950 2,590 8,600 2,727 3,532 2,703 2,703 3,351 3,180 21,460 Mean velocity. Ft. per sec. 1.01 .73 2.86 5.01 4.88 4.44 1.28 .83 3.33 1.10 1.38 .94 .91 1.16 1.40 5.31 Gage height. Feet. 1.25 .87 4.84 13.70 13.10 9.60 1.50 1.12 3.87 6.56 1.29 2.05 1.20 1.20 1.70 1.76 16.95 Discharge Sec.-ft. 2,921 1,717 18,880 86,420 80,520 54,080 3,770 2,140 13,750 28,640 2,997 4.889 2,531 2 467 3,892- 4,450 114,000 108 RIVER DISCHARGE. Rating table for Potomac River at Point of Rocks, Md., from April 1, 1902, to December 31, 1906. Gage Dia- Differ- Gage Dis- Differ- Gage height. Dis- Diffei* height. charge. ence. height. charge. ence. charge. ence. Feet. Sec. -ft. Sec.-ft. Feet. Sec.-n. Sec.-n. Feet. Sec.-ft. Sec.-ft. 0.50 900 2.40 6,620 390 4.60 17,430 1,160 .60 1,090 190 .50 6,920 400 .80 18,610 1,180 .70 1,295 205 .60 7,330 410 5.00 19,820 1,210 .80 1,515 220 .70 7,750 420 .20 21 ,060 1,240 .90 1,750 235 .83 8,180 430 ' .40 22,300 1,240 1.00 2,000 250 .90 8,620 440 .60 23,560 1,260 .10 2,263 260 3.00 9,070 450 .80 24,840 1,280 .20 2,530 270 .10 9,530 460 6.00 26,140 1300 .30 2,810 283 .20 10,000 470 .20 27, im 1.320 .40 3,100 290 .30 10.480 480 .40 28,780 1,320 .50 3,40.1 303 .40 10,970 490 .60 30,100 1,320 .60 3,703 300 .50 11,470 500 .80 31,460 1,360 .70 4,010 310 .60 11,980 510 7.00 32,820 1,360 .80 4.330 320 .70 12,490 510 .60 3fi,340 3.520 .90 4,670 340 .80 13,010 520 8.00 39,980 3,640 2.00 5,020 350 .90 13,530 520 .50 43,740 3,760 .10 5,383 360 4.00 14,070 540 9.00 47,600 3,860 .20 5,750 370 .20 15.150 1,080 .50 51^60 3,960 .30 6,130 380 .40 16,270 1,120 10 00 66,600 4,040 Note: The above table is applicable only for opsn-chainel conditiois. It £■? based on discharge measurements made during 1902 to 1907. It is well defined between gage heights 1.0 feet and 17.0 feet. Above gage height 10 feet the rating curve is a tangent, ther difference being 830 per tenth. Daily gage heights and discharges of Potomic River at Point of Rocks, Md., for July to December, 1904. July. August. September. October. November. December. Day. . . . Is si P| "4 Si ^i 1 Feet. Sec.-ft. Feet. Sec. -ft. Feet. Sec.-ft. Feet. Sec.-ft. Feet. Sec. -ft. Feet. Sec.-ft. 1 1.4 3,100 1.4 3,100 0.9 1,750 0.6 1,090 0.6 1,090 0.8 1,515 2 1.3 2,810 1.3 2,810 .8 1,515 .6 1,090 .6 1,000 .8 1,515 3 1.3 2,810 1.2 2,530 .8 1,515 .6 1,000 .7 1,295 .8 1,515 4 1.3 2,810 1.2 2,530 .8 1,515 .6 1,090 . 7 1,205 .8 1.515 5 1.2 2,530 1.2 2,530 .9 1,750 .6 1,090 7 1,205 .8 1.515 6 1.5 3,400 1.2 2,530 1.0 2,000 .6 1,090 7 1,205 .8 1,515 7 1.5 3,40,1 1.3 2,810 .9 1,750 .6 1,090 7 1.295 .8 1.515 8 1.6 3,700 1.4 3,100 .8 1,515 .6 1,000 7 1.295 .8 1.515 9 1.6 3,700 1.5 3,400 .7 1,295 .5 000 . 7 1,205 .8 1,515 10 1.7 4,010 1.4 3,100 .7 1,295 .5 000 7 1,295 .0 1,750 11 2.9 8,620 1.3 2,810 .7 1,295 .5 900 .7 1,295 .0 1,750 12 2.6 7,330 1.3 2,810 ,8 1,515 .6 1,000 .7 1,205 .0 1.750 13 3.4 10,970 1.2 2,530 1.0 2,000 .7 1,205 .7 1,205 9 1,750 14 3.1 9,530 1.2 2,530 .0 1,750 .7 1,295 .8 1,515 .0 1,750 15 3.0 9,070 1,1 2,260 .0 1,750 .6 1,000 .8 1515 .0 1,750 16 2.8 8,180 1,1 2,260 1.0 2,000 .6 1.000 .8 1.515 1,750 17 2.4 6,520 1,1 2,260 1.0 2,000 .5 000 .7 1,205 .9 1,750 18 2,0 5,020 1.0 2,000 .0 1750 .6 000 S 1.515 ,9 1,750 10 1.8 4,330 1.0 2,000 .8 1,515 .5 900 8 1.515 .0 1.750 20 1.6 3,700 1.0 2,000 .7 1,295 .6 1,000 .8 1.515 1.0 2,000 21 1.4 3,100 1.0 2.000 .8 1.515 1.0 2,000 1,295 1.0 2.000 22 1,4 3,100 .9 1,750 1.0 2,000 .9 1,750 1,205 1.0 2,000 23 1.3 2,810 .9 1,750 .0 1,760 .8 1.515 1.205 1.0 2,000 24 1.3 2,810 1.0 2,000 .8 1,616 .7 1.295 1.205 1.0 2,000 25 1.3 2,810 1 .0 2,000 .8 1,616 .7 1,295 1.205 1.1 2,260 26 1.4 3,100 1.2 2,530 .8 1,616 .7 1.205 1.295 1.4 3.100 27 1.4 3,100 1.1 2,260 .7 1,295 .7 1,295 1,205 1.5 3,400 28 1.4 3,100 1.1 2,260 .7 1,296 .7 1,205 1,205 1.8 4,330 29 1.5 3,400 1.0 2,000 .7 1,295 .6 1,000 !s 1,615 1.8 4,330 30 1.5 3,400 1.0 2,000 .7 1,295 .6 1.000 ,8 1,515 1.0 4,670 31 1.5 3.400 .9 1,750 .6 1,000 36,080 2.0 5,020 Total. . . 130,670 74,200 47,760 40.200 68.245 Mean . . 4,506 1 2,304 1,502 1,164 1,340 2.201 DISCUSSION AND USE OF DATA. 109 MonlMy discharge of Potomac River at Point of Rocks, Md., for 1904. Discharge in second-feet. Run-oef. Month. Maximum. Minimum. Mean. Second-feet per sq. mi. Depth in inches. Acre-feet. July . . . 10,970 3,400 2,000 2,000 1,515 5.020 10,970 2,530 1,750 1,295 900 1,090 1,515 900 4,305 2,394 1,592 1,164 1,340 2,201 2,199 .467 .248 .165 .121 .139 .228 .228 .538 .286 .184 .140 .155 .263 1.556 277,300 147,200 September October 94,730 71,570 November 79,740 135,300 The period 805,840 GAGING STATIONS WITH CHANGEABLE BEDS. The determination of the daily discharge of streams with changeable beds is more difficult than of those with permanent beds. The method used varies with the rapidity of the changes. The base data for such determinations are the same as those used for permanent beds, but more frequent discharge measurements are necessary, as otherwise the results obtained are only roughly approximate. PEKIODICALLY CHANGING BEDS. For stations with beds which shift slowly or are changed only during floods, station rating curves can be prepared as above described for periods between changes, and satisfactory results can be obtained with two or three measurements a month, provided measurements are taken soon after such changes take place. CONSTANTLY CHANGING BEDS. For streams with continually shifting beds, as the Colorado and Rio Grande, discharge measurements should be made every two or three days and the discharge for the intervening days estimated by interpola- tion, modified by the gage heights for these days. There are two methods of making these interpolations, the Stout and the Bolster methods, known by the names of their inventors. Stout method. — In the Stout method an approximate station rating curve and rating table are prepared from the discharge measurements and applied to modified or so-called corrected daUy gage heights. The gage heights are corrected by means of a curve (fig. 27) determined by plotting as ordinates the differences between the actual gage heights at the time of the various discharge measurements and the gage height 110 RIVER DISCHARGE. corresponding on the approximate curve to the respective measured discharges, and as abscissas the corresponding days of the months. Through these points an irregular curve is drawn, from which can be found the correction for days other than those on which measurements were made. The correction is positive if the discharge is greater than that given by the station rating curve, negative if less. Each daily gage height is then corrected by the amount indicated on the correction curve, and the discharge corresponding thereto is taken from the approx- imate rating table. Bolster method.— In the Bolster method the discharge measurements for the entire year are first plotted with discharges as abscissas and gage heights as ordinates. The points so plotted are considered chrono- logically and, even though scattered, will usually locate one or more fairly well-defined curves, called standard curves (fig. 27). In general the number and position of these standard curves is determined by the radical changes in the stream bed due to floods. When beds change very rapidly it is necessary to change the position of the rating curve from day to day, making practically a new curve daily. This daily curve is of the same form as the standard curve and is parallel to it with respect to ordinates. For a day when a measurement is made the, rating curve passes through such plotted measurement. In order to locate a rating curve for other days a line connecting consecu- tive measurements is drawn and divided into as mam- equal parts as there are days intervening between the measurements, on the assump- tion that the change in conditions of flow between any two consecutive measurements is uniform from day to day. The daily rating curve will then pass through these points of division, and the discharge is read directly from these curves by applying to them the observed daily gage heights. In order to facilitate the use of the method and to make it as rapid in application as the common method for permanent stations the stand- ard curve or curves, together with a vertical line of reference, should be transferred from the original station sheet to tracing cloth, which can be readily shifted vertically to any desired position by always keeping the two reference lines coincident with oach other. In applying and modifying this method judgment must be used for long time intervals of no measurements, or for radical changes in the stream bed caused by Muddcii floods. Tlie tables on pages 112-113 and figure 27 illustrate the Bolster and the Stout metiiods of obtaining daily discharge. DISCUSSION AND USE OF DATA. Ill Gage Helmut in feat vs - >, ^. ,^ \ S \ 1" re > s ^ V <\^ S \ ^ 1. f \ \ s \ \ s \ ''^ N \ •I) — X A \ V ?. 9 Ms ■■31 s \^ \ \ \^. 1 ^ \ \ V - \o A \ \^ 'z. r\j > ;^ \^ \; N> O \ G •t^ ,NJ \ \ Juf elO \ \t, \^ \ N*^^ 3 \ - \: \ ' ,> \ V !n i - \ 7J \f \ V*^ 3' \ N*^ .\ ^ \ V V - \ v^ % \ ) \ xn Jul e20 - \o> \ \ \ s: *>9 <-f \ \ \^ 3 \ \ \ \ rr N ■T\ \ \ \ \ I. \*^ \ \ \ \ \ feet 112 RIVER DISCHARGE. List of meaaurements to illustrate the Stout and the Bolster methods of determining daily discharge. No. Date. Gage height. Discharge. Feet. Sec.-ft. 1 June 1 2.55 3700 2 6 .55 500 3 14 1.4 1200 4 22 1.2 600 5 July 2 1.5 500 6 18 3.8 6460 7 20 2.2 2330 8 22 .4 200 9 31 .9 150 Daily gage heights and discharges to illustrate the Stout and the Bolster methods of determining daily discharge. June. July. Day. Observed Discharge, Corrected Discharge, Observed Discharge, Corrected Discharge, hMghts. Bolster gage- Stout heights. Bolster heights. Stout method. heights. method. method. method Feel. Sec. -ft. Feet. Sec.-fl. Feet. Sec.-n. Feet. Sec.-fl. 1 3.0 4870 3.3 4970 1.6 530 .85 520 2 2.5 3580 2.8 3650 1.5 500 .85 520 3 2.0 2490 2.3 2530 1.5 570 .85 520 4 1.5 1610 1.8 1640 1.6 730 .95 605 5 1.0 930 1.3 960 1.6 780 1.0 650 6 .1 390 .65 365 1.8 1050 1.25 905 7 .6 510 .85 520 1.7 970 1.2 850 8 .6 490 .85 520 - 1.7 1020 1.25 905 9 .7 550 .95 605 1.9 1320 1.55 1280 10 .8 620 1.0 650 2.0 1510 1.7 1490 11 1.0 800 1.2 850 2.2 1890 2.0 1970 12 1.5 1400 1.65 1420 2.6 2720 2.45 2850 13 1.4 1240 1.55 1280 3.0 3700 2.9 3900 14 1.4 1200 1.5 1210 3.6 5440 3.5 aaan 15 1.3 1020 1.35 1020 3.7 5850 3.65 6000 16 1.1 760 1.15 800 3.6 5370 3.5 .■>550 17 1.0 620 1.0 650 3.2 4610 3.2 4690 18 1.0 680 .95 605 3.7 6150 3.7 6150 19 1.1 640 1.0 650 4.0 7080 4.0 7080 20 1.2 690 1.05 700 3.0 4160 3,0 4160 21 1.2 650 1.0 650 1.8 1640 1.8 1640 22 1.3 690 1.05 700 .8 480 .8 480 23 1.5 850 1.2 850 .3 120 .3 150 24 1.8 1170 1.45 1140 .3 100 .25 130 25 1.7 990 1.3 960 .4 110 .35 175 26 1.6 830 1.15 800 .4 90 .3 150 27 1.6 780 1.1 750 .8 130 .4 200 28 1.6 740 1.05 700 .7 ISO .45 230 29 1.6 700 1.0 650 .8 170 .45 230 30 1.6 660 .95 606 .9 180 .4 200 31 1.0 200 .4 200 Totals. 33050 33400 69320 59930 Means . 1102 1113 1914 1933 DISCUSSION AND USE OF DATA. 113 Rating table to illustrate the Stout method of determining daily discharge. Gage Dis- Gage Di^- Gage Dis- Gage Dis- Gage Dis- height. charge. height. cliarge. height. charge. height. charge. Sec.-ft. height. charge. Feet. Sec. -ft. Feet. Scc.-ft. Feet. Sec.-fl. Feet. Feet. Sec. -ft. 0.00 60 1.00 050 2.00 1070 3.00 4160 4.00 7080 .10 80 .10 750 .10 21S0 .10 4423 .20 no .20 850 .20 2330 .20 4690 .30 150 .30 960 .30 2530 .30 4970 .40 200 .40 1080 .40 2740 .40 5260 .50 260 .50 1210 .60 2960 .50 6550 .60 330 .60 1350 .60 3180 .60 5850 .70 400 .70 1490 .70 3410 .70 6150 .80 480 .80 1640 .80 3650 .80 6460 .90 560 .90 1800 .90 3900 .90 6770 ICE-COVERED STREAMS.^ Ice occurs in rivers in three forms — surface ice, anchor ice and frazil. Surface ice may occur as a complete cover, supported by the water, or bridged from bank to bank, free from or partly supported by the water, as in ice jams due to piling up of ice, or as alternate layers of ice and water. Anchor ice may be attached to the bed of the river where it has been formed, or it may be floating in suspension. Fxazil usually occurs floating in suspension. The presence of ice in a stream in any form may destroy the open- water relation of discharge to stage by causing backwater and thus increasing the stage for a given discharge. Therefore discharge measure- ments of a stream in which ice is present will always plot either at the left of or on the open-water curve. Under no circumstances will they plot to the right provided the measurement represents the correct flow. It is not necessary that ice be present at the measuring section or at the normal control section to destroy the relation of stage to discharge. The existence of ice far below the control section may establish a temporary control which will affect the station rating. The data necessary for computing flow during periods of ice are — 1. Measurements of discharge made during the period. 2. Records of stage read to the surface of the water in a hole cut through the ice. 3. Records of temperature and precipitation. 4. Full notes in regard to the ice. The complex manner in which ice may form and the varying condi- tions presented by streams preclude the formulation of any method that can be universally employed to determine winter flow. In general the following method s may be used: a See Water-Supply Paper No. 337, U. S. Geo'. Survey. 114 RIVER DISCHARGE. 1 . The readings of gage heights to the water surface may be directly applied to the open-water rating curve. 2. The observed gage heights may be applied directly to a special rating curve based on winter discharge measurements and gage heights to water surface. 3. Discharge measurements may be used in connection with gage heights and with data showing climatic conditions and the occurrence of ice. This method may be applied either by the eye or graphically, as will be explained, for determining corrections to the gage heights neces- sary for making the open-channel rating curve applicable. FIRST METHOD. The use of the first method to determine the daily discharge of a frozen stream — the application of water-surface gage readings to the open-water rating curve — is advisable only when the stream is open at the control section and no backwater exists at the gage. If the control section is entirely free from ice the relation between slope, stage, and discharge will not be appreciably changed even by complete ice cover between the control section and the gage. In using this method the engineer should closely inspect the gage- height records and compare them with temperature records to detect the presence of backwater. If discharge measurements made in several winters have shown that ice rarely occurs at the control section and that the regular open- water curve is applicable fewer measurements are needed with this method than with any other. An open-control section, how- ever, with ice above, implies as a rule that the control section is at rapids at which anchor ice is likely to form . In order to detect the presence of anchor ice during extremely cold periods the gage should be read twice a day. Readings higher in the morning than in the after- noon indicate the presence of anchor ice, and care must be taken to read the gage soon after the point of maximum daily temperature, when the control section is likely to be clear. SKCOND MKTHO]). The conditions favorable to the use of the second method — in which observed gage heights are applied directly to a special rating curve based on winter discharge measurements and gage heights to the water sur- face — are most likely to be found on the larger rivers, where the slope and cross-section may be fairly uniform for long stretches. In general, however, this method should be used with great care and the period of DISCUSSION AND USE OF DATA. 115 applicability of the curve should be closely determined by discharge measurements. On a large stream that freezes uniformly and that varies little in flow all discharge measurements made when the ice has reached its perma- nent condition may plot on a curve, but it is evident that this curve will not correctly represent the relation of stage to discharge in the period of transition from open water to solid ice, and vice versa. It will also not represent conditions if between the times of measurement the character of the ice cover has changed greatly as a result of changes in tempera- ture. If backwater is caused by a combination of anchor and surface ice, discharge measurements made at certain times might give a smooth curve that would in reality not apply except on the days of measure- ment. This method should be used only when many discharge measurements have been found to plot on a smooth curve and when conditions of temperature and ice are stable for long periods. THIRD METHOD. Eye method. — The method most commonly employed at the present time to determine the flow of streams either partly or completely covered with ice is that which utilizes the discharge measurements and data regarding climatic conditions and the occurrence of ice in connection with observed gage heights by means of eye-inspection of records of tem- perature, precipitation, and gage heights, estimating the daily discharge for the period between times of measurement, and adjusting the deter- minations by comparing with results obtained at near-by stations. The monthly mean of such determinations is also compared with monthly means at adjacent stations in order that any large error may be detected. The accuracy of this method depends largely on the uniformity of stream flow between times of measurements, the number of measure- ments, and the engineer's knowledge of general conditions. Care must be taken that the discharge, as estimated, is not greater than would be given by the application of gage heights to the open-water rating curve. In general this method should give more accurate results than the second method, because it considers the time and temperature factors. The method will give good results at stations in localities where tem- peratures are fairly constant over long periods of time and where the flow is affected by surface rather than by anchor ice. Under such con- ditions fewer measurements and gage readings are required than at 116 RIVER DISCHARGE. stations situated where climatic conditions are irregular. Temperature records from the nearest Weather Bureau station are generally sufficient. The disadvantage of this method is that it is impossible to check its results, as no record is left of steps employed. Graphic method.'^ — As ice causes backwater it is only necessary to determine the magnitude of the backwater effect in order to find the true fiow at a given stage. Since the formation of ice is due entirely to temperature, the amount of backwater will in general vary with temperature. The magnitude of the backwater effect at any given time can be determined by measurements of discharge. If such measurements are made at stated intervals during the winter the backwater effect between times of measurement can be determined by constructing a curve of backwater. In constructing this curve (see fig. 28) proceed as follows: 1. Plot the observed daily gage heights. 2. Plot the mean daily temperatures. 3. Plot the daily precipitation. 4. Plot on the curve of observed daily gage heights the gage heights corresponding to the measured discharges as determined from the open- water rating table. The differences between these gage heights and the observed gage heights measure the backwater effects for the days in Question. 5. Plot the backwater effects as determined under 4 and through these plotted points construct a backwater curve, following the same general shape as the inverted temperature curve, taking into account the daily precipitation (if rain), ice jams, and other unusual conditions that may affect the records of stage. 6. From the backwater curve construct the curve of corrected gage heights, from which the true discharge can be obtained by applying the open-water rating table. Aside from giving more accurate results, this method has an advantage over any other method in furnishing a complete record of all the steps taken, thus making it possible for a second person to review or check the estimates. The accuracy of the results obtainable by this method will depend on tlie frctiuency of the discharge measurements, ^\'hen winter conditions are comparatively constant, fewer measurements will be required, as the principal uncortaintios occur during transition periods from cold to warm weather. A special form, see fig. 29, is desirable for use in computing winter flow. "■The graphic method wus flrst proposed by W. Q. Iloyt, Assoc. M. Am. See. C. E., Eng. News Vol. 69, pp. 725-727, Apr. 10, 1913. DISCUSSION AND USE OF DATA. 117 Backwater, tn feet Temperature, 'fahrenheit Gage height, infect o K S. o, S. ro w *► I PRECIPITATI IN IN INCHES 1 ■z. ? o < f ^ iC / < z s V^ ~x^ ^ t ~3 > 3 V =- c j -~^ 1 iB U / c ( ^ ^ y r " ■ o o ; ., ^ 2 -== n t ! 1 /' i ~~~~-i < > TO. Ei o / ) __,J — -^ tra IT 4 3 m c x^ ■• V 2 J p ^> — -^^ ' "v T 3 h- V ' 3 TJ _ ■ "Y i i) ! t 3 ™ L - 0) - \ ^ 0) 1 — -^ ^ , ' 3 _ a y < - ;;5 J •1 .^r <, 3 '3 - ■c. ^v *c 1^^ < ^ ^ F IT T C o c =• — /" ^-' .-.: ■-^ ^ 3 / 11 "*,._ t.- T ^ "T s / • / / ? ) T 2 lU « c: < „? » T^ "■JV- c i_ . O* 00 5 io q -/ee/ -/iy^rograph p dt S o ^ g S S ^ g C ^ s \ ^ ss ^ ci. ■ — Z3 f -s ■U ^ o -c -is s. Oi -O. g -= _, t ^ s ^ — > •s i 5" - — ' t- s^ § 1 t f ::::= =- 3) N, ¥ < ^ < . ^ i?5 1 i ^ >.s ^ ^ ~ \ ^' c — =- \ <. « 8 o - ^ S ^■' •^ V < ^ ■ r-i \ r **. 5> ' ^ ' 6 (^ ^ - \ (^ g \ ^ it V < § !S v I ^ - "f5 \ ( ^ IS \ ^s X ■ ■ -^ o i \, •>* ) \ \ "l X \ ■ -s \ it --S iS2 e- "" "^v ' — - - l^ ^'" ^) J ^ fi h c > r ^ c 5S' Oisc^arge in tfTousanef ^eco/7£/-/^ef for Duraf/on Curye. 124 BIVER DISCHARGE. case uhe duration as well as the quantity of the flow is essential. In order to obtain a reliable idea of the conditions of flow that may be expected, several years' records of daily flow should be available for study and comparison. The duration of flow for a given year maybe determined by tabulating, as shown in the following table, the values of the various daily flows in order of their magnitude, and then tabulating the number of days of the year on which each flow occurs. The sum of the numbers in the " Number of days " column up to any given flow will give the number of days when the flow is less than that indicated in the " Discharge " column, or the number of days deficiency. The column should be filled out showing deficiency for each discharge. By plotting the discharge as abscissas and the number of days defi- ciencies as ordinates, a curve (fig. 30) can be constructed which shows the number of days during the year when the discharge is below any given amount. The horsepower corresponding to the various discharges can then be computed and tabulated on the sheets with the discharge, which will show the number of days when an auxiliary will have to be used for given development. In computing the horsepower the loss of head caused by backwater, if any, should be taken into account. Discharge and horsepower table j •>r Potomac River at Point of Rocks, Md., for 1904. DischarEB in sec. -ft. Horse- power (80% e£f.) per toot tall. Number days duration between consecutive values of discharge ' in first column. Days of c •-3 i J3 i 'S ^ >1 1 d5 a s *-> 1 1 1 a; a 1 deficient discharge. 900 990 1,100 1,330 1.540 1,760 1,980 2,200 2.750 3,300 3,850 4,400 4,950 5,500 6,600 7,700 8,800 9,900 11,000 13,200 15,400 17,600 19,800 22,000 27,500 33,000 38,500 82 90 100 120 140 160 180 200 250 300 350 400 450 500 600 700 800 900 1,000 1,200 1,400 1,600 1,800 2,000 2,500 3,000 3,500 2 2 1 '2 *j i 1 i 3 1 i 7 4 3 1 2 3 3 3 1 2 1 ■3 3 2 4 5 4 1 4 '3 i i 10 6 4 3 2 2 i '2 5 2 ■3 2 4 2 1 1 1 2 2 2 'i 1 12 8 2 'i 1 1 2 2 1 3 8 12 7 1 8 10 7 5 6 15 7 1 1 i '2 20 8 9 10 '5 1 1 1 2 1 1 6 17 35 28 21 ig 14 21 35 11 3 13 26 19 14 14 9 17 11 6 5 7 7 5 3 e" 23 58 86 107 "i26" 140 161 196 207 210 223 249 268 282 296 305 322 333 339 344 351 358 363 366 Total davs 31 29 31 30 31 30 31 31 30 31 30 31 366 DISCUSSION AND USE OF DATA. SUGGESTIONS FOR ESTIMATING DISCHARGE. 125 The engineer is often called upon for estimates of flow of streams on which few if any measurements of discharge have been made. In such cases it is necessary to prepare estimates of discharge and run-off for the stream basin by comparison of that basin with others for which records are available. When no measurements of discharge are available the estimates are made by determining from records at other stations the probable dis- charge and run-off per square mile from the area under consideration. This multiplied by the drainage area gives the discharge. Such com- parisons can be safely made, however, only when the streams used are in the same section of the country and are similar in character. The table, pp. 146-149, give the run-off per square mile from areas in the northeastern United States. When few measurements are available coefficients may be determined by means of which the discharge can be computed from the records at a neighboring station. Rainfall data are of use as a check on estimates of flow, and they also show years of high and low water. As noted in Chapter VI, care should be exercised in their use. HYDROGRAPHS. , In order to show graphically the daily and seasonal distribution of flow of a stream for comparative purposes, hydrographs (fig. 30) are prepared by plotting the daily discharge for each day during the year and connecting the points so plotted by a curve. These curves are of use not only in studying the variations in flow from year to year, but may also be used in storage problems, where the total quantity of water is an essential factor. The mass curve may also be used to advantage in the study of storage. (See Water-Supply Paper No. 197, U. S. Geol. Survey.) MEASUREMENT OF DRAINAGE AREAS FROM MAPS. In connection with most hydrologic studies it is necessary to obtain an estimate of the area of the drainage basin under consideration, and it will usually be necessary for the engineer to measure such areas. Accompanying most planimeters are tables giving either (1) the proper settings of the arm for maps of various scales so that the plani- meter readings will give the area directly, or, (2) the settings so that the readings will give square inches and coefficients to be used in con- 126 RIVER DISCHARGE. nection with maps of various scales for reducing these readings to square miles. In measuring drainage areas, however, it is more satis- factory to calibrate the planimeter, with the arm at any setting, directly from the map on which the area is to be measured rather than to use those tables. This method is applicable to maps constructed either on the Mercator or on the polyconic projection. By it considerable time is saved in making the measurement and greater accuracy is obtainable, as errors due to shrinkage or stretch of paper and those due to the planimeter itself, are eliminated. The calibration is readily made by determining the number of revo- lutions of the planimeter wheel for a quadrangle of equal extent in latitude and longitude for which the area is given in standard tables similar to those shown on pages 127 and 128. The area at the given latitude corresponding to a revolution of the planimeter wheel for the map used, may then be determined by dividing the area of the meas- ured quadrangle by the number of revolutions of the planimeter wheel, thus calibrating the instrument for that latitude and map. In the calibration a quadrangle should be chosen, the middle parallel of which passes approximately through the center of gravity of the area. This is necessary in order to equalize the variation in area due to differ- ences in latitude. In case the area extends over several degrees of latitude, it may be necessary to divide it into two or more parts and calibrate the planimeter for each part. In determining an area it is necessary to measure only the portions which do not occupy full quadrangles as the areas for full quadrangles can be. taken directly from the tables. In using the planimeter, start at any observed wheel reading, without attempting to set the arm at zero. Move the pointer around the area in a clockwise direction and observe the final wheel reading. Change the position of the planimeter wheel on the paper, observe the initial reading and move the pointer around the area in a counter-clockwise direction and observe the final wheel reading. The differences between the initial and final readings in the two runs respectively should be very small and their mean will be the mean reading for the area. The double tracing of the area in this manner gives a check on the reading and when applied as explained removes the error due to lag of the instrument. In some cases it is convenient to calibrate the planimeter, using the area of a State or county instead of the area of a quadrilateral. Areas of quadrilaterals of various sizes may be found in " Geographic Tables and Formulas," United States Geological Survey, from which the tables DISCUSSION AND USE OF DATA. 12 1 Areas of quadrilaterals of the earth's surface of SO' extent in latitude and longitude. Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. o / 00 1, 188. 10 11 / 00 1, 166. 84 22 / 00 1,103.68 15 1,188.08 11 15 1,165.86 22 15 1,101.77 30 1, 188. 05 11 .30 1, 164. 86 22 30 1, 099. 84 45 1, 188. 00 11 45 1, 163. 85 22 45' 1,097.88 1 00 1,187.92 12 00 1, 162. 81 23 00 1, 095. 91 I 15 1,187.82 12 15 1,161.75 23 15 1,093.92 1 30 1, 187. 70 12 30 1, 160. 67 23 30 1, 091. 90 1 45 1,187.56 12 45 1, 159. 56 23 45 1, 089. 87 2 00 1,187.39 13 00 1,158.44 24 00 1, 087. 81 2 15 1,187.20 13 15 1,157.29 24 15 1, 085. 74 2 30 1, 186. 99 13 30 1, 156. 12 24 30 1,083.64 2 45 1,186.76 13 45 1, 154. 93 24 45 1,081.52 3 00 1,186.51 14 00 1,153.72 25 00 1, 079. 39 3 15 1, 186. 24 14 15 1,152.48 25 15 1, 077. 23 3 30 1, 185. 95 14 30 1,151.23 25 30 1, 075. 05 3 45 1, 185. 62 14 45 1, 149. 95 25 45 1, 072. 85 4 00 1, 185. 28 15 00 1, 148. 65 26 00 1,070.64 4 15 1,184.92 15 15 1, 147. 33 26 15 1,068.40 4 30 1, 184. 53 15 30 1,145.99 26 30 1,066.14 4 45 1, 184. 13 15 45 1,144.63 26 45 1, 063. 86 5 00 1, 183. 70 16 00 1,143.25 27 00 1,061.56 5 15 1, 183. 24 16 15 1,141.84 27 15 1,059.24 5 30 1, 182. 77 16 30 1,140.41 27 30 1,056.90 5 45 1, 182. 28 16 45 1, 138. 96 27 45 1, 054. 54 6 00 1,181.76 17 00 1, 137. oO 28 00 1,052.16 6 15 1,181.22 17 15 1,136.00 28 15 1,049.76 6 30 1, 180. 66 17 30 1,134.49 28 30 1,047.34 6 45 1, 180. 08 17 45 1, 132. 96 28 45 1, 044. 90 7 00 1,179.48 18 00 1,131.41 29 00 1,042.44 7 15 1, 178. 85 18 15 1,129.83 29 15 1,039.97 ,7 30 1,178.20 18 30 1,128.24 29 30 1,037.47 7 45 1,177.53 18 45 1, 126. 62 29 45 1,034.95 8 00 1, 176. 84 19 00 1,124.98 30 00 1,032.41 8 15 1, 176. 13 19 15 1,123.32 30 15 1,029.85 8 30 1,175.39 19 30 1,121.64 30 30 1,027.27 8, 45 1,174.63 19 45 1,119.93 30 45 1,024.68 9 00 1, 173. 86 20 00 1,118.21 31 00 1, 022. 06 9 15 1,173.06 20 15 1,116.47 31 15 1,019.43 9 30 1, 172. 23 20 30 1,114.71 31 30 1,016.77 9 45 1,171.39 20 45 1,112.92 31 45 1,014.10 10 00 1, 170. 52 21 00 1,111.11 32 00 1, Oil. 40 10 15 1, 169.63 21 15 1, 109. 28 32 15 1,008.69 • 10 30 1,168.73 21 30 1,107.44 32 30 1, 005. 96 10 45 1, 167. 80 21 45 1,105.57 32 45 1, 003. 20 128 RIVER DISCHARGE. Areas of (juadrilaterals of the earth's surface of SO' extent in latitude and longi- tude (continued). Middle lati- tude of quadrilateral. Area in square miles. Middle lati- . tude of quadrilateral. Area in square miles. Middle lati- tude of quadrilateral. Area in square miles. 33 / 00 1, 000. 43 44 00 860. 25 65 f 00 687.70 33 15 997.64 44 15 856.-67 55 16 683.44 33 30 994. 83 44 30 853.07 65 30 679. 17 33 45 992.00 44 45 849. 46 55 46 674. 89 34 00 989. 16 45 00 845. 82 56 00 670.60 34 15 986. 29 45 15 842.18 56 16 666.29 34 30 983. 41 45 30 838. 61 56 30 661. 97 34 45 980. 50 45 45 834.83 56 46 657.64 35 00 977. 58 46 00 831. 13 67 00 653.29 35 15 974. 64 46 15 827. 42 57 16 648. 93 35 30 971. 68 46 30 823. 68 67 30 644.55 35 45 968. 70 46 45 819. 94 57 46 640.17 36 00 965. 70 47 00 816. 18 68 00 636.77 36 15 962. 68 47 15 812.40 58 15 &31.36 36 30 959.65 47 30 808:60 58 30 626. 93 36 45 956.60 47 45 804. 79 58 46 622.49 37 00 953. 52 48 00 800.97 69 00 618. 06 37 15 950.43 48 15 197. 13 59 15 613. 69 37 30 947. 32 48 30 793. 27 69 30 609.11 37 45 944.21 48 45 789. 39 69 46 604.62 38 00 941. 05 49 00 785.50 60 00 600.13 38 15 ■937. 88 49 15 781. 60 60 15 595.62 38 30 934.71 49 30 777: 68 60 30 591.09 38 45 931.51 49 45 773. 74 60 45 586.56 39 00 928.29 50 00 769. 79 61 00 582.01 39 15 925.06 50 15 765. 83 61 15 577.46 39 30 921. 80 50 30 761.85 61 30 672.88 39 45 918. 53 50 45 757. 85 61 45 568.30 40 00 915. 25 51 00 753.84 62 00 563.71 40 15 911.94 51 15 749. 82 62 15 559.11 40 30 908. 61 51 30 746. 78 62 3p 654.49 40 45 905.27 51 45 741. 72 62 45 549.86 41 00 901. 91 52 00 737. eS 63 00 545.23 41 15 898. 54 52 15 733. 57 63 15 640.68 41 30 895. 14 52 30 729.47 63 30 636.92 41 45 891.73 52 45 725.36 63 45 531.26 42 00 888. 30 53 00 721.23 64 00 526.57 42 15 884. 85 53 15 717.08 64 15 621.88 42 30 881.39 6d 30 712. 93 64 30 517. 17 42 45 877.91 53 45 708. 76 64 46 512.46 43 00 874. 41 H 00 •704.57 65 00 507. 74 43 15 870.90 64 15 700.38 65 15 503.01 43 30 867.37 54 30 696. 16 65 30 498.26 143 45 863.82 54 45 691.94 65 45 493.51 DISCUSSION AND USE OF DATA. 129 on pages 127 and 128 have been obtained. Standard areas of various States are given in Bulletin 302, United States Geological Survey, and areas of counties can be obtained from Rand and McNally Atlas maps. Unfortunately, in measuring drainage areas in many sections of the country, maps of sufficient detail are not available for determining accurately the boundaries of the areas. In general, maps from various sources may be rated as to reliability in the following order: (1) Results of special detail surveys. (2) Topographic sheets. United States Geological Survey. (3) United States Land Office maps. (4) United States post route maps. (5) Rand and McNally Atlas maps. (6) Miscellaneous State and county maps. LOGARITHMIC PLOTTING. • In ordinary plotting, the co-ordinates or distances from the axes rep- resent values of the variables. In logarithmic plotting, the co-ordinates represent values of the logarithms of the variables. Thus figure 31 is the result of plotting directly the following simultan- % - ° Values of X CM Fig. 31. » " Hydraulic Laboratory Manual," by Professors Ernest W. Schoder and Kenneth B. Turner, Cornell University. 130 EIVER DISCHARGE. eous values of X and }', the plotted points having been joined by a smooth curve: X Y .50 .162 .90 .45 1.20 .74 1.60 1.22 2.00 1.80 Let us now tabulate the logarithms of the above values. Log X Log Y 9.6990(— 10) 9.2095(— 10) 9.9542(— 10) 9.6532(— 10) .0792 9.8692(— 10) .2041 .0864 .3010, .2553 > o LogX Fig. 32. DISCUSSION AND USE OF DATA. 131 It should be noted that the logarithms of numbers less than 1 are negative. Instead, however, of writing the logarithm of 0.50 as — 0.3010 (i. e. log i=0 — 0.3010), we change it to a whole negative number plus a IX)sitive decimal, i. e. either to — 1+0.6990 (because lug y7=0.6990 — 1), written 1.6990, or to 9.6990—10 (the —10 being usually omitted in writing, but always understood). In figure 32 these simultaneous values of the logarithms are plotted. The numbers marked along the axes to the left of and below the origin are in accordance with the usual scheme of writing the negative loga- rithms. In figure 32 the plotted points give a straight line, while in figure 31 with the direct plotting of the simultaneous values there is obtained a curve resembling a parabola. Herein appears one advantage of loga- rithmic plotting. In figure 31 we have no ready means of determining the equation of the curve, but in figure 32, since we have a straight line, the equation can be fuund readily as follows: The equation of a straight line is of the form 2/=ax+6 (1) where a is the slope of the line and b is the intercept on the F axis, i. e. when 2;=0, y=b. So, by measuring the slope (the tangent of the angle made with the X axis) and the intercept, we can write out the correct equation of any straight line. It is to be noted that the slope of a line may be negative as well as positive. If the line is in the second and fourth quadrants the slope is negative. Or, from another standpoint, when y increases with an increase in x the slope is positive and when y decreases with an increase in X the slope is negative. Now, if we know, or assume, the equation F=mX„ (2) we may write also (log Y) =n{log X)+(log m) (3) because if quantities are equal, their logarithms are equal. Equation (3) is of the same form as (1), i. e. a straight line equation. In (3) the slope of the straight line is n and the intercept on the {log Y) axis is {log m) i. e. when {log X)=0, {log Y)={log m). Hence an equation like (2) , which gives a parabola-like curve when corresponding values of Xand Fare plotted, gives a straight line when the logarithms of Xand Fare plotted. Conversely, when the logarithms of Xand F have been plotted, and the points found to lie on a straight line, we know that the equation is of the form F=mX- 132 BIVER DISCHARGE. the slope of the line being equal to the exjxjnent n and the intercept on the {log Y) axis being equal to (log m). To find m when (log m) is known a table of logarithms is used. The above reasoning holds good for all real values of the exponent n, whether positive or negative, whole number or fraction, m is assumed to be positive, as it usually is in equations that occur in engineering. We deal with only positive values of the original variables, X and Y, since the logarithm of a negative number is an imaginary quantity. With the above facts demonstrated we can proceed to write the equa- tion of the line in figure 32. The slope is -2^=1.75. (See Fig. 32.) The intercept on the (log Y) axis is negative and by the chosen scale the distance below the origin equals — 0.277, or, by the system of representing negative logarithms, it equals 9.733( — 10) as may be read directly on figure 32. Therefore the equation of the straight line is (log F)=1.75(% X) +(9.733—10). Taking the anti-logarithms of both sides, we have F=0.54Xi" , which is the desired equation in terms of Xand Y, the original variables. Let us now make use of logarithmic scales along the axes of figure 32, (See Fig. 33), and note the results. On a logarithmic scale the divisions and marking are such that a division with some particular number represents (by its distance from the starting point) the logarithm of that number, just as on the common slide rule. Figure 34 shows an equal division scale and a logarithmic scale side by side. A careful study of these scales in their relation to each other will fix in mind the principle involved. Sq by using the logarithmic scales it is not necessary, for instance, to scale off the intercept, as was done in figure 32, and then to look up the corresponding number in a table of logarithms. In figure 33 on the logarithmic scale at the left, horizontally opposite the intersection of the sloping line with the (log Y) axis, we see the division representing 0.54. This is the same value of m previously obtained by the longer roundabout method. So also in figure 33, opposite each plotted point, we see, on the left and bottom logarithmic scales, the divisions representing the values of Xand Y given at the beginning of this discussion. It thus appears that the logarithmic scales enable us both to plot in proper position the logarithms of given numbers without using a table and also to read off DISCUSSION AND USB OF DATA. 13? directly the number whose logarithm is represented by a given distance, e. g. an intercept. Hence for purposes of logarithmic plotting we do not need the equal divisions along the axes, as in figures 32 and 33, but can advantageously o o d oo 1 1 1 nil M MlllllVl/ S- I /A- / ^ Slope = ^.= I.7S d c> o o' d d Logarithmic Scale . Values of X Fig. 33. substitute the logarithmic scales. This brings us to the method of ruling Logarithmic Cross-Section Paper or a Logarithmic Diagram. As ordinary cross-section paper is made by drawing two sets of lines, equally spaced, perpendicular to each other, so logarithmic paper is made by 1.34 EIVER DISCHARGE. Fig. M It appear drawing two sets of lines spaced according to a logarithmic scale. The ' ' base ' ' of such paper, and of a loga- rithmic scale in general, is the distance represent- ing 1.0 in logarithms. Thus the "base" of the lower scales on the common 10-inch slide rule is 10 inches (sometimes 25 centimeters). The "base" of the upper scales of the slide rule is 5 inches. A logarithmic scale has the same salient fea- tures as a common logarithmic table. Thus a table of logarithms contains the logarithms of all numbers between 1 and 10, advancing by inter- vals of, e. g., .01 or .001 or .0001, etc. We con- sider such a table complete, but really it is not, because we modify the tabular logarithms by adding or subtracting one or more whole units (jhe characteristic) whenever the number is more than 10 or less than one. Under the same con- ditions we may consider a logarithmic scale to be complete when its divisions extend from 1 to 10. We can provide for the position of the decimal point by shifting one ' ' base ' ' length for each place that the decimal point is moved, because changing the decimal point one place on a num- ber changes its logarithm by 1.0. Then on a logarithmic scale the position of the division representing the number wovdd be moved one " base." But in plotting we do not wish to bother with a scale that must be shifted about on the paper. The paper should be ruled so it will furnish its own scale at all points. Evidently, then, loga- rithmic scale cross-sections consist of a succession of panels one base square. All panels are ruled alike, just as on the upper scales of a slide rule the right half is a repetition of the left half. The logarithmic scale in figure 34 illustrates a suc- cession of five base distances each divided alike, and giving a range of values from .01 to 1000. s from figure 33 that the axes are situated where the logarith- S.0 -= r-.OI e.i ■= - S.2 ^ zr 8.3 -i f-.OZ 6.4 ^ : 8.5 -| E-.03 8.6 4 I-.04 8.7 -= S-.OS 8.8 .| E-.06 8.9 -| E-.oa 9.0 -| f-0.1 >N 9.( _E - ^1 9.2 -= ~ 2 9.3 ^ f-0.Z !■ 9.4 -| : !?• 9.S -| E-0.3 g* 9.6 -= |-0/» 1- 9.7 ~£ S- 0.5 1 9.8 -^ ^ 0.6 3 99 -= ^ 0.8 ir 0.0 -1 f- 1 0.1 0,2 -| \ s a 0.3 -= '—Z 1 0.4 5* f^ 0.6. .= E-3 i2 0.6 _= i- 4 ^ .;&• 0.7 -= ^5 5 — 6 ,t\ 0.8 -^ 's- 0.9 ■% r-8 1 1.0 — = i-IO 2; = •.s 4.1 "= - 3 I.Z -^ z" ^ a. 1.3 -= =-Z0 ;5- 1.4 -= :: ^ 1.5 _E E-30 E>- 1.6 -= =-40 ,**- S" 1,7 ~ ^50 s i.a ~ E-60 ,^, 1.9 -| E-80 ^ 2.0 -i f-lOO ,^ 2.1 2.2 -5 r 2.3 ■^ 1-200 ZA -i : Z.B J =- 300 2.6 -| |-400 2.7 -S — 500 2.8 .= E-600 23 -a E-800 .30- -^ ^1000 DISCUSSION AND USE OF DATA. 135 mic scales are marked 1. This is so because {log 1)=0. So on loga- rithmic paper the line for {log X)=0 is marked with the value of X, viz., 1. Therefore on logarithmic paper, in plotting lines from equa- tions or finding equations from plotted lines, the origin always is at the intersection of the lines marked 1, and the intercept is to be taken on the Faxis, which is the line marked X=l. SI 9 -09 08 / 7 6 S t -0.7 -n/i / ' — 4 / ,■ 0^ \ A ,' 0.* ■0.3 02 0.1 ■ -9.9 ..9.8 -97 -9.6 ..S.S 9* \ r- ? \ ,,- / \ ,,' '' / ^-' -' / i.n ^^ -' / 0.9 on \ ,' / 0.7 ^^ \ / c^ ,' \ / ( ■ 0.4 a ,"' " \ / \ / s \ / 0? -9J 32 9.1 -<>n / / \ / \ — 0.1 / r \ < i <: •i ^ i i c ^ .= i s 3 ri ? S s ^ ' 5 ^ ? ? c — \ ■> c c ' ? \ s 5) St *0 ^O K OoOlO o C o a cs ov Fig. 35. (Y, xi- ''I v» ^ ■ > > 0.282 . These equations are read directly from figure 35, or indirectly from DISCUSSION AND USE OF DATA. lo7 figure 36 by first writing out the straight line equations of the loga- rithms, namely : {log r)=1.72 {log X) + {2.22— \0). {log 7) =0.65 {log X) +0.1. {log F)=— 1.11 {log X) + {9. 45— 10). By taking the anti-logarithms of each side of these equations we obtain those given above. The advantage of using the logarithmic paper is obvious. It is to be noted that the slope of a line on logarithmic paper is a ratio of two distances, and that these distances must be measured with an ordinary scale, not with the logarithmic scale of the paper. Following are a few relations involving powers and roots, and in the representation of which logarithmic plotting is useful : Plow in pipe : — ■' d 2g ^ rfi-» ^ V=AV^s. Plow in open channel :- Velocity of jet : — F=Cv'2^ Head corresponding to velocity : — Power in a nozzle stream : — ^=i FyV 2g~' WHEEE STREAM-GAGING DATA CAN BE FOUND.' As a result of hydrographic studies by the Pederal Government, by States, by special commissions, and by individuals, data in regard to stream flow and the conditions affecting it are now available for streams in nearly all sections of the country. These data are contained in publi- cations which should form a part of every engineer's library, and should be freely used in order to avoid duplication of work. " Notes on Hydrology, by Daniel W. Mead, professor of hydraulic engineering, Wisconsin University, contains many tables and references in regard to hydrologio data. 138 RIVER DISCHARGE. These publications are prepared and issued by — 1. United States Geological Survey. 2. United States Census. 3. United States Weather Bureau. 4. Corps of Engineers, United States Army. 5. State officials. 6. Special commissions. 7. City officials. Re-ports of the United States Geological Survey. — The United States Geological Survey has for many years carried on systematic measure- ments of flow of streams and publishes annually a report of the results of such stream measurements. In connection with this work much other data, such as river profiles, quality of water, etc., are collected, and from time to time as information becomes available, special reports are pre- pared, which either bring together all the hydrographic data for partic- ular drainage areas, or treat of special hydrographic subjects. These are published in the series of Water-Supply and Irrigation Papers. Reports of ths United States Census. — Volumes 16 and 17 of the Tenth Census are devoted to water powers, and contain the results of detailed studies of the important rivers of the United States. During the Census of 1900 schedules were prepared showing the amount of utilized water power in the United States. These schedules have never been published, but the data may be obtained on application to the Census Bureau. Rzports of the United States Weather Bureau. — The reports of the United States Weather Bureau contain a large amount of data in regard to precipitation, evaporation, and other factors which affect the run-off of streams. A summary of these data is published each year in the Annual Report of the Chief of the Weather Bureau. The Weather Bureau also publishes each month a "Climate and Crop Report," which gives daily temperature, precipitation, and other information for a limited area, usually one State; and the "The Weather Review," which gives under one cover a monthly summary of the data collected in all sections of the country and special articles in regard to various climatic conditions. Besides collecting these data in regard to climate, the Weather Bureau maintains a flood service, in connection with which a large number of river-height observation stations are maintained for the records of daily fluctuations of stage. These data have beon printed under the title "Daily River Stages," of which volumes 1 to 11 have been published. DISCUSSION AND USE OF DATA. 139 Reports of the Chief of Engineers, United States Army. — The Army Engineers have made extensive investigations in regard to the flow and slope of many of the larger rivers in the United States, among which are the Mississippi, Missouri, Niagara, and St. Lawrence. Data collected in these investigations are published in the Annual Reports of the Chief of Engineers, United States Army, and in reports of special commissions working under the direction of the Chief of Engineers. The Army Engineers also have a large amount of manuscript data relative to the various streams, which may be obtained on application. Reports of State officials. — A large amount of valuable information has been collected and published by various States. Among these publications may be mentioned the following: Reports of the New York State Engineer. Hydrology of the State of New York, by G. ,W. Rafter (1905). Reports of the Illinois State Board of Health. Report of the Geological Survey of New Jersey, vol. 3 (1894)^ Reports of the State Board of Health of Massachusetts. Reports of the Metropolitan Water and Sewage Board of Massachu- setts. Wells, "Water Powers of Maine" (1869). Bulletins of the Geological Survey of North Carolina. Reports of the Commission of Public Works of California. Reports of special commissions. — A large number of special hydro- graphic problems have been investigated by commissions appointed by Federal, State, or city governments. Among these reports may be mentioned : Report of New York City Water Supply, by John R. Freeman (1900). Report of the Commission on Additional Water Supply of New York City (1904). Report of Commission on Charles River dam (1903). Report of the U. S. Deep Waterways Commission (1900). Report of the State Water Storage Commission of New York (1903). Reports of city officials. — Nearly all large cities have investigated and reported upon the water supply in their locality in connection with the municipal waterworks. These reports may usually be obtained by application to the city engineer. How to obtain Government publications. — Most Government publica- tions may be obtained or consulted in the following ways : (1) A limited number of every issue is delivered to the Department under which the work was done. Copies of these reports may be 140 RIVER DISCHARGE. obtained either free of charge or for a nominal sum on application to the Department publishing them. (2) Every member of Congress is allotted a certain number, from which they may be obtained, free of charge, on application. (3) Other copies are deposited with the Superintendent of Documents, Washington, D. C, from whom they may be purchased practically at cost. (4) Copies are furnished to the principal public libraries in the large cities throughout the United States, where they may be consulted by those interested. CHAPTER VI. CONDITIONS AFFECTING STREAM FLOW. Water, in its ceaseless round from atmosphere to earth and return, in its courses over or through the land or through vegetation, affords an endless number of interesting problems for study. In this discussion, ^ which pertains essentially to stream flow, there will be considered only the conditions affecting the quantity and distribution of water from the time it reaches the earth in some form of precipitation until it flows into the ocean or is returned to the atmosphere. The amount and dis- tribution of the water in the streams, which is derived primarily from precipitation, are modified by evaporation, temperature, geology, topog- raphy, vegetation, and artificial control. Since the effects of these influencing factors can not as a rule be differentiated from one another, no data can in general be given to show their magnitude; tendencies only can be discussed. It is important to observe that while precipitation and evaporation largely affect the distribution of the run-off, they also practically control its total amount. The other factors, except in so far as they affect precipitation and evaporation, exert their influence principally on the distribution of flow and but slightly on the total quantity of discharge. PRECIPITATION. All the water that appears in streams has at some time been condensed and precipitated from the atmosphere. The quantity, intensity, and distribution of precipitation are therefore prime factors influencing the quantity and distribution of the run-off. Rain gages for measuring precipitation consist of a collecting cylinder, which exposes a circular surface for collecting the rainfall, and a storage vessel in which the water is retained until measured. The standard rain gage of the United States Weather Bureau (fig. 37 and PI. VIII, A) is best suited for the measurement of precipitation under ordinary conditions. This gage consists of a receiver, an overflow attachment, and a measuring tube. In this rain gage the exposed area is 8 inches in diameter and is 141 142 RIVER DISCHARGE. connected by means of a reducing funnel with the measuring tube, which has an inside area of cross-section of j^ the area of the surface of the receiver. The measured depth of water in this tube is therefore 10 times the depth of precipitation. Other rain gages are arranged for weighing the collected waters and for easily reducing the observed weights to inches of depth. Rain gages are usually non-recording and must be visited daily whenever precipitation takes place. The attendant measures the precipitation either directly, by measuring the depth, or indirectly, by weighing the water which has been collected since his last record, empties the gage, and replaces it for further use. Satisfactory recording rain gages that require only occasional attention and that are therefore suited to the collection of records in uninhabited and mountainous sections have not yet been devised. Inaccuracies in precipitation records may result from one of two causes — (1) poor exposure of the gage or (2) incorrect collec- tions and measurement of snowfall. Rain gages in slightly different positions, if badly exposed, catch very different amounts of rainfall. Two gages placed within a few yards of each other may show a difference of 20 per cent in rainfall in a heavy rainstorm. Wind seems to be the principal factor in producing this difference. The stronger the wind the greater the difference is likely to be. In a high loca- tion eddies of wind produced by walls of buildings divert rain that would otherwise fall in the gage. A gage near the edge of the roof, on the windward side of a building, shows less rainfall than one in the center of the roof. The vertical ascending current along the side of the \\all extends slightly above the level of the roof, and part of the i'i<;.:i7.—Kuin(iagc and Support, rain is Carried away from the gage. In the center of a large, flat roof, at least 60 foot square, the rainfall collected by a gage does not differ materially from what is collected at the level of the ground. A gage on a plain with a fence 3 feet high around it at a distance of 3 feet may collect 6 per cent more rain than without the fence. The gage should therefore, if possible, be set in an open lot. Plate VIII, ^' A ill I mi I litfrtiSi" A. PRECIPITATION AND EVAPORATION STATION, MADISON, WIS. B. SNOW OBSERVATION STATION, WHITE MOUNTAINS, N. H. CONDITIONS AFFECTING STREAM FLOW. 143 unobstructed by large trees, buildings, or fences. Low bushes and fences, or walls that break the force of the wind in the vicinity of the gage are, however, beneficial, if at a distance at least as great as the height of the object. Such a place, in general, affords the best exposure. Gages should be exposed on roofs of buildings only when necessary, and then the roof should be flat, or nearly so. Satisfactory measurements of the snowfall of individual storms are seldom obtained because of the difficulty in collecting in a receptacle the true amount of snow falling in wind. In order-to measure snowfall, therefore, it has been found most satisfactory to arrange a platform, on which the snow is allowed to fall, and to collect and melt a vertical sample of known area, thus determining its water equivalent. The tube and scale method, devised by the United States Weather Bureau (PI. VIII, B), for determining the water equivalent of accumulated snow represents the latest and best practice and will give satisfactory results when sufficient observations are made. The amount of water collected on the small surface presented by a rain gage is assumed to represent the precipitation over a large area. Since, as explained above, slight differences may occur in the amount of water collected, and consequently, in the recorded rainfall, any data in regard to the precipitation over an area may be in error. Moreover, ob- servation stations are generally located in the lower, inhabited sections, and even if accurate records are obtained at the gage, they may not cor- rectly represent the precipitation on the more elevated portions of the basin. It follows, therefore, that the application of a few records to a large area may result in considerable error. The United States Weather Bureau has collected precipitation records for many stations. The plan followed contemplates the establish- ment of a precipitation station in each county; therefore, in most of the areas considered the horizontal distribution of the stations is fairly uniform and representative. This is not generally the case, how- ever, with the vertical distribution of the stations, as the location of the gage depends in large measure on the accessibility of a reliable observer and a telegraph station for use in reporting excessive rains. Neither the observer nor the telegraph is generally available at high alti- tudes. Most of the stations have therefore been located at low or medium elevations, and little is yet known concerning the effect of elevation on precipitation. The records of precipitation show great variations from season to season and from place to place, with no ascertainable sequence or order. They show also great variations between different sections of the country and for different altitudes and exposures in the same sections. The 1-^4 RIVER DISCHARGE. mean yearly and seasonal rainfall for any locality is, however, fairly constant and has been determined for many observation stations from records extending over a series of years. The average precipitation and the range of departure from the aver- age has been determined with reasonable accuracy for many localities in thu United States. In PL IX'' are shown lines of equal rainfall which liiivo been drawn from the means of records collected in several years at many observation stations. The departures from the mean conditions can be determined for any place only by study of detailed records of precipitation. Although a discussion of the conditions that aflfect precipitation will not be attempted here, it seems desirable to call attention to the effects of variations in latitude, altitude, and topography on the amount and distribution of precipitation, in order that the user of such records may be able to estimate the probable errors in the application of avail- able records to an extended area. The effects of latitude and altitude on precipitation are similar, since they are the principal factors governing temperature, which affects both the amount of moisture received by the atmosphere and its precip- itation. Other conditions being equal, precipitation decreases toward the poles, probably on account of lesser evaporation with decrease of temperature and consequent smaller absolute amounts of moisture in the air. It increases with altitude to the usual height of rain clouds, above which it probably decreases. The evaporation from water surfaces is in many places so great that the air above such surfaces generally contains a large amount of moisture. If such moisture-laden air is carried by prevailing winds over adjacent lands, and especially if the lands contain mountains high enough to deflect the air currents to those altitudes in which the temperature is sufficiently low to cause precipitation, there will be heavy precipitation in such mountains and between them and the water surfaces. By this process the winds are so robbed of moisture that the lands beyond the mountains receive much smaller amounts of precipitation. On the other hand, if the prevailing winds are away from the land or if no mountains are near to deflect the air currents upward, the adjacent land surfaces may be arid. A study of the actual annual and seasonal variations of rainfall is of great importance, and a comparison of such rainfall with the measured stream flow is of interest in hydraulic investigations. Such compari- sons show that grc^at errors will probably result from attempts to esti- mate stream flow from precipitation data, and the estimates made » Sl'O Water-Siipply I'apci- No. ;!01, V. S. Geol, Surv.'y. PLATE IX MAP OF UNITED STATES, SHOWING MEAN ANNUAL PRECIPITATION Blue lines and figures indicate average annual precipitation in depth in inches PtepafOd by Honry Gannett mainly from data of the United States Geological Survey and United States Weather Bureau CONDITIONS AFFECTING STREAM FLOW. 145 should never be used as the only basis for computations of the amount of water available for power or irrigation. In using rainfall data the conditions affecting the accuracy of the records, previously noted, must be considered, as well as the possible sources of error stated below. The record obtained by a single rain gage shows only the measured precipitation on a few square inches of surface. This record, even if accurately made, may not be representative of a considerable area. In order to ascertain with certainty the average precipitation over a large area many rain gages should be employed. Under ordinary con- ditions of practice, however, the gages in any drainage basin are gener- ally few in number, and as a result the extremes of precipitation, which always occur in comparatively small areas, may not be recorded. No means have yet been devised for obtaining reliable data in regard to precipitation during the winter months, and practically no data have been collected to show the amount of snow storage at the end of each month. Hence the records of snowfall are especially unreliable, while the lack of information in regard to the amount of water held in the form of snow on the ground makes it necessary to study the winter conditions as a whole. In any use of rainfall data it is necessary to assume that for any period of time the mean rainfall over the whole of an area is either the arithmetical or weighted mean of the rainfall during that period as observed at the various stations in that area. Since all rainfall records are liable to great errors the weighting of the data is not generally warranted. In order to compare rainfall and run-off both records should be ex- pressed in "depth in inches" over the drainage basins considered and should of course pertain to the same periods of time. Such data have usually been computed and recorded for calendar months. This period is, however, too short for comparative purposes and may lead to appar- ently erroneous results, because heavy precipitation which occurs at the end of the month will not appear as run-off until the following month. A year is a better period but is not entirely satisfactory. The calendar year is undesirable as a comparative period, because the con- ditions of snow and ground storage are not the same at the end of every December. The year beginning with October is a much better period, since on the first of that month the storage conditions are more nearly uniform from year to year, because there is at that time no snow storage, and surface and ground storage are usually at a minimum. The largest disturbing factors in the relation between run-off and rainfall are 146 RIVER DISCHARGE. Monthly and yearly maximum, minimum, and mean loss, for an Precipitation, in Inches. [Note: — M = Mean; Drainage. Connecticut, above Or- ford; S 300 sq. miles. . . . Housatonic, above Oay lordsville; lOSO sq. miles Susquehanna, above Har- risburg; 24 OSOsq. miles. Susquehanna, above Wukes-Barre; 9810 sq. miles Susquehanna, above Wil- liacnsport; 5 640 sq. miles Ohio, above Wheeling; 23 820 sq. miles Potomac, above Point of Bocks; 9 650 sq. mUes. . Shenandoah, above Mill' villi; 3 one sq. miles.... James,abDve Cartersville; 6230 sq. miles James, above Buchanan; 2060sq. miles James, above Glasgow; 830 sq. miles Appomattox, above Mat toax; 745 sq. miles Boannke, above Boanoke; 390 sq. miles Boanoke, above Ban dolph; S 080 sq. miles. . . October. 3.98 3.33 2.90 2.66 2.21 2.47 3.46 2.52 2.61 2.70 2.71 2.61 B. 4.12 2.12 6.49 2.74 5.74 0.9S 6.04 1. 6. 0.89 6.78 0.51 6.41 0.57 7.10 0.4H 8.85 0.5i 8.07 0.48 8.70 0.32 7.60 0.35 6.32 0.13 B.S4 0.65 NOVEMBBB. 2.17 2.41 2.74 8.09 2.08 2.42 2.22 B. 6.54 1.05 4. 0.89 4 ' 0.92 4.70 1.18 4.91 0.64 5.67 0.65 4.10 0.79 4.16 0.81 8.57 0.93 5.20 0.71 5.27 0.73 8.99 1.06 4.60 1.04 3.15 1.22 Decembsb. M. B. 2.80 2.97 3.30 3.15 3.13 2.67 2.61 3.28 8.00 2.87 8.76 3.96 4.77 1.86 6.76 2.72 5.63 1.04 6.58 2.24 6.48 1.25 5.07 1.84 B.71 0.74 6.12 0.23 7.19 1.41 7.63 0.30 7.i 0.17 8.08 1. 7.45 0.50 7.84 1.78 Jahuaby. H. 8.06 2.73 2.57 2.63 3.24 2.53 2.58 3.20 2.79 3.28 2.86 3.10 2.94 1. 4. 1.65 4.40 1.77 3.40 1.69 8.69 1.61 4.97 1.72 3.78 1.55 4.08 1.41 4. 2.21 4.51! 1.77 4. 1.80 4.82 2.00 4.08 1.64 4.36 2.19 Febbuaby. M. B. 2.56 2.87 2.80 2.72 3.19 2.91 3.12 3.52 3.66 3.57 8.11 3.92 3.18 0.71 4.24 0.76 4.55 0.93 8.46 1.17 4.00 1.05 6.54 1.19 5.88 0.46 6.% 0.38 6.08 0.59 6.80 0.63 5.48 0.49 6.22 0.94 7.10 0.62 5.63 0.88 Mabch. M. 3.44 4.10 8.35 s.eo 4.09 8.39 8.42 S. 8.88 8.88 8.89 8.63 4.01 8.57 4.77 2.05 5.20 8.04 4.68 1.21 4.77 8.17 5.20 8.42 5.63 1.40 4.44 2.08 5.12 2.08 6.38 2.59 5.66 2.39 6.96 2.37 6.49 2.44 6.49 2.29 Run-off, in Inches. Drainage. OCTOBEK. M. E, NOVEUBEB. M. December. M. K. jAmjABT. M. B. Fkbrdabt, M. E. Mabcb. Connecticut, above Or- ford Housatonic, above Gay- lordsville Susquehanna, above Har- risburg Susquehanna, above Wukes-Barre Susquehanna, above Wil liamsport Ohio, above Wheeling. . . . Potomac, above Point of Bocks Shenandoah, above Hill ville James, above Carters- ville '.. James, above Buchanan. James, above Glasgow. . . Appomattox, above Mat- toax Boanoke, above Boanoke. Boanoke, above Ban- dolph 1.24 1.89 0.90 1.16 0.85 0.72 0.52 0.82 0.89 0.60 0.67 0.63 0.86 1.03 1.94 0.45 3.25 (0.40) 2.17 0.16 3.22 0.13 2.68 0.15 8.70 0.12 1.68 0.14 2.99 0.20 2.84 0.21 2.83 0.1S 2.48 0.2:3 1.44 0.27 8.00 0.20 1.82 0.30 1.23 1.89 1.08 0.96 1.14 1.21 0.44 0.48 0.75 0.71 O.o;) 0.01 0.78 0.81 2.61 0.50 1 0.96 2.18 0.28 1.47 0.60 1.84 O.SO 2.97 0.24 0.99 0.15 1.05 O.SO 1.27 0.26 2. -IB O.'.O 1.07 0.24 l..'i2 0.!!8 i.ri 0.24 1.08 0.82 1.28 2.68 1.75 2.68 1.75 1.99 1.06 1 05 1.61 1.21 1.46 1.29 1.71 2.34 0.47 4.13 (1.03) 8.58 (1.40 4.91 O.flO 4.14 0.33 3.64 0.58 8.06 0,26 8.18 0.29 8.29 0.46 4.82 0.26 4.50 0.31 2.54 0.58 4.23 0.35 3.1)1 0.71 0.76 2.82 1.94 2.89 1.96 2.78 1.30 1.21 1.80 1.41 1.75 1.43 1.11 0.27 8.81 0.98 3.79 0.67 8.45 2.14 8.23 1.01 4.30 1.; 2.49 0.51 2.63 0.47 2.76 0.68 2.51 0.42 2.79 0.63 2.78 0.61 3.34 0.22 0.78 1.98 0.61 1.61 2.66 1.90 3.12 2.00 1.53 2.11 2.34 2.84 2.29 2.34 1.03 0.26 (3.68) 0.49 4.04 0.53 3.92 1.57 4.52 0.56 7.29 0.78 4.00 0.89 8.63 0.16 8.74 0.64 5.84 0.51 8.99 0.48 8.60 0.45 6.63 0.64 3.49 1.02 CONDITIONS AFFECTING STREAM FLOW. 147 rainfall, run-off in percentage of rainfall, and average year. R = Range.] Apkil. Mat. Juke. Jolt. Adgcst. September. Year. OH Ml d S M. E. M. E. M. E. M. R. M. E. M. E. Total. E. 8.54 4.78 5.27 5,08 4.59 5,76 41.80 2.77 1.37 6.12 2.99 0.27 6.24 8.78 2.10 10.42 4.84 8.78 7 25 3.88 8.22 7.28 3.73 1,08 6.42 86.76 88.48 51.49 5 S.71 2.25 4.46 2.97 1.12 7.70 5.46 1.80 6.41 5.00 8.ra 7.24 5.56 8.45 8.48 4.70 1.94 5.61 47.88 89.77 45.17 5 2.76 1.27 4 67 8.98 1.27 5.39 3.98 2.77 6.38 4.11 2.42 7 88 4.16 1.92 6 51 3.04 1.41 4.82 39.38 31.82 44,13 14 2.70 1.50 4.69 2.73 1.11 5.41 4.46 2.94 8.03 5.05 4.03 7.58 4.49 2.78 8.62 2.90 1.40 4.70 39.85 31.17 44.11 6 3.89 1.33 6.50 3.20 1.7. 7.4S 4.11 2.94 5.80 4.62 2,77 9.08 4.14 2 26 6.83 2.83 1.05 6.48 40.02 83.04 55.56 10 S.28 1.5T 8.05 4.04 2.18 6. 47 4.32 2.50 6.57 4.55 2.64 6.63 3.74 1,30 7.00 8.0? 1.56 6.09 41.71 33.47 44,81 21 2.61 1.84 8.21 8.77 1.97 5.S2 4.13 1.81 7.63 4.15 2.28 8.2! 3.50 1.89 7.73 2.65 1.32 7.22 86.86 29. S7 48.08 10 2.55 1.18 6.92 8.85 2.28 6.70 4.90 2.09 7.73 4.14 2,17 7.47 3.58 1.41 10,22 2.95 1.01 4.11 88.83 30.47 54,88 10 8.07 1.72 6.52 3.75 1.78 6.31 5.13 3.55 7.57 4.08 2,35 8.48 4.50 1.64 8.71 3.24 1.98 6.20 42.98 30.58 53.31 7 2.86 1.57 7.08 4.20 1.25 6.18 4.78 8.34 8.71 4.42 2,27 8.22 3.87 1.61 7.47 3.17 1.06 8.70 41.17 30.45 51.48 10 2.70 1.19 5.99 4.04 1.83 7.26 4.78 2.7i 5.04 4.09 2.18 7.05 3.82 1.46 13.06 3.24 0.78 4.20 40.76 82,48 52,98 10 3.09 1.08 6.50 3.98 1.72 7.46 3.99 8.20 8.14 4.13 1.94 11.64 6.24 2.70 10.72 2.89 2.29 5.18 42.98 80.80 58.30 5 2.80 1.67 6.04 4.18 0.93 6.33 4.77 1.90 5.98 4.91 3.08 5,09 3.80 0.98 11.21 3.32 1.22 8.29 42.88 35.19 58.95 9 S.35 1.48 4.07 1.92 4.53 2.8d 4.92 2,08 5.15 2.40 2,77 1.86 48.80 34.00 5 Apbil. Mat. JnsB. JULT. August. Ybab. "S2 M. R. L. E. M. E. M. E. M. R. M. E Total. E. d 7.10 4.80 3.20 1,51 1 58 1.82 27.04 4.70 3.64 6.43 3.10 1.16 4.50 1.69 1.02 4.28 1.U9 0.49 2.49 1.09 0.69 2.19 l.OS 0.37 2.25 21.68 16.01 36.94 5 4.83 3.82 4,83 2.40 1.11 4,54 2.24 0.92 3.03 1.47 0.58 3.25 1.41 0.87 1 60 1.51 1.08 1.42 29.43 23.76 28.03 6 3.48 2.34 4.46 2.07 0,81 2,52 1.25 0,.50 1.79 0.88 0.34 3.41 0.77 0.24 1.53 0.61 0.17 1.44 21.09 16.34 27.18 14 S.17 2.49 5,45 1.13 0.40 3 15 1.07 0.40 2.44 1.01 0.28 4,11 0.68 0.12 1 44 0.72 0.15 1.24 23.19 15.15 27.60 6 8.50 2,24 8,84 1.68 0.60 5.10 1.20 0,54 3,37 1.23 0,36 3,49 0.87 0.27 1,88 0.52 0,18 2.50 22.28 16.57 34.20 10 3.20 1,80 4,60 1.94 0,51 8,22 1.80 0.31 2.18 1.08 0,28 1..52 0.76 0,16 2,66 0.53 0,15 0.88 22,68 16.29 21.46 21 1.98 0,76 4.79 1.34 (0,31) 3 8ti 0.99 0.37 3.07 0.76 0.29 1.71 0.89 0.23 3.15 0.34 0.16 0.93 14.22 8.16 19.78 10 1.77 0.72 4.45 1.39 0,53 3.45 1.16 0.62 3.05 0.83 0.34 1,45 0.81 0.38 8. 08 0.43 0.33 1,26 13.04 7.86 24.73 10 2.18 1.01 4.98 1.63 0,94 3,55 1.50 0,68 3,15 0.99 0,38 3,02 1.02 0.30 2.71 0.67 0.29 0,99 18.21 10.69 26.30 7 2.02 0.88 4.20 1.77 0.58 2.83 1.17 0,49 8,00 0.98 0.24 2.82 0.81 0.22 2,49 0.50 0,21 2.14 16.91 11.45 21.33 10 1.79 0,80 3,67 1.51 0,58 3.19 1.15 0.30 1.51 0.99 0.24 1,31 0.84 0,25 4,01 0.63 0.17 1.18 15.99 13.15 25.15 10 2.18 0,85 4,90 -1.44 0.92 4 38 0.90 0.48 2,54 o.rd 0.39 3,54 1.42 0.53 5.73 0.83 0.87 1.58 16.48 10.92 29.66 5 1.89 0,58 3,49 1.79 0.78 3 18 1.14 0.54 l,7.j 1.16 0.39 2.43 1.33 0.26 4.94 0.80 0.22 1.45 17.69 8.8S 25.16 9 1.88 0.81 1.65 1.10 1.37 1.05 1.45 0.79 1.80 0.82 1.02 0,65 18.66 10,99 5 148 RIVER DISCHARGE. Monthly and yearly maximum, minimum, and mean loss, for an Run-off in Pebcentage of Rainfall. [Note— M = Mean: Drainage. Connecticut, above Or- ford Housatonic, above Gay- lordsville Susquehanna, above Har- nsburg Susquehanna, above Wtlkes-Barre Susquehanna, above Wil- liamsport Ohio, above Wheeling. Potomac, above Point ol liocks Shenandoah, above Mill- vlUe JaTiies, above Carters- ville James, above Buchanan. James, above Glasgow. Appomattox, above Mat- coax Hoanoke, above Roanoke. Roanoke, above Ran- dolph October. NOVBHBEB Dboembeb. Jandabt. M. R. M. R. M. R. M. R. 92 182 103 55 41 n 57 83 46 17 88 13 04 175 67 149 47 (13) 58 22 61 (87 > 76 ilV 44 105 100 SO fi 41 11 .59 19 71 32 53 85 140 201 85 4 40 22 77 40 112 76 64 68 102 116 29 10 42 12 56 15 75 SO 72 114 99 129 87 6 39 12 64 27 86 46 162 41 76 98 24 8 19 fi 40 10 51 30 623 64 883 78 33 10 23 12 40 9 47 (27) 181 69 70 74 25 13 ■SB 23 46 21 56 31 92 75 67 75 24 H 29 14 43 11 49 24 381 64 653 78 26 H 28 11 42 12 49 84 160 47 71 77 23 11 29 13 89 17 53 SO 208 77 92 90 81 9 81 15 39 7 SO 13 180 89 S3 71 40 23 36 17 43 24 S3 36 Febbuaby. R. Ill 72 98 64 66 31ABCH. M. 88 23 (87) (39) 209 41 197 (47) 146 43 151 St 163 S3 139 (26) 108 3'4 105 16 168 51 88 48 152 16 116 (31) 114 143 134 148 187 120 82 61 81 86 70 62 72 65 163 45 203 87 277 60 223 78 200 74 191 82 149 41 148 23 128 44 172 40 127 87 76 2S 115 27 108 41 Loss, IN Inches. Drainage. Connecticut, above Or- (ord Housatonic, above Clay- lordsville Susquehanna, above Bar- rlsourg Susquehanna, above Wilkes- Barre Susquehanna, above Wil- liamsport Ohio, above Wheeling. . . . Potomac, above Point of Rocks Shenandoah, above Mill- vlUe Jjmes, above Caners- viUe James, above Buchanan. James, above Glasgow. . . Appomattox, above Mat- toaz Boanoke, above Roanoke. Roanoke, above Ran- dolph OCTOBBB. 2.12 2.17 2.05 1.94 l.fiS 1.65 l.flS 1.8(1 1.68 R. 2.60 0.18 3.24 0.98 4.16 0.66 8.46 1.27 4.71 0.40 3.06 0.39 4.78 0.57 4.91 -2.51 (6.01) -0.17 2.85 0.20 0.22 -0.00 6.16 -0.21 8.96 -0.14 8.72 —0.86 NoTEUBEB. December. 0.94 1..55 1.45 1.60 1.8! 1.60 1.14 1.71 1.66 1.66 1.71 1.41 R. M. R. 8.03 0.41 8.33 -0.67 3.42 -0.11 3. 40 0.17 3. .58 0.21 4. TO — 0.8T 3.86 O.BI 3.48 0.29 2.07 0,29 8.88 0.50 8 0,42 2.67 0,66 3.91 0.43 2.13 0.14 1. 1.70 1.22 0.77 1.40 1.14 1.61 1.66 1.77 1.70 1.67 2.80 1.68 2.24 2.43 —0.06 2. 0.96 2.76 0.00 1.70 —0.93 3.82 —0.03 2.25 0.03 2.65 0.18 3.00 —0.65 3.90 0.96 8.07 0.71 3.10 ■0.94 6.77 0.86 3,33 0,04 4.23 1.05 Jasdaby. 1.62 0.7S 0.T9 —0.32 0.67 0.46 1.23 1.3: 1.40 1.48 1.45 1.52 1.43 1.47 1.97 0.91 1.99 -1.05 1.84 -0.62| 0.83 -i.ra 1.50 —0.80 1.91 -O.ft'* 2.09 0.05 2.11 0.55 1.C3 0.8i S.(;5 0.72 1.. 0.86 2.09 0.76 2.61 0.39 2.06 0.82 Febbhaby. M. 1.06 0.95 0.69 0.76 o.o; 0.91 1.59 1.41 1.57 1.58 2 15 0.10 2.36 (0.20) 2.14 —1.21 0.65 1.93 l.fS -0.84 0.9 J -1.S8 2.32 —0,75 (8.67 —0.13 2.31 —0.05 2.00 —0.08 2.80 — 1..S4 1.6U 0.40 4.10 —0.32 2.73 ^.14 Habch. -0.47 1.78 B. 1.92 8.91 0.66 4.48 1.65 1.1S'-S.58 0.80 -I.TSM.SS 1.02 -1.60' 4.(6 0.69 —0.68 o.e? 1. 0.72 0.68 1.07 1.88 1.18 l.Sl — 3.1S 2.60 -2.15 1 2, 40) -1.78 1.96 -0.92 2.62 -2.27 2.55 -0.86 2.27 0,71 2.53 1.00 2.86 0.09 CONDITIONS AFFECTING STREAM FLOW. 149 rainfall, rwi-off in percentage of rainfall, and average year. R = Range.] April. MiT. JCNK. JULT. August. Septbsibbr. Tear. 2 M. R. M. R. M. R. M. R. M. R. M. R. Mean. R. i^ 266 430 68 38 39 34 65 170 lao 187 104 65 118 45 20 113 25 13 61 28 16 40 28 22 80 69 46 78 3 185 105 824 81 72 72 41 20 86 29 U 47 25 18 4? 32 17 78 62 53 63 5 124 25 200 62 21 50 81 10 58 20 9 43 18 6 24 20 6 74 56 44 65 14 117 96 276 41 26 69 24 10 6fi 20 7 64 16 4 82 26 11 56 58 47 68 6 121 85 156 62 34 82 29 12 67 27 12 58 21 7 56 18 7 39 56 42 63 10 98 58 104 48 18 67 80 10 48 23 9 34 20 6 38 17 6 28 64 44 61 21 76 85 113 36 ''A' 24 11 41 18 9 48 20 10 41 13 4 41 39 22 58 10 69 31 101 36 14 66 24 13 54 20 11 87 23 10 30 15 6 44 36 21 50 10 71 48 123 43 32 79 2U 18 52 24 13 38 28 11 39 21 8 80 42 33 68 7 76 40 128 42 19 69 23 14 52 22 8 38 22 5 83 16 8 82 41 28 63 10 66 37 lis 37 18 64 24 9 41 24 10 32 23 6 31 19 6 49 39 33 48 10 69 42 89 86 24 U5 C3 13 57 18 9 43 23 14 53 29 14 87 38 80 56 5 66 25 87 43 75 66 24 14 38 24 12 46 35 8 44 24 7 44 41 23 57 9 56 31 41 23 1 80 21 29 16 35 24 87 25 43 32 5 April. May. June. July. August. SSPTEUBER. Year. "SS M. R. M. R. M. R. M. fi. M. R. M. R. Total. R. — O.70 1.67 4.23 3.81 8 63 8.74 18.81 —1.94 -8.62 -0.20 —0.11 —1.39 1.74 2.09 1.05 6.14 3.25 2.41 5.06 2.79 2.00 5.71 2.70 0.71 6.19 15.10 13.84 22.56 5 —0.92 —2.20 1.37 0.57 -0.22 3.16 3.22 —0.25 5.57 3.53 1.56 4.41 4.15 2.08 5 25 3.19 0.39 4.81 18.43 13.39 21 04 5 —0.67 —2.84 0,21 1.89 0.58 2.87 2.73 0,40 5.30 3.28 1.94 4,53 3.39 1.22 6 10 2.43 0.58 3.76 18.29 13.64 18.61 14 —0.46 — ! 50 0.47 l.CO 0,71 2.26 3.39 1,32 6.05 4.04 3.47 4,58 3.83 2.53 5.18 2.18 0.43 4.39 16.66 14.52 20.89 6 —0.61 -2 54 2.00 1.53 0.94 8.14 2.91 1.25 4,91 3.39 2.41 6.07 8.27 0.96 5,44 2.31 0.87 4.50 17.70 15.70 24.86 10 0.07 -1.56 1.60 2.10 0.95 3.77 3.02 1,33 4.49 8.60 2.26 5.41 2.98 1.09 6 21 2.63 0.81 5.84 19.02 16.18 29.09 21 0.63 —0.14 1.82 2.43 1.S6 3.97 8.16 1.33 5 14 S.S9 1.9S 5 11 2.81 1.27 4 58 2 31 1.03 6.83 22.64 13.87 33,05 10 0.78 — n.30 2.47 2.46 1.46 8.59 3,71 1.49 5.37 3.31 1.78 4.93 2.75 1.03 7,14 2.62 0.76 3.54 24.09 14.68 30.79 10 0.89 -0.02 1.54 2.12 0.60 4.10 8.63 2.67 5,77 3.07 1.94 5.46 3.48 1.24 6.00 2.67 1.33 5.21 21.77 18.90 32.38 7 0.64 -0.37 2.88 2.43 0.26 3.47 8.60 2,79 6.87 3.44 1.87 4 18 a. 86 1.30 4.98 2.67 0.83 4.56 24.20 14.89 30.46 10 0.91 -0.45 2.61 2.63 0.41 4.07 3.63 1.92 4.04 3.10 1.91 6.42 2.97- 1.15 9 05 2.61 0.50 3.46 24.77 16.29 36.10 10 0.95 -0.41 1.70 2.52 0.79 4,91 3.09 2,19 6.83 3.40 1.51 8 10 4.82 2.17 4,99 2.07 1.22 4.81 26.50 19.88 31.71 5 0.91 0.20 2.55 2.39 —0.23 4 95 3.63 0.81 4.75 3.76 2.44 6.30 2.47 0.72 fi.27 2.53 0.84 1.99 24.99 15.91 29.38 9 1.47 0.24 2.42 0.65 S.16 1.78 3.47 1.87 8.86 1.58 1.75 1.21 25.14 16.00 5 150 RIVER DISCHARGE. ground, surface, and snow storage. As data in regard to them are not available as a rule, it has been impossible to allow for their effects. The table" (pp. 146-149) shows, for various drainage areas in the northeastern United States, the monthly and yearly rainfall, run-off, and loss for each of the years for which run-off records are available. The records of precipitation were in some instances incomplete, and figures for several months in the period considered were missing. In such cases the mean of the records for the stations available was taken as the mean for the month in question. Interpolation for supplying missing rainfall data adds nothing to the accuracy of the record and is probably never justifiable by theory or facts. The records of mean annual run-off for all important stations in the United States have been compiled in uniform manner, and the results used in the construction of a run-off map shown in PI. X.^ EVAPORATION. All precipitated water, in some portion of its course over the earth's surface, is subjected to the effects of evaporation, whereby a portion is returned to the atmosphere again and thus disappears from the surface waters. The principal conditions on which the amount of evaporation depends are the temperature of the atmosphere and of the surface from which evaporation takes place, the relative humidity of the air, and the wind movement. The greatest of these factors is temperature, although the others are important. The greater the wind movement the lower the relative humidity, and the higher the temperature the greater the evap- oration. Consequently the rate of evaporation from land surface and from rivers, lakes, canals, or reservoirs varies widely in different local- ities, and in the same locality in different seasons. The determination of the amount of evaporated water received by the air from land .surfaces is very difficult, and no satisfactory direct measurements have been made. The best information available in regard to this phenomenon has been obtained by subtracting from the total annual precipitation, e.xpressed in inches of depth on the basin, the total annual run-off expressed in the same unit. The difference represents closely the total loss by evajxjration from the land and water surfaces of the basin (see table on pp. 1411-149). The measurument of evaporation from water surfaces offers consider- able difficultie s, but approximate records have been col lected at many « See Prooeedlnga of the American Society of t'ivll Ensrlneers. Vol. XXXIII, May, 1907. » Sec Water-Supply Paper No. 801, U. S. Qeol. Survey. PLATE X MAP OF UNITED STATES, SHOWING MEAN ANNUAL RUN-OFF Blue lines and figures indicate average annual run-off in depth in inches Prepared by Henry Gannett nnainly from data of the United States Geological Survey CONDITIONS AFFECTING STREAM FLOW. 151 points. These records are of great value in studies of artificial storage, since the total annual storage is diminished by the annual evaporation from the water surface. The method adopted for measuring the evaporation from a body of water consists in measuring the loss of water from a pan (PL VIII, A), which is so placed that the contained water has as nearly as possible the same temperature and exposure as that of the water which it is intended to represent. In order that the proper conditions of temperature and exposure may be most nearly attained the pan is either floated in the water at a place where the wind velocity is the average for the body of water under consideration, or, in occasional cases, is sunk nearly to its top in marshy ground. In general, the condition that the pan should be in a place of average wind velocity must be sacrificed to the practical requirement that the water about the pan when it is floated shall be so still that water will not slop in or out and that accurate observation of its height can be made. The location should therefore be chosen with a view to securing a body of relatively quiet water around the . pan. The pan should be floated as deep as possible and the water in the pan maintained as near the top as possible, consistent with the requirement that the wind does not drive water in or out of the pan by direct splashing. It is usually not possible to maintain the height above IJ inches below the rim. The height of water in the pan may be read by means of an inclined scale of such form that the readings, which must be made to hundredths of an inch of vertical elevation, are magnified by the inclina- tion of the scale. It is better, however, to use a point projecting from the center of the pan, fixed at a uniform height, the water in the pan being restored night and morning to such a height that the point is just submerged. The height of water in the pan is thus maintained at practically the same distance below the rim, and the magnitude of errors of observation is reduced. For the purpose of ascertaining the amount of evaporation a small cup is provided, the cubical contents of which is exactly equivalent to that of the pan at a depth of one one-hundredth of an inch. Such a cup, of cylindrical form, is 4.13 inches high and 2 inches in diameter for a pan 36 inches square. When an observation is to be made the pan should be level. The cup should then be filled with water. This is emptied into the pan and the operation is repeated until the point is exactly submerged. The number of cupfuls emptied into the pan is the amount of water, in hundredths of an inch that is evaporated. If a rain storm has occurred and the point in the center of the pan has been 152 RIVER DISCHARGE. submerged, water must be dipped out of the pan and the exact nuiflber of eupfuls noted. Reports of the observations should contain data on wind movement, temperature of water inside and outside the pan, amount of precipi- tation, and amount of water added to or removed from the pan. The annual evaporation from water surfaces varies from 20 to 40 inches in the humid Eastern States to 70 to 100 inches in the arid West. In all sections of the country and under all conditions, practically all of the precipitation is either evaporated or appears ultimately as sur- face water. The only exceptions are the small amounts which are lost permanently to the ground or which undergo chemical change by vegetable growth or by entering into composition with other minerals. The major part of all ground water becomes a part of the surface water again by flowing from springs, or is transmitted directly to the atmos- phere by transpiration from vegetation. The difference between annual rainfall and run-off thus represents very closely the annual evaporation. The effects of evaporation extend, therefore, both to the total flow of streams, as indicated above, and to the distribution of flow by the different rates of evaporation for different seasons. The major part of summer precipitation returns in a relatively short time to the atmosphere, while the winter precipitation remains longer on the surface and practically all runs off either directly as winter or spring flow, or later as summer flow from ground water. A comparison of rainfall and run-off for the summer and winter seasons, as shown in the table on page 153, illustrates forcibly the effect of evaporation on the regimen of the streams and the remarkable constancy of the total yearly evaporation in the sections covered by the data. It also shows the direct variation of the yearly evaporation with the mean annual temperature and the remarkably small losses during the period of low temperatures. TEMPERATURE. Temperature is the chief factor affecting evaporation and rainfall and thereby affects both the tot;;l run-off and its distribution. Low temperature exerts a further effect, mainly on the distribution of flow, by forming snow and ice and temporarily storing the precipitated moisture. Storage resulting from low temperature is an important factor in the regimen of streams in high latitudes and in mountainous areas. A CONDITIONS AFFECTING STREAM PLOW. 153 fe\\»^ieterminations of the quantity of such storage have been made by collecting cylindrical samples of the snow and ice, extending from the surface of the snow to the ground, and melting each such sample to determine the equivalent depth of water. The relation between depth of snow and equivalent depth of water varies with the temperature at the times of the snowfalls and also, generally much more, with the length of time the snows have remained on the ground, because the weight of snow above and the absorption of rains, if any, or of water from melting snows, serve to compact the snow and thereby to increase the water equivalent for a given depth. Rainfall, run-off, run-off in percentage of rainfall, and loss, for the winier and the sumpier months, for the mean year.'^ Winter Months, Deo. to Apr., Incldsite. Summer Months, June, July, August. i Station. 1 1 5? u u 3 1 1 o a 1 li £0 10 1 1 1 Connecticut, at Ortord, N. H. lioi satoiio, at Gaylordsville, 12.89 17.80 14.48 14.47 15.48 16.-1Z 14.14 14.38 16. as 15.99 15.89 16.87 16.60 17.58 11.19 17.13 13.58 18.48 14.76 15.16 9.14 7.72 10.76 10.37 9.57 9.89 9.84 9.53 87 96 94 114 95 93 65 S4 63 65 60 69 60 54 1.70 0.68 0.90 —2.01 0.72 1.07 5.00 n.S6 6,19 5.68 6.38 6.98 6.66 8.00 12.00 16.08 12.23 14.00 12,87 12.01 11.80 12.6'' 13.69 18.87 18.69 14.36 13.48 14.60 3.87 5.12 2.85 2.74 3.30 3.12 2.44 2.P0 8.51 2.97 2.98 3.05 3.63 4.62 32 32 23 20 26 25 21 22 26 23 23 21 27 38 8.13 10.90 9.40 11.86 9.57 9.49 9.36 9.80 10.18 9.90 9.71 11.31 9.85 9.98 15.10 18.43 Susquehaniia, at Harrisburg, Pa 18.29 Susquehanna, at Willces- 16.66 Susquehanna, at Williams- 17.76 ■OUo, at Wheeling, W. Va. . . Potomac, at Point of BocIjs, Md 19.02 22.64 Shenandoah, at Millville. W.Va James, at Cartersville, Va.. . . James, at Buchanan. Va 2forth (of James) Glasgow, Va 84.69 84.77 24.26 84.77 26.60 24.99 25.14 Appomattox, at Mattoax, Va. Eoanolce, at Eoanolte, Va. . . . Koanoke, at Eandolph, Va.. "For the number of years records see table on pp. 136-139. GEOLOGY. Aside from its effect on topography, which results directly from it, geology has an important influence on the regimen of stream flow in two ways, which relate to the nature and depth of the soil and the dip of the strata. It affects both the total run-off and its regimen. Rain that falls upon a sandy soil enters it almost immediately, with a minimum loss through evaporation, is retained there tempo- 154 RIVER DISCHARGE. rarily, and readily and gradually flows from it to springs and rivers. Clay and loam receive water much less readily and give it up much. less freely. Large areas and depths of sand are therefore among the best natural regulators of stream flow. Basins of bare rock, on the other hand, shed immediately the major portion of the water that falls upon them. Between these two extremes- Df rock and sand are all grades of clay, silt, and loam, of varying depths, affecting very decidedly the regimen of the streams that drain them. The dip of the strata and their porosity are often important OD account of their effect on the courses of streams and on the concen- tration of fail, but also on the amount of water absorbed by the ground to appear elsewhere as springs in the same or another drainage basin, or to be lost permanently to the ground, unless it is brought to the surface Eigain by means of some deep well. TOPOGRAPHY. The general topography of the country affects largely both the total amount and the distribution of the run-off. Its influence on the total run-off is derived principally from its effect on precipitation. Mountain ranges frequently cause the precipitation of large quantities of moisture upon them, thereby decreasing the moisture and the clouds in the atmosphere, which they intercept, so that Uttle precipitation occurs beyond the range. By their storage of snow, mountainous areas form the principal reservoirs for the -w.ater supply of western streams. The nature of the slopes of the basin and stream affects principally the distribution of run-off. Steep slopes discharge their water rapidly and as a rule store relatively small amounts of ground water. Flat areas, on the other hand, if pervious, absorb much of the water that falls upon them and yield it up gradually. Rivers draining steep slopes and having steep beds are therefore "flashy" in character, having great ranges in stage and very small minimum discharges. Rivers that drain flat countries, containing swamp or sand areas, fluctuate less rapidly, having fairly uniform stage and relatively large minimum discharge. The shape and si?e of a drainage basin has a decided effect on the streams draining it. The flow from basins which are so large that they cover considerable, latitude may be materially affected thereby on account of the difference in the times at which the snows are melted. Rivers flowing southward may discharge the snow water without serious freshet, since the snows melt gradually, beginning in the southern part CONDITIONS AFFECTING STREAM FLOW. 155 and gradually extending toward the north. On the other hand, rivers flowing northward are more liable to freshets from the accumulation of water as the higher temperatures advance north, and to ice-jams and consequent freshets from backwater therefrom, because of the greater thickness and strength of the more northern ice. Rivers flowing east and west are more liable to have the same temperature conditions through- out the whole basin and consequently an accumulation of waters result- ing from freshets simultaneously in all tributaries. The shape of the basin, whether long or palmate, affects in a similar way the accumu- lation of freshet waters. The shape of the basin and the direction of its axis relative to the direction of motion of prevailing storms is often an important factor in determining the magnitude of freshets. Basins whose axes lie in such direction of motion of storms and whose streams flow in the direction of such motion rather than against it are especially liable to excessive freshets. The surfaces of lakes and ponds affect the regimen of streams in two ways — first, by decreasing the total annual run-off, on account of the great evaporation from their surfaces, and second, by equalizing flow and making the discharge more regular. They are also important on account of their availability for artificial storage. Swamp areas affect streams in much the same way, especially as regards their regimen, VEGETATION. Vegetation affects very largely the regimen of streams. Its influence does not probably extend to rainfall but pertains principally to effects on surface and ground storage and evaporation. The ground storage is increased on account of the greater receptivity^ of a soil loosened and opened by roots and a surface covered with fallen leaves and litter. The roots and cover retard the flow of water over the surface and thereby promote the absorption of the water by the soils. The effect of forests on ground storage is therefore a minimum on open, sandy soils, which would readily absorb water under all conditions, and a maximum on heavy, compact soils and clays, which do not take up water easily. The differences between evergreen and deciduous forests or between large and small trees in their effects on ground storage are probably small. Young trees and bushes, or even grass and weeds, produce approximately the same effects in this respect as virgin forests. In their effects on temperature and resultant evaporation, and especially 156 RIVER DISCHARGE. on snow storage, the differences in forests are great. In the latter respect, especially, dense evergreen growths have much more marked effects than open or deciduous growths. Unfortunately the magni- tudes of their effects have not been measured, and the conclusions in regard to them are based rather on general observations than on measured differences in stream flow. The variety of conditions existing within basins of considerable size makes exact determinations of the effect of the various factors very difficult. Many attempts have been made to study the magnitude of the effects of forests on stream flow, but without satisfactory success. In order that such observations may result in definite conclusions it is necessary that conditions of climate, geology, and topography shall be the same, and that the only differences shall pertain to forestation. Such conditions are not readily found or produced. ARTIFICIAL CONTROL. Artificial control of the flow of surface water may be effected either by storage in ponds, lakes, or reservoirs, or by drainage of swamp or wet areas by drains or open ditches. Artificial storage is generally cheapest and its results greatest in glaciated regions, where natural ponds and lakes available for increased storage are numerous. By means of such artificial storage freshet flows are diminished and low flows increased. By artificial drainage, on the other hand, the opposite effects are produced. It is believed that a considerable proportion of the effects on stream flow usually ascribed to deforestation and cultivation are due to the artificial surface and subsurface drainage which has been accomplished incidental to cultivation. TABLES. TABLES. There are available a large number of tables for facilitating the com- putations in various hydraulic problems. It is often necessary, how- ever, for the engineer to prepare special tables adapted to the problem in hand. Among the tables available are a number having wide appli- cation, which are given on the following pages. These tables have been adapted from Water-Supply Papers of the U. S. Geological Survey. In connection with the use of these tables attention is called to Barlow's tables and to Crelle's Rechentaf eln. The former tables give for numbers from 1 to 10,000 the squares, cubes, square roots, cube roots, etc. The latter give products of all numbers between 1 and 1000, and can be used both for multiplication and division. LIST OF TABLES. Table I. Discharge in second-feet over rectangular sharp-crested weirs having complete end contractions. [Formula: Q=3 .33 (Z - .2H) H^] Table II. Discharge in second-feet per foot of crest over rectangular sharp- crested weirs without end contractions. [Formula: Q=3 .33 I H^ Table III. Discharge in second-feet per foot of crest length for certain broad- crested weirs. [Formula: Q=2 .64 I H^ Table IV. Discharge in second-feet per foot of crest over sharp-crested rectan- gular weirs without end contractions. [Formula: Q=(0 .405 +'5^^) (1 + 0.55 ;^'^ IH V2^] Table V. MultipHers to be used in connection with Table IV to obtain the discharge over broad-crested weirs of rectangular cross-section of type a, Fig. 38. Table VI. Multipliers to be used in connection with Table IV to obtain the discharge over broad-crested weirs of trapezoidal cross-section of types 6 and c, Fig. 38. Table VII. Multipliers to be used in connection with Table IV to obtain the discharge over broad-crested weirs of compound cross section of types d to m in- clusive, Fig. oS. Table VIII. Three-halves powers of numbers. Table IX. For converting discharge in second-feet per square mile into run- off in depth in inches over the area. Table X. For converting discharge in second-feet into run-off in acre-feet. Table XL For converting discharge in second-feet per day into run-off in miUions of gallons. Table XII. For converting run-off in miUions of gallons into discharge in second-feet per day. Table XIII. For converting run-off in acre-feet into run-off in million gallons. Table XIV. For converting run-off in million gallons into rim-off in acre-feet. Table XV. Values of c for use in the Chezy formula: F=c VRs. Table XVI. Square roots of numbers ( VB, Vs) for use in Kutter's formula. Table XVII. Convenient equivalents. 159 160 RIVER DISCHARGE. Tabu I. — Discharges in second-feet, over rectangular sharp-crested weirs having Head. 10,010 ' .021 .031 .042 .052 .052 .073 .083 .094 .104 1. 1[ li n 2 2i 21 2i 21 2 22 2 23 2 24 3 25 3i ■3V 31 3i 3' 3 3J 4 4 4 4 4 4 .5 5i 5' 5i 5' s; 6 6i 6i 8J 8} a: 7 7i T 7 7 78 7" 7 8 .115 ,125 .135 .146 ,156 ,167 ,177 .187 .198 ,208 .219 .229 .243 ,250 .260 ,271 ,281 .292 ,302 ,312 .323 ,333 ,344 .354 ,365 ,375 ,385 .396 .406 .417 .427 .437 .448 .458 .469 .479 .490 .500 .510 .521 .531 .542 .552 563 .573 ,583 ,594 ,604 ,615 .625 .635 ,646 ,656 ,667 ,688 ,708 .729 .750 .792 ,833 0,0011 0033 .0060 .0092 .0128 .0167 .0209 .0254 ,0301 ,0349 ,0401 .0454 .0508 .0564 .0622 ,08SO .0749 ,0793 ,0882 ,0924 Length of weir. .a .a 01 ,0017 0. ,0050 , ,0091 .0139 .0194 .0254 .0318 .0387 .0460 ,0536 .0616 .0699 ,0784 ,0873 ,0965 ,106 .115 ,125 ,135 ,145 .155 .166 .177 .187 .198 .209 ,220 ,232 0026 0075 0137 0210 0293 0384 0482 0587 0699 0816 .0939 ,107 ,120 ,134 ,148 ,162 ,177 ,193 ,208 ,224 ,241 ,257 .274 .291 .309 .327 .345 .363 .381 .400 .419 .438 .457 .477 .496 ,516 1.029 1.060 1 . 00353 . 00997 .0183 .0281 .0392 .0514 .0646 .0788 .0938 .110 .126 .144 .161 ,180 ,199 ,219 ,239 ,260 ,282 ,303 ,326 ,349 ,372 ,395 ,420 ,444 ,469 ,494 ,520 ,545 .572 ,598 ,625 ,652 .680 .707 .735 .764 .793 .821 .850 .879 .908 .938 .968 ).0125 ,0229 ,0352 ,0491 ,0644 ,0810 .0988 .118 .138 ,159 ,180 ,203 ,226 ,251 ,276 ,301 ,328 ,355 ,383 ,411 ,440 ,469 ,499 .530 .561 .593 .625 .658 .691 ,724 ,758 .793 ,828 ,863 ,899 ,935 ,971 1,009 1,045 1.082 1.120 1.158 196 1.235 1.274 1.314 1.354 1.394 434 1,475 1,516 1.557 1.598 1.640 1.682 1.725 1.767 1,809 1.851 00 1. 1.0150 .0275 .0422 .0599 .0774 .0974 .119 .142 ,166 ,191 .217 .244 ,273 ,302 ,332 .364 .395 .428 .462 .496 ,531 ,567 ,604 ,641 ,679 ,717 ,756 ,796 ,836 ,877 ,919 ,961 ,003 ,046 ,090 .134 .178 224 269 .315 .361 ,407 ,455 ,502 ,550 .599 .649 .897 .747 1,798 1.848 1.898 1.949 001 2.053 2,106 158 210 263 316 2,370 2,423 2,477 2,586 2,697 2,818 2,919 .a 1,0200 .0367 .0564 .0788 .103 .130 .159 .189 .222 .255 .291 .327 .365 .405 .446 .488 .531 .575 .620 .667 .714 ,762 ,812 ,862 ,913 ,966 1,018 1,072 1.127 183 239 296 354 413 1.472 1.532 593 1.655 717 1.779 843 906 971 037 103 170 237 304 372 2.442 2.511 2.581 2.652 2.723 2.796 ' 867 2.940 3.012 3.085 3.160 3,234 3,308 3,384 3.535 3,689 3,844 4,001 4,320 4,644 &3 (NO eo « o> ^ (M I-* •-' 0.00029 0.00354 1 6; 6566 J .0666 6.6766 6. '0806 6. '6666 '6!i66 '6!i26 '6'i46 o'.ieb '6.'i86 '6. '266 .00083 .01001 2 .0918 .110 .129 .147 .166 .184 .221 .258 .294 .331 .368 .00153 .0184 3 .141 .170 .198 .226 .255 .283 .340 .396 .453 .510 .566 .00236 .0283 4 .198 .237 .277 .316 .356 .395 .475 .554 .633 .712 .791 .00330 .0396 5 .260 .312 .364 .416 .468 .520 .624 .728 .832 .936 1.040 .00433 .0520 6 .327 .392 .458 .624 .589 .655 .786 .917 1.048 1.179 1.310 .00546 .0656 7 .399 .479 .559 .640 .720 .800 .960 1.120 1.23 J 1.441 1.601 .00667 .0801 8 .476 .572 .667 .763 .859 .954 1 . 145 1.337 1.528 1.719 1.910 .00796 .0956 9 .557 .669 .781 .893 1.005 1.117 1.341 1.565 1.789 2.013 2.237 .00933 .112 10 .643 .772 .901 1.030 1.160 1.289 1.547 1.805 2.064 2.322 2.580 .0108 .129 11 .732 .879 1.026 1.174 1.321 1.468 1.762 2.057 2.351 2.646 2.940 .0123 .147 12 .825 .991 1.157 1.323 1.489 1.655 1.967 2.319 2. 650 2.982 3.314 .0138 .166 13 .922 1.107 1.293 1.478 1.664 1.849 2.220 2.691 2.962 3.333 3.704 .0155 .185 14 1.022 1.228 1 433 1.639 1.845 2.050 2.462 2.873 3.284 3.696 4.107 .0171 .206 15 1.125 1.352 1.679 1.805 2.032 2.258 2.711 3.166 3.618 4.071 4.524 .0189 .227 16 1.232 1.480 1.723 1.976 2.225 2.473 2.969 3.465 3.962 4,468 4.954 .0207 .248 17 1.342 1.612 1.882 2.153 2.423 2.693 3.234 3.775 4.316 4,866 5.397 .0225 .270 18 1.455 1.748 2.041 2.334 2.627 2.921 3.537 4.093 4,68.; 5.266 5.853 .0244 .293 19 1.570 1.887 2.203 2.520 2.837 3.153 3.787 4.420 5.053 5.686 6.320 .0264 .317 20 1.689 2.029 2.370 2.711 3.051 3.392 4.074 4.755 5.436 6.118 6.799 .0284 .341 21 1.810 2.175 2.540 2.906 3.271 3.636 4.367 5.098 5.823 6.559 7.290 .0304 .366 22 1.934 2.324 2.715 3.105 3.496 3.886 4.667 5.448 6.22G 7.010 7.792 .0325 .391 23 2.060 2.477 2.893 3.309 3.725 4.142 4.974 5.807 6.030 7.472 8.304 .0347 .416 24 2.190 2.632 3.075 3.517 3.960 4.402 5.287 6.172 7.068 7.943 8.828 .0369 .443 25 2.321 2.791 3.260 3.729 4.199 4.668 5.607 6.646 7.484 8.423 9.362 .0391 .469 26 2.455 2.952 3.449 3.946 4.442 4.939 5.932 6.926 7.919 8.913 9.906 .0414 .497 27 2.592 3.117 3.641 4.166 4.690 5.215 6.264 7.313 8.362 9.411 10,460 ,0437 .525 28 2.731 3.284 3.837 4.390 4.943 5.495 6.601 7.707 8.813 9.918 11,024 ,0461 .553 29 2.872 3.464 4.036 4.617 5.199 5.781 6.944 8.108 9.271 10.435 11.698 ,0486 .582 30 3.016 3.627 4.238 4.849 5.460 6.071 7.293 8.515 9.737 10.960 12.182 ,0609 .611 31 3.162 3.802 4.443 5.084 5.726 6.366 7.648 8.929 10.211 11.493 12.774 .0634 .641 32 3.310 3.981 4.652 5.323 5.994 6.665 8.007 9.350 10.692 12.034 13.376 .0659 .671 33 3.460 4.161 4.863 5.565 6.267 6.969 8.373 9.776 11.180 12.684 13.988 .0586 .702 34 3.612 4.345 5.078 5 811 6.544 7.277 8.743 10.209 11.676 13.142 14.608 .0611 .733 35 3.766 4.531 5.296 6.060 6.825 7.590 9.119 10.648 12.178 13 . 707 15,237 .0637 .765 36 3.922 4.719 5.516 6.313 7.110 7.906 9.500 11.093 12.687 14.281 15.874 .0664 .797 37 4.081 4.910 5.739 6.569 7.398 8.227 9.886 11.545 13 , 203 14.862 16,520 .0691 .829 38 4.242 5.104 5.967 6.829 7.691 8.553 10.278 12.002 13 . 727 15.451 17,176 .0719 .862 39 4.404 5.299 6.195 7.090 7.986 8.882 10.673 12.464 14.256 16.047 17.838 .0747 .896 40 4.568 5.497 6.427 7.356 8.285 9.215 11.074 12.933 14.791 16.650 18,509 .0775 .929 41 4,733 5.697 6.661 7.624 8.588 9.551 11.479 13.406 15.333 17.260 19.187 .0803 .964 42 4.901 5.899 6.897 7.895 8.894 9.892 11.888 13.886 15.881 17.877 19.874 .0832 .998 43 5.071 6.105 7.138 8.171 9.204 10.238 12.304 14.371 16.438 18.504 20.571 .0861 1.033 44 5.243 6.312 7.380 8.449 9.518 10.586 12.724 14.861 16.999 19.136 21.273 .0891 1.069 45 5.416 6.521 7.626 8.730 9.835 10.939 13 . 149 15 .358 17.567 19.776 21.985 .0921 1.105 46 5.592 6.733 7.873 9.014 10.155 11.295 13 . 577 15.868 18.140 20.421 22.702 .0951 1.141 47 5.769 6.947 8.124 9.301 10.478 11.656 14.010 16.365 18.720 21 074 23.429 .0981 1.177 48 5.948 7.162 8.376 9.591 10.805 12.020 14.448 16.877 19.306 21 . 735 24.164 .101 1.214 49 6.128 7.380 8.631 9.883 11.135 12.386 14.890 17.393 19.897 22.400 24.903 .104 1.252 50 6.311 7.600 8. 889 10.179 11.468 12.758 15.336 17.915 20.494 23,073 25,652 ,107 1.289 51 6.494 7.822 9.149 10.477 11.804 13.132 15 . 787 18.442 21.097 23,762 26,407 ,111 1.328 52 6.679 8.045 9.411 10.777 12.143 13.509 16.241 18 . 973 21.705 24,437 27,169 ,114 1.366 53 6.866 8.271 9.676 11.081 12.485 13.890 16 . 700 19.509 22,319 25,129 27.938 ,117 1.405 54 7.055 8.500 9.944 11.388 12.832 14.276 17 . 164 20.052 22,941 25,829 28.717 .120 1.444 55 7.245 8.729 10.213 11.696 13.180 14 663 17.631 20 . 59S 23 , 565 26,532 29.499 .124 1.484 56 7.438 8.962 10.485 12.009 13 . 532 15.056 18.103 21.150 24 , 197 27,244 30.291 .127 1.524 57 7.631 9.195 10.759 12.323 13.886 15.460 18.578 21 . 70S 24,833 27,961 31.083 .130 1.564 68 7.826 9.430 11.034 12.639 14 . 243 15.848 19.056 22 . 265 25 , 474 28,683 31.892 .134 1.604 59 8.022 9.667 11.312 12.958 14.603 16.249 19.539 22.830 26,121 29,412 32.703 .137 1.646 60 8.220 9.907 11.593 13.280 14.967 16.653 20.027 23.400 26,774 30,147 33.520 .141 1.687 61 8.419 10.148 11.876 13.604 15.332 17.061 20.517 23.974 27,431 30,887 34.344 .144 1.728 62 8.619 10.390 12.160 13.930 15.700 17.471 21.011 24.552 28 , 093 31,633 35.174 .148 1.770 63 8.821 10 . 634 12.447 14.259 16.072 17.884 21.510 26 . 135 28,760 32,385 36.010 .151 1.813 64 9.230 11.128 13.026 14.924 16.823 18.721 22.517 26.314 30,110 33,906 37.703 .168 1.898 65 9 645 11.630 13.615 15.600 17.686 19.571 23.541 27.512 31.482 36.462 39.423 .165 1.985 66 10.065 12.138 14.211 16.285 18.358 20.432 24.578 28.725 32.872 37.019 41.166 .173 2.073 67 10.490 12.653 14.815 16.978 19.141 21.304 25.630 29.956 34,28238.607 42.933 .180 2.163 68 11.356 13.702 16.048 18.393 20.739 23.084 27.776 32.467 37.158141.849 46.640 .196 2.346 69 10 o±A Id 777 17 S10 19 843 22.377 24.910 29.976 35.043 40.109 45.175 50.242 .211 2.533 70 162 RIVER DISCHARGE. Table II. — Discharge in second-feet per foot of crest over rectangular sharp-crested weirs without end contractions. Formula: Q=Z.ZZIH^. Head H, feet. .00 ,01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 0. 0000 0.0033 0.0094 0.0173 0.0266 0.0372 0.0489 0.0617 0.0753 0.0899 .1 .1053 .1215 .1384 ,1561 .1744 ,1935 ,2131 .2334 .2543 .2758 .2 .2978 .3205 .3436 .3673 .3915 ,4162 .4416 .4672 .4934 .5200 .8. .6472 .6748 .6028 .6313 .6602 ,6895 .7193 .7495 .7800 , .8110 .4 .8424 .8742 .9084 .9390 .9719 1.0052 1.0389 1.0730 1,1074 1.1422 .6 1.1773 1.2128 1.2487 1.2849 1.3214 1.3583 1.3965 1.4330 1,4709 1.5091 .6 1.5476 1.5865 1.6257 1.6652 1.7050 1.7451 1.7856 1.8262 1.8673 1.9086 .7 1. 9603 1.9922 2.0344 2.0770 2. 1198 2.1629 2.2063 2.2500 2.2940 2.3382 .8 2.3828 2.4276 2.4727 2.6180 2.5637 2.6096 2.6568 2.7022 2.7490 2.7959 .9 2.8432 2.8907 2.9385 2.9866 3.0348 3.0834 3.1322 3.1813 3,2306 3.2802 1.0 3. 3.300 3.3801 3.4304 8.4810 3.6318 3.5828 3.6342 3.6857 3.7375 3.7895 1.1 3.8418 3.8943 3.9470 4,0000 4.0532 4.1067 4.1604 4.2143 4.2384 4.3228 1.2 4.3774 4. 4322 4.4873 4.6426 4.6981 4.6638 4.7098 4.7660 4,8224 4.8790 1.3 4.9368 4.9929 5. 0502 5.1077 5.1654 5.2233 6.2814 5.3398 6.3984 5.4572 1.4 5.5162 5.5754 5.6348 6.6944 5.7542 5. 8143 5.8745 5.9350 5.9957 6.0565 1.5 6. 1176 6. 1789 6.2404 6,3020 6.3633 6.4260 6.4883 6.5508 6.6135 6.6764 1.0 6.7394 6.8027 6.8662 6.9299 6.9937 7.0578 7.1221 7.1865 7.2512 7.3160 1-V 7. 3810 7.4403 7.5117 7.6778 7.6431 7. 7091 7.7752 7.8416 7.9081 7.9749 1.8 8.0418 8.1689 8.1762 8.2437 8.3118 8.3792 8.4472 8.5154 8:5838 8.6524 1.9 8. 7212 8.7901 8.8692 8.9286 8.9980 9.0677 9. 1375 9.2075 8.277'/ 9.3481 2.0 9.4187 0.4S94 9.6603 9.6314 9.7026 9. 7741 9.8457 9.9174 9,9894 10.0620 2.1 10.1340 10. 2060 10.2790 10. 3520 10.4250 10,4980 10,5710 10.6460 10,7183 10.7920 2.2 10.8660 10.9400 11.0150 11.0890 11,1640 11,2390 11,8140 11.3890 11.4640 11.5400 2.3 11.6160 11. 6910 11.7670 11.8430 11.9200 11,9960 12.0730 12.1500 12.2270 12.3040 2.4 12. 3810 12.4590 12.6360 12.6140 12.6920 12,7700 12.8480 12.9270 13,0050 13.0840 2.6 13.1630 13.2480 13.3210 13.4010 13.4800 13.6600 12.6400 13. 7200 13.8000 13.8800 2.6 13. 9610 14.0410 14.1220 14.2030 14,2840 14.3050 14.4470 14.5280 14.6100 14.6920 2.7 14.7740 14.8560 14.9380 15.0210 15, 1030 15. 1860 15.26:0 15.3620 15.4350 15.5190 2.8 16. 6020 15.6860 16.7690 16.8530 15.9380 16.0220 16.1060 16.1910 16,2750 16.3600 2.9 16.4460 16.5300 16.6160 16.7010 16.7870 10.8720 16.9680 17.0440 17.1300 17.2170 8.0 17.3038 17.3899 17.46C8 17,5684 17. 6503 17.7376 17.8248 17.9124 18.0000 18.0876 3.1 18.1754 18.2634 18.8516 18.4399 18.5285 18.6170 18. 7056 18.7945 18.8838 18.9727 3.2 19.0619 19. 1516 19. 2410 19,3307 19.4206 19.6105 19.6007 19.6910 19, 7S12 19.8718 8.3 19.9624 20.06.'^3 20.1442 20.2354 20.3267 20,4179 20.5C95 20.6011 20,6930 20.7849 3.4 20.8777 20.9690 21.0613 21.1538 21.2464 21,3390 21.4319 21. 5248 21.6180 21. 7118 3.6 21.8045 21. 8980 21.9917 22.0866 22.1795 22,2734 22.3677 22.4618 22.55C4 22.6510 8.6 22.7456 22.8405 22.9354 23.0306 23, 1259 23,2211 28.3167 28.4123 :3.5081 23.6040 8.7 23.6999 23. 7962 23. 8924 23.9887 24,0.s.62 24,1818 24.2787 24,3766 24.4728 24.5697 8.8 24.6073 24.7646 24.8621 24.9600 'JB. 0576 25.1665 25. 2537 25.8520 26.4502 25.5488 8.9 26.6473 26.7469 25.8748 25.9437 211.0429 26,1422 20.2414 26. 3410 26.4406 26.5401 4.0 26. 6400 26.7399 26.8101 26.9404 27,0406 27, 1112 -'7. 2417 27,8423 27.4432 27.5411 4.1 27.6463 27.7466 27.8478' 27. 9494 28,0509 28,1526 28,2544 28.3563 28.4682 2S.6604 4.2 28.6620 28. 7652 28.8678 28,9703 29.0732 29, 1761 29.2790 29. 3823 29.4855 29.5890 4.3 29.6926 29.7902 29.9001 80.0040 30.1079 80,2118 30,3163 30.4205 80.5261 30,6297 4.4 30. 7342 80.8391 30.9440 31.0493 81. 1545 31.2697 31,3649 81.4705 31.5764 81,6820 4.5 81.7878 81.8941 82.0003 82.1065 82.2128 82,3198 82,4259 32.6324 32. 6393 32,7462 4.6 82. 8634 82.9607 83.0679 33.1765 83.2880 33.3906 33.4985 33.6064 83.7143 33,8225 4.7 83.9307 84.0373 84. 1475 34.2500 34,8646 34.4735 34.6824 84.6913 C4.8005 84,9097 4.8 85.0193 86.1288 86.2354 35, 8480 36,4578 35.6677 85. 6780 85. 7882 35.8984 36,0086 4.9 36.1182 36.2297 86.8406 86,4616 36.5624 36. 6736 86.7846 36,8961 37.0073 87.1188' | TABLES. 163 Table II. — Continued, Head H, feet. .00 .01 .02 .08 .01 .05 .06 .07 .08 .09 5.0 37. 2304 37. 3423 37.4542 37.5661 37.6783 37.7905 37. 9027 38.0163 38. 1275 38.2404 5.1 38.3629 38. 4658 38.5787 38.6919 88.8052 38. 9184 39.0319 39.1456 39.2691 39. 3726 5.2 39.4865 39. 6004 39. 7146 39.8288 89.9430 40.0676 40. 1718 40.2867 40. 4012 40. 51S1 6.3 40. 6310 40. 7462 40.5281 40.9766 41.0919 41.2074 41.3230 41. 4386 41.6544 41. 6703 5.4 41. 7866 41.9024 42.0186 42.1362 42.2517 42.3683 42.4848 42.0C17 42.7186 42. 8356 5.5 42. 9523 43.0700 43.1871 43.3043 43.4219 42.5394 43.6573 43.7752 43.8931 44.0109 5.6 44.1292 44.2474 44.3659 44.4845 44.6030 44. 7216 44. 8404 44.9593 4.5.0782 46. 1974 5.7 45.3166 45.4859 46.5654 45.6746 46.7945 46. 9140 46.0339 46. 1638 46, 2740 46.3939 5.8 46. 5141 46.6347 46.7552 46.8757 46.99(3 47. 1172 47.2380 47. 3589 47.4798 47. 0010 5.9 47.7226 47.8438 47. 9663 48.0869 48. 2084 48.3303 48. 4522 48. 6744 48.6963 48.8186 6.0 48. 9407 49.0632 49.1858 49.3083 48.4312 49.5537 49.6766 49. 7999 49.9230 50. 0462 6.1 50.1694 60.2930 50. 4162 60. 6401 50.6637 50. 7875 60.9114 51.0356 51.1595 51.2837 6.2 51.4082 51. 5324 51.6670 51. 7818 61. 9034 62.0313 52.1631 52.2813 52. 4062 52, ,^314 6.3 52.6570 62.7822 52.9077 63.0336 53.1591 63.2850 53.4109 63. 6371 53. 6630 53. 7892 6.4 53.9157 54.0419 64.1684 64.2950 54.4219 54.5487 64.6766 54.8025 54. 9297 65.0569 6.5 55. 1832 55.3116 55.4392 55.5667 55.6943 65.8221 55.9500 56.0779 56. 20C1 56. 3343 6.6 56.4625 56.6910 66.7192 56.8478 66.9766 57. 1065 67. 2340 67. 3233 57. 4921 67, 6213 6.7 57. 7505 57.8801 58.0093 58.1388 68.2687 58.3982 58.5281 68.6580 58. 7882 68,9180 6.8 59.0482 59.1788 59. 3090 59.4428 59. 570u 59. 7009 59.8314 59. 9623 60.0935 60, 2244 6.9 60.3556 60.4868 60.6183 60,7499 60.8814 61.0129 61. 1445 61, 2763 61. 4082 61, 5404 7.0 61. 6736 61.8048 61.9370 62. 0692 02. 2017 02. 3343 62. 4671 62. 6000 62, 7329 62,8667 7.1 62.9986 63.1318 63.2650 63.3992 63.5317 63. 66.63 63.7991 63.9327 64,0666 64,2004 7.2 64.3343 64.4686 64. 6027 64.7369 64.8711 65.0056 66. 1268 65.2750 05,4095 65.5444 7.3 65.6793 66.8145 65. 9493 66.0845 66.2197 66. 3552 66. 4908 66. 6263 06, 7618 66, 8977 7.4 67. 0336 67. 1694 67.3053 67.4415 67.5777 67. 7139 67.8504 67.9869 68, 1235 68,2600 7.5 .68.3969 68.5337 68.6706 68.8078 68. 9447 69.0818 69. 2794 60. 3566 69,4941 69, 6316 7.6 69.7695 69. 9070 70.0449 70. 1827 70.3209 70. 4591 70.5973 70. 7355 70. 8737 71,0123 7.7 71.1508 71.2896 71.4282 71.6670 71.7059 71.8451 71. 9843 72.1236 72.2627 72.4743 7.8 72.5414 72.6809 72.8208 72.9603 73. 1002 73. 2400 73. 3802 73. 6201 73. 6603 73.8005 7.9 73.9410 74.0815 74.2220 74.3626 74.5031 74. 6439 74. 7848 74.9260 75.0669 75.2081 8.0 75.3492 76. 4908 76.6320 75.7735 76.9150 76.0569 76.1987 76. 3406 76,4824 76. 6243 8.1 76. 7665 76.9087 77.0509 77.1934 77.3360 77.4784 77.6210 77.7638 77,9067 78.0496 8.2 78.1924 78.3366 78.4788 78. 6220 78. 7656 78. 9087 79.0522 79.1957 79, 3396 79.4834 8.3 79.6273 79. 7711 79.9153 80.0592 80.2034 80.3479 80.4921 80.6366 80, 7811 80.9260 8.4 81.0705 81.2164 81.3602 81.5054 81.6603 81. 7966 81. 9406 82. 0862 82. 2314 82.3769 8.5 82.6224 82.6682 82.8141 82. 9600 83.1058 83.2617 83.3979 83.5440 83.6902 83.8367 8.6 83.9833 84.1298 84.2763 84.4228 84.6697 84.7166 84.8634 85.0106 85.1578 85.3049 8.7 85.4521 85.6996 85.7472 85.8947 83.0465 86.1897 86.3376 86.4864 86. 6336 86. 7815 8.8 86.9297 87.0778 87.2264 87. 3745 87.5231 87.6716 87.8204 87.9689 88,1178 88.2666 8.9 88.4192 88.6647 88. 7139 88.8630 89. 0126 89.1617 £9. 3113 89.4608 89, 6103 89. 7602 9.0 89. 9100 90.0699 90.2064 90.3699 90.5101 90.6602 90.4778 90. 9609 91, 1115 91.2620 9.1 91.4125 91.8633 91. 7142 91.8650 92.0159 92.1671 92. 3183 92.4694 92, 6206 92. 7721 9.2 92.9237 93.0782 93.2267 93.3785 93. 6304 93.6822 93.8341 93.9863 94,1384 94, 2906 9.3 94.4428 94.6950 94. 7475 94. 9000 96.0529 95.2054 95.3682 95.5111 96, 6633 95,8171 9.4 95.9703 90.1234 96.2766 96. 4298 96.6833 96. 7363 96.8903 97.0442 97,1977 97. 3516 9.5 97.5057 97.6596 97.8138 97.9679 98. 1021 98. 2763 98.4308 98. 6863 98, 7398 98,8943 9.6 99.0492 99.2040 99.3589 99.5141 99. 6089 99. 8241 99.9793 100.1344 100,2899 100,4456 9.7 100.6010 100.7666 100. 9123 101.0678 101.2237 101. 3799 101.6357 101.6919 101,8481 102,0042 9.8 102.1607 102. 3169 102.4734 102.6299 102.7868 102.9433 103. 1001 103.2570 103. 4141 103, 6710 9.9 103.7282 103.8863 104.0429 104.2000 104.3676 104. 6121 104.6726 104.8304 104.9882 105,1461 10.0 105.3039 105.4618 105. 6199 105.7781 106.9363 106.0946 106.2630 106.4116 106.5700 106.7285 Note:— By increasing the quantities in this table by 1 per cent the discharge by the Cippoletti 1„ m—Q -it iTjf^ will hfi obtained. 164 RIVER DISCHARGE. Table III. — Discharge in second-feet per foot of crest length for certain broad-crested weirs. Formula: Q=2 .64 IH^ Head //, feet 1 2 3 4 6 6 7 8 10 0.00 0.000 2.64 7.47 13.7 21.1 29.5 38.8 48.9 59.7 71.3 83.5 .01 .003 2.08 7.52 13.8 21.2 29. o 38.9 49.0 59.8 71.4 83.6 .02 .007 2.72 7.58 13.8 21.3 29.7 39.0 49.1 59.9 71.5 83.7 .03 .014 2.76 7.64 13.9 21.4 29.8 39.1 49.2 60.1 71.6 83.9 .04 .021 2.80 7.69 14.0 21.4 29.9 39.2 49.3 60.2 71.7 84.0 .05 .030 2.84 7.75 H.l 21.6 30.0 39.3 49.4 60.3 71.9 84.1 ,0G .039 2.88 7.81 14.1 21.0 30.0 39.4 49.6 60.4 72.0 84.2 .07 .049 2.92 7.86 14.2 21.7 30.1 39.5 49.6 60.6 72.1 84.4 .08 .060 2.96 7.92 14.3 21.8 30.2 39.6 49.7 60.6 72.2 84.5 .09 .071 3.00 7.98 11.3 21.8 30.3 39.7 49.8 00.7 72,3 84.6 0.10 0.083 3.04 8.03 14.4 21.9 30.4 39.8 49.9 60.8 72.5 84.7 .11 .096 3.09 8.09 11.5 22.0 30.5 39.9 50.0 61.0 72.6 84.9 .12 .110 3.13 8.15 14.5 22.1 30.6 40.0 60.2 61.1 72.7 a-j.o .13 .124 3.17 8.21 11.6 22.2 30.7 40.1 50.3 61.2 72,8 85.1 .U .138 3.21 8.26 14.7 22.2 30.8 40.2 50.4 61.3 72.9 85.2 .16 .163 3.26 8.32 14.8 22.3 30.8 4D.3 50.5 61.4 73.1 85.4 .16 .169 3.30 8.33 14.8 22.4 30.9 40.4 50.6 61.6 73.2 .S,i,5 .17 .185 3.34 8.44 14.9 22.5 31.0 40.6 60.7 61.6 73.3 85.6 .18 .202 3.38 8.50 13.0 22.6 31.1 40.6 50.8 61.8 73.4 a5.7 .19 .218 3.43 8.56 15.0 22.6 31.2 40.7 50.9 61.9 73.6 86.9 0.20 0.236 3.47 8.61 16.1 22.7 31.3 40.8 61.0 62.0 73.7 86.0 .21 .264 3.51 8.67 15.2 22.8 31.4 40.9 61.1 62.1 73.8 86.1 .22 .272 3.56 8.73 15.2 22.9 31.5 41.0 61.2 62.2 73.9 86.2 .23 .291 3.60 8.79 15.3 23.0 31.6 41.0 61.3 62,3 74.0 86.4 .24 .310 3.64 8.86 16.4 23.0 31.7 41.1 51.4 62.4 74.1 86.5 .25 .330 3.69 8.91 16.5 23.1 31.8 41.2 51.5 62.6 74.3 86.6 .26 .350 3.73 8.97 15.6 23.2 31.8 41.3 61.6 62.7 74.4 86.8 .27 .370 3.78 9.03 16.6 23.3 31.9 41.4 61.7 62,8 74.5 86.9 .28 .391 3.82 9.09 16.7 23.4 32.0 41.5 51.9 62.9 74.6 87.0 .29 .412 3.87 9.15 15.8 23.4 32.1 41.6 62.0 63.0 74.8 87.1 0.30 0.434 3.91 9.21 16.8 23.6 32.2 41.7 52.1 63.1 74.9 87.3 .CI .456 3.96 9.27 15.9 23.6 32.3 41.8 82.2 63.2 75.0 87.4 .r.2 .478 4.00 9.33 16.0 23.7 32.4 41.9 52.3 63.4 75.1 S7.5 .Z3 .500 4.05 9.89 10.0 23.8 32.5 42,0 52.4 63.6 75.2 87.6 .34 .524 4.10 9.46 16.2 23.9 32.6 42.1 62.5 63.6 75.4 87,8 .35 .547 4.14 9.61 16.2 24.0 32.7 42.2 52,6 63. T 75.6 87.9 .36 .670 4.19 9.67 15.3 24.1 32. ,S 42.3 62.7 03.8 75.6 88.0 .87 .694 4.23 9.63 10.3 21.1 32,8 42,4 52.8 63.9 75.7 88.2 .38 .618 4.28 9.69 16.4 24. 2 32, 9 42.5 52.9 64. 75.8 88.3 .39 .643 4.33 9.75 10.6 21,3 33.0 42.6 63.0 64.2 76.0 88.4 0.40 0.608 4.37 9.82 16.0 21.4 33.1 42,7 63.1 64.3 70.1 88.5 .11 .693 4.42 9.f'R 16.6 24. 4 33.2 42. S 53.2 64.4 76.2 88.7 .42 ..719 4.47 9.94 16.7 21,6 33.8 42.9 63.4 64.5 76.3 88.8 .43 .744 4.51 10.0 16.8 21,6 33.4 43.0 53.5 64.6 76.4 88.9 .11 .771 4.56 10.1 10.8 24.7 33.5 43.1 53.6 617 76.0 89.0 .45 .797 4.61 10.1 16.0 24.8 33.6 43.2 53.7 64.8 76.7 89.2 .46 .824 4.66 10.2 17.0 24,9 33.7 43.3 63.8 66.0 76.8 89.3 .47 .861 4.70 10.2 17.1 24.9 33.8 43.4 53.9 65.1 76.9 89.4 .48 .878 4.75 10.3 17.1 25.0 33.9 43.6 64.0 65.2 77.0 89.6 .49 .905 4.80 10.4 17.2 25.1 84.0 43 6 54.1 65.3 77.2 89.7 1 TABLES. Table ///.—Continued. IQFi Head if, feet. 1 2 3 4 6 < I 8 9 10 0.50 0.934 4.85 10.4 17.8 25.2 34.0 43.7 54.2 66.4 77. S 89.8 .51 .961 4.90 10.5 17.4 25.3 34.1 43.8 54.3 65.5 77.4 90.0 .52 .990 4.95 10.6 17.4 25.4 34.2 44.0 64.4 66.6 77.6 90.1 .53 1.02 5.00 10.6 17.5 25.4 34.3 44.1 64.6 65.8 77.7 90.2 .54 1.05 5.04 10.7 17.6 26.5 34.4 44.2 54.7 66.9 77.8 90.3 .65 1.08 5.09 10.8 17.7 25.6 34.5 44.3 54.8 66.0 77.9 90.6 .66 1.11 6.14 10.8 17.7 25.7 34.6 44.4 54.9 66.1 78.0 90.6 .57 1.14 5.19 10.9 17.8 25.8 34.7 44.5 56.0 66.2 78.2 90.7 .68 1.17 5.24 10.9 17.9 25.9 34.8 44.6 56.1 66.3 78.3 90.8 .69 1.20 5.29 11.0 18.0 26.0 34.9 44.7 55.2 66.6 73.4 91.0 0.60 1.23 5.34 11.1 18.0 26.0 35.0 44.8 55.3 66.6 78.6 91.1 .61 1.26 5.39 11.1 18.1 26.1 35.1 44.9 66.4 66.7 78.8 91.2 .62 1.29 5.44 11.2 18.2 26.2 35.2 46.0 55.6 66.8 78.8 91.4 .63 1.32 5.49 11.2 18.2 26.3 35. 3 45.1 55.6 66.9 78.9 91.5 .64 1.35 5.64 11.3 18.3 26.4 35.4 45.2 56.7 67.0 79.0 91.6 .65 1.38 6.00 11.4 18.4 26.5 35.4 45.3 55.9 67.2 79.1 91.8 .66 1.42 5.05 11.4 18.5 26.0 35.5 46.4 56.0 67.3 79.3 91.9 .67 1.45 5.70 11.5 18.0 26.6 35.6 45.5 66.1 67.4 79.4 92.0 .63 1.48 6.75 11.6 18.6 26.7 35.7 45.0 56.2 07. 5 79.5 92.1 .69 1.51 6.80 11.6 18.7 26.8 35.8 45.7 56.3 67.6 79.6 92.3 0.70 1.65 5.85 11.7 18.8 26.9 35.9 45.8 56.4 67.7 79.8 92.4 .71 1.68 5.90 11.8 18.9 27.0 30.0 45.9 56.6 67.9 79.9 92.5 .72 1.61 5.96 11.8 18.9 27.1 36.1 46.0 56.6 68.0 80.0 92.7 .73 1.65 6.01 11.9 19.0 27.2 36.2 46.1 66.7 68.1 80.1 92.8 .74 1.68 6.06 12.0 19.1 27.2 36.3 46.2 66.8 68.2 80.2 92.9 .75 1.71 6.11 12.0 19.2 27.3 36.4 46.3 67.0 68.3 80.4 93.0 .76 1.75 6.16 12.1 19.2 27.4 36.6 46.4 67.1 68.4 80.5 93.2 .77 1.78 6.22 12.2 19.3 27.5 36.6 46.5 57.2 68.6 80.6 93.3 .78 1.82 6.27 12.2 19.4 27.6 36.7 46.6 57.3 08.7 80.7 93.4 .79 1.85 6.32 12.3 19.5 27.7 36.8 46.7 67.4 68.8 80.9 93.6 0.80 1.89 6.38 12.4 19.6 27.8 36.9 46.8 57.5 68.9 81.0 93.7 .81 1.92 6.43 12.4 19.6 27.8 37.0 46.9 67.6 69.0 81.1 93.8 .82 1.96 6.48 12.5 19.7 27.9 37.1 47.0 67.7 69.2 81.2 94.0 .83 2.00 6.64 12.6 19.8 28.0 37.2 47.1 67.8 69.3 81.4 94.1 .84 2.03 6.69 12.6 19.9 28.1 37.3 47.2 58.0 69.4 81.5 94.2 .85 2.07 6.64 12.7 19.9 28.2 37.4 47.3 58.1 69.6 81.6 94.4 .86 2.10 6.70 12.8 20.0 28.3 37.4 47.4 68.2 69.6 81.7 94.5 .87 2.14 6.75 12.8 20.1 28.4 37.5 47.5 68.3 69.7 81.9 94.6 .88 2.18 6.80 12.9 23.2 28.6 37.6 47.0 58.4 69.9 82. 94.7 .89 2.22 6.86 13.0 20.2 28.5 37.7 47.7 58.5 70.0 82.1 94.9 0.90 2.25 6.91 13.0 20.3 28.6 37.8 47.8 58.6 70.1 82.2 95.0 .91 2.29 6.97 13.1 20.4 28.7 37.9 48.0 58.7 70.2 82.4 95.1 .92 2.33 7.02 13.2 20.6 28.8 38.0 48.1 58.8 70.3 82.5 95.3 .93 2.37 7.08 13.2 20.6 28.9 38.1 48.2 69.0 70.4 82.6 95.4 .94 2.41 7.13 13.3 20.6 29.0 38.2 48.3 59.1 70.6 82.7 95.5 .95 2.44 7.19 13.4 20.7 29.1 38.3 48.4 59.2 70.7 82.9 96.6 .96 2.48 7.24 13.4 20.8 29.2 38.4 48.5 59.3 7o!8 83.0 95.8 .97 2.52 7.30 13.5 20.9 29.3 38.6 48.6 59.4 70.9 83.1 96.9 .98 2.56 7.36 13.6 21.0 29.3 38.6 48 7 59.5 71.0 83.2 96.0 .99 2.60 7.41 13.6 21.0 29.4 38.7 48.8 59.6 71.2 83.4 96.2 1.00 2.64 V.47 13.7 21.1 29.5 38.8 48.9 59.7 71.3 83.5 96.3 Note: — ^This table is applicable for use with broad-crested weirs exceeding 2 feet of crest width and for heads from 0.5 foot up to 1.5 or 2 times the breadth of weir crest. 166 RIVEK DISCHARGE. DETERMINATION OF DISCHARGE OVER VARIOUS TYPES OF BROAD-CRESTED WEIRS. From the weir experiments at the Cornell Hydraulic Laboratory, as outlined in United States Geological Survey Water-Supplj"^ Paper No. 200, Mr. E. C. Murphy has derived coefficients to be used in connec- tion with a discharge table computed by Bazin's formula for sharp- crested weirs for determining the discharge over certain types of broad- crested weirs. Table IV gives the discharge per foot of length of crest by Bazin's formula for weirs having a height varying from 2 to 30 feet, and tables V, VI, and VII give the multipliers to be used with this table to give the discharge over broad-crested weirs. Example: Sup- pose the discharge is to be computed over a rectangular weir that is 10 feet long, 12 feet high, 6 feet crest width, and has an observed head of 2.4 feet. Table IV shows that for a height (p) of 12 feet and a head (H) of 2.4, the discharge (Q) is 12.42 second-feet. Table V shows that for a height (p) of 12 feet, a crest width (c) of 6 feet, and head (H) of 2.4 feet the multiplier is 0.797. Hence, the discharge is 12.42x0.797x10=99.0 second-feet. Table IV. — Discharge in secondrfeet per foot of crest over sharp-crested rectangular weirs without end contractions." Formula: Q= ('o .405 +-^.^^\ A + 0.55 ^!.. , ) IH V^ffT [fl=head, in feet, P=height of weir, in feet]. a \P 2 4 e 8 10 20 30 0.1 0.13 0.13 0.13 0.13 0.13 0.13 0.13 .2 .33 .33 .33 .33 .33 .33 .33 .3 .58 .58 .68 .68 .58 .58 .58 .4 .88 .88 .87 .87 .87 ,87 .87 .6 1.23 1.21 1.21 1.21 1.21 1.20 1.20 .6 1.62 1.59 1.58 1.58 1.57 1.67 l.,'i7 .7 2.04 1.99 1.98 1.98 1.97 1.97 1.97 .8 2. ,50 2.43 2.41 2.41 2.40 2.40 2.40 .9 3.00 2.90 2.88 2.86 2.86 2. ,S5 2,85 1.0 3.53 3.40 3.36 8,35 3.34 8,33 8.38 1.1 4.10 3.93 3.88 3.86 3.85 8,84 3.83 1.2 4.69 4.48 4.42 4.40 4. 38 4.36 4.36 1,3 6.32 6.07 4.99 4.96 4.94 4.92 4.91 1.4 5.99 6.68 6.68 5.65 6.62 6.49 5.48 oThis table should not be used where water on the downstream side of the weir is above the level of the crest, nor unless air circulates freely between the overfalllng sheet and the downstream face of the weir. If a vacuum forms under the falling sheet the discharge may be 6 per cent greater than given in this table. TABLES. Table 77.— Continued. 1H7 >< 2 1 6 8 10 20 30 1.6 6.69 6.30 6.20 6.16 6.13 6.08 6.07 1.6 7.40 6.97 6.84 6.78 6.75 6.69 6.68 \7 8.15 7.66 7.60 7.43 7.39 7.33 7.31 1.8 8.93 8.37 8.18 8.09 ■ 8.06 7.98 7.96 1.9 9.74 9.11 8.89 8.79 8.74 8.65 8.63 2.0 10.58 9.87 9.62 9.51 9.44 9.34 9.32 2.1 11.44 10.65 10.37 10.24 10.17 10.06 10.02 2.2 12.33 11.46 11.14 10.99 10.91 10.78 10.75 2.3 13.25 12.29 11.93 11.77 11.67 11.52 11.48 2.4 14.20 13.15 12.75 12.66 12.45 12.28 12.24 2.5 15.18 14.03 13.69 13.37 13.25 13.06 13.02 2.6 16.17 14.92 14.44 14.20 14.07 13.86 13.80 2.7 17.19 16.84 16.31 16.05 14.90 14.65 14.60 2.8 18.23 16.79 16.21 15.92 15.76 15.48 15.42 2.9 19.29 17.75 17.12 16.81 16.63 16.32 16.25 3.0 20.38 18.74 18.06 17.71 17.62 17.18 17.10 3.1 21.60 19.74 19.01 18.64 18.42 18.05 17.96 3.2 22.64 20.77 19.98 19.58 19.34 18.93 18.83 3.3 23.80 21.82 20.98 20.54 20.28 19.83 19.72 3.4 24.98 22.89 21.99 21.62 21.24 20.75 20.63 3.5 26.20 23.98 23.01 22.51 22.22 21.69 21.55 3.6 27.42 25.09 24.06 23.52 23.20 22.62 22.48 3.7 28.67 26.23 25.13 24.55 24.21 23.68 23.43 3.8 29.94 27.38 26.22 26.60 25.23 24.66 24.39 3.9 81.23 28.55 27.32 26.66 26.27 25.54 25.87 4.0 32.64 29.74 28.45 27.74 27.32 26.55 26.36 4.1 33.87 30.96 29.59 28.84 28.39 27.66 27.34 4.2 35.22 32.18 30.75 29.96 29.48 28.59 28.36 4.3 36.59 33.43 31.92 31.09 30.68 29.63 29.38 4.4 37.99 84.70 33.12 32.24 31.70 30.68 30.42 4.5 89.40 36.98 34.33 33.40 32.83 31.74 31.47 4.6 40.83 37.29 35.66 34. .58 33.98 32.82 32.53 4.7 42.28 38.61 36.80 35.78 35.14 33.92 33.61 4.8 43.75 39.96 38.07 37.00 36.32 35.04 34.70 4.9 45.23 41.32 39.35 38.23 37.52 36.17 35.80 6.0 46.73 42.69 40.65 39.48 38.74 37.21 36.91 5.1 48.26 44.09 41.96 40.73 39.97 38.45 38.03 6.2 49.79 45.50 43.29 42.01 41.20 39.61 39.17 5.3 61.36 46.93 44.64 43.30 42.45 40.78 40.31 5.4 52.94 48.38 46.00 44.60 43.71 41.96 41.47 5.5 64.54 49.85 47.38 45.93 45.00 43.16 42.64 6.6 56.15 61.34 48.79 47.27 46.31 44.38 43.83 6.7 57.78 52.83 50.19 48.62 47.62 45.60 45.02 5.8 69.42 54.34 61.62 49.99 48.94 46.83 46.22 5.9 61.09 55.88 53.07 51.38 60.29 48.08 47.44 6.0 62.77 67.43 54.53 52.78 51.64 49.34 48.67 6.1 64.46 59.00 66.00 54.20 63.02 50.61 49.91 6.2 66.18 60.58 67.60 55.63 64.40 51.90 61.16 6.3 67.91 62.18 69.01 57.07 56.80 53.20 52.42 6.4 69.65 63.79 60.53 58.53 57.22 54.50 53.70 168 BIVER DISCHARGE. TcMe /F.— Continued. >< i 4 6 8 10 £0 SO 6.5 71.42 65.42 62.07 60.01 58.65 55.82 54.98 6.6 73.19 67.07 63.63 CI. 50 60.09 57.16 56.27 C.7 74.99 68.74 65.20 63.00 61.55 58.50 57.68 6.8 76.80 70.42 66.78 64.53 63.02 69.96 58.90 6.9 78.62 72.11 68.38 66.06 64.50 61.23 60.22 7.0 80.46 73.82 70.00 67. CO 66.00 62.61 61.56 7.1 82.32 75.55 71.63 69.17 67.62 64.00 62.91 7.2 84.18 77.29 73.28 70.74 69.04 65.40 64.27 7.3 86.07 79.04 74.94 72.34 70.58 66.81 65.64 7.4 87.97 80.81 76.61 73.94 72.14 68.24 67.02 7.5 89.89 82. CO 78.30 7:.. 66 73.70 69.68 68.41 7.6 91.82 84.40 80.01 77.19 75.28 71.13 69.81 7.7 93.76 86.22 81.73 78.84 76.88 72.59 71.23 7.8 95.72 88.05 83.46 80.50 78.48 74. C6 72.05 7.9 97.70 89.90 85.21 82.18 80.11 75.55 74.09 8.0 99.68 91.75 86.97 83.87 81.74 77.04 75.53 8.1 101.69 93. C3 88.75 85.67 83.39 78.55 76.98 8.2 103.70 95.61 90.54 87.29 85.25 80.06 78.44 8.3 105.73 97.42 92.34 89.02 86.72 81.69 79.92 8.4 107.78 99.34 94.16 90.76 88.41 83.13 81.40 8.6 109.84 101.27 96.00 92.52 90.11 81.69 82.90 8.6 111.91 103.21 97.84 94.29 91.82 86.25 84.41 8.7 113.99 105.17 99.70 96. C7 93.55 87.82 85.92 8.8 116.09 107.14 101.57 97.87 95.28 89.40 87.44 8.9 118.20 109.13 103. 46 9X68 97.04 91.00 88.98 9.0 120.33 in. 13 105. 36 101. 50 98.80 9^61 90.62 9.1 122.47 113. 15 107.28 103.34 100.58 94.23 92.08 9.2 124.62 115.18 109.21 105.19 102.37 95.86 93.65 9.3 126.79 117.22 111.15 107. 06 104.17 97.49 95.22 9.4 128.97 119.27 113.10 108.93 105. 99 99.14 96.80 9.5 131.16 121.34 115.07 110.82 107.82 100.80 98.40 9.6 133.36 123.42 117.05 112.72 109.65 102. 4S 100.00 9.7 135.58 125.51 119.04 114.64 ni.50 104.16 101.62 9.8 137.82 127.63 121.05 116.57 113.87 105.65 103.25 9.9 140.06 129.74 128.07 118.51 115.25 107.56 104.88 10.0 142.81 131.87 125. 10 120.40 117.14 109.27 106.62 TABLES. 169 Table V. — Multipliers to be used in connection with Table IV to obtain the discharge over broad-crested weirs of rectangular cross-section of type a, fig, 38 . tp = Height of weir; c = width of crest; ff =ob8erved head, all in feet.] •V: 4.6 2.6 4.6 6.6 11.25 .48 11.25 .93 11.25 1.66 11.25 3.17 11.25 6.88 11.25 8.98 11.25 12.24 11.26 16.30 0.5 0.821 0.801 .794 0.786 .815 0.790 .790 1.0 0.765 0.708 .997 .899 .808 .795 .791 1.5 .789 .709 1.00 .982 .878 .796 .796 .793 .814 .792 2.0 .814 .710 1.00 1.00 .906 .815 .797 .792 .797 .793 2.5 .635 .711 1.00 1.00 .985 .844 .797 .790 .796 .793 3.0 .857 .711 1.00 1.00 1.00 .870 .797 .788 .794 .791 3.5 .878 .712 1.00 1.00 1.00 .90 .812 .787 .794 .791 ■ 4.0 .899 .714 1.00 1.00 1.00 .93 .834 .786 .792 .789 5.0 .940 .716 1.00 1.00 1,00 .97 (") .78 .79 .78 6.0 .986 .718 1.00 1.00 1.00 .98 («) .78 .78 .78 7.0 1.00 1 00 1 00 (") C°) 77 78 77 8.0 1.00 1.00 9.0 1.00 1.00 1.00 C) 10.0 1.00 1.00 1.00 C") .77 .77 .77 a Value doubtful. Table VI. — Multipliers to be used in connection with Table IV to obtain the discharge over broad-crested weirs of trapezoidal cross-section of types b and c, fig. 38. [p=Height of weir, in feet; c = width of crest, in feet: s = upstream slope; 5' = downstream slope; fl^=observed head, in feet.] Type h, fig. as . Type c, flg. 38 . 4.9 .33 2:1 4.9 .66 2:1 4.9 .66 3:1 4.9 .66 4:1 4.9 .66 5:1 4.9 .33 2:1 5:1 4.9 .66 2:1 2:1 4.65 7.00 4.67:1 11.25 6.00 6:1 8 s' H 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1.137 1.131 1.120 1.106 1.094 1.085 1.072 1.064 1.048 1.068 1.080 1.085 1.088 1.087 1.084 1.081 1.066 1.066 1.061 1.052 1.047 1.043 1.038 1.036 1.039 1.039 1.033 1.026 1.020 1.017 1.012 1.009 1.009 1.009 1.006 .997 .991 .988 .984 .980 1.095 1.071 1.044 1.024 1.009 1.003 1.014 1.023 1.071 1.066 1.053 1.047 1.047 1.050 1.062 1.055 1.042 1.033 1.024 1.012 .995 .983 .977 .974 .97 .97 .97 .96 .96 ,96 1.060 1.069 1.054 1.012 .985 .979 .976 .973 .97 .96 .96 .95 .95 .95 6.0. 7.0 8 9 10.0 ]70 RIVER DISCHARGE. f-0- 1 .4303 1 9672 4.1200 6.7453 9.7696 13.1457 16.8402 20.8278 25.0883 29.6052 34.3647 39.3550 ..58 .4417 1.9800 4. 1441 6.7787 9.8016 13.1811 16.8787 20.8691 25.1322 29.6610 34.4135 39.4060 .69 .4532 2.0049 4.1682 6.8021 9.8337 18.2166 10.9172 20.9104 25.176229.6980 84.4623 89.4571 0.60 0. 4648 2.0238 4. 1924 6.8305 9.8659 13.2520 16.9557 20.9518 25.2202 29.7445 34.6111 39.5082 .61 .4764 2.0429 4.2166 6.8590 9.8981 13.2875 16.9943 20.9931 25.2642 29.7910 34.5599 39.5593 .62 .4882 2.0619 4.2408 6.8875 9.930S 13.3231 17.0328 21.0345 25.3082 29.8375134.6088 39.6104 .68 .6000 2.0810 4.2651 6.9161 9. 9626 13.8587 17.0714 21.0759 25.3322 29.8841 34.6677 39.0615 .64 .5120 2.1002 4.2896 6.9447 9.994S 13.3943 17.1101 21.1174 25.3963 29.930« 34.7066 39.7127 .65 .5-240 2.1196 4.3139 6.9733 10.0272 13.4299 17.1488 21.158S 25.4404 29.977! 34.7557 39. 7639 .66 .5362 2.1388 4.3383 7.0020 10.0596 18.4656 17.1874 21.2004 25.484E 30.023! 34.8045 39.8161 .67 .6484 2. 1681 4.8628 7.0307 10.092C 13.5013 'l7.2172 21.2419 25.528- 30.0704 34.8635 89.8663 .68 .6607 2.177E 4.S874'7.059E 10.1244 13.5370 17.2649 21.2834 25.5725 30. 1171 34.9026 39.9176 .69 .5732 2.197C 4.4119 7.0888 10.156E 13.5728 17.3037 21.3260 25.6171 30.ie3f 34.9516 S9.a>>89 TABLES. TahU F///.— Continued. 173 1 2 S 4 5 7 8 9 10 11 0.70 0.B857 2. 2165 4.4366 7.1171 10. 1894 13. 6080 17. 3426 21.3666 26.6613 30.2105 36.0006 40.0202 .71 .5983 2.2361 4.4612 7. 1460 10.2214 13. 0444 17.3814 21. 4083 26.7056 30.2572 35.0497 40. 0715 .72 .6109 2.2568 4.4859 7. 1749 10. 2545 13. 6803 17.4202 2. 4499 25.7499 30. 3040 36.0988 40.1228 .73 .6237 2. 2765 4.5107 7. 2038 10.2871 13.7161 17.4591 21,4916 25.7942 30.3607 35. 1479 40. 1742 .74 .6366 2.2952 4.5355 7.2328 10.3197 13.7521 17.4981 21. 5333 26. 8395 30. 3975 35.1971 40. 2266 .75 .6495 2. 3150J4. B604 7.2618 10.3524 13. 7880 17.6370 21. 6751 25. 8828 30.4444 35. 2462 40.2770 .76 .6626 2.3349 4.5863 7.2909 10.3851 13.8240 17. 5700 21.6169 25.9272 30.4912 35.2964 40.3284 .77 .6757 2.3548 4. 6102 7.3200 10. 4178 13.8600 17.6150 21.6687 26.9716 30.6381 35.3446 40.3798 .78 .6889 2. 3748l4. 6362 7. 3492 10.4606 13. 8961 17.6541 21. 7005 26. 0161 30.5850 35. -3939 40.4313 .79 .7022 2. 3949 4. 6602 7. S783'l0. 4804 13. 9321 17. 6031 21.7423 26.0605 30. 0319 35.4431 40.4828 0.80 0. 7155 2.4150 4.6853 7.4076^10.6103 13. 9682 17. 7322 21.7842 26.1060 30.6789 35.4924 40.5343 .81 .7290 2.4351J4.7104 7.4368 10.5492 14.004417.7714 21. 8261 26.1495 30,7268 36.5417 40.6859 .82 .7425 2.4553 4.7356 7. 4661 10.6812 14. 0406 17. 8105 21.8681 26.194130.772835.5911 40.6374 .83 .7562 2. 4766 4,7608 7.4955 10.6160 14.0768'l7.8507 21. 9100 26. 2386 30. 819836. M04 40. 689P .84 .7699 2.49-69 4. 7861 7. 5248 10.6480 14.113o'l7.8889 21.9520 26. 2832.30. 8669'35. 6898 40.7406 .85 .7837 2. 5163 4.8114 7.6542 10.0810 14.149317.9282 21.9940 26. 3278^30. 9139'36. 7392 40.7922 .86 .7975 2.5367 4.8367 7. 6837 10. 7141 14.185617.9674 22.0361 26.3726 30.9610 36.7886 40.8439 .87 .8115 2. 5672 4.' 8021 7. 0132 10.7472 14.221918.0067 22.0781 26.4171 31. 0081 35. 8380 40.8955 .88 .8255 2.6777 4.8875 7.6427 10. 7803 14.268218.046122.1202 26. 4618 31.0563 35.8876 40. 9472 .89 .8396 2.6983 4.9130 7.6723 10.8134 14. 2946 18.0854 22.1623 26.6065 31.1024 35.9370 40.9989 0.90 0.8538 2.6190 4.9385 7.7019 10.8466 14. 3311 18.1248 22.2045 26.5623 31. 1496 36. 9865 41.0507 .91 .8681 2.0397 4.9641 7.7315 10. 8798 14.3676 18. 1642 22. 2467 26.5900 31.1968 36.0360 41.1024 .92 .8824 2.6604 4. 9897 7.7702 10.9131 14. 4040 18.2037 22.2889 26.640B 31.244136.0856 41.1542 .93 .8969 2. 6812 6.0154 7. 7909 10.9464 14.4405 18.2432 22. 3311 26.6866 31.2913 361352 41. 2060 .94 .9114 2.7021 6.0411 7.8207 10. 9797 14.4770 18.2827 22.3733 26. 7305 31. 3386 36 1848 41. 2578 .95 .9259 2.7230 5.0668 7.8805 11.0131 14. 6136 18. 3222 22.4156 26.7753 31.385o'36 2344 41.3097 .96 .9406 2.7440 5.0926 7.8808 11. 0464 14.5602 18 3617 22.4679 26. 8202 31.4332'36.2841 41.3615 .97 .9553 2.7650 5. 1184 7.9102 11.0799 14.5869 18. 4013 22.5003 26.8651 31.4806'36.3337 41.4134 .98 .9702 2.7861 6.1443 7.9401 11.1133 14. 6235 18 4409 22.6426 26.9100 31.528o'36.3S34 41.4653 .99 .9850 2. 8072 5. 1702 7. 9700 11.1468 14.6602 18.4806 22. 6850 26. 9560 31.5754'36.4331 41.6173 1.00 1.0000 2.8284 5. 1962 8.0000 11.1803 14. 6969 18. 5203 22.6274 27.0000 81.622836.4829 41. 5692 Table IX. — For converting discharge in second-feet per square mile into run-off in depth in inches over the area. Period in days. Second-feet per square mile. 1 38 !J9 30 31 1. . . . . . . Inches. .03719 .07438 .11157 . 14876 . 18595 .22314 .26033 .29752 .33471 Inches. 1.041 2.083 3.124 4.165 5.207 6 248 7.289 8.331 9.372 Inches. 1.079 2,157 3 "36 4.314 5.393 6.471 7.550 8.628 9,707 Inches. 1.116 2.231 3.347 4.463 5.579 6.694 7.810 8.926 10.041 Inches. 1 153 2 2 306 3. .. 3 459 4 4 612 5 5 764 6 6 917 7 8.070 8 9.223 9 10.376 Note. — For partial month multiply tha values for one day by the number of days. 174 RIVER DISCHARGE. Tabu X. — For converting discharge in second-feet into run-off in acre-feet. Second-feet. Period in days. 1 as 89 30 31 1 Acre-ft. 1.983 3.967 5.950 7.934 9.917 11.90 13.88 15.87 17.85 Acre-ft. 55.54 111.1 166.6 222.1 277.7 333.2 388.8 444.3 499.8 Acre-ft. 57.52 115.0 172.6 230.1 287.6 345.1 402.6 460.2 517.7 Acre-ft. 59.50 119.0 178.5 238.0 297.5 357 416.5 476.0 535.5 Acre-ft. 61.49 123 2 , 3 184.5 4 5 307 4 6 368 9 7 430 4 8 491 9 9 553 4 NoiE. — For partial month multiply values for one day by the number of days. Table XI.— For converting discharge in second-feet per day into run-off in millions of gallons. 1 second foot, or 7.4805 gallons per second for 1 day, or 86,400 seconds = 646,300 gallons. Units. Tens. 1 S 3 4 5 6 7 S 9 0.65 1.29 1.94 2.59 3.23 3.88 4.52 5.17 5.82 1 6.46 7.11 7.76 8.40 9.05 9.69 10.34 10.99 11.63 12.28 2 12.93 13.57 14,22 14.87 15.51 16.16 16.80 17.45 18.10 18.74 3 19 39 20.04 20,68 21.33 21.97 22.62 23.27 23,91 24.56 25.21 4 25.85 26.50 27,15 27.79 28.44 29.08 29.73 30,38 31.02 31.67 5 32.32 32.96 33,61 34.25 34.90 35.55 36.19 36.84 37.49 38,13 6 38.78 39.43 40, 07 40.72 41.36 42.01 42.66 43.30 43.95 41,60 7 45.24 45.89 46,53 47.18 47.83 48.47 49.12 49.77 50.41 51,06 8 51.71 52 35 53,00 53.64 54.29 54.94 55.58 56.23 56.88 57.52 9 58,17 58.81 59,46 60.11 60.75 61.40 62.05 62.69 63. 3t 63 £9 Table XII. — For converting run-off in millions of gallons into discharge in sccotid- feel per day. 1 million gallons per 24 hours = . foRy 86 4T)Q '^"^^'^ feet per second, or 1.547 second feet. Units. Tens. 1 1.65 ■4 3 4 6 G 7 8 9 3,09 4,64 6.19 7.74 9 28 10.83 12.38 13.93 1 15.47 17.02 18,67 20.11 21.66 23.21 24 76 26.30 27.85 29.40 2 30 , 94 32.49 34,04 35.59 37.13 38,68 40 23 41.78 43.32 44.87 3 46 -12 47.98 49,51 51.06 52.61 54,15 55,70 57.25 58.79 60.34 4 61 s;) 63.44 64 98 66.53 68.08 69,63 71,17 72.72 74.27 75.81 6 77,36 78.91 80,46 82.00 83.55 85.lrf 86 64 88.19 89.74 91.29 6 92,83 94 , 38 95,93 97.48 99.02 100.. '-.7 102.12 103.66 105.21 106.76 7 108,31 109,86 111,40 112.95 114.49 116.04 117.59 119.14 120.68 122.23 8 123,78 126.33 126,87 128,42 129.97 131.51 133.06 134.61 136.16 137.70 9 139.26 140,80 142,34 143.89 145.44 146.99 148.53 150.08 151.63 153.18 TABLES. 17a Table XIII. — For converting run-off in acre-feet into run-off in million gallons. 1 acre-foot = 43,560 cubic feet=*M6|Xi728^ ^^ 75,271,680 ^^ 325 gso galbns. Units. Tens. 1 a 3 4 6 6 7 8 9 0.326 0.652 0,978 1.303 1.629 1.955 2.281 2.607 2.933 1 3.258 3.584 3.910 4.236 4.562 4.888 5.214 5.640 5.865 6 191 2 6.517 5.843 7.169 7.495 7.820 8.146 8.472 8.798 9.124 9.450 3 9.776 10.101 10.427 10.753 11.079 11.405 11.731 12.056 12.382 12 708 4 13.034 13.360 13.686 14.012 14.337 14.663 14.989 15.315 15.641 15.967 S 16.293 16.618 16.944 17.270 17.596 17.922 18.248 18.574 18.899 19.225 6 19.551 19.877 20.203 20.529 20 , 854 21.180 21.506 21.832 22.158 22.484 7 22.S10 23 . 135 23.461 23.787 24.113 24.439 24.765 25.090 25.416 25 . 742 8 26.03S 26.394 26.720 27.046 27.372 27.697 28 . 023 28.349 28 . 675 29.001 9 29.327 29.652 29.978 30.304 30 630 30.958 31.282 31.608 31.933 32 259 Table XIV. — For converting run-off in million gallons into run-off in acre-feet. One million United States liquid gallons or 231 million cubic inches = 133,680,555 cubic feet, or ",?'^„*°-3.0689 43.560 Units. Tens. 1 8 3 4 5 6 7 8 9 3.07 6.14 9.21 12,28 15.34 18,41 21.48 24,, 55 27.62 1 30.69 33.76 36.83 39.90 42.96 46,03 49.10 52.17 55,24 58.31 2 61.38 64.45 67,52 70.58 73.65 76,72 79,79 82.86 85,93 89.00 3 92.07 95.14 98.20 101.27 104.34 107.41 110,48 113.55 116.62 119.69 4 122.76 125 82 128.89 131.96 135.03 138.10 141,17 144.24 147.31 150.38 5 153.44 156.51 159.58 162.65 165.72 168.79 171,86 174.93 178,00 181.06 « 184.13 187.20 190.27 193.34 196,41 199.48 202.55 205.62 208,68 211.75 7 214.82 217,89 220 . 96 224.03 227.10 230,17 233.24 236.30 239.37 242.44 8 245.51 248.58 251.65 254.72 257.79 260,86 263.92 266.99 270.06 273.13 9 276.20 279.27 282.34 285.41 288.48 291 54 294.61 297,68 300.75 303.82 Table XV. — Values of c for use in the Chezy formula V= cy/Rs. Slope. R. n .020 n .025 n .030 n .035 n .040 n .045 n .050 n .055 n .063 r3.28 91 73 60 52 46 40 36 33 30 1 10 111 92 78 69 62 55 50 46 42 .0001 { 20 122 102 89 79 71 65 60 55 51 1 50 134 114 100 91 83 76 71 67 63 L 100 140 121 108 98 91 84 79 74 70 C 10 108 89 76 67 60 53 49 45 41 1 20 1 50 [ 100 117 98 85 76 68 61 57 53 49 126 108 94 85 78 71 66 62 58 131 113 99 90 83 77 ■ 72 68 64 r 10 107 88 75 66 59 53 48 44 41 ! 20 115 96 83 73 66 60 55 51 48 .0004 1 50 L 100 123 104 91 82 75 68 63 59 66 127 108- 96 87 80 73 68 64 61 r 10 105 87 74 65 58 52 47 44 40 1 20 1 50 113 94 81 72 65 59 54 50 47 120 101 89 79 72 66 61 57 54 L 100 124 105 94 85 77 71 66 62 59 r 10 105 86 74 65 58 51 47 43 40 20 112 93 80 71 64 58 53 49 46 1 50 119 100 87 78 71 65 60 66 53 L 100 122 104 91 82 75 69 65 61 58 Note. — For B = 3.2S feet, n constant, i; is constant for all values of slope, ereater than 0.01. or fall of 52.8 feet per mile, o remains nearly constant. For slopes 176 RIVER DISCHARGE. Table XVI. — Square roots of numbers {\/R y s) for use in Kutter's formula. See PI. V, Chapter III. R \/B R VR R 4//e R VB , R VB i V^ 0.05 0.224 3.05 1,746 6.06 2.460 9.05 3.008 20.25 4.500 .00002 .00447 0.10 0.316 3.10 1,761 6.10 2.470 9.10 3.017 20.50 4.528 .000025 .005 0.15 0.387 3.16 1,776 6.15 2.480 9.15 3.026 20.76 4.555 .0000275 .00524 0.20 0.447 3.20 1.789 6.20 2.490 9.20 3.033 21.00 4.583 .00003 .0054S 0.25 0.500 3.25 1.803 6.25 2,500 9.26 3.041 21.26 4.610 .000036 .00692 0.30 0.548 3.30 1.817 6.30 2.510 9.30 3.060 21.50 4.637 .00004 .00632 0.35 0.592 3.35 1.830 6.35 2.520 9.36 3.058 21.76 4.664 .000045 .00671 0.40 0.632 3.40 1.844 6.40 2.530 9.40 3.066 22.00 4.690 .00005 .00707 0.45 0.671 3.45 1.857 6.45 2.540 9.46 3.074 22.25 4.717 .00006 .00775 0.50 0.707 3.60 1,871 6.50 2.550 9.50 3.082 22.50 4.743 .00007 .00837 0,55 0.742 3.65 1.884 6.65 2.559 9.55 3.090 22.75 4.770 .00008 .00894 0.60. 0.775 3.60 1.897 6.60 2.569 9.60 3.098 23.00 4.796 .00009 .00949 0.65 0.806 3.85 1.910 6.65 2.579 9.65 3.106 23.25 4.822 .0001 .01 0.70 0.837 3.70 1.924 6.70 2.588 9.70 3.114 23.50 4.848 .00012 .0110 0.75 0.866 3.75 1.936 6.76 2.598 9.75 3.122 23.75 4.873 .00014 .0118 0.80 0.894 3.80 1.949 6.80 2.608 9.80 3.130 24.00 4.899 .00016 .012ft 0.85 0.922 3.85 1.962 6.86 2.617 9.85 3.138 24.25 4.924 .00018 .0134 0.90 0.949 3.90 1.975 6.90 2.627 9.90 3.146 24.60 4.950 .0002 .0141 0.95 0.975 3.95 1.987 6.96 2.636 9.05 3.154 24.76 4.975 .00025 .0158 l.OC 1.000 4.00 2.000 7.00 2.646 10.00 3.162 25.00 5.000 .0003 .0173 1.05 1.025 4.06 2.012 7.05 2.665 10.25 3.202 25.25 5.025 .00035 .0187 1.10 1.049 4.10 2.025 7.10 2.665 10.60 3.240 26.60 6.050 .0004 .02 1.15 1.072 4.16 2.037 7.15 2.674 10.75 3.279 25.75 5.074 .0005 .0224 1.20 1.096 4.20 2.049 7.20 2.683 11.00 3.317 26.00 6.099 .0006 .0245 1.25 1.118 4.25 2.062 7.25 2.693 11.25 3.354 26.25 5.123 .0007 .0265 1.30 1.140 4.30 2.074 7.30 2.702 11.50 3.391 26.50 5.148 .0008 .0283 1.35 1.162 4.35 2.086 7.36 2.711 11.75 3.428 26.75 5.172 .0009 .03 1.40 1.183 4.40 2.098 7.40 2.720 12.00 3.464 27.00 5.196 .001 .031R 1.45 1.204 4.45 2.110 7.46 2.729 12.26 3.500 27.26 6.220 .0012 .034S 1.50 1.225 4.50 2.121 7.50 2.739 12.50 3.536 27.50 5.244 .0014 .0374 1.55 1.245 4.55 2.133 7.65 2.748 12.75 3.671 27.76 5.268 .0016 .04 1.60 1.266 4.60 2.145 7.60 2.757 13.00 3.606 28.00 5.292 .0018 .0424 1.65 1.286 4.65 2.156 7.65 2.766 13.25 3.640 28.25 5.315 .002 .0447 1.70 1.304 4.70 2.168 7.70 2.775 13.60 3.674 28.50 5.339 .003 .054S 1.75 1.323 4.75 2.179 7.75 2.784 13.76 3.708 28.75 5.362 .004 .0632 1.80 1.342 4.80 2.191 7.80 2.793 14.00 3.742 29.00 6.385 .005 .0707 1.85 1.360 4.85 2.202 7.86 2.802 14.25 3.775 29.25 6.408 1.90 1.378 4,90 2.214 7.90 2.811 14.50 3.808 29.50 5.431 1.95 1.396 4.95 2.226 7.95 2.820 14.76 3.841 29.76 5.454 2.00 1.414 5.00 2.236 8.00 2.828 16.00 3.873 30.00 5.477 2.05 1.432 5.06 2.247 8.05 2.837 15.25 3.906 30.26 5.500 2.10 1.449 5.10 2.258 8.10 2.846 15.50 3.937 30.50 5.623 2.15 1.466 5.15 2.269 8.16 2.856 15.76 3.969 30.75 6.545 2.20 1.483 5.20 2.280 8.20 2.864 16.00 4.000 31.00 6.568 2.25 1.500 5.25 2.291 8.25 2.872 16.25 4.031 31.25 6.590 2.30 1.517 5.30 2.302 8.30 2.881 16.50 4.062 31.60 5.612 2.35 1.533 5.35 2.313 8.36 2.890 16.76 4.093 31.75 5.635 2.40 1,649 5.40 2.324 8.40 2.898 17.00 4.123 32.00 5.657 2.45 1.565 5.45 2.335 8.46 2.907 17.26 4.163 32.25 5.679 2.50 1.581 5.60 2.345 8.50 2.915 17.50 4.183 32.60 5.701 2.65 1.697 5.55 2,366 8.66 2.924 17.75 4.213 32.75 5.723 2,60 1.612 5.60 2.366 8.60 2.933 18.00 4.243 33.00 5.745 2.66 1.628 6.65 2.377 8.66 2.941 18.26 4.272 33.25 6.766 2.70 1,643 6.70 2.387 8.70 2.960 18.60 4.301 33.50 5.788 2.76 1.658 5,76 2.398 8.75 2.958 18.75 4.330 33.75 5.809 2.80 1.673 6.80 2.408 8.80 2.966 19.00 4.359 34.00 5.831 2.86 1.688 5,86 2.419 8.86 2.976 19.26 4.387 34.25 5.862 2:90 1.703 6,90 2.429 8.90 2.983 19.60 4.416 34.50 6.874 2 05 1.718 6,95 2.439 8.96 ■2.992 19.75 4.444 34.75 6.895 3.00 1.732 6.00 2.449 0.00 3.000 20.00 4.472 35.00 5.916 TABLES. Table XVII. — Convenient equivalents. 1 second-foot equals 40 California miner's inches. (Law of March 23, 1901.) 1 second-foot equals 38.4 Colorado miner's inches. 1 second-foot equals 40 Arizona miner's inches. 1 s3Cond-foot equals 7.48 United States gallons per second; equals 448.8 gallons per minute; equals 646,272 gallons for one day. 1 second-foot equals 6.23 British imperial gallons per second. 1 second-foot for one year covers one square mile 1.131 feet deep; 13.57 inches deep. 1 second-foot for one year equals 31,536,000 cubic feet. 1 second-foot equals about 1 acre-inch per hour. 1 second-foot falling 10 feet equals 1.136 horsepower. 100 California miner's inches equal 15.7 United States gallons per second. 100 California miner's inches equal 96.0 Colorado miner's inches. 100 California miner's inches for one day equal 4 .96 acre-feet. 100 Colorado miner's inches equal 2.60 second-feet. 100 Colorado miner's inches equal 19.5 United States gallons per second. 100 Colorado miner's inches equal 104 California miner's inches. 100 Colorado miner's inches for one day equal 5.17 acre-feet. 100 United States gallons per minute equal 0.223 second-foot. 100 United States gallons per minute for one day equal 0.442 acre-foot. 1,000,000 United States gallons per day equal 1.55 second-feet. 1,000,000 United States gallons equal 3.07 acre-feet. 1,000,000 cubic feet equal 22.95 acre-feet. 1 acre-foot equals 325,850 gallons. 1 inch deep on 1 square mile equals 2,323,200 cubic feet. 1 inch deep on 1 square mile equals 0.0737 second-foot per year. 1 inch equals 2.54 centimeters. 1 foot equals 0.3048 meter. 1 yard equals .9144 meter. 1 mile equals 1.60935 kilometers. 1 mile equals 1,760 yards; equals 5,280 feet; equals 63,360 inches. 1 square yard equals 0.836 square meter. 1 acre equals 0.4047 hectare 1 acre equals 43,560 square feet; equals 4,840 square yards. 1 acre equals 209 feet square, nearly. 1 square mile equals 259 hectares. 1 square mile equals 2.59 square kilometers. 1 cubic foot equals 0.0283 cubic meter. 1 cubic foot equals 7.48 gallons; equals 0.804 bushel. 1 cubic foot of water weighs 62.5 pounds. 1 cubic yard equals 0.7646 cubic meter. 1 gallon equals 3.7854 liters. 1 gallon equals 8.36 pounds of water. 1 gallon equals 231 cubic inches (liquid measure). 1 pound equals 0.4536 kilogram. 1 avoirdupois pound equals 7,000 grains. 1 troy pound equals 5,760 grams. ^'^ RIVER DISCHARGE. 1 meter equals 39.37 mches. Log. 1.5951654. 1 meter equals 3.280833 feet. Log. 0.5159842. 1 meter equals 1.093611 yards. Log. 0.0388629. 1 kilometer equals 3,281 feet; equals five-eighths mile, nearly. 1 square meter equals 10.764 square feet; equals 1.196 square yards. 1 hectare equals 2.471 acres. 1 cubic meter equals 35.314 cubic feet; equals 1.308 cubic yards. 1 liter equals 1.0567 quarts. 1 gram equals 15.43 grains. 1 kilogram equals 2.2046 pounds. 1 tonneau equals 2,204.6 pounds. 1 foot per second equals 1.097 kilometers per hour. 1 foot per second equals 0.68 mile per hour. 1 cubic meter per minute equals 0.5886 second-foot. 1 atmosphere equals 15 pounds per square inch; equals 1 ton per square foot; equals 1 kilogram per square centimeter. Acceleration of gravity equals 32.16 feet per second every second. 1 horsepower equals 550 foot-pounds per second. 1 horsepower equals 76.04 kilogram-meters per second. 1 horsepower equals 746 watts. 1 horsepower equals 1 second-foot falling 8.80 feet. IJ horsepowers equal about 1 kilowatt. To calculate water power quickly: '- — -~ ^Net horsepower on water wheel, realizing 80 per cent of the theoretical power. To change miles to inches on map : Scale 1:125000, 1 mile= 0.50688 inch. Scale 1 :90000, 1 mlle= 0.70400 inch. Scale 1:62500, 1 mile= 1.01376 inches, fcale 1:45000, 1 mile= 1.40800 inches. INDEX. Pack. Accuracy of stream-flow data . . 12'J Acre-leet, table for computing from million gallons . 17'i tabic fnr converting into million gallons , 175 Acre-foot, use of, as unit of run-off 121 value of . 177 Appomattox River, basin of, average rain- fall and run-off in . . 146-149, 158 Area curves, construction of 92-95 definition of . ... 92 figures showing . . 93, 9 [, 96, 98, 100 use of, in constructing rating cur\es 94, 99 Areas, measurement of . 125, 129 of quadrilaterals . . 127-12S Artificial channels, discharge measure- ments in . 76 Automatic gages . 30-36 Page. Bazin fornuilas, discussion of , 88, 89 use of, in computing discharge over sharp-crested weirs . 166 Bench marks, establishment and use of . 23-36, 85 Boat stations, establishment of . . 41 Bolster method of interpolating discharge, description of . . 110-113 figure illustrating 111 Cable car, plate showing ... Cable stations, euuipment of, description of plate showing . . . Car, cable, description of . plate showing ... Census. See United States Census Chenango River, vertical velocity-curves on, figure showing Chezy formula, use of, in determining velocity . values of c for, table showing . Cippoletti weir, construction of . discharge over, determination of . figure showing . formula applicable to . City ofHcials, reports of . . Coefficient of roughness. See Roughness, coefficient of. Commissions, special, reports of . . Computation, methods of, in discharge measurements . . 34, 36 37-41 36 89-40 34,36 1, 77 175 84 163 83 (Connecticut River, basin of, average rain- fall and run-off in . 146- Controls, artificial . Control section . . ('ostof records, conditions affecting Cross-section, determination of standard . typical, figure showing Cross-section paper, use of Cultivation, effect of, on stream flow Current meters, care of description of . discharge measurements by means of . plate showing . rating of . use of, in determining velocity Current-meter rating curves, figure show- ing . Current-meter rating station, plate show- ing . .... Current-meter stations, reauisite condi- tions for . Daily discharge. See Discharge, daily. Dams. See Weirs. Diagrams, value of, as compared with rating tables Discharge, daily, computation of . relation of, to gage height table for computing, from run-off . tables for converting, into run-off units of .... Discharge measurements, data obtained in , use of methods of making Drainage, artificial, for controlling stream flow Duration of flow. See Stream flow, dura- tion of. Ellet, Charles . ... End contraction, allowance for, in weir formulas Engineers. Chief of. United States Army, reports of Equipment for gaging streams, descrip- tion of . . . Error, sources of, in estimating stream flow Estimates of stream flow, sources of error ■149, 1.53 42, 43 45. 46 46 50, 51 51 65 97-104 l,-.6 16-20 6-22 61-76 6 20-22 51-61 21,23 22 44 90 91-120 83 174 173, 174 121 91-140 49-80 61-67, , 90, 113-120 suggestions for . 1.56 87 139 5-43 122 122 125 179 180 RIVER DISCHARGE. Page. Evaporation, discussion of, as affecting stream flow . . . . 160-162 elVi'cL on, ol cliii.racter of soil . 153-154 ('ll'.'cl oil, of veKctation . 156-160 nieas\iri>inent of . 4:), 150-152 seasonal variations in . . 152 Float stations, requisite conditions for . . 76,77 Floats, description of ... 5, 6 use of, in determining velocity 76, 77 Flow of stream. See Stream flow. Forests, effect of, on stream flow , 155, 156 Formulas for discharge measurements 64 discussion of .... 65 See also Bazin formula ; Cliezy formula ; Francis formula^ Kutter for- mula: Weir formulas. Francis formula, discussion of . . 87, 88 first use of . ... . . 2 Freshets, conditions causing . . . 154, 165 Friez gage, plate showing . 30 Fteley current meter, discription of . . 7, 8 plate showing . . . . 6 Gage height, relation of, to discharge . . . 91 limits of use . .... 104-107 Gage readers, instructions to . . . . 23-36, 80, 81 Gages, datum of . 23-36 description of 23-36 installation of 28, 36, 48, 85 methods of using 80, 81 use of, with stilling box 30 Gaging stations. See Velocity-area sta- tions: Weir stations. Gallons per minute, use of, as unit of dis- charge 121 Geological Survey. See United States Geological .Survey. Geology, discussion of, as affecting stream flow . . ... 163, 154 Government publications, method of ob- taining 139, 140 Gurly gage, description of 81-34 plate showing ..... 30 Haskell current meter, description of . . . 7, 8 plate showing . . 6 High water, discharge measurements at 88, 69 Hook gage, description of 25, 26 figure showing 26 Horsepower. See Power. Ilousatonic River, basin of, average rain- fall and run-off In , . . 146-149,158 Hydraulics, historical sketch of . . . . 1,2 Hydrograph ol Potomac River, figure showing 123 Hydrographs, construction of 125 Ice conditions, dally discharge under, computation of 113-120 discharge measurementa under .... 69-80 Page. Indicators, current- met«r, description of . 12, 13 Initial point. See Soundings. Instruments for gaging stream, descrip- tion of 5-43 for determining climatologlcsil data . 43 Integration method, determination of mean velocity by 61 .Tames River, basin of, average rainfall and run-off in . . 146-149, 153 Kutter formula, diagram for applica- tion of 78* square roots for u?e in. table of . 176 use of, in constructing rating curves 102 in determining velocity 77, 78 Lakes, effect of, on stream flow . - . 155, 156 Logarithmic cross-section paper, use of H3, 104, 129-137 Low water, discliarge measurements at 65, 68 Maps, measurement of areas on . 125-129 Mean velocity-curves, construction of . 9.5-97 figures showing . . .96. 98. 100 use of, in constructing rating curves 97, 99, 101 Meters, ciu-ient. See Current meters. Methods, outline of, used in stream gaging 3. 4 Metric terms, equivalents of . 178 Million gallons, table for computing, from acre-feet . . 175 table for converting, into acre-feet . 175 Miner's inch, use of, as unit of discharge 121 values of 177 Murphy, E.C., coefficients obtained by, for computing discharge over broad-crested weirs . . 166-171 Ohio River, basin of, average rainfall and run-off in . .146-149.153 discharge, mean velocity and area curves on, figure showing . 100 discharge meiisurements of . . 101 Ponds, effect of, on stream flow . ... 155. 156 Potomac River, bnsiu of, average min-fall and run-off in. . . .146-149,153 curves of discharge and duration of flow, figure showing 123 dlaoliargo and horsepower table for . 124 discharge, moan velocity, and area citrvos on, figure showing . . 98 discharge measurements on . . . .108,109 station rating table for . . . . 108 Powell, J. W., on stream gaging .... 2 Power, determination of amount avail- able ... . 122-124 rule for calculating . ... 178 INDEX. 181 Page. Precipitation, conditions affecting 144 discussion of, as affecting stream flow . 141-1,')0 effect on, of topograpliy . . . .154 mean annual, in United States, map siiowing . . 141 measurement of . . 43, 141-143 seasonal variations in . . 143-149 Precipitation station, plate showing 142 Price current meter, description of 9-16 plate showing 6 Badius, hydraulic, determination of (dia- gram) . 78 symhol used for . . ... 51 Rain gage, description of . . 141-143 illustration showing . 142 use of . . . . 142, 143, 145 Rainfall, relation of, to run-off . . 145-150, 153 See also Precipitation. Rating curves, construction of . . 97-104 figures showing . . 96, 98, 100, 102 Eating tables, application of . 104-108 construction of .... .104 value of, as compared with diagrams . 90 Recorders, current-meter, use of 12, 13 Recording gages . 30-36 Roanoke River, basin of, average rainfall and run-off in . . 146-149, 153 measurements of . . 67 Rome, water supply of, in first century 1 Roughness, coeflicient of, determination of (diagram) . 10 symhol used for . 51 value of . . . ... 79, 80 Run-off, effect on, of character of soil . 153, 154 effect on, of topography . 154,155 relation between rainfall and . 145-150, 153 tables for computing, from discharge . 173, 174 tables for converting, into discharge . 174, 175 units of . 121 P.VGE. Staff gage, description of . 24, 2.") State officials, reports of , . 139 Station rating tables. See Rating tables. Stay lines, description of 16, 42 Stevens gage, description of . 31-33 plate showing ... .30 Stilling box, description of 30 Stop-watches, use of . . . 13 Storage, artificial, for controlling stream flow . . .156 due to snow and ice, measurement of . 152, 153 effect on, of vegetation . . 155 Stout method of interpolating discharge. description of . 109, 110, 112, 113 figure illustrating . Ill Stream flow, computation of . 64-67, 89, 90, 91-120 conditions affecting . . . 141-156 control of, by artificial means . 156 duration of, curve of, figure showing . 123 determination of . . 122-124 See also Discharge. Stream-gaging data, accvu-acy of 122 sources of . . . . . 137-140 Surface method, determination of mean velocity by 60 Susquehanna River, basin of, average rain- fall and run-off in . . 146-149, 153 cable station on, plate showing . 1 12 Swamps, effect of, on stream flow . . 155 Tables, miscellaneous . . . ... 157-178 Temperature, discussion of, as affecting stream flow . 152-155 effect of, on evaporation . 152, 153 Three-halves powers, table of . . . 171-173 Three-point method, determination of mean velocity by . . 61 Topography, discussion of, as affecting stream flow 154, 155 Two-point method, determination of mean velocity by . . 60 Second-foot, deflnition of . . . 3 use of, as unit of discharge 121 values of . . . 177 Shenandoah River, basin of, average rain- fall and run-off in . 146-149, 153 Six-tenths depth method, determination of mean velocity by . 59, 60 Slope, determination of (diagram) 78 symbol used for . ... 51 Slope measurements, determination of velocity by . 77, 78 Slope stations .... 77, 78 Snowfall, measurement of . .143,145 Sounders. See Indicators. Soundings, appliances for, description of 22 errors in . . . . 51 method of making ... 50, 51 Square roots, table of 176 United States, mean annual rainfall in, map showing . . 144 United States Census, reports of . . . 138 United States Geological Survey, reports of 138 weight gage used by, description of . 26-30 work of, on hydrography . . 2 United States Weather Bureau, rain gage used by .141,142 reports of . 138 Vegetation, discussion of, as affecting stream flow . . 155-156 Velocity, determination of . 51-61 distribution of, in vertical line . 54-59 instruments for measuring, descrip- tion of . . . . 5-22 laws governing ... . 52-55 mean, relation of, to surface velocity . 55 182 RIVER DISCHARGE. Paoe. Velocity-area stations, classes of conditions at, permanence in . cost of records at (iiscliarge measurements at establishment . .... Velocity-urea stations, discussion of selection of site . . ... Velocity-curves, mean. 5ee Mean velocil.v curves. Vertical, determination of . determination of mean velocity by figures showing . J'-'i. form of tables showing . . . oii. 57, Velocity of approach, allowance for, in weir formulas . . . Vertical velocity-curves. See Velocity- curves, vertical. Wading stations, methods used at . plate showing Watches, stop. See Stop-watches. Water power. See Power. 41 44,45 •16 49-HO 48. 49 -14-Hl 44-47 .5;i, ,'J4 ,13-59 5H, 72 64 71], 71 65, 68 36 Weather Bureau. See United States Weather Bureau. Weight gage, description of . figure showing Wfights for current melers. descriptiua of W'i'ir formulas, discussion of Weir stations, discharge measurements at plate showing . \\'eirs, broad-crested, description of broad-crested, discharge over, table showing . disclrarge over, tables for comput- ing figure showing . fornmlas applicable to Cippoletti. See Cippoletti weir, rectangular, formulas applicable to . Weirs, sharp-cre.sted, description of . discharge over, tables sho\\ing . IGl-KM, trapezoidal, formulas applicable to . use of, in discharge measuremenis Wind, effect of, on precipitation measure- ments . 26-30 27 12 86-89 82-90 85 84-86 IM. 165 169. 171 170 S9 ST ,88 Si !.84 160 166-168 88 68 142. 143 ESTABLISHED INCORPORATED 1845 1900 FIELD INSTRUMENTS FOR CIVIL ENGINEERS AND LAND SURVEYORS WATER STAGE REGISTERS CURRENT METERS HOOK GAGES W- & L. E. GURLEY TROY, NEW YORK BRANCH FACTORY SEATTLE, WASHINGTON JOHN WILEY & SONS 43 and 45 East 1 9th St., New York City LONDON : CHAPMAN & HALL. LTD. MONTREAL. CANADA : RENOUF PUBLISHING CO. THE IMPROVEMENT OF RIVERS. A Treatise on the Methods Employed for Improving Streams for Open Navigation and for Navigation by Means of Locks and Dams. By B. F. Thomas, United States Assistant Engineer, Member of the American Society of Civil Engineers ; and D. A. AVait, United States Assistant Engineer, Member of the American Society of Civil Engineers. Second Edition, Re- vised to date and Rewritten, with much new matter and many new figures and plates added. 4to, profusely illustrated, including figures in the text and full-page and folding plates. Cloth, J6.00 net. DOMESTIC WATER SUPPLIES FOR THE FARM. By Myron L. Fullbr, S. B., Specialist on Underground Water Supplies, formerly in charge of Underground Waters in Eastern United States for U. S. Geological Survey, Author of "Underground Waters in the Eastern United States," etc. 8vo. $1.50 net. HYDRAULIC TABLES. The Elements of Gagings and the Friction of Water Flowing in Pipes, Aqueducts, Sewers, etc., as Determined by the Hazen and Williams formula ; and the Flow of Water Over Sharp-edged and Irregular Weirs, and the Quan- tity Discharged, as Determined by Bazin's Formula and Experimental Investi- gations upon Large Models. By Gardner S. Wn.i.iAMS, M. Am. Soc. C. E., Professor of Civil, Hydraulic, and Sanitary Engineering, University of Michigan; and Allen Hazen, M. Am. Soc. C. E., Civil Engineer. Second Edition, Revised and Enlarged. 8vo, vi+104 pages. Cloth, $1.50. PUBLIC WATER SUPPLIES. Requirements, Resources, and the Construction of Works. By F. E. TuRNEAURE, Dr. Eng. , Dean of the College of Engineering, University of Wisconsin, and H. L. Russell, Ph. D., Dean of the College of Agriculture, University of Wisconsin. With a Chapter on Pumping-Machinery, by D. W. Mead, C. E., Professor of Hjjdraulic and Sanitary Engineering, Uni- versity of Wisconsin. Second Edition, Revised and Enlarged. 8vo, xv-t- 808 pages, 220 figures. Cloth, $5.00. ' TREATISE ON HYDRAULICS. By MANsi'iEi.n Mkuriman, Member of American Society of Civil Engi- neers. Nintli Edition, Revised and Reset with the assistance of Thaddeus Merriman, Member of American Society of Civil Engineers. 8vo, x + 565 pages, 224 figures. Cloth, $4,00 net. LEUPOLD & VOELPEL MANUFACTURERS OF Scientific Instruments 107 East 70th Street N. PORTLAND, OREGON Stevens Continuous Water Stage Recorders Fuller Integrator Tor rapid rleterniinatioii of mean ordinate^ of lines sncli as antomatic ssLse records. L. & V. Transits L. & V. Levels