S 621 
 .S35 
 Copy 1 
 
 OFFICIAL PUBLICATION OF 
 
 IOWA STATE COLLEGE OF AGRICULTURE 
 
 AND MECHANIC ARTS 
 
 Vol. XVII. September 25, 1918 No. 17 
 
 THE THEORY OF 
 UNDERDRAINAGE 
 
 W*&>:$6 
 
 i 
 
 By 
 W. J. SCHLICK 
 
 BULLETIN 50 
 ENGINEERING EXPERIMENT STATION 
 
 Ames, Iowa 
 
 Acceptance for mailing at special rate of postage provided for in Section 1108, 
 Act of October 3, 1917. Authorized September 23, 1918. 
 
PURPOSE OF THE STATION 
 
 THE purpose of the Engineering Experi- 
 ment Station is to afford a service, 
 through scientific investigations, evolution of 
 new devices and methods, educational techni- 
 cal information, and tests and analyses of ma- 
 terials : 
 
 For the manufacturing and other engineer- 
 ing industries of Iowa; 
 
 For the industries related to agriculture in 
 the solution of their engineering problems; 
 
 For all people of the State in the solution of 
 the engineering problems of urban and rural 
 life. 
 
OFFICIAL PUBLICATION OF 
 
 IOWA STATE COLLEGE OF AGRICULTURE 
 
 AND MECHANIC ARTS 
 
 Vol. XVII. September 25, 1918 No. 17 
 
 THE THEORY OF 
 UNDERDRAINAGE 
 
 By 
 W. J. SCHLICK 
 
 BULLETIN 50 
 ENGINEERING EXPERIMENT STATION 
 
 Ames, Iowa 
 
 Acceptance for mailing at special rate of postage provided for in Section 1103, 
 Act of October 3, 1917. Authorized September 23, 1918. 
 
^ 
 
 OARD OF EDUCATION <Q ^ 
 
 » 
 
 Members 
 
 Hon. D. D. Murphy, President Elkader 
 
 Hon. Geo. T. Baker Davenport 
 
 Hon. Chas. R. Brenton Dallas Center 
 
 Hon. P. K. Holbrook Onawa 
 
 Hon. Edw. P. Schoentgen Council Bluffs 
 
 Hon. H. M. Eicher Washington 
 
 Hon. Frank P. Jones Villisca 
 
 Hon. Paul Stillman Jefferson 
 
 Hon. W. C. Stuckslager Lisbon 
 
 Finance Committee 
 
 Hon. W. R. Boyd, President Cedar Rapids 
 
 Hon. Thomas Lambert Sabula 
 
 Hon. W. H. Gemmill, Secretary Des Moines 
 
 ENGINEERING EXPERIMENT STATION 
 Station Council 
 
 (Appointed by the State Board of Education) 
 
 Raymond A. Pearson, LL. D President 
 
 *Anson Marston, C. E Professor 
 
 Louis Bevier Spinney, B. M. E Professor 
 
 Samuel Walker Beyer, B. S., Ph. D Professor 
 
 Warren H. Meeker, M. E Professor 
 
 Fred Alan Fish, M. E. in E. E Professor 
 
 Allen Holmes Kimball, M. S Professor 
 
 Thomas Harris MacDonald, B. C. E. . . Chief Engineer, Iowa Highway Commission 
 
 Station Staff 
 
 Raymond A. Pearson, LL. D President Ex Officio 
 
 * Anson Marston, C. E Director and Civil Engineer 
 
 Samuel Walker Beyer, B. S., Ph. D Director, Mining Engineer and Geologist 
 
 Charles S. Nichols, C. E Assistant to Director, Sanitary Engineer 
 
 Louis Bevier Spinney, B. M. E Illuminating Engineer and Physicist 
 
 Warren H. Meeker, M. E Mechanical Engineer 
 
 Fred Alan Fish, M. E. in E. E Electrical Engineer 
 
 Allen Holmes Kimball, M. S Architectural Engineer 
 
 William J. Schlick, C. E .Drainage Engineer 
 
 T. R. Agg, C. E , Highway Engineer 
 
 John Edwin Brindley, A. M., Ph. D Engineering Economist 
 
 *Max Levine, S. B Bacteriologist 
 
 Roy W. Crum, C. E Structural Engineer 
 
 *Homer F. Staley, M. A Ceramic Engineer 
 
 D. C. Faber, E. E Mechanical, Electrical, and Industrial Engineer 
 
 * John S. Coye, S. B Chemist 
 
 J. S. Dodds, C. E Assistant Highway Engineer 
 
 H. V. Wright, B. S. in Chem. E. Chemist 
 
 *B. Kamrass Assistant Engineer, Road Materials 
 
 A. O. Smith Mechanician 
 
 ft. Of 9f 
 
 *Leave of absence during the war. ,. , n „- «*«#• 
 
 MAN 25 |919 
 
TABLE OF CONTENTS 
 
 I. INTRODUCTION AND HISTORICAL SKETCH. 
 
 Page 
 Art. 1. Importance of Underdrainage in Iowa 5 
 
 2. Early History of Underdrainage 5 
 
 3. Purpose of this Bulletin 7 
 
 4. Acknowledgments 8 
 
 II. SOILS. 
 
 Art. 5. Soil Areas in Iowa g 
 
 6. Mechanical Composition of Soils 13 
 
 Viewpoints of the Drainage Engineer and the Agriculturist 13 
 
 Texture and Structure 13 
 
 7. Soil Texture 13 
 
 Soil Separates 13 
 
 Soil Separates in Common Soils 13 
 
 Soil Separates in Crop Adaptations 15 
 
 Size of Soil Grains .' 15 
 
 Effective Diameter .!!!!! 16 
 
 Uniformity Coefficient '.'.'.'. 16 
 
 Number of Soil Grains '.'.'.'. 17 
 
 Surface Area of Soil Grains 17 
 
 8. Soil Structure . ' [' ' ' 17 
 
 9. Porosity 18 
 
 Porosity and Size of Soil Grains I!.'."!!!.'!!!!!!!!!!!! 18 
 
 Porosity and Structure 18 
 
 10. Porosity and Perviousness ...... j 19 
 
 III. SOIL MOISTURE. 
 
 Art. 11. Source of Soil Moisture 19 
 
 12. Moisture Content of Soils 20 
 
 Moisture Content and Crop Production 20 
 
 13. Forms of Soil Moisture ' 21 
 
 14. Gravitational Moisture .'. 21 
 
 Gravitational Moisture Content of Soils. ......'.'. '91 
 
 The Watertable 23 
 
 15. Capillary Moisture ' 23 
 
 Capillary Moisture Content 23 
 
 Available Capillary Moisture ' 25 
 
 Capillary Moisture and Drainage 95 
 
 16. Hygroscopic Moisture 05 
 
 Hygroscopic Moisture Content ' gr. 
 
 17. Loss of Soil Moisture .....'.'!!."!!!!!.'!.'.'!!! 26 
 
 IV. SOIL WATER MOVEMENTS. 
 
 Art. 18. Soil-water Movement and Underdrainage 9R 
 
 19. Forms of Soil-water Movement 9c 
 
 20. Thermal Movements '. 97 
 
 Evaporation 9 7 
 
 21. Capillary Movement ......... 27 
 
 Form of Movement and Factors Governing it.' ! " ' 27 
 
 Relation of Capillary Movement to Underdrainage ' 28 
 
 Rate and Extent of Capillarv Movement. .. "' '98 
 
 00 „ Capillary Movement and Depth of Underdrains .' 29 
 
 22. Gravitational Movement o« 
 
 Form of Movement '.'.'.. f q 
 
 Channels for Movement [ .[ on 
 
 Effect of Temperature and Barometric Pressure 90 
 
 Effect of Soil Texture ,; 
 
 Effect of Structure .' .' ™ 
 
 The Viscosity of the Moving "Water. . . 00 
 
 Do Tile Drains "Draw?" ..!..!!!!! 33 
 
 23. 
 
 xt * How Water Moves from the Surface to the Drain 
 
 Natural Underdrainage, Seeps and Springs 94 
 
 Rate of Groundwater Movement or 
 
 Relation of Groundwater Movement to Underd'rainage" " " %r 
 
 or t. I — £ ^ "»*ci uia.iiia.se, oeejjs a,iiu opringS 94 
 
 25. Rate of Groundwater Movement or 
 
 Rela T E, i ° n of Groundwater Movement to Underdrainage! '. ' %d 
 
 Effect and Spacing of Laterals ,2 
 
 Effect and Depth of Laterals , 
 
 The Time Factor ..-{.., gg 
 
V. RUNOFF. 
 
 Page 
 
 Art. 27. Definitions 40 
 
 28. Factors Affecting- Runoff 40 
 
 Rainfall 41 
 
 Topography of the Watershed 42 
 
 Character of Soil 42 
 
 Evaporation and the Transpiration of Plants 43 
 
 Climate and the Seasons 43 
 
 29. Economic Rate of Runoff 43 
 
 30. Runoff Data and Values 44 
 
 VI. FLOW IN UNDERDRAINS. 
 
 Art. 31. Cause of Flow and Factors Affecting Rate 46 
 
 32. Formulas for Flow in Underdrains 47 
 
 Kutter's Formula 47 
 
 Use of Kutter's Formula 49 
 
 Poncelet's Formula and Elliott's Modifications 50 
 
 Use of Elliott's Formula 51 
 
 33. Advantages of Each of the Two Formulas 52 
 
 VII. RESULTS OF UNDERDRAINAGE. 
 
 Art. 34. Financial Results 53 
 
 35. Physical Results 54 
 
 36. General Results 56 
 
 LIST OF FIGURES. 
 
 1. Principal Soil Areas of Iowa 9 
 
 2. Crop Adaptation and Composition of Some Soils 15 
 
 3. Ideal Arrangement of Spherical Soil Particles 18 
 
 4. Proportional Amounts of the Three Forms of Soil Moisture 21 
 
 5. Diagram Illustrating the Condition Obtaining After a Rain When the Soil 
 
 Pores Are Filled With Air 24 
 
 6. Diagram Illustrating the Movement of Water from the Surface to the Drain 34 
 
 7. Diagram Illustrating Effect of Closer Spacing of Laterals 38 
 
 8. Capacities of Drains as Given by Kutter's Formula with "n"=.015. .(facing) 48 
 
 9. Diagram Showing the Effect of Drainage Upon the Height of Corn 56 
 
 LIST OF TABLES. 
 
 I. Soil Separates 13 
 
 II. Physical Composition of Common Soils 14 
 
 III. Physical Composition of Common Soils 15 
 
 IV. Properties of Common Soils 17 
 
 V. Moisture Capacity of Soils 20 
 
 VI. Moisture Content of Soils 22 
 
 VII. Gravitational Water Capacities of Soils Near Hanford, Cerro Gordo 
 
 County, Iowa 22 
 
 VIII. Available Moisture in Soils 25 
 
 IX. Per Cents of Hygroscopic Moisture at 21" C, or Approximately 70° F. . . . 26 
 X. Pounds of Water Per Day Per Square Foot of Soil Raised from Differ- 
 
 erent Depths 28 
 
 XL The Coefficient of Roughness in Average Iowa Drains 48 
 
The Theory of^Underdrainage 
 
 I. INTRODUCTION. 
 
 1. Importance of Underdrainage in Iowa. There has probably 
 been no single factor, in the agricultural and commercial development 
 of Iowa, of greater importance than drainage, and particularly under- 
 drainage. It has been estimated on good authority that the lands in 
 Iowa needing drainage include at least 7,100,000 1 acres, and that 
 this work will cost $400,000,000'-, a sum equal to the cost of the 
 Panama Canal. Practically all of this 7,100,000 acres will require un- 
 derdrainage to put it in the condition for maximum crop production. 
 
 It seems from the best available estimates that not much over 50 
 per cent of the ultimate drainage work in Iowa has been completed. 
 One Governor of Iowa, in his inaugural address, estimated that up to 
 1911, 125,000 3 miles of underdrains had been constructed in Iowa, 
 at a probable cost of $105,000,000. Up to the same year, the drainage 
 work in one Iowa County, Winnebago, was estimated to have cost 
 $1,700,000*. Late in 1918 it was stated that when work then in 
 course of construction was completed, Kossuth County would have 
 expended more than $7,000,000 for drainage improvements. 
 
 While these figures are only estimates, they are as reliable as any 
 which are available, and they serve to show the vast importance of 
 drainage work, and particularly of underdrainage work, in this state. 
 It is probable that during the next decade at least two hundred mil- 
 lions of dollars will be required for drainage work in Iowa, and that 
 the major portion of this will be expended for underdrainage systems. 
 
 2. Early History of Underdrainage. One of the earliest records of 
 underdrainage is found in the writings of the Roman, Columnela, who 
 lived in the first century of the Christian Era. The Drainage Journal, 
 Vol. XXIV, gives the following translation from that writer's 
 works* : "We know of two kinds of ditches, those which are wide 
 open and those which are hidden.. For hidden ditches one will dig 
 trenches three feet deep, which shall be filled with pebbles or pure 
 gravel, and then the whole will be filled with earth taken from the 
 trench." That the Roman peoples did not, however, fully realize the 
 need for drainage, or its benefits, is shown by the existence of the 
 noted Pontine Marshes at the time of the fall of the Roman Empire. 
 
 In the middle of the seventeenth century, Walter Blith of England, 
 in writing on drainage, said that drains to be efficient must be laid 
 
 Proceedings, Iowa State Drainage Association, 1912. 
 Proceedings, Iowa State Drainage Association, 1912. 
 Proceedings, Iowa State Drainage Association, 1911. 
 Proceedings, Iowa State Drainage Association, 1910. 
 *Geo. M. Thompson, Proceedings, Iowa State Drainage Association, 1911. 
 
three or four feet deep. In these writings he recommended the use 
 of trenches filled with fagots or stones. A little later, about 1730, 
 James Smith of Deanston, Scotland, and Joseph Parks, Engineer for 
 the Royal Agricultural Society of England, made numerous experi- 
 ments which gave drainage development an added impetus. The En- 
 cyclopedia Brittanica in speaking of Smith and his work states that 
 "L_he insisted on the necessity of providing each field which needed 
 draining at all with a system of underground channels, .and so near 
 together that the whole rain at any time on the surface should sink 
 down and be carried off by the drains." Smith believed that the dis- 
 tance between drains should be regulated by the retentiveness of the 
 soil, but recommended parallel drains, 10 to 40 feet apart and 30 inches 
 deep. In his earlier works, he recommended trenches filled with 12 
 inches of stones which would pass a three inch ring. In his later work 
 he advised the use of burned clay tile, or "field pottery," in the shape 
 of a letter U inverted and generally used without the bottom plate, 
 or "sole," which was commonly used later. At about the same time 
 Parks advocated drains further apart and at a depth of at least four 
 feet. Both of these men were strong advocates of underdrainage, but 
 they encountered and held different opinions upon one of the prob- 
 lems still confronting us today; namely: the determination of the 
 most advantageous spacing and depth for lateral drains. 
 
 The earliest tile drainage in the United States was probably that 
 of John Johnson of New York. While on his way to the coast to 
 leave Scotland, Mr. Johnson saw some tile being burned, and on mak- 
 ing inquiry was so impressed with the idea that he brought some 
 of" the tile to this country with him. He laid his first tile in 1835. The 
 results were so gratifying that he continued the work till in 1851 he 
 had 16 miles of tile drains. In the meantime, he imported a tile 
 moulding machine, after which tile could be obtained at a price, which 
 as he expressed it, left the farmer no excuse for wet land. It seems 
 probable that Mr. Johnson laid his tile lines very close together and 
 it is known that he used very small tile (not to exceed two inches in 
 diameter) with collars. 
 
 With the westward emigration from the New England States 
 to Ohio and Indiana, and later from there to Iowa and Illinois, came 
 the practice of tiling the wet lands of the fertile Mississippi Valley. 
 There has been a constant and rapid progress in this work during the 
 last quarter of a century till now these two states, and particularly 
 Iowa, have taken the lead in underdrainage development. The knowl- 
 edge of the forms and movements of soil moisture, or groundwater, 
 and their relationships to underdrainage and to crop production has 
 increased greatly, and the engineering features of underdrainage de- 
 sign have been made more accurate through investigations which 
 have developed new methods and formulas, or shown how to use 
 old ones more correctly. 
 
3. Purpose of this Bulletin. The general knowledge of the rela- 
 tionships between soil characteristics, the forms and movements of 
 soil moisture, underdrainage and crop production is so small that 
 many engineers and landowners either consider these factors as al- 
 most wholly unrelated or do not consider the possibility of an inter- 
 relationship at all. In reality these factors, in so far as they are of 
 especial significance in underdrainage work, are all closely inter-re- 
 iated and inter-dependent. 
 
 Some readers may feel at first that much of the material presented 
 in this bulletin is an encroachment on the sphere of the agriculturist, 
 but such is not the case. The underdrainage systems of Iowa are 
 constructed primarily in agricultural lands to increase the potential 
 production of those lands. The study of soils and soil moisture and 
 their relation to crop production is essentially agricultural, but the 
 relation of these to drainage is a part of drainage engineering and a 
 knowledge of them is essential to the engineer employed in under- 
 drainage work. 
 
 The question of the most advantageous spacing and depth for 
 underdrains, regarding which James Smith and Joseph Parks held 
 different views nearly a century ago, is not debated so much now as 
 it is ignored by landowners and engineers who unthinkingly follow 
 some precedent or local custom. The question of the proper rate of 
 runoff is treated in much the same manner and is usually decided 
 upon as an independent feature of the design, and this decision 
 altered to meet the landowner's ideas as to the amount he thinks his 
 drainage system should cost. The proper spacing and depth for 
 lateral underdrains are dependent upon the amount of the surplus soil 
 moisture and the rate of its movement through the soil. These 
 in turn are dependent quite largely, in each locality, upon the 
 character of the soil. The same principles which determine the 
 proper spacing and depth for the lateral underdrains also determine 
 the rate of runoff from these drains, and a correct understanding of 
 these principles is dependent upon a general knowledge of soils and 
 soil moisture. 
 
 It is the purpose of this bulletin to present those principles which 
 determine the efficiency of the operation of a well-constructed under- 
 drainage system. Only those phases of the whole study of soils and 
 soil moisture that are essentially a part of drainage engineering are 
 discussed, and these are treated from a drainage standpoint. It is not 
 intended that any part of this bulletin be taken as a discussion of 
 these principles from a strictly agricultural standpoint. 
 
 Some additional matter of a more strictly drainage engineering 
 nature has been included so as to make a more complete presentation 
 of the principles governing the design of underdrainage systems. 
 
 It is hoped that these discussions will be of value both to the engi- 
 neer and to the landowner and that they will lead to a more general 
 and correct understanding of the principles of the intelligent design 
 of underdrainage systems. 
 
4. Acknowledgements. Much of the material in this bulletin, par- 
 ticularly those chapters relating to soils and the forms and movements 
 of soil moisture, is a compilation of material gathered from other 
 sources. These subjects and their relation to crop production come, 
 primarily, in the field of the agriculturist ; the discussions of these 
 points are taken principally from agricultural text books. The only 
 claim for originality in this connection is in the presentation of the 
 whole subject from a drainage standpoint. 
 
 The suggestions and criticisms offered by Mr. A. Marston, for- 
 merly Dean and Director of the Division of Engineering, Mr. W. H. 
 Stevenson, Professor of Agronomy and Mr. S. W. Beyer, Dean and 
 Director of Engineering, all of the Iowa State College, have been of 
 much value in preparing and arranging the subject matter presented. 
 Acknowledgement is also made of the valuable assistance given by 
 Professor Stevenson and Mr. R. E. Smith, Associate Professor of 
 Soils, in reviewing those chapters relating to soils and soil moisture. 
 
 II. SOILS. 
 
 A clear understanding of the nature and movements of soil water 
 as related to both agriculture and drainage requires some knowledge 
 of the various kinds of soils and of their physical or mechanical com- 
 position. Such elementary phases of the subject as are thought 
 necessary for a comprehensive study of the succeeding discussions 
 will be presented here. 
 
 5. Soil Areas of Iowa. The typical soil areas of Iowa might be 
 listed as follows: 
 
 Wisconsin Drift. 
 
 Iowan Drift. 
 
 Southern Iowa Loess and Kansan Drift. 
 
 and (5) Missouri and Mississippi Loess. 
 
 Moraines. 
 
 Gumbo. 
 
 Bottom Lands or Alluvium. 
 
 Peat. 
 
 a: 
 
 (2: 
 
 (3: 
 (4: 
 
 (6^ 
 
 (7) 
 
 (8) 
 
 (9) 
 
 Each of these different soil areas has its peculiar properties and 
 each presents a different problem in drainage due, primarily, to dif- 
 ferences in topography and the physical or mechanical composition of 
 the soil. The map (Fig. 1) showing the location of the six larger 
 areas and the description of each area are taken in most part from 
 published reports of the Iowa Agricultural Experiment Station. The 
 data as to the peat areas are taken from the published report of in- 
 vestigations by the State Geological Survey. 
 
 (1) Wisconsin Drift Area. The soil of this area is the till deposited 
 by the Wisconsin Glacier, the last of the great Keewatin ice-sheets 
 to invade Iowa. This drift area includes all or part of 30 counties in 
 

 W^m&0£& 
 
10 
 
 the western portion of the north-central part of the state. This area, 
 geologically speaking, is very new and its natural drainage very in- 
 complete. A few large streams, notably the Des Moines River and 
 its large tributaries, cross it but have not had time to extend their 
 tributaries very far back from the main streams. Nearly the whole 
 area is a wide prairie with numerous sloughs and ponds, except for 
 the eastern and western edges where stretches of low hills, the re- 
 mains of terminal moraines, occur. 
 
 The soil of practically all of this area is a black loam top soil, 
 sometimes of a sandy or clayey nature, with a yellow clay or sandy 
 yellow clay subsoil. A few small areas of partially decayed peat are 
 found in the swales and sloughs. Owing to the newness of this drift 
 the rocks are only partially decomposed causing the formation of light 
 alkali spots around the edges of a few ponds and sloughs which have 
 surface drainage but not' adequate underdrainage. Nearly all of 
 this area requires, and much of it now has, artificial drainage, both by 
 underdrains and open ditches. Thorough underdrainage has been 
 found to be a very efficient remedy for the alkali trouble. 
 
 (2) Iowan Drift Area. The Iowan Ice-sheet invaded Iowa at an 
 earlier period than the Wisconsin, and extended considerably further 
 east, so that the Iowan Drift Area now exposed covers an area just 
 east of soil area No. 1. The Iowan Drift Area comprises all or part of 
 29 Counties. This area is nearer maturity than the Wisconsin Drift 
 Area and has more complete natural drainage, as is evidenced by the 
 absence of ponds and sloughs, and by the deeper and more pronounced 
 natural water courses. 
 
 The soil of the Iowan Drift area is much the same as that of the 
 Wisconsin. The top soil is generally a black loam, sometimes sandy 
 or gravelly, while the underlying strata are sand, sandy clay or clay. 
 Some sections of this area have a substratum of sand or gravel at a 
 depth of four to six feet which often is a great aid to underdrainage, 
 though this layer is quite often overlain with a layer of clay or sandy 
 clay 6 inches to 18 inches in thickness. Practically no peat and but 
 very few "alkali spots" are found in this area. 
 
 (3) Southern Iowa Loess and Kansas Drift Area. This area is 
 shown in Fig 1 as the Southern Iowa Loess Area, and includes prac- 
 tically all of the state south of the Wisconsin and Iowan Drift Areas, 
 between the Missouri and Mississippi Loess Areas. The subsoil for- 
 mation is of the till from the great Kansan Ice-sheet which covered 
 Iowa long before either of the other ice-sheets mentioned. At a later 
 time the deposit known as the Iowa Loess was placed over this deposit 
 of till. This area is much older than either of the other drift areas 
 and has numerous well defined natural drainage channels, though 
 many nearly flat areas of both bottom land and upland now exist. 
 
 The top soil of this area is the loess deposit and may be described 
 as a fine black loam. It is usually found now only on the divides, 
 
11 
 
 erosion having removed it from the hillsides. Where found upon the 
 fairly level divides it usually has a depth of about two feet. The sub- 
 soil is the till from the Kansan Glacier, and upon the badly eroded 
 portions this former subsoil is now the top soil. This till is a very 
 close clay, usually yellowish red to red brown in color. It is so im- 
 pervious as to have given the name "Hardpan Area" to much of this 
 section. Neither the loess nor the till underdrain as readily as the 
 soils in other portions of the state, though the efficiency of the under- 
 drainage systems increase with the length of service. 
 
 (4) and (5) Missouri and Mississippi Loess Areas. These two 
 areas are similar so far as the characteristics of interest in this dis- 
 cussion are concerned, and hence are classed together. The location 
 and extent of these areas are shown by Fig. 1. These areas contain 
 many examples of the two topographical features characteristic of 
 deep loess deposits ; namely, the well-rounded convex curves of the 
 slopes and ridges, and the vertical escarpments. Although this soil 
 erodes easily, it still has the property of standing nearly vertical in cuts, 
 either natural or artificial, as is evidenced by the steep bluffs along 
 the Missouri River. 
 
 The soil of these loess areas is rather porous and loose. It often 
 allows of such rapid aeration that the humus is decayed so rapidly 
 that the desired amount cannot be accumulated. From an agricultural 
 standpoint, this area is marked by infertile tracts often of as much 
 as 50 acres, the infertility being accredited to the loss of the surface 
 layer of soil. The loess is not unusually as much as 100 feet deep, 
 so that it can be readily underdrained. 
 
 (6) Moraines. The areas of morainal drift now exposed in Iowa 
 lie in narrow belts on the eastern and western edges of the Wisconsin 
 Drift Area and two small areas within this drift area. These areas 
 were formed principally at the extremities of the ice-sheet and in con- 
 sequence have better developed systems of natural drainage channels 
 and a correspondingly smaller need for underdraining. 
 
 The soil of these morainal areas is very similar to that in the ad- 
 joining drift areas, except that it contains a larger percentage of 
 coarse material and more boulders. 
 
 From the standpoint of underdrainage these morainal areas are 
 comparatively unimportant. Because of the development of the nat- 
 ural drainage systems only those areas of bottom land along the 
 streams are wet enough to need underdrainage. 
 
 (7) Gumbo Areas. The Gumbo areas of Iowa are a very small por- 
 tion of the whole state and are found in only two localities. A narrow 
 strip from two to five miles wide, extends from the center of Wood- 
 bury County to the center of Pottawattamie County, parallel to the 
 Missouri River and about seven miles east of it. In Washington, Mus- 
 catine, Henry, Des Moines, Van Buren and Lee Counties are sev- 
 
12 
 
 eral irregular but small areas. Gumbo is found in both upland and 
 lowland areas, and is practically the same, from a drainage stand- 
 point, wherever found. 
 
 The soil of these gumbo areas is very fine grained and waxy, and 
 is usually black in color. The lowland gumbo is usually finer grained 
 than that of the uplands, though the latter is often just as sticky 
 and waxy as the former. 
 
 Strange as it may seem, this soil seems to drain more readily than 
 the black loam soils of other areas. Reports show that underdrains 
 placed as much as 200 feet apart have given satisfactory results, and 
 where ever underdrains have been laid in Iowa gumbo, there is re- 
 ported to be little doubt that lateral drains 100 to 150 feet wide will 
 give satisfactory results. 
 
 8. Bottom Lands or Alluvium. These terms are applied to the soil 
 formations in the present and former flood plains of streams. Owing 
 to the mode of formation the characteristics of these soils vary 
 greatly. The top soil is usually a fine black loam ; the subsoil may be 
 anything from a very close clay to a coarse gravel, though each of the 
 separate layers is usually of fairly uniform composition and fairly dis- 
 tinct. 
 
 If the subsoil is of close clay, as often occurs, this soil is more 
 difficult to drain than any of the other types of Iowa soil, unless it be 
 those sections of Southern Iowa where the close clay of the Kansan 
 Drift is at or near the surface. It can be successfully underdrained, 
 however, if the proper spacing and depth of drains be used. 
 
 (9) Peat. The peat areas of Iowa may be divided roughly into two 
 classes ; the thick deposits found in the morainal belt along the east- 
 ern side of the Wisconsin lobe, and the shallow beds in the counties 
 to the west. 
 
 The peat beds in the morainal belt vary in thickness, when wet, 
 from three or four feet to twenty or thirty feet and occasionally more. 
 The peat in the shallow deposits further west is rarely over three 
 feet thick, even when wet. The subsoil of the peat areas is almost 
 universally a marly clay. 
 
 The Report of the Iowa Geological Survey, Vol. XVII, gives the 
 areas of the peat beds of Iowa, by Counties, as follows : 
 
 Clay 
 
 Dickinson 
 
 Emmet - 
 
 Hamilton 
 
 Hancock 
 
 Kossuth 
 
 Trace 
 
 50 acres 
 400 acres 
 .Trace 
 
 375 acres 
 625 acres 
 Franklin 
 
 Palo Alto - 
 Webster 
 Winnebago 
 Wright 
 Worth 
 
 Cerro Gordo • 
 590 acres 
 
 Trace 
 
 800 acres 
 4055 acres 
 
 800 acres 
 1540 acres 
 1610 acres 
 
 Owing to the impurities in these peats they are generally avail- 
 able for agricultural uses within two or three years after they are 
 
13 
 
 thoroughly drained. Tile drainage is not a difficult matter wherever 
 it is possible to place the tile in or upon the subsoil. The instability 
 of the wet peat, and its great shrinkage upon drying make under- 
 drainage of the deeper peat beds uncertain because of construction 
 and maintenance difficulties. 
 
 6. Mechanical Composition of Soils. Viewpoints of the Drainage 
 Engineer and the Agriculturist : The agriculturist in considering the phys- 
 ical properties of the soil of any region will divide his information 
 into that relating to the top soil, or the seed-bed of cultivatable crops, 
 and that relating to the subsoil. The drainage engineer may or may 
 not divide the soil in this way depending upon the thickness of the 
 top layer of soil. If this surface layer is four or five feet thick the 
 lower stratum will have little effect upon the underdrainage unless its 
 perviousness or imperviousness be extreme. The drainage engineer 
 will look rather upon the soil as a whole, and base his conclusions 
 upon its general physical properties, considering of course any un- 
 usual formations. In some cases he may need to consider more than 
 two layers or strata. The drainage engineer should not ignore the 
 study of the agricultural possibilities of the soil in any proposed drain- 
 age district because upon this will usually depend the feasibility, from 
 an economic standpoint, of the proposed work. 
 
 Texture and Structure: The physical character of a soil is usually 
 expressed by the terms texture and structure. The term texture is used 
 to refer to the size, or range in sizes, of the individual soil grains, while 
 the term structure refers to the arrangement of these particles. 
 
 7. Soil Texture. Soil Separates: The various classes of soils, ordi- 
 narily designated as clay, loam, sandy clay, etc., derive their physical 
 characteristics and textural classes and groups from the size of the 
 individual grains of which each is composed. The size of grain which 
 places a soil in one of these classes is chosen arbitrarily, though those 
 adopted by the United States Bureau of Soils are usually taken as a 
 standard. The soil whose grains, as determined by analyses, are all 
 between the upper and lower limits of size set for one class, is termed 
 a soil separate. The list of the soil separates and the limits of sizes of 
 grains for each as adopted by the Bureau of Soils are given in Table 1. 
 
 TABLE I. SOIL SEPARATES. 
 
 Diameter of Grains, 
 Separate Millimeters 
 
 Fine gravel 2.0 - 1.0 
 
 Coarse sand 1-0 - 0.5 
 
 Medium sand JJ-"}_ " 0-^5 
 
 Pine sand 0.25 - 0.10 
 
 Very fine sand 0.10 - O.Oo 
 
 gilt 0.05 - 0.005 
 
 Clay ".'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'...... - 005 " °- 00 
 
 (1 milimeter = 0.03937 inch.) 
 
 Soil Separates in Common Soils: These soils separates must not be 
 confused with the ordinary soil groups, (clay, loam, sandy loam, etc.) 
 even though the names are similar. Each of the various soils, as 
 
14 
 
 popularly designated, is made up of varying percentages of the soil 
 separates given in Table I. Tables II and III show the percentages 
 of the various separates present in some of the common soils together 
 with some of their physical properties. All the data in Table III, ex- 
 cept the per cents of pore space and the numbers of soil grains per 
 gram, are the results of analyses of samples of these soils. 
 
 TABLE II. 
 PHYSICAL COMPOSITION OP COMMON SOILS. 
 
 
 1 
 
 • ~ ijt 
 
 Fine 
 Gravel 
 
 2 
 
 Coarse 
 Sand 
 
 3 
 
 Medium 
 Sand 
 
 .4 
 
 Fine 
 Sand 
 
 5 
 Very 
 Fine 
 Sand 
 
 6 
 Silt 
 
 7 
 Clay 
 
 Coarse 
 
 More than 25% 
 (1 4- 2) 
 
 
 
 
 0-15% | 0-10% 
 
 Sand 
 
 More than 50% 
 (1 + 2 + 3) 
 
 Less than 20% 
 (6 + 7) 
 
 Medium 
 Sand 
 
 Less than 20% 
 (1 + 2) 
 
 
 
 
 0-15% | 0-10% 
 
 
 More than 20% 
 (1 + 2 + 3) 
 
 Less than 20% 
 (6 + 7) 
 
 
 Less than 20% 
 (1 + 2 + 3) 
 
 
 
 0-15% | 0-10% 
 
 Fine 
 Sand 
 
 Less than 20% 
 (6 + 7) 
 
 
 More than 20% 
 (1 + 2 + 3) 
 
 
 
 
 
 10-35% | 5-15% 
 
 Sandy 
 Loam 
 
 More than 20% 
 
 and less than 50% 
 
 (6 + 7) 
 
 
 Less than 20% 
 (1 + 2 + 3) 
 
 
 
 10-35% | 5-15% 
 
 Fine 
 
 Sandy 
 
 Loam 
 
 More than 20% 
 
 and less than 50% 
 
 (6 + 7) 
 
 
 
 - ■ 
 
 
 
 
 1 15-25% 
 
 Loam 
 
 Less than 
 55% 
 
 
 
 More than 50% 
 (6 + 7) 
 
 Silt 
 Loam 
 
 
 
 
 \ 
 
 More 1 Less 
 than 55%|than25% 
 
 
 
 
 
 1 
 
 25-55% | 25-35% 
 
 Clay 
 Loam 
 
 More than 60% 
 (6 + 7) 
 
 Sandy 
 
 
 1 
 
 1 
 
 1 
 
 1 
 
 Less | More 
 than 25%|than 20% 
 
 Clay 
 
 I^ess than 60% 
 (6 + 7) 
 
 Silt 
 Clay 
 
 
 
 
 
 More |25%-35% 
 than 55% | 
 
 
 
 
 
 1 
 
 
 More 
 than 35% 
 
 Clay 
 
 
 
 More than 60% 
 (6 + 7) 
 
 Taken from "Principles of Soil Management," Lyon and Fippin. 
 
15 
 
 
 
 
 TABLE III. 
 
 
 
 
 
 
 PHYSICAL, 
 
 COMPOSITION OP 
 
 COMMON SOILS. 
 
 
 
 
 
 
 
 
 
 
 
 
 Surface 
 
 . 
 
 Per cent 
 
 of Separate Present 
 
 N 
 
 
 Number of Area 
 
 
 
 
 
 Very 
 
 
 
 
 Grains in 
 
 of 1 
 
 Fine 
 
 Coarse 
 
 Medium 
 
 Fine 
 
 fine 
 
 
 
 Pore 
 
 1 gram, 
 
 Cu. Ft., 
 
 Soils — gravel 
 
 sand 
 
 sand 
 
 sand 
 
 sand 
 
 Silt 
 
 Clay 
 
 Space 
 
 millions 
 
 sq. ft. 
 
 Coarse Sand ...5.0 
 
 13.0 
 
 27.0 
 
 30.0 
 
 11.0 
 
 8.5 
 
 5.5 
 
 40.0 
 
 3,276 
 
 40,500 
 
 Medium Sand ..5.0 
 
 13.0 
 
 20.0 
 
 32.5 
 
 14.0 
 
 9.0 
 
 6.5 
 
 41.8 
 
 3,956 
 
 44,500 
 
 Sandy Loam ...5.0 
 
 10.0 
 
 11.0 
 
 26.0 
 
 11.0 
 
 22.0 
 
 15.0 
 
 51.0 
 
 6,485 
 
 66,600 
 
 Fine Sandy Loam 2.0 
 
 2.5 
 
 5.0 
 
 20.0 
 
 27.5 
 
 32.0 
 
 11.0 
 
 50.0 
 
 4,902 
 
 62,000 
 
 Silt Loam 1.0 
 
 1.5 
 
 2.5 
 
 6.0 
 
 11.0 
 
 56.0 
 
 22.0 
 
 53.0 
 
 9,639 
 
 104,000 
 
 Clay Loam . . . .3.0 
 
 5.0 
 
 5.0 
 
 12.0 
 
 10.0 
 
 28.0 
 
 37.0 
 
 54.0 
 
 16,371 
 
 136,000 
 
 Clay 0.0 
 
 2.0 
 
 2.5 
 
 5.5 
 
 7.0 
 
 37.0 
 
 46.0 
 
 56.0 
 
 19,525 
 
 142,000 
 
 (Compiled from data given in "Principles of Soil Management," Lyon & Pippin.) 
 
 Soil Separates and Crop Adaptation: Figure 2 shows the crop adapta- 
 tion and composition of some soils whose analysis gave the data from 
 which the curves were plotted. By watching the yields of various 
 crops and noting the general characteristics of any soil and then re- 
 ferring to these curves it should be possible to determine something 
 of its physical composition. 
 
 5 
 
 Very Fine 
 
 oand 
 
 Fig. 2. Crop Adaptation and Composition of Some Soils. 
 
 However, it should be borne in mind that these data, both as to 
 physical composition of the soil and the crop to which it is best 
 adapted, refer more particularly to the seed bed or surface layer than 
 to the total depth that must be considered in connection with under- 
 drainage. 
 
 Size of Soil Grains: The sizes of the individual particles which com- 
 pose any natural soil vary greatly. For example, the sandy loam listed 
 in Table II has particles of fine gravel, which may vary in size from 
 
16 
 
 2.0 m.m. to 1.0 m.m. and the clay, whose particles are less than 0.005 
 m.m. in diameter. If the largest limit be taken for the clay particles, 
 it would require 5050 of them to span one linear inch. The variation 
 in sizes of the grains composing all soils is not as great as that just 
 referred to, though the variation is great for all natural soils. 
 
 Effective Diameter: All formulas for the movement of water through 
 the soil take into account either directly or indirectly, the size of the 
 grains composing the soil in question. Where the size of grains is 
 used directly it is expressed as the "effective diameter" or the "effec- 
 tive size." This is a diameter such that if grains of this diameter 
 were substituted for the soil in question the porosity would remain 
 the same. The effective diameter is also defined as the diameter 
 of the grain which has 10% of the grains smaller than itself and 90% 
 larger. In other words, the effective diameter or effective size of 
 grain in any soil, however determined or defined, is a size such that 
 if grains of this size were substituted for the soil in question a soil of 
 the same hydraulic properties, as far as the movement of ground- 
 water is concerned, would be produced. 
 
 Uniformity Coefficient: In his formula for the movement of water 
 through filter sands, Mr. Allen Hazen introduces a factor known as 
 the "Uniformity Coefficient" in order to give expression to the variety 
 of sizes of the grains of any sample. To determine this coefficient, 
 first find the size of grains such that 60% of the material is of smaller 
 grains and 40% of larger grains. This result divided by the effective 
 diameter of grain for the entire sample gives the uniformity coeffi- 
 cient. In his determination on filter sands, Mr. Hazen made a sieve 
 analysis, and then plotted a curve using the diameter of grains as 
 absessae and the per cent by weight passing through the various 
 sieves as ordinates. From this curve it was easily possible to loca'te 
 the effective size of grain and the size which divided by the effective 
 size would give the uniformity coefficient. 
 
 It is doubtful if, with the present methods of determining the size 
 of soil grains, it would be possible to apply this method to natural 
 field soils. The grains in natural soils are too small to permit of suc- 
 cessful sieve analysis so that it is probable that the best method of 
 determining the effective size and uniformity coefficient would be to 
 determine the per cents of the various soil separates present and then 
 compute the value of the effective size and the uniformity coefficient. 
 Such a result would be only approximate at best and for calculating 
 soil water movement would probably not be desirable. 
 
 In his book on Soil Physics, Professor King gives the data in Table 
 IV for samples of the various soils. It will be noticed that there is 
 a little apparent variation in the data in this table and that in Table 
 III, but this is probably due to slight differences in the samples of 
 the various soils analyzed. 
 

 Surface 
 
 Per 
 
 Area of 1 
 
 Cent of 
 
 Cu. ft. of 
 
 Pore 
 
 Soil Grains, 
 
 Space 
 
 sq. ft. 
 
 52.94 
 
 173,300 
 
 48.00 
 
 110,500 
 
 44.15 
 
 91,960 
 
 49.19 
 
 70,500 
 
 47.10 
 
 53,490 
 
 44.15 
 
 46,510 
 
 38.83 
 
 36,880 
 
 34.45 
 
 15,870 
 
 34.91 
 
 8,381 
 
 17 
 
 TABLE IV. 
 
 PROPERTIES OP COMMON SOILS. 
 
 Effective 
 Size of 
 Soil Grains, 
 Kind of Soil. M. M. 
 
 Finest Clay Soil 004956 
 
 Fine Clay Soil 008612 
 
 Heavy Red Clay Soil 01111 
 
 Loamy Clay 02542 
 
 Clayey Loam 01810 
 
 Loam 02197 
 
 Sandy Loam 03035 
 
 Sandy Soil 07555 
 
 Coarse Sandy Soil 1432 
 
 Number of Soil Grains: The number of grains in a sample of soil 
 may be readily computed when the mean diameter of the grains and 
 the specific gravity of the soil particles are known. The value of 
 2.65 for the latter is fairly constant for the soil particles, but it is not 
 correct for a volume of the soil. The data as to the numbers of soil 
 grains in 1 gram of soil given in Table III were computed in this 
 way from data obtained from an analysis of each sample. 
 
 Surface Area of Soil Grains: The surface area of the particles com- 
 posing a given weight of a soil may be computed from the number 
 of particles and their mean diameter, each particle being taken as a 
 true sphere. The relation of the fineness and number of particles to 
 the surface area is well illustrated by the data in Tables III and IV. 
 The finer the grains the greater is the number of particles and the 
 total surface area of particles. This fact has a very important bear- 
 ing on the capacity for, and movement of, capillary moisture. 
 
 8. Soil Structure. The term structure is used to refer to the ar- 
 rangement or grouping of the soil particles. Upon the structure de- 
 pends, to a large extent, the per cent of pore space and the size and 
 number of pores. This effect will be treated more fully under a dis- 
 cussion of porosity. 
 
 In any soil in natural condition, especially the top or cultivated 
 layer, the individual particles are found not as simple grains but as 
 groups of grains or granules. If these grains be arranged very com- 
 pactly in the granules the effect is to produce a soil which has the 
 same properties in regard to the movement of water and air as a 
 larger grained soil. Arrangement No. 4 of Fig. 3 is an illustration of 
 the effect of such a grouping into granules. Some soils have varying 
 sized grains which become mixed as do the particles in a well mixed 
 concrete. The smaller particles fill the spaces between the larger ones 
 so completely as to make it a nearly compact mass. When many of 
 the fine-grained soils are subjected to long continual saturation by 
 standing water, the finer particles move downward till they lodge 
 in the soil pores. This action produces a very compact layer which is 
 often termed "hard pan." When a soil, which is composed of grains 
 of properly graded sizes, is worked while wet, as by the tramping of 
 
18 
 
 stock, the smaller particles are carried into the spaces between the 
 larger grains. This produces a condition commonly known as 
 "puddled." 
 
 9. Porosity. Porosity and Size of Soil Grains: The relation of the 
 soil grains to the percentage of pore space is well shown by the data in 
 Tables III and IV. The clay soils having the smallest sized grains 
 have the largest per cent of pore space, while the sands and gravels 
 having the larger sized grains have small per cents of pore space. This 
 
 Fig. 3. Ideal Arrangement of Spherical Soil Particles. 
 (1) and (2), columnar order, 47.64% of pore space; (3) oblique order, 25.95% 
 of pore space; (4), compound spheres in oblique order, 74.05% of pore space; 
 (5), three sizes of spheres with closest packing, about 5% of pore space. 
 
 may lead to the question of why the sandy soils appear 1 to be more 
 porous than the clays. It is well known that a sandy soil will drain 
 out much more readily than a close fine-grained clay soil. This ap- 
 parent contradiction is due to the fact that pore space in the clay soil 
 is divided up into such minute channels that water or air passes 
 through them with difficulty, while in the sandy soil with its smaller 
 amount of pore space the pores or channels are much larger and 
 afford a much freer passage for either air or water. The effect of the 
 amount of pore space and size of pores will be discussed more fully 
 in the following chapters. 
 
 Porosity and Structure: The porosity of any soil depends not only 
 upon the size but also upon arrangement of the individual particles. 
 The principle is well illustrated by the data in Tables III and IV and 
 by Fig. 3 which shows the effects of arrangement if all particles be 
 considered as spheres. Arrangements 1 and 2, Fig. 3, have the same 
 per cent of pore space but in the first arrangement there are only 16 
 pores while in the latter there are 64. The spheres in these two cases 
 have diameters of 1 and J / 2 respectively. If the diameter be again 
 reduced so that it is % the per cent and total amount of pore space 
 remains the same but the number of pores is increased to 256. _ The 
 effect of this reduction upon the movement of soil water or soil air 
 is readily seen as in the first case it is divided into only 16 streams 
 while in the second case it is divided into 64 streams, each propor- 
 tionately smaller than those of the first arrangement. If the particles 
 be arranged in the oblique order shown as Arrangement 3, the pore 
 
19 
 
 space is reduced to a minimum for spheres of uniform size. But if the 
 structure be that shown in Arrangement 5, the pore space is further 
 reduced because the smaller particles continually fill the spaces be- 
 tween the larger ones. The effect of the grouping into granules is 
 shown in Arrangement 4, which gives the largest per cent of pore 
 space of any of the arrangements shown. 
 
 Figure 3 must not be taken as illustrating the arrangements of par- 
 ticles in any natural soils. These diagrams are only given to show the 
 effects of different arrangements upon the total pore space and the 
 size of pores. The particles in any natural soil would not conform to 
 any of these arrangements but would be modifications and combina- 
 tions of all or of several of them. 
 
 10. Porosity and Perviousness. Because of a misunderstanding of 
 their true meaning, these two terms are often used as synonyms. 
 These terms are neither synonyms nor antinyms, though they are 
 more nearly antinyms than synonyms ; in a number of soil samples the 
 most porous, the soil with the highest per cent of porosity, is normally 
 the least pervious. 
 
 The porosity of a soil depends upon the total amount of pore space, 
 and has no reference to the size or hydraulic efficiency of the channels 
 formed by these pore spaces. The perviousness, or permeability, of a 
 soil depends upon the readiness with which liquids or gasses (usually 
 water or air) will pass through the soil. This depends upon both the 
 size and the hydraulic efficiency of the channels formed by connected 
 pores. Normally, the soil with the smallest individual grains has the 
 highest per cent of pore space. In such soils, as very fine grained 
 clay soils, the soil pores are so small and are so disconnected that the 
 soil is practically impervious. On the other hand, the coarser grained 
 soils, as sand or granular loam soils, have a much smaller per cent 
 of pore space, but the pores are larger and form such efficient hydraulic 
 channels (comparatively) that soil air and soil water pass through 
 them rapidly. 
 
 In loam soils, porosity is determined largely by the soil texture 
 and the permeability by the soil structure; the porosity normally de- 
 creases as the permeability increases or vice versa. 
 
 III. SOIL MOISTURE. 
 
 In discussing soil moisture and its movement only such phases of 
 the subject as have an especial relation to underdrainage will be con- 
 sidered. The subject in its entirety is so complex that only an ele- 
 mentary treatment is either possible or desirable here. 
 
 11. Source of Soil Moisture: Of the water which falls to the 
 earth's surface as rainfall, one portion runs away over the surface to 
 the natural drainage channels, another portion seeps into the ground, 
 and the third portion evaporates from the place where it falls. It is 
 
20 
 
 this second portion, that which is taken up by the soil, which is of 
 particular interest in this discussion. 
 
 12. Moisture Content of Soils: The capacities of soils to take up 
 and hold moisture vary greatly with the different soil types and 
 formations. The soils with the larger percentages of porosity hold 
 the larger amounts of moisture. The moisture content is usually ex- 
 pressed as a percentage of either the dry weight or of the volume of 
 soil, or as a depth in" inches, which is simply a modified way of ex- 
 pressing it as a percentage of the volume. Table V shows the varia- 
 tion of the moisture capacity of a soil with the fineness of _ the soil 
 grains. The maximum and minimum moisture content each increases 
 as the size of the soil grains decreases. Any treatment, such as 
 underdrainage, as will tend to increase the moisture capacity of a 
 soil without too great injury in some other respect is desirable. 
 
 TABLE V. 
 
 MOISTURE CAPACITY OP SOILS. 
 
 Amount of Available Water 
 
 Depth, 
 
 Water Capacity Cu. in. inches 
 
 Min. Max. per in top 4 
 
 per cent per cent Per cent cu. ft. ft. of soil 
 
 Light Sandy Loam Early Truck Soil 3 8 5 122 3.4 
 
 Silt Loam Bluegrass Soil 15 25 10 218 6.0 
 
 Clay Black Cretaceous Prairie Soil 23 40* 17 274 7.6 
 
 (From "The Principles of Soil Management," Lyon & Fippin.) 
 
 Moisture Content and Crop Production: The amount of moisture 
 necessary for crop production varies greatly with the soil texture and 
 structure, the crop and the climate. Lyon and Fippin state in their 
 text, "The Principles of Soil Management," that " — other things being 
 equal, more water will be required in an arid region than in one of 
 humid climate ; more in a warm region than in a cold region ; more in 
 a clay soil than in a sandy soil ; more in a windy section than in a 
 region of still atmosphere; more with a high soil-moisture content; 
 more on a poor soil ; and lastly, more water is used per pound of dry 
 matter produced in a small crop than is required in a large crop. Not 
 only is the total seasonal requirement to be considered, but the maxi- 
 mum demand of the crop at any period of its growth must be met." 
 
 Investigations by Hunt and by King show that one acre of corn 
 in Illinois will, in July, take 1.55 inches of water from the soil in one 
 week. This indicates the large amount of water required by this 
 one crop. The other crops common to Iowa agriculture, unless it be 
 grasses, all require more water than does corn for the total crop 
 growth. 
 
 Professor King of the University of Wisconsin has determined that 
 the average crop under the best management requires water equiva- 
 lent to 3.7 to 15 inches of rainfall for the average yield. From Table 
 
 'Assumed. 
 
21 
 
 V it is seen that the surface four feet of even the clay soil does not 
 hold quite one-half enough moisture for some crops, while the other 
 two soils hold even less. This means that for an average yield the 
 average crops require that the moisture content of the soil shall be 
 replenished during the growing season. 
 
 13. Forms of Soil Moisture. Soil moisture is of three different 
 classes: (1) Gravitational water, or that which is free to move under 
 the influence of gravity ; (2) Capillary or film moisture, which is held, 
 by surface tension, against the influence of gravity; and (3) Hygro- 
 scopic moisture or that which condenses from the atmosphere upon 
 the surface of the soil particles. Fig. 4 shows the proportional 
 amounts of these forms of moisture in a soil and the availability of 
 each for plant use. 
 
 Hydroscopic Capillary Gravitational 
 
 <0| 
 
 ~~\( ^ r \ 
 
 J\. 
 
 Unavailable Available Injurious 
 
 Fig. 4. Proportional Amounts of the Three Forms of Soil Moisture.* 
 
 14. Gravitational Moisture. Land drainage has been aptly defined 
 as the removal of the surplus moisture from the soil. (Usually this 
 is only the means to an end, as the benefits of drainage are due to 
 those actions made possible by the removal of the surplus moisture). 
 Underdrainage is the removal of this water by artificial or natural 
 means under the surface. As it is only the gravitational soil water 
 which is free to move under the influence of gravity, and which is 
 unavailable for and injurious to plant growth, the need for drainage 
 is proportional to the amount of this form of moisture present in the 
 soil. 
 
 When the supply of soil moisture is replenished by rainfall that 
 part in excess of what can be held capillarily becomes gravitational 
 moisture. As the water percolates from the surface downward the 
 thickness of the films of capillary moisture near the plane of satura- 
 tion is gradually increased till the whole pore space is filled. None of 
 the soil moisture becomes gravitational till after the full capillary 
 moisture capacity has been supplied. This of course takes no account 
 of the relatively large amount of water which passes from the satu- 
 rated surface through the shrinkage cracks, small root cavities and 
 worm bores. 
 
 Gravitational Moisture Content of Soils: The gravitational water- 
 content is directly proportional to size of the spaces and is also the 
 difference between the total moisture content and the capillary and 
 *From "The Principles of Soil Management," Lyon and Fippin. 
 
22 
 
 hygroscopic moisture contents. If the pore spaces become too small 
 they may be almost entirely filled by capillarity as in the fine grained 
 clay soils. In general it may be said that the gravitational water 
 capacity decreases as the total amount of pore space increases, because 
 the largest total percentage of pore space is ordinarily found in the 
 soil having the smallest grains and the smallest individual pore spaces. 
 
 TABLE VI. 
 MOISTURE CONTENT OP SOILS. 
 
 Max. Gravita- 
 
 Weight Maximum Maximum tional Capacity 
 
 Per Cubic Pore "Water Capillary Depth, 
 
 Foot, Space, Capacity, Capacity, inches in 
 
 Kind of Soil. Pounds per cent per cent per cent Per cent top 4 ft. 
 
 Dune Sand 80 52 40.5 10.7 29.8 18.3 
 
 Coarse Sand 81 51 39.5 10.6 28.9 18.0 
 
 Pine Sandy Loam 83 50 38.0 18.0 20.0 12.7 
 
 Silt Loam 83 50 38.0 20.9 18.9 12.1 
 
 Clay 68 59 54.5 30.4 13.9 7.3 
 
 Muck Soil 15 80 333.0 250.0 83.0 9.6 
 
 Note.- — Percentages are figured by weights. (From "Principles of Soil Manage- 
 ment," Lyon & Fippin.) 
 
 The above principles are well illustrated by the data in Table VI. 
 It is seen here that the gravitational water capacity varies directly as 
 the porosity until the clay is reached. In this fine grained soil the 
 pore spaces are so small as to be more nearly filled by capillary mois- 
 ture. The quantities given in the columns headed "Max. Gravitational 
 Capacity" are the amounts which might be removed by drainage. In 
 considering the data in the columns headed, "Max. Gravitational Ca- 
 pacity," it should be borne in mind that these values are for a saturated 
 soil and represent the maximum amounts of water which are sub- 
 ject to removal by drainage from each of these soils. If an acre of 
 the "Dune Sand" be saturated to a depth of over four feet, the water in 
 this top four feet would be equal to 18.3 in. in depth over the entire 
 acre. This amount is that which a drainage system should carry 
 away in order to restore this acre of land to the best condition. 
 
 Some determinations were made of the percentage of porosity of 
 the soils, in natural field condition, of the fields at Hanford, Cerro 
 Gordo County, Iowa, to which a part of the original data in Bulletin 
 No. 52 refers. 
 
 This value of the porosity as given by these determinations, is very 
 nearly equal to the gravitational water content of these soils, as they 
 had all or part of their maximum capillary water content when the 
 determinations were made. The results of these determinations are 
 summarized in Table VII. 
 
 TABLE VII. 
 
 GRAVITATIONAL WATER CAPACITIES OF SOILS NEAR HANFORD, CERRO 
 
 GORDO COUNTY, IOWA. 
 
 Gravitational 
 
 Depth Water 
 
 of Sample Capacity, 
 
 Kind of Soil. Below Surface Per cent 
 
 Black Top Soil 3 in. 18.5 
 
 Clay, a little sand 2.5 ft. 5.8 
 
 Whitish Yellow Clay 3.5 ft. 2.5 
 
 Blue Clay 4.5 ft. 6.6 
 
 Sandy Clay 3.0 ft. 13.9 
 
 Sandy Clay 4.0 ft. 18.6 
 
23 
 
 A.s is shown in Fig. 4 only a very small part of the gravitational 
 moisture in the soil is available for plant use, and the major portion 
 of it is injurious to vegetable life. Below the plane of saturation it 
 completely fills the pore spaces in the soil, thus excluding the air. 
 Many authorities on agriculture contend that aeration, or the passage 
 of air through the soil, is one of the most important factors of crop 
 production as far as it is controlled by the condition of the soil. 
 
 Watcrtable: The surface of the gravitational water in the soil, or 
 the surface of the saturated layer, is commonly called the watertable. 
 It is also referred to as the groundwater level, groundwater in this 
 sense meaning gravitational soil moisture, or surplus moisture. 
 
 It sometimes happens that the presence of air in the soil causes two 
 planes of saturation. After a rain there are sometimes a saturated 
 surface layer and a true groundwater level at a greater depth. The 
 pore spaces of the intermediate layer of soil are filled with air which 
 excludes the water till such time as the air can pass out through the 
 upper saturated layer. Figure 5 illustrates this condition as shown by 
 an experiment by Professor King. The arrows indicate the movement 
 of both the water and the air ; as soon as the surplus water in the 
 saturated surface layer has worked down to the readjusted true water- 
 table, the surface of the latter will not curve upward toward the ex- 
 perimental well as is shown in the diagram. Under the conditions 
 illustrated the water is passing from the well to the lower saturated 
 layer, hence the upward curve of the w r atertable near the well. 
 
 Between periods of rainfall the movement of capillary soil mois- 
 ture is from the watertable upward. In this one particular, that of 
 furnishing a source of supply for capillary moisture, the gravitational 
 moisture is very beneficial. 
 
 15. Capillary Moisture. In so far as plant life is concerned this is 
 the most valuable form of soil moisture and, in fact, the only form 
 which is available for the sustaining of plant growth. It is held, against 
 the force of gravity, in the small pore spaces between the soil grains 
 and as a thin film surrounding each individual particle or group of par- 
 ticles. Every one has noticed the rise of water in a small bore glass 
 tube when the lower end is immersed in water, the height to which the 
 water rises increasing as the size of the opening in the tube decreases. 
 It is the same force, surface tension, which holds the capillary water 
 in the soil. 
 
 Capillary-Moisture Content. In the field the grains of soil are sur- 
 rounded by connecting thin films of moisture and the finer the soil 
 particles the greater the surface area which holds this film of mois- 
 ture. This variation of the capillary moisture capacity of soils with 
 different sized grains is illustrated by the data in Table VI, already 
 referred to. 
 
 An idea of the amount of water held in this film, and the thickness 
 of the film, may be obtained by considering the fine clay soil where 
 
24 
 
 "LTcSuperscrt^ura : tec/.\ '■ 
 
 Zone of Soil . 
 
 • » • * . 
 
 _ ■ oir wh/cn . 
 • * • - . » * 
 
 • s\ • • - * 
 
 t " /i jr escapmq\ .* 
 
 » - - . * . ■ * 
 
 m 
 
 ff- Surface So//>~±: 
 
 with confined ../ • 
 
 impedes peroolahon. ■ 
 
 , * . /a?/o jve// ' . * 
 
 • » * 
 
 Fig. 5. Diagram Illustrating the Condition Obtaining After a Rain When the Soil 
 Pores Are Filled With Air. 
 
25 
 
 the effective diameter of soil grains is 0.005 m.m. or less. Professor 
 King has determined (See Table IV) that for 1 cubic foot of such soil 
 the area of the surface of the soil grains is 173700 sq. ft. or approxi- 
 mately four acres. Water equivalent to four inches in depth over 
 one square foot could be held in one cubic foot of this soil if the thick- 
 ness of the film was 173,000 inches, or about one-half the thickness 
 of a soap bubble just before it expands to the bursting point. 
 
 Available Capillary Moisture. However, not all of even the capillary 
 moisture is available for plant use. A certain portion of it is held so 
 intimately that the small roots cannot draw it from the soil. This 
 fact is illustrated by the data in Table VIII, which is compiled with 
 data given in Lyon and Fippin's "The Principles of Soil Manage- 
 ment." The values in the column headed "Approximate % of Mois- 
 ture at which Crops will Wilt," are the amounts of water which are 
 held so intimately in the soil as to be unavailable for plant use. The 
 sum of the values in this column and those of either the succeeding 
 columns represent very approximately the total combined capillary 
 and hygroscopic water capacities of those soils to which they refer. 
 
 TABLE VIII. 
 
 AVAILABLE MOISTURE IN SOILS. 
 
 Approximate Available Moisture 
 
 Dry Per cent of Depth 
 
 Porosity, Water Crops inches in 
 
 Kind of Soil. Percent Will Wilt Percent top 4 ft. 
 
 Dune Sand 52.2 3.0 7.7 4.6 
 
 Coarse Sand 51 3.0 7.6 5.2 
 
 Fine Sandy Loam 50 5.0 13.0 8.5 
 
 Silt Loam 50 10.0 10.9 6.9 
 
 Clay 59 17.0 13.4 7.0 
 
 Muck Soil 80* 80.0 170.0 20.5 
 
 Capillary Moisture and Drainage. Capillary moisture has no direct 
 relation to underdrainage though it has a very definite and important 
 bearing upon the results and effects of drainage. When the plane of 
 saturation is lowered by the use of underdrains the moisture necessary 
 for crop production must be supplied by capillarity. 
 
 16. Hygroscopic Moisture. This is the least important of the 
 three forms of soil moisture and in amount it is relatively very small. 
 It is the moisture which condenses from the air onto the soil grains, 
 the condensation taking place either at the surface or in the- soil, if 
 it be so open as to allow of a circulation of air. 
 
 Hygroscopic-Moisture Content. The amount of this form of mois- 
 ture in a soil is a function of the surface area exposed and conse- 
 quently is greater in the finer grained soils. The amount also varies 
 inversely as the temperature in the soil. Table IX shows the amounts 
 of hygroscopic water held by three soils, each of which was a soil 
 separate obtained by careful analysis. 
 
 *Assumed. 
 
26 
 
 TABLE IX. 
 
 PER CENTS OF HYGROSCOPIC MOISTURE AT 21°C., OR APPROXIMATELY 70°F. 
 
 "Very fine sand 18 
 
 Silt 7.3 
 
 Clay 16.5 
 
 Taken from "The Principles of Soil Management," Lyon & Fippin. 
 
 Comparison of these data with others in the text from which these 
 were taken show that all soils hold a considerably larger percentage 
 of capillary water than of hygroscopic water. The importance of this 
 form of moisture is further reduced by the facts that it is varying in 
 amount and unavailable for plant use. It has practically no bearing 
 at all upon the underdrainage of the soil. 
 
 17. Loss of Soil Moisture. The total amount of moisture in the 
 soil at any one time is a function of the supply and the loss. The sup- 
 ply may be either from rainfall or from percolation from higher 
 ground; the loss will be from percolation, evaporation or transpiration 
 of plants. Relatively the loss by percolation is much larger than 
 either or both of the other two. As a general rule it may be said that 
 where the soils are such that percolation is very slow the losses by 
 evaporation will be high comparatively. 
 
 The loss due to percolation naturally has to do with the movement 
 of gravitational water so will be discussed under the head. 
 
 The losses due to evaporation are in the nature of thermal move- 
 ments and will be discussed under that head. 
 
 IV. SOIL-WATER MOVEMENTS 
 
 18. Soil-water Movement and Drainage. The relations of the dif- 
 ferent movements of soil water to underdrainage are the same as those 
 of the forms of soil moisture to which they refer. The gravitational 
 movement, or the percolation of the groundwater, is the one by which 
 the surplus water reaches the drain, and is, consequently, the most 
 important in this connection. Just as capillary moisture has an im- 
 portant relation to the effects of underdrainage, so has the capillary 
 movement, as it is the effectiveness of this movement which deter- 
 mines whether or not the underdrained soil shall be constantly sup- 
 plied with the moisture necessary for plant growth. 
 
 19. Forms of Soil-water Movement. The previous discussion of 
 the types of soil water will readily suggest the forms of soil-water 
 movements. Each of the three forms of soil water has a distinct type 
 of movement. These movements are : (1) Gravitational, or the move- 
 ment of gravitational water under the influence of gravity ; (2) Capil- 
 lary, or the movement of capillary moisture due to capillarity or sur- 
 face tension ; and (3) Thermal, or the movement due to changes in 
 temperature. This latter movement is in the form of water vapor, 
 though changes in temperature have some effect upon the other two 
 types of movement. 
 
27 
 
 These three types of soil-water movement will be discussed in the 
 reverse of the order in which they were stated. Because of its very 
 important and direct relationship to underdrainage the discussion of 
 gravitational movement will be left till the last then be given more at- 
 tention than the other two. 
 
 20. Thermal Movements. This movement takes place as the 
 movement of water vapor and consequently is relatively very small. 
 If the bottom of a column of soil be heated, the cold portion directly 
 above the heated portion will be found to have added moisture. The 
 moisture from the heated layer has been converted into water vapor 
 and as such has passed up through the heated soil to the cold portion 
 where it has been recondensed. If none of this soil column had been 
 cold enough to condense this vapor it would have passed upward and 
 outward to the air. Such an action would have resulted in the loss of 
 soil moisture by evaporation. 
 
 Evaporation. Evaporation of soil moisture may take place not only 
 at the surface as is popularly supposed but also in the deeper pores 
 of the soil. When a dust mulch is maintained the evaporation is very 
 apt to take place at the surface of the moist layer. The loss due to 
 this movement depends upon the rate at which diffusion into the 
 atmosphere takes place. Buckingham found that the loss due to evap- 
 oration from sandy, silty, or clayey soils where the porosity was near 
 50% varied from 4.3 inches per year for the sandy soils to about 1 
 inch per year from the clayey soils. In the ordinary agricultural 
 soils of Iowa this loss is so small as to be of very little importance in 
 a study of soil moisture as related to underdrainage. 
 
 21. Capillary Movement. In the discussion of capillary soil mois- 
 ture, its importance to plant life and its relation to underdrainage were 
 explained. Its movement naturally bears the same relation to these 
 as the moisture itself. It is of vital importance to crop production 
 but of very little importance to the operation of underdrainage. 
 
 Form of Movement and Factors Governing It. The form in which 
 capillary moisture occurs in the soil has been explained as a thin film 
 of moisture surrounding the individual soil particles. Its movement 
 then is a film movement and depends upon an unbalanced condition 
 in the pull exerted upon these films. Any moisture which is moved 
 in this way naturally moves as a film and consequently is small in 
 amount. This movement always takes place from the wetter soil to 
 the dryer regardless of the direction. 
 
 The soil factors governing this movement are texture, structure 
 and dampness. The finer the soil particles the more surface is ex- 
 posed and consequently the greater capillary pull is exerted. In gen- 
 eral it may be said that the extent of capillary movement is inversely 
 proportional to the fineness of the soil grains. It is also true, that 
 when the soil grains are very fine the spaces between them become so 
 very minute and the thickness of the film of moisture so reduced as 
 
28 
 
 to so increase the friction that the movement is very slow. It is also 
 necessary for water to wet any substance to which it is held by capil- 
 larity, hence if the soil particles are somewhat dry the moisture is not 
 held to them strongly until after they become damp, as all natural 
 field soils have a certain resistance to wetting'. 
 
 The rate and extent of this movement are also affected, to some 
 degree, by the temperature changes. The surface tension is greater 
 for low temperatures than for high, causing both a greater rate and 
 a greater extent of movement at the lower temperatures. On the 
 other hand, warm water is more limpid than cold and will conse- 
 quently pass through the small pore spaces more readily. 
 
 Relation of Capillary Movement to Under 'drainage. The most im- 
 portant phase of this movement in relation to underdrainage is the 
 distance which a sufficient quantity of water for crop production will 
 be raised. It is the effect of any drainage to lower the permanent 
 watertable after which the moisture for sustaining plant life must be 
 furnished capillarily. If the watertable is held at too low a stage an 
 insufficient amount of moisture will be raised to the upper soil layers 
 and the crops may suffer. In such a case the underdrainage system 
 will have been too effective and its results will be no better than those 
 conditions which obtained before any drainage was attempted. 
 
 Rate and Extent of Capillary Movement. As has been stated the rate 
 and extent of capillary movement depend upon the distance the water 
 is raised and the nature of the soil through which the movement takes 
 place. In Part II of the 19th Annual Report of the United States Geo- 
 logical Survey is given experimental data from which Table X was 
 compiled. These data illustrate the principle that the rate of move- 
 ments varies inversely with the extent and distance of the movement. 
 The lower rate of movement in the clay soil from each lift is probably 
 due to the greater friction and greater resistance to movement in the 
 finer grained soil. 
 
 table x. 
 
 POUNDS OF WATER PER DAY PER SQUARE FOOT OF SOIL RAISED FROM 
 
 DIFFERENT DEPTHS. 
 
 ■ Depths 
 
 Soil. 1 foot 2 feet 3 feet 4 feet. 
 
 Medium Fine Sand 2.37 2.07 1.23 0.91 
 
 Medium Clay Loam 2.05 1.62 1.00 0.90 
 
 The report referred to above states further that though there were 
 very few reliable data on this subject those at hand indicated that for 
 natural field soils the movement is fairly rapid when the lift does not 
 exceed four feet. If the rate given for that lift in Table X be main- 
 tained throughout the year a quantity of water equivalent to 63.8 
 inches in depth would be raised. Experiments already referred to 
 show that corn in Illinois used water during July equivalent to a depth 
 of 1.55 inches or 1.15 pounds per square foot per day. When this 
 moisture is to be supplied by capillarity, as is the case during periods 
 between rains, the lift should not exceed 2.5 to 3.0 feet, if the crop is 
 
29 
 
 to be fully supplied. It has also been previously stated that for the 
 average yield under the best methods of cultivation the average crop 
 requires from 3.7 to 15 inches in depth of moisture or from 19.24 to 78 
 pounds of water. If the average growing season be taken at 80 days 
 this would mean that from .24 to .96 pounds of moisture would be 
 required per day per square foot. This data in Table X indicates that 
 to meet this demand the lift for capillary moisture should be about 4 
 feet. However, the amount of moisture needed by a crop varies so 
 greatly with stage of its growth and with the season that the above 
 figures can be only approximate. 
 
 Capillary Movement and Depth of Undcrdrains. From the standpoint 
 of the supply of capillary moisture the above data indicate that the 
 ideal underdrainage system for the average Iowa soil which is to be 
 used for the ordinary field crops is one which will maintain the 
 groundwater level at a depth of from 2.5 to 3.0 feet below the average 
 elevation of the crop roots. However, this optimum depth varies 
 slightly for the various crops and soils. This depth seems to afford 
 the maximum storage capacity without so lowering the watertable as 
 to reduce the capillary movement too greatly. There are, however, 
 other factors than the supply of capillary moisture which must be 
 considered in determining the depth of underdrains. 
 
 22. Gravitational Movement. Form of Movement: It was stated in 
 the discussion of gravitational soil water that the need for drainage 
 was directly proportional to the amount of this form of moisture pres- 
 ent. Consequently, the nature and rate of this movement will be a 
 very important factor, and in most cases the deciding factor, in the de- 
 sign of the underdrainage system. It is true that the optimum posi- 
 tion of the watertable with relation to capillary movement should be 
 considered, but it is probable that the rate at which the surplus, or 
 gravitational, water is removed will be of greater importance. 
 
 The gravitational movement is the result of the gravity pull upon 
 the soil water, and, as both the capillary and the hygroscopic mois- 
 ture are held against gravity, it is only the gravitational soil moisture 
 which is affected. This moisture and its movement are usually re- 
 ferred to as "groundwater" and "groundwater movement" or "perco- 
 lation." 
 
 The direction of this movement depends entirely upon the soil 
 formations. Being a gravity movement the direction is always as 
 nearly vertically downward as the soil conditions will permit. From 
 the previous discussions of soil composition and formations it will 
 be readily seen that the channels afforded by the soil pores will not be 
 straight and where the percolating water encounters a more or less 
 impervious layer the direction may be so changed as to have only a 
 very slight slope ; or if the percolation is through a porous layer be- 
 tween two nearly impervious layers which are undulating or which 
 approach the surface closely, the movement may be upward, as- in 
 the case of the outlet to a spring. 
 
30 
 
 Channels for Movement. In all natural field soils the percolation of 
 the groundwater, especially downward from a saturated surface layer, 
 occurs in two ways ; through the soil pores and through the shrinkage 
 cracks, small root cavities and worm bores. The movement through 
 the soil pores is subject to both theoretical and experimental investi- 
 gation. The flow through the comparatively large channels afforded 
 by the shrinkage cracks, etc., is indeterminate. The presence of these 
 openings can be detected in the soils of any field, but the amount of 
 channel capacity thus afforded could be determined only by a great 
 number of careful mechanical analyses. The rate of flow through 
 these larger openings is comparatively great because they afford a 
 much more efficient channel. 
 
 The following discussion of groundwater movements will be con- 
 fined entirely to the flow through the soil. In a later discussion of 
 runoff from underdrained areas the total flow through the soil, both 
 through the soil and through the large channels mention, will be con- 
 sidered. 
 
 The flow of water through the channels afforded by the pores of 
 the soil is subject to the same laws as the flow through a pipe, a tile 
 drain or an open ditch. In each case the velocity of flow depends upon 
 the slope and the resistance which the sides of the channel offer to the 
 passage of water. The rate of flow is the product of the velocity and 
 the cross-sectional area of the moving stream. 
 
 The size, shape and hydraulic efficiency of the soil-water channels 
 depends upon the texture and structure of the soil. However, while 
 these are the only soil factors influencing the movement of gravita- 
 tional soil water, some external forces have a definite influence upon 
 the rate of this movement. 
 
 Effect of Temperature and Barometric Pressure. Changes in temper- 
 ature affect the rate of movement both through the effect upon the 
 air and upon the moving water. Likewise the barometric pressure 
 tends to increase or decrease the rate of flow as the barometer rises 
 or falls. The wind may cause a suction or an increased pressure at 
 the outlet, the flow being effected accordingly. 
 
 The exact amount of the affect of temperature upon the rate of 
 percolation of soil water, except for the effect upon the water itself, is 
 indeterminate, though it may be approximated by experimentation. 
 A lowering of the temperature of the soil air will cause it to contract 
 causing a suction which tends to hold the soil water. An abrupt 
 warming of the soil air will have the opposite effect. Consider, for ex- 
 ample, the conditions obtaining in a well underdrained soil. In the 
 evening the outer air cools much more rapidly than that in the soil. 
 This cooler air is the denser and flows to the more rarefied and 
 warmer air in the soil. When the cool outer air passes from the tile 
 into the soil, the soil air cools and contracts causing a suction which 
 tends to hold the soil water. In the morning the outer air warms 
 more rapidly than the soil air, and due to the circulation within the tile 
 and the soil, the soil air is warmed, causing it to expand and tend to 
 
31 
 
 force out the soil water. In the 19th Annual Report of the United 
 States Geological survey are given some records of the variation in 
 the rate of discharge from a tile drain due to the change in tempera- 
 ture during the day. When the rates of discharge and temperature 
 are plotted as curves they are found to be approximately parallel, the 
 rate of discharge increasing during those hours when the tempera- 
 ture should be expected to increase and decreasing towards evening. 
 It should be borne in mind, however, that these changes were due 
 to the effect of temperature change upon both the soil air and the outer 
 air and upon the water itself. 
 
 The variation in the rate of discharge from a tile drain or a spring, 
 due to barometric changes, is very similar to that due to temperature 
 changes. The rate of flow increases and decreases as the barometer 
 rises and falls. The changes in the pressure in the outer air are 
 transmitted through the tile to the soil air causing a suction or pres- 
 sure as it contracts or expands. In the same publication referred to 
 above are given curves showing the change in rate of discharge from 
 underdrains and springs and the barometric changes for the same 
 periods. In each case the curves are nearly parallel except that the 
 changes in the barometric pressure occur more rapidly than the 
 changes in rate of discharge. Professor King found from these records 
 that the effect of changes in barometric pressure were sufficient to 
 vary the rate of discharge as much as 8% for springs and as high as 
 15% for underdrains. 
 
 The changes in rates of groundwater movement due to tempera- 
 ture and barometric changes are interesting rather than valuable in a 
 discussion of underdrainage. The changes due to each are usually 
 comparatively small and are compensating. The present knowledge 
 of the movement of water in the tile and of other factors of drainage 
 engineering is not sufficiently accurate to demand any changes in the 
 design of an underdrainage system to care for the variations from 
 these causes. It is probable, however, that for extremely large under- 
 drained areas this variation in the rate of flow would be noticeable, 
 especially if accurate discharge records were kept. 
 
 Effect of Soil Texture. The influence of the texture of a soil upon 
 the movement of groundwater is due to the variation in the size of 
 the soil pores resulting from differences in the sizes of soil grains. 
 The finer the soil grains are the smaller the pore spaces and, conse- 
 quently, the higher the resistance which they offer to the passage 
 of percolating water. The rate of percolation varies directly as the 
 size of the soil grains until in some very fine grained soils the pores 
 become so small as to be completely filled with capillary moisture. 
 
 As has been stated the movement of gravitational soil water is gov- 
 erned by the same laws as the flow through a pipe under gravity head. 
 In the pipe the velocity of flow is determined by the slope and the re- 
 sistance which the pipe offers against the passage of water. This re- 
 sistance, considering only that within a straight pipe, is due to the 
 friction between the water and sides of the pipe and so varies directly 
 
32 
 
 as the wetted area of pipe surface. From the laws of the variation of 
 the area and circumference with the diameter, it is readily seen that 
 the resistance in a small pipe is proportionally much greater than that 
 in a large pipe. 
 
 The application of the above principles to the movement of water 
 through soils may be illustrated by considering Fig. 3 as representing 
 sectional views of soils and considering each grain as a cylinder of 
 unit length and of the same diameter as the spherical soil grains. If 
 the diameters of cylinders arranged as shown in Arrangements 1 and 
 2 of Fig. 3 be taken as 1 inch and ]/$ inch, respectively, the cross-sec- 
 tional area of the pore spaces will in each case be 3.4336 square inches, 
 while the surface area of these pores will be 50.2556 square inches and 
 201.0224 square inches respectively. In other words, decreasing the 
 diameter 4 times leaves the total cross-sectional area of the pore space 
 the same but increases the surface area 4 times and, if the frictional 
 resistance be taken as the same per unit of area in each case, the re- 
 sistance is 4 times as large with the small grains as with the larger. 
 
 The above discussion is of general principle only, when applied to 
 soils in natural field condition, because there the grains are not ar- 
 ranged in any such regular order and are not of uniform size. But 
 the principle that the ratio of the exposed surface area to the cross- 
 sectional area of the pore space increases at a more rapid rate than 
 the diameter of soil grains decreases holds true, though this ratio may 
 vary considerably. It is these ratios which will determine, to a 
 large extent, the ratios of the flows through different soils. Every one 
 has noticed how much more quickly the water left upon a loose sandy 
 soil will disappear than that left upon a field of close grained clay 
 soil. This is only an illustration of the above principles. 
 
 Effect of Structure. The effect of different arrangements of soil 
 grains upon the rate and extent of the movement of groundwater is 
 governed by the same principles as that referring to the effect of var- 
 ious sized soil grains. If the arrangement is such as to give a large 
 exposed surface area in proportion to the cross-sectional area of the 
 pore space the flow is small. If the same assumption be made as in 
 considering the soil grains of 1 inch and % inch diameters in the 
 preceding paragraph, grains of 1 inch diameter and arranged as in Ar- 
 rangements 1 and 3 of Fig. 3, the cross-sectional area of each pore will 
 be .2146 square inches and .04 square inches respectively. In other 
 words, the area of the pore space for 1 inch grains arranged in 
 columnar order is 5 times that for the same sized grains arranged in 
 oblique order. The areas of the exposed surfaces in these two cases, 
 considering each grain as a cylinder of unit length, are 3.1416 square 
 inches and 1.5758 square inches respectively. The ratio of the ex- 
 posed surface to the area of the pore is 14.6 for the columnar arrange- 
 ment and 39.4 for the oblique order. It is thus seen that with the 
 oblique arrangement the pore space is both smaller and less efficient 
 than in the columnar arrangement. 
 
33 
 
 In the section on "Soils" the property of some soils to form 
 granules, or groups of grains, was discussed. As far as the percolation 
 of groundwater is concerned, a soil of granular structure is a large 
 grained soil, and, as such, allows a much more rapid groundwater 
 movement than it would if composed of the individual grains. There 
 are some small pore spaces within the granules themselves but these 
 are so small as to allow of only a very small flow in comparison to that 
 passing through the pores between the granules. 
 
 The Viscosity of the Moving Water. The effect of temperature upon 
 the movement of gravitational water is of considerable importance. 
 The viscosity of water decreases as the temperature rises, and, conse- 
 quently, the flow increases with the temperature of the water. Hazen 
 found in his experiments with filter sands that the relative flow at 
 different temperatures varied from .70 at 32° to 1.0 at 50° and 1.45 at 
 77° . All temperatures were measured in degrees fahrenheit. In other 
 words, raising the temperature from 32° to 77° approximately doubles 
 the flow. This fact more than anything else, accounts for the variation 
 in the flow from tile drains. However, the temperature within the 
 underdrained soils varies much less than that of the air. It is prob- 
 able that during the growing season in Iowa the temperature of 
 drained soils is very nearly constant at 50° fahrenheit. At least, if 
 temperature were to be taken into account directly in computing the 
 flow through Iowa soils, it would seem safe to make such calculations 
 with a soil temperature of 50° F. 
 
 23. Do Tile Drains "Draw?" How far will a tile drain "draw?" 
 The statement that the underdrains in one field "draw" better, or 
 farther, than those in another field is often heard. Actually the drains 
 do not draw at all, if by "draw" it is meant that the tile exert a pull 
 lending to suck the water out of the soil pores and into the drain. 
 The underdrains serve simply as a collecting channel, or outlet, for the 
 percolating water. If one field is drained farther back from the line of 
 tile than another field it signifies simply that the conditions as to 
 depth and capacity of the tile, or of the soil are such as to cause a more 
 leady movement of the groundwater in the one case than in the other. 
 
 How Water Moves from the Surface to the Drain. It is the opinion 
 of many persons, who have given the subject little serious considera- 
 tion, that the water falling upon the surface of an underdrained area 
 moves in a diagonal direction till it is directly over the tile and then 
 enters it from the top. This is not the case, as no water ordinarily en- 
 ters the tile from the top except that which falls upon the surface di- 
 rectly above the drain and then only when the soil conditions are such 
 as to allow of a nearly vertical percolation. 
 
 The path taken by a drop of water passing from the surface to the 
 drain is illustrated by Fig. 6. The surplus water in the surface layers 
 passes as nearly directly downward as soil conditions will permit until 
 it reaches the watertable, and then moves laterally so as to enter the 
 drain from the bottom. Its movement after reaching groundwater 
 
34 
 
 level is somewhat uncertain, but the paths illustrated in Fig. 6 are 
 the general paths of this movement. The water below the plane of 
 saturation is under a certain hydraulic or hydrostatic head and fol- 
 lows the path of least resistance, which, in this case, is into the drain. 
 The only case when water generally will enter the drain from the 
 top is when the tile is or has been surcharged and the soil above has 
 become saturated. 
 
 Surface of Ground 
 
 i.i , .1 
 
 I 
 
 Impen/iou5 Stratum 
 
 Fig. 6. Diagram Illustrating the Movement of Water from the Surface to the 
 
 Drain. 
 
 24. Natural Underdrainage, Seeps and Springs. An area is said 
 to have natural underdrainage when there is a subsoil stratum of sand 
 or gravel at a depth of from 2' to 6' below the surface. In such area 
 the surplus water from rainfall may pass down through the top soil to 
 this sand layer and through it to an outlet. The thoroughness of such 
 drainage depends upon the readiness with which the surplus water in 
 the top soil layer reaches the layer of sand and the rate at which it 
 passes away through this sand layer. 
 
 However, such lands, especially if they are very flat, usually re- 
 quire artificial underdrainage if they are to be efficiently drained. If 
 the top soil is fairly loose and porous and if the said substratum is 
 not at too great a depth, say from 4 to 5 feet, the drains may be placed 
 at the top of the sand stratum and at considerably greater distances 
 apart than if placed in the top soil. Care must be taken in such design 
 to see that the tile are well supported whenever placed in any sand 
 stratum. 
 
35 
 
 Every one has noticed seepy or spouty spots on the sides or at the 
 foot of the steeper slopes. These wet places are especially evident 
 where there is a porous layer overlying a stratum of very close clay, 
 both of which outcrop upon the slope. The surplus soil water works 
 down into the porous layer and then follows it to the outcrop, that 
 being the only outlet. In some few cases these wet places are caused 
 by the flow from a porous layer which is both overlain and underlain 
 by impervious layers. In this case the soil water enters the porous 
 layer at a point higher up the slope where the overlying impervious 
 layer is very thin or above the point of its beginning. 
 
 The drainage of these wet spots is accomplished by tracing the 
 porous stratum for a few feet back from the outlet and then construct- 
 ing intercepting tile drains. In some instances the drains may be laid 
 at a sufficient depth in the wet areas so as to intercept the seep water 
 as it rises to the surface. 
 
 Springs, as they are ordinarily considered, are not usually a factor 
 to be considered in the design of underdrainage. The location is gen- 
 erally such that the flow will not interfere with any cultivatable lands 
 and, as the flow is more often than not a fairly constant quantity, pro- 
 vision for them can be made without difficulty. 
 
 The character of the soil formation causing springs is very similar 
 to that causing the second class of "spouty" spots mentioned in a 
 preceding paragraph. In cases where a spring causes conditions de- 
 manding relief by underdrainage, an intercepting drain is necessary 
 if the flow is to be prevented from coming to the surface. 
 
 25. Rate of Groundwater Movement. Several investigators have 
 endeavored to express the laws governing the flow of water through 
 soil, or other porous media, in a mathematical formula. Such formulas 
 contain constants or factors representing the character of the soil 
 (as the fineness of soil grains, and the porosity), the length and cross- 
 sectional area of the column of soil through which the flow occurs, the 
 loss of head in passage and the temperature, or the viscosity, of the 
 moving water. In one formula all of these factors may be represented 
 by separate quantities while in others one or more of the soil factors 
 and the temperature factor may be represented by a constant. 
 
 These formulas, in their original form, are unsuited for application 
 to drainage work because of their great refinement. To be practically 
 and readily usable a formula for drainage uses will require no data 
 which are not easily obtainable and will not be more accurate than 
 the original data or the other formulas which will be used in the de- 
 sign of the system. The effective size of soil grain for a given sample 
 of natural soil can be determined only by a careful laboratory analysis, 
 which is both impractable and undesirable in drainage design. Such 
 an analysis would give data of a much greater degree of refinement 
 than the other data which will be used in the design. Much the same 
 thing is true also of the determination of the porosity, if the absolute 
 value is to be determined, though the space available for the move- 
 
36 
 
 ment of the surplus moisture can be determined without great diffi- 
 culty. 
 
 Darcy's Formula.One of the earliest attempts to determine, and state, 
 the laws of the flow of water through soils was made in 1856 by Darcy, 
 a Frenchman. He announced that the flow of water in a certain 
 direction through a column of soil is proportional to the difference in 
 pressure at the two ends of the column and inversely proportional to 
 the length of the column.* Darcy expressed his conclusions in the 
 
 P 
 
 formula v = k — 
 
 h 
 where v=the velocity of the moving water. 
 
 p=the difference in pressure at the two ends of the column. 
 h=the length of the column. 
 
 k=a constant whose value depends upon the character of the 
 soil, especially the size of the soil grains, and which must 
 be determined experimentally. 
 
 The principles expressed by Darcy has been incorporated in all 
 subsequent formulas for the movement of groundwater. In reality, 
 Darcy did no more than say that, other things being equal, the rate 
 of flow was proportional to the hydraulic grade which is true of the 
 movement of water under all conditions. 
 
 Mr. Allen Hazen, Consulting Engineer, of New York, has derived 
 a formula for the movement of water through filter sands. His 
 formula is the same as Darcy's with added factors representing the 
 effective size of soil grains and the effect of temperature. According 
 to Mr. Hazen's statements his formula is true for only sands with 
 grains within certain limits of size, the lower limit being much larger 
 than the grains of natural field soils. 
 
 Mr. Charles S. Slichter of the United States Geological Survey 
 has derived a theoretical formula for the movement of water through 
 porous media. As far as is known, Mr. Slichter's formula* is the only 
 purely theoretical investigation of this subject which has ever been 
 published. His theoretical derivation was made in conjunction 
 with an experimental investigation by Prof. F. H. King, of the Uni- 
 versity of Wisconsin. In some trials, the flow through certain soils 
 was computed by Mr. Slichter and measured in the laboratory by Mr. 
 King. These results gave such close checks as to prove that this 
 formula was correct if used for soils which had been accurately an- 
 alyzed. This formula requires so careful a laboratory analysis of the 
 soil through which the movement is to be calculated as to prohibit its 
 use in drainage work. 
 
 26. Relation of Groundwater Movement to Underdrainage. Since 
 only gravitational moisture, or groundwater, is free to move under 
 the influence of gravity, this is the only moisture which can be re- 
 
 *U. S. Geological Survey, Water Supply Paper No. 67. 
 
37 
 
 moved by the drains. The rate of its movement through the soil to 
 the drains is the controlling factor in determining the efficiency of the 
 drainage. The primary function of the underdrains is to make pos- 
 sible this movement by providing an outlet for it. 
 
 According to Darcy's principle, the velocity of the movement of 
 water through a particular soil depends upon the hydraulic slope of 
 the moving water. It follows then that any change in the lateral 
 system which causes a change in this hydraulic slope will cause a 
 corresponding variation in the velocity of the movement of the ground- 
 water that is flowing through the soil to the drains. As the rate of 
 this movement determines the efficiency of the drainage, it follows 
 that the lateral system should be so designed as to give the desired 
 control of this movement, or of the rate of removal of the surplus 
 moisture. In other words, the spacing and depth of the laterals in a 
 particular field controls the rate of the movement, and of the removal 
 of the surplus moisture, and this in turn determines the volume of 
 flow which determines the capacity required in the mains and sub- 
 mains. 
 
 The application of Darcy's principle to the design of underdrainage 
 systems may be summarized in the. three statements given below. 
 Each of these is based upon the premise that all factors, except that 
 stated as a variable, remain constant. From the nature of the prob- 
 lem, it naturally follows that the converse of each of these statements 
 is equally true. 
 
 (a) The rate of the movement of the groundwater to the drain varies in- 
 versely with the distance between the laterals. 
 
 (b) The rate of this movement varies directly with the depth of the under- 
 drains (actually varies with the vertical distance from the crest of the 
 watertable to the water in the drain). 
 
 (c) The rate of runoff from the underdrainage system varies directly with 
 the rate of the movement of the groundwater to the drain. 
 
 The first two of these principles will be discussed in the following 
 paragraphs. The relationship of the spacing and depth of laterals 
 to the rate of runoff will be taken up in succeeding articles. 
 
 Effect of Spacing of Laterals. Darcy's principle states that the ve- 
 locity of water moving through any given soil varies directly with the 
 hydraulic slope of the moving water. (In this connection the hy- 
 draulic slope is the quotient obtained by dividing the vertical distance 
 from the crest of the watertable, or plane of saturation, to the free 
 surface of the water in the drain by the horizontal distance between 
 these two points.) This means simply that if the distance between the 
 laterals be decreased, other conditions remaining the same, the 
 hydraulic slope of the moving groundwater is increased and that it 
 will move to the drain at a more rapid rate. This will tend to remove 
 the surplus moisture at a more rapid rate which, in turn, means that 
 the soil is in the condition required for proper plant growth a larger 
 percentage of the time. This increase in the rate of the movement of 
 
38 
 
 groundwater also requires that the mains and submains of the sys- 
 tem be designed to care for larger flows. Suppose, for example, that 
 the drains in a particular field are 100 feet apart. If intermediate 
 drains were constructed so that laterals would be only 50 feet apart, 
 the rate of flow to the drains, for any position of the watertable, would 
 be just twice that when the drains were 100 feet apart. 
 
 The form of the surface of the plane of saturation, or the water- 
 table, has already been explained. Fig. 7 illustrates the condition just 
 described. The lines D and E represent two positions of the water- 
 table when only drains A and C are constructed. After the inter- 
 mediate drain B has been constructed, the positions of the watertable 
 are illustrated by lines F, G, H and I. It can be seen from this dia- 
 gram how the hydraulic slope of the water moving to the drain is 
 made steeper by decreasing the distance between the laterals. 
 
 This diagram also illustrates the way in which the closer laterals 
 cause an increase in the area of soil which is free from surplus mois- 
 ture. The importance of this latter fact is emphasized by the fact 
 that plant roots can neither live nor draw food from a saturated soil. 
 
 A B C 
 
 Fig. 7. Diagram Illustrating Effect of Closer Spacing of Laterals. 
 
 The form of the watertable between drains and the rate of move- 
 ment of groundwater will vary with differing soil conditions. The 
 relationship discussed above cannot be applied directly to systems in 
 different fields. If the soil conditions are similar approximately cor- 
 rect comparisons can be made. This principle is of more value in 
 considering the various systems that might be used in one field and in 
 explaining the general proposition of the relative efficiencies of dif- 
 ferent underdrainage systems. 
 
 Effect of Depth of Laterals: The discussions just given will explain 
 the relationship between the depth of laterals and the rate of move- 
 ment of the surplus soil water. Few, if any, underdrainage systems 
 are so designed and constructed th^t the plane of saturation will not 
 
39 
 
 rise to the surface during or after heavy rains. It is apparent then, 
 that if the soil is uniform, that placing the laterals deeper will cause 
 an increase in the rate of movement of surplus moisture as will a de- 
 crease in the distance between laterals. However, other considera- 
 tions control the depth of laterals to within such close limits that this 
 relationship is of less importance than that of the spacing in laterals. 
 
 In considering the effect of placing the laterals at a greater depth 
 the effect of the variation in the soil at different depths must be con- 
 sidered. For example, if the subsoil is a very close clay, the move- 
 ment of groundwater though this stratum will be much slower than 
 through the more open top soil. This increase in the resistance to the 
 flow may be sufficient to more than counterbalance the increase due to 
 the steeper hydraulic grade. In some soils, such as were referred to 
 above, drains only two feet deep may appear to be just as effective, 
 or in extreme cases, more effective, than drains four feet deep. A 
 greater depth than this is desirable in order to increase the depth of 
 soil that is in condition to furnish plant food. This close subsoil us- 
 ually contains valuable plant food which must be made available if 
 the field is to produce the maximum crops. The close soils become 
 more open and drain more readily after the drains have been in opera- 
 tion for a time, and experience shows that this improvement continues 
 as time goes by. The solution of the problem presented by such a 
 field is to place the laterals closer together and hold to the four foot 
 depth. 
 
 It will be readily seen from Fig. 6 or 7 why the average position 
 of the watertable is lowered as the drains are placed deeper. The 
 drains cannot lower the plane of saturation below their own level, and, 
 practically, cannot hold it to their own level during the growing sea- 
 son when rains are usually frequent. The plane of saturation must 
 have an appreciable slope (the hydraulic slope upon which depends 
 the rate of flow to the drain) toward the drain, or the rate of move- 
 ment of the soil waters will be so slow as to be of small consequence. 
 The food requirements of the crops and the plant food generally avail- 
 able then demand that drains be not less than four feet deep except in 
 unusual cases. In these discussions no consideration has been given 
 those cases where the depth of the drains may be controlled by con- 
 struction features, this discussion being confined to the relationship of 
 the depth of the drains to the rate and extent of the removal of the 
 surplus soil moisture. 
 
 The Time Factor: The relationship of the spacing and depth of lat- 
 erals to the rate of the movement has been explained. The increase 
 in this rate which results from certain changes in the lateral system 
 has an important bearing upon the crop production and upon the cost 
 and degree of thoroughness of the cultivation. In each soil, each posi- 
 tion of the watertable represents a certain amount of surplus mois- 
 ture. If changes in the lateral system cause the removal of this sur- 
 plus moisture at a more rapid rate, the loss due to this surplus is cor- 
 
40 
 
 respondingly, reduced. If the surplus moisture is removed more rap- 
 idly there is a larger average depth of soil available to support the 
 growing crop. The removal of the surplus moisture at a more rapid 
 rate allows the field to be prepared and the crop to be planted earlier. 
 The more rapid removal of the surplus after each rain allows the field 
 to be cultivated with less loss of time because the ground is too wet 
 for proper cultural operations. In short, the more rapid removal of 
 the surplus moisture means a decrease in the total time during which 
 the plane of saturation is too high to permit of the maximum plant 
 growth and proper cultural operations. This point is of especial im- 
 portance when the underdrained area is to be used for truck crops. 
 
 5. RUNOFF. • 
 
 27. Definitions. The portion of the rainfall or snowfall which 
 passes over or through the ground to the natural or artificial drainage 
 channels is termed runoff. It is that part which passes through the 
 soil to the drains which is of particular interest in this discussion. 
 
 The rate of runoff is variously expressed as a percentage of the 
 rainfall, as the depth in inches removed from the watershed per 24 
 hours, and as cubic feet per second, or per 24 hours, from each unit of 
 watershed area. 
 
 It is probable that the method most common in present day drain- 
 age practice is to express the rate of runoff as the depth in inches 
 removed from the watershed in 24 hours. This depth is often re- 
 ferred to as the runoff coefficient or the drainage coefficient, or in the 
 abbreviated form, of a "^-inch runoff." This method of expressing 
 the rate of runoff will be used in this bulletin. 
 
 28. Factors Affecting Runoff. The relationship of the form of 
 the lateral system to the rate of the movement of the surplus moisture 
 through the soil has been explained. Since the runoff from an under- 
 drainage system is the surplus soil moisture which flows through the 
 soil and collects in the drain, it follows that the rate of runoff is di- 
 rectly dependent upon the spacing and depth of the laterals. The 
 efficient operation of the underdrainage system demands that it be 
 so designed that it will remove the surplus moisture at a sufficiently 
 rapid rate; if this is not done the primary object of the construction 
 is not attained. The climatological, topographical and physical fea- 
 tures which determine the amount of rainfall concentrated on the area 
 to be underdrained and the soil characteristics which determine the 
 rate of movement through the soil, jointly determine the form of the 
 lateral system necessary to secure the desired control of the ground- 
 water. Those factors which are ordinarily considered to control the 
 rate of runoff should be considered to control the type of the lateral 
 system and then the probable rate of flow from each system should 
 be determined as accurately as possible and used as the rate of runoff 
 for which the capacities of the various lines of the system are designed. 
 
41 
 
 The principal natural or physical factors controlling the amount 
 and rate of movement of surplus soil moisture are : rainfall, topog- 
 raphy of the watershed, character of the soil, evaporation and trans- 
 piration of plants and seasons and climate. The general relation of 
 each of these to the form of the lateral system and its resulting effect 
 upon the rate of runoff will be discussed in the above order. 
 
 Rainfall. Since rainfall is the source of supply of soil moisture, the 
 amount of surplus moisture to be removed by the drains naturally 
 varies with the rainfall. In sections where the rainfall is heavy, a 
 proper control of the soil water will demand a closer lateral spacing, 
 these conditions resulting in a high rate of runoff. The total annual 
 runoffs from two underdrainage systems, of similar size and design, 
 draining similar watersheds so located that the annual precipitation is 
 30 inches and 60 inches, will be approximately in the ratio of one to 
 two. 
 
 However, the total amount of surplus moisture to be removed dur- 
 ing the year is of very much less importance in this connection than 
 is the probable maximum amount which must be removed per unit of 
 time in order to secure proper soil conditions during the cropping 
 season. Both the ordinary maximum daily precipitation and the rate 
 at which it falls must be recognized as controlling factors. If the 
 underdrainage system is to be constructed in a locality where the 
 daily rainfall is ordinarily heavy during the cropping seasons, but 
 consists of severe short showers, as thunder storms, the water will 
 reach the earth much more rapidly than it can be taken up by the soil. 
 Under such conditions much of the rainfall must necessarily flow away 
 over the surface, with the result that there will be but a compara- 
 tively small amount of surplus moisture to be removed by the under- 
 drains. The rate of underdrainage runoff due to a rain of one inch 
 in one hour will often be much smaller than that due to a rain of one 
 inch falling, slowly but steadily, in a period of six to twelve hours. In 
 the latter case more nearly the total amount of water falling will pass 
 down into the soil and on to the drains. 
 
 The effect of hard dashing rains was well illustrated by the records 
 from two adjoining drainage systems in Southern Iowa, where the 
 Engineering Experiment Station was conducting an investigation dur- 
 ing the summer of 1914. The soil in which these drains were laid is 
 rather close but has been underdrained sufficiently long to be much 
 more open, and to drain more readily, than in its natural state. From 
 early spring till the latter part of May the soil was very dry, though 
 it had been wet when the crop, oats, was planted. The rainfall during 
 Tune and July was as follows: Tune 10, 0.50 in.; June 13, 2.12 in.; 
 June 22, 0.50 'in.; July 6, 1.25 in.; July 12, 2.06 in., and July 16, 1.0 in. 
 Each of these rains was a heavy downpour lasting but a short time. 
 The water reached the surface so rapidly that a very large proportion 
 of it passed away as surface runoff. So small a portion of this water 
 entered the soil that at no time during June or July was there any flow 
 
42 
 
 in the outlet mains of these systems. If the rate of precipitation in 
 these storms had been slow it is very possible that after the rains of 
 July 12 or 16, the outlet main would have been flowing full. 
 
 In the design of an underdrainage system consideration should be 
 given to all the factors which tend to control the amount of surplus 
 moisture to be removed by the drains, and the rate at which it moves 
 through the soil to them. Where the rainfall is such as will ordinarily 
 cause the saturation of the soil to a high level during a considerable 
 period, the spacing of the laterals must be such as will cause a rapid 
 movement of the groundwater to the drains and the runoff coefficient 
 used in calculating the sizes of the tile required must be correspond- 
 ingly large. 
 
 Topography of the Watershed: The area and slopes of the water- 
 shed have a very great influence upon the amount of surplus mois- 
 ture to be removed by the drains. If the slopes are steep a large part 
 of the rainfall passes away over the surface. If the underdrained area 
 is a flat with an untiled tributary area with steeper slopes, a portion 
 of both the surface and natural underground runoff from the tribu- 
 tary area will be collected in and on the flat. This condition is the 
 same in effect as subjecting the flat to heavier rainfall. The amount 
 of such increase will depend upon the slope and proportional area of 
 the tributary watershed. The effect of such additions upon the design 
 of the lateral system and upon the rate of runoff has already been dis- 
 cussed in the previous paragraphs. 
 
 The size of the underdrained area, unless it be very large, will us- 
 ually have but little effect upon the rate of runoff. The time neces- 
 sary for water to pass through the drains themselves is very small 
 compared to that required for the passage through the soil to the 
 drain. If the spacing and depth of drains, the soil conditions and 
 the relative elevation of the plane of saturation are the same in all 
 parts of the underdrained area, the flow will reach all laterals at the 
 same rate. The rate of the movement of the water through the 
 drain is so rapid, compared with this movement through the soil, that 
 it seems very probable that the rate of runoff will not be affected ma- 
 terially by the size of the underdrained area. It must be remembered 
 however, that this statement is true only when applied to areas exactly 
 similar in all respects except size. 
 
 The effect of topography should be studied, in each particular case, 
 to determine its relation to an increase or decrease of the normal 
 amount of surplus moisture and then the underdrainage designed to 
 remove the surplus moisture at the desired rate. 
 
 Character of Soil: The relation of the properties and characteristics 
 of soils to the rate of movement of soil moisture has already been 
 discussed. Since the rate of runoff is but another expression of the 
 rate of the movement of the surplus moisture through the soil, these 
 discussions need not be repeated here. Considering each of the three 
 physical properties of soil separately, the other two being constant 
 
43 
 
 in each case, the rate of runoff varies inversely as the size of the soil 
 grains, directly as the closeness of their arrangement and directly as 
 the porosity. 
 
 The foregoing statements mean that a fairly fine grained soil that 
 is loose will store a considerable quantity of moisture and will allow of 
 its percolation at a fairly rapid rate; that a fine grained, close soil, 
 such as clay or close "gummy" black soil, will allow of only a very 
 slow percolation but has a large reservoir capacity, though consider- 
 able time is required for the pore spaces to become filled ; that a large 
 grained porous soil, as sandy loam, will hold but a small quantity of 
 drainage water in storage, but allows of its percolation at a rapid rate. 
 The relation between rainfall, including surface runoff collected on 
 the underdrained area, the storage capacity and the rate of percola- 
 tion determines the rate of underdrainage runoff. 
 
 Evaporation and the Transpiration of Plants: The amount of water 
 which would otherwise reappear as runoff, but which is removed from 
 the soil by these two agencies, varies with the climate, the nature and 
 the amount of the vegetation and the character of the soil. It should 
 be remembered, however, that unless the soil is saturated clear to the 
 surface so that evaporation may take place directly, neither of these 
 agencies will affect the amount of drainage water except indirectly. 
 The relation of evaporation and the use of water by vegetable life, to 
 the moisture content of the soil has been discussed in previous chap- 
 ters which need not be repeated here. It has been estimated that, 
 in the Upper Mississippi Valley, the average maximum daily loss 
 from these two causes will not exceed one-tenth of an inch. How- 
 ever, both of these depend to a large extent on the plant growth. The 
 water required by some plants is much more than that necessary for 
 others. If the vegetable growth is dense and rank, the shading of the 
 surface may be such as to reduce evaporation to a minimum. 
 
 The amount of water removed annually from the soil by evapora- 
 tion and used by plants may be large in amount, but it is always small 
 in comparison to the underdrainage runoff. 
 
 Climate and the Seasons: That the climate and the seasons have an 
 important bearing upon the rate of runoff is readily seen from the dis- 
 cussions already given. In Iowa in the early spring the rainfall is or- 
 dinarily large and the losses through evaporation and transpiration 
 are small, causing a comparatively high rate of runoff. In the sum- 
 mer the rainfall may be large, but these losses are also large, result- 
 ing in a lower rate of runoff. In the fall, if the amount of rainfall be 
 large the rate of runoff will also be high, as the evaporation and 
 transpiration losses are small. In other words, the effects of climate 
 and seasons upon the rate of runoff are the combined effects of the 
 resulting rainfall and the evaporation and transpiration losses. 
 
 29. Economic Rate of Runoff: Conditions sometimes prevail such 
 that to provide capacities in the drains equal to the flow of surplus 
 
44 
 
 moisture resulting - from the maximum rate of rainfall, would require 
 a larger investment than that upon which the average benefits from 
 the drainage would pay an adequate return. These unusually severe 
 storms, or series of storms, may occur at such infrequent intervals 
 that it is economically desirable to suffer whatever loss may be due 
 to the inadequacy of the drains during such storms than to provide 
 the drainage system necessary at such times. The drainage systems 
 should be designed to care for the maximum runoff for whcih it is 
 economically possible to make provision. This rate of runoff, some- 
 what below the actual maximum, is often referred to as the economic 
 rate of runoff. 
 
 In this connection it should be remembered that the more rapidly 
 the surplus soil moisture is collected in the laterals, the higher will 
 be the rate of runoff for which the capacities of the various lines 
 should be calculated. Higher values for farm land and products make 
 more efficient, more rapid, and more thorough underdrainage both de- 
 sirable and possible, economically. The increasing of the general 
 knowledge of underdrainage and its benefits are responsible for a con- 
 stant tendency toward more efficient drainage. All of these things 
 will demand that the mains and submains be designed to care for 
 larger rates of runoff. As an underdrainage system properly con- 
 structed of good materials will last for a great many years, it will be 
 cheaper to provide at first for a larger rate of runoff than seems neces- 
 sary at that time, than to make replacements or additions within a 
 few years when the recognized conditions demand the more effi- 
 cient drainage service. 
 
 30. Runoff Data and Values: The designers of farm underdrain- 
 age systems have been confronted with a paucity of reliable data as to 
 the runoffs from underdrained areas. Consequently they have had to 
 depend upon observation of the operation of existing systems, making 
 the capacities larger or smaller than those in some other system as 
 the conditions appeared to demand. This condition has led to much 
 work being designed for the care of a certain rate of runoff without 
 really studying the particular project, or its differences from some 
 other system. It has been the purpose of the foregoing pages of this 
 bulletin to explain the whole subject so that the designer might make 
 a rational study of each project, or proposed system, and then design 
 the underdrainage system, using all available data, from publications 
 and observations, with full knowledge of the significance of all espe- 
 cial conditions obtaining in the particular problem. 
 
 The data as to the rates of runoff from farm underdrainage sys- 
 tems given in Bulletin 52, Iowa Engineering Experiment Station, 
 comprise practically the only published, comprehensive records for 
 such systems. A few other data from older investigations, principally 
 of larger county systems, are to be found, but because of their nature 
 and the general advancement in drainage practice, these are now not 
 
45 
 
 applicable without making many allowances for the advancement in 
 drainage work. 
 
 The data in the publication just referred to show that the rate of 
 runoff now generally used is not applicable to all cases, or, that the 
 tvpe of the lateral system and the completeness of the drainage have 
 a marked effect upon the rate of flow to the drains. In fact, these 
 data are concrete evidence of the influence of nearly all the factors 
 discussed in the foregoing chapters. 
 
 These data show that if one rate of runoff is to be used as a basis 
 from which to reach decision in each particular problem, this rate 
 should be slightly larger than the rate of % inch now in quite com- 
 mon use ; in some cases this rate will need to be increased materially. 
 The tendency is ever toward more thorough drainage, so that con- 
 siderable care should be exercised to insure that the main drains of 
 the system will have sufficient capacity for the completed and ex- 
 tended system of the next few years. Much of the benefit of closer 
 lateral spacing may be counteracted by mains of too small a 
 capacity. 
 
 The problems encountered in the design of a large county drain 
 are capable of less exact study. The flow through the main lines of 
 a county drain are only the combined flows from the various separate 
 farm systems. These drains now usually are provided with inlets 
 for admitting surface water, which add to the problem of deciding 
 upon the probable capacity required. It is obviously impracticable 
 and impossible for the engineer to study each individual farm and at- 
 tempt to decide upon the rate of flow from the underdrainage sys- 
 tem which the owner will install. Some landowners will install no 
 farm drainage systems ; others will construct more or less complete 
 systems, depending upon their opinions as to the needs for under- 
 drainage and the value of the systems to their farms. From his 
 knowledge of the general underdrainage requirements and the local 
 sentiment for and against thorough underdrainage, the engineer 
 should be able to reach a fairly accurate conclusion as to the capaci- 
 ties to be required in the main lines of the county system. He 
 should not forget, however, that there is a growing knowledge of 
 underdrainage, with a resulting demand for ever increasing thorough- 
 ness of drainage. It is the moral duty of every engineer to be a con- 
 stant advocate of more thorough drainage in his community. There 
 is now no apparent reason to expect the present tendency toward bet- 
 ter drainage to reach its climax or to turn for many years. The effect 
 of this growth and development should not be ignored when design- 
 ing any drainage system. 
 
 In designing large county drains provided with intakes for admit- 
 ting surface water the engineer should increase his underdrainage rate 
 of runoff sufficiently to care for the surface flow admitted. If this is 
 not done the whole capacity of the drain will often be used for the 
 surface flow and the tributary underdrains remain inoperative till this 
 accumulated surface flow is removed. 
 
46 
 
 VI. FLOW IN UNDERDRAINS. 
 
 The foregoing pages have presented a discussion of the forms of 
 soil moisture, their movements, their relation to the various soil prop- 
 erties, crop production and drainage, the relationship of the rate of 
 movement to the surplus moisture, crop requirements and soil prop- 
 erties to the form of the lateral system and the resulting relationship 
 of all these to the rate of runoff, or to the capacities required in the 
 various lines of the system. This section will take up a discussion of 
 the factors controlling the rate of flow through the drain and the 
 methods of computing this. 
 
 31. Cause of Flow and Factors Affecting Rate : The pull of grav- 
 ity is the sole cause of the flow of water, except where pumps of some 
 sort are used. It is gravity which causes water to run down hill or a 
 ball to roll down an inclined plane. 
 
 The rate, or velocity, of the movement in the case of either the 
 water or the ball, depends upon the steepness of the slope down 
 which the movement takes place and the resistances which the path 
 offers. In the case of the flow through a tile drain, the velocity de- 
 pends upon the slope, or grade, of the moving water and the rough- 
 ness of the inside of the drain. Obviously, the quantity of flow per 
 unit of time is the product of the cross-sectional area of the moving 
 column and the rate of movement. 
 
 Hydraulic Grade: In these, as in all such hydrological problems, the 
 hydraulic slope or grade is the one which determines the velocity of 
 the flow. The hydraulic head, when flow is due to gravity only, is 
 the difference in elevation of the free water surface at the two ex- 
 tremities of the portion of the flow under consideration ; the hydraulic 
 grade is the quotient obtained by dividing the hydraulic head by the 
 horizontal distance between the upper and lower limits of this flow. 
 
 This hydraulic grade may or may not be parallel to the grade at 
 which the tile were laid ; it will be parallel to this constructed grade 
 only when the tile are flowing just full at both ends and neither end 
 is submerged. However, it is customary to calculate the capacity of a 
 drain when it is flowing full at a grade equal to that at which the tile 
 were laid. 
 
 Resistance to Floiu: The principal resistances to flow in a tile drain 
 are the roughness of the inside of the tile, the irregularities due to 
 careless laying, the irregularities due to tile of nonuniform shape and 
 size and sharp or irregular changes in direction. The roughness of 
 the inside of the tile is an inherent quality or property of the tile being 
 used, and can be changed only by the action of the flow. The irregular- 
 ities of laying cannot be entirely eliminated, but by careful workman- 
 ship this resistance can be reduced very greatly. The irregularities 
 due to unsymmetrical or ununiform tile can be almost wholly elimi- 
 nated by proper inspection of the tile before they are laid. Any channel 
 composed of unconnected short sections, as a tile drain, will have 
 
47 
 
 larger resistance to flow than a channel composed of a continuous 
 tube of like material. The resistance due to sharp and irregular bends 
 can be greatly reduced by making all changes in direction by means 
 of longer, easier and regular curves ; changes in the direction of the 
 drain .cannot be avoided practically, but by using proper curves this 
 resistance is reduced to a very small amount, both actually and com- 
 paratively. 
 
 All formulas for the flow in a tile drain take into account the effect 
 of these resistances, usually by means of a constant which varies, with 
 the roughness of the inside of the drain, or with the size of the tile, or 
 both. In designing a drain it is customary to consider the resistances 
 present in a drain constructed of average good materials and in an 
 average good, workmanship-like manner. 
 
 32. Formulas for Flow in Underdrains : All formulas used for 
 calculating the velocity of the flow through a tile drain have been de- 
 rived, partially at least, from the results of experiments. For this rea- 
 son, all such formulas contain constants whose values must be chosen 
 with reference to the conditions obtaining in the problem to be 
 solved. (The constant mentioned above as expressing the effect of the 
 resistance due to the roughness of the inside of the drain is an ex- 
 ample.) Great care must be exercised in choosing the values of these 
 constants in order that the values which are truly applicable be used. 
 
 Several different formulas are used, by drainage engineers in Iowa, 
 for computing the capacities of tile drains. However, as only two of 
 these are in general use, only these two will be discussed here. Any 
 one wishing to study other formulas can find them stated and ex- 
 plained in published works on hydraulics. 
 
 Ratter's Formula: Probably the most widely used and most reliable 
 formula for calculating the flow in tile drains is a combination of the 
 simple basic formula proposed by Chezy and the more complex for- 
 mula proposed by Kutter and Ganguilet for determining the value of 
 the constant in the Chezy Formula. This combination is usually 
 spoken of simply as Kutter's formula. Some new formulas for the 
 flow in circular channels have been derived and found to be more 
 satisfactory than Kutter's formula for the particular cases studied. 
 As yet no new formulas especially adapted to the calculation of flows 
 in tile drains have been published. Kutter's formula is probably ac- 
 cepted as the most accurate one available in a very great majority of 
 such hydraulic problems. 
 
 Chezy's Formula is : 
 
 V=CVr^ 
 where V=the velocity in feet per second, 
 
 C=a constant, depending primarily, on the resistance to flow 
 
 from different causes, 
 r=the mean hydraulic radius, 
 s=the hydraulic slope or grade. 
 
48 
 
 The constant in this formula was determined by Kutter and 
 Ganguilet to be : 
 
 .00281 1.811 
 41.6 + + 
 
 C= 
 
 .00281 
 (41.6+ )n 
 
 1 
 
 where s=the hydraulic slope, 
 
 n=the coefficient of roughness, 
 r=the mean hydraulic radius. 
 
 The mean hydraulic radius, r, is determined by dividing the area 
 of the cross-section of the flow by the area of the wet perimeter per 
 unit length of channel. In circular pipes flowing full, r equals one- 
 fourth the internal diameter. 
 
 The value of the "coefficient of roughness," n, varies from .010 for 
 very smooth continuous pipe to .020, or even more, for poorly con- 
 structed drains. The best available information and the best drainage 
 practice favors the use of a value of .015 for the coefficient of rough- 
 ness of average good tile drains. 
 
 In Table XI is given summary of the results obtained in an in- 
 vestigation of the value of "n" for several Iowa drains. These data 
 were collected in 1909 by Messrs. Rightmire and Chappel as a thesis, 
 the work being done under the direction of the Iowa Engineering Ex- 
 periment Station. The data given below are taken from the complete 
 report of these investigations given in the Engineering Experiment 
 Station Bulletin, Vol. IV, No. IV. 
 
 In these investigations the discharge from the drain being investi- 
 gated was measured by means of a weir. The hydraulic slope and 
 depth of flow were determined for five consecutive stations of about 
 equal length. With these data the value of "n" for each station was 
 computed, and the average of these taken as the value for the drain. 
 
 TABLE XI. 
 THE COEFFICIENT OF ROUGHNESS IN AVERAGE IOWA DRAINS. 
 
 Size Material "n" Character of Grade Depth of Flow 
 
 2'x32" Cement .01504 Irregular 23y 2 " to 24 1-3" 
 
 2'x24" Cement .01638 .01% to .09%, irreg. V 2 " to 2%" 
 
 2'x20" Cement .01146 Regular 7%"to9%" 
 
 2'xl8" Clay, hard burned .01172 .3% to .6%, regular 4" to 7%'' 
 
 2'xl4" Clay, hard burned .01525 1% to 2%, irreg. 1%" to 3" 
 
 l'xl2" Clay, hard burned .01683 .15% to 1.1%, irreg. 1 X A" to 2%'< 
 1'xlO" Clay .0164 1.2% to 1.7%, fairly 
 
 irregular % to 1' 
 
 These data are too few to be conclusive, but they seem to bear out 
 the use of the value of .015 for "n" with well laid Iowa drains. It is 
 
49 
 
 quite certain that this value of "n" is too large for some very care- 
 fully constructed drains, but in such cases the error is not large and 
 is on the side of safety. As far as is shown by the above data, the 
 or 1 ' variation of "n" is with the regularity of the grade and possibly 
 n the length of the individual tile, as the number of joints is in- 
 ... ased with shorter tile. 
 
 Use of Mutter's Formula: In actual use of this formula the value 
 of the constant "C" is not computed, but is taken from either a dia- 
 gram or from tables. Having the value of "C" the velocity is easily 
 computed, or taken from a table, and from it the discharge determined. 
 Tables and Diagrams giving the values of "C" for different slopes 
 and depths of flow are given in many texts and handbooks, so are 
 not repeated here. Trautwine's "Civil Engineer's Pocket Book" gives 
 very complete data of this kind. 
 
 Another method of simplifying the use of this formula is by means 
 of diagrams, or curves, which show the discharges for various sizes of 
 drains at various slopes. These diagrams can be prepared for any 
 shaped channel with any depth of flow at any slope, and for any de- 
 gree of roughness as indicated by the coefficient "n." Such a dia- 
 gram for tile drains from 4 inches to 48 inches in diameter flowing 
 full at hydraulic grades of from 0.02 feet to 5.0 feet per 100 feet, when 
 "in" equals .015, is given as Fig. 8. At the right of the diagram has 
 been added a scale showing the number of acres drained, at different 
 rates of runoff, for different discharges in cubic feet per second. This 
 diagram is as accurate as is possible considering the probable errors 
 of plotting and reading the curves. Any engineer desiring to use 
 such a diagram in his work should prepare one to a larger scale on 
 mounted paper which is not subject to great change under different 
 temperature and humidity conditions. 
 
 In preparing these diagrams it is preferable to plot them to a 
 logarithmic scale, as this gives a straight line for the discharge for 
 each size of tile. In this way the diagram may be prepared by plot- 
 ting the discharge for each size of tile at three grades and then con- 
 necting these points with straight lines. The scales at the right of the 
 diagram are prepared simply by platting the number of acres 
 drained at different rates of runoff opposite the equivalent discharge 
 in cubic feet per second. 
 
 This use of the diagram may be explained by two examples : 
 
 1. What is the discharge from a 15 inch drain at a grade of 0.20% 
 or 0.20 feet per 100 feet? Follow up the vertical line from the notation 
 0.20 at the bottom of the diagram till this line intersects the dis- 
 charge line for 15 inch tile and then across horizontally to the scale 
 at the left, where the result is found to be approximately 2.28 cubic 
 feet per second. 
 
 2. What size of tile, laid at a .015% grade, will be required to 
 drain 500 acres at a j^-inch runoff? Follow up the vertical line repre- 
 senting a grade of .015% till this intersects the horizontal line from 
 
Discharge in Cubic Feet per Second 
 
 $ § SS § 
 
 1 ' ' ' | ■ ■ ' ' | 'I I I | I I I I | I I I I | I I I I | II I I | — I | I | I | I | I | I I I I | | I I I | I I I l | II M | I I II 
 
 ,,*,* ,, 5 § g § §■ g § 8 8 § 8 I 8 § 8 
 
 ' ' ' ' ' ' ' ' l I ! I | i i i i | I I I I | ii I I 1 1 1 i i| — | | I j I | i | i | r t i i | i i i i | 1 1 i i [ 1 1 n [ i i M 
 
 2 ° ° ooooooo o 855 
 
c 
 > 
 
 sg 
 
 H fD 
 
50 
 
 500 acres at a ^-inch runoff on the scale at the right. This intersec- 
 tion shows that a 24 inch tile is slightly too small and a 26 inch tile 
 too large. The engineer must use his judgment in deciding between 
 these two sizes, though in a case of this kind, it is often better to 
 have drains too large rather than too small. In designing a drainage 
 system all drains should be designed to have the required capacity 
 when the hydraulic grade is parallel to the constructed grade, or 
 when flowing full but under no head other than that afforded by the 
 slope of the drain. If this is done, the drain will have extra capacity 
 for the flow from unusual storms and spring freshets when the water 
 will be backed up at the upper end of the drain causing a steeper 
 hydraulic slope. Another reason for not designing the drain to work 
 under extra head is that the pressure will often cause water to pass 
 cut through cracked tile and wash or soften the earth so as to allow 
 these cracked tile to spread and collapse. 
 
 Poncelefs Formula and Elliott's Modifications: The other formula, 
 or rather a set of formulas, in general use among Iowa drainage engi- 
 neers is termed, very often incorrectly, Elliott's formula. This set of 
 four formulas proposed by Mr. C. G. Elliott, formerly chief of Drain- 
 age Investigations, U. S. Department of Agriculture, consists of Pon- 
 celet's formula and three modifications suggested by Mr. Elliott. 
 
 Poncelet's Formula: 
 
 /d h 
 
 v = 48 V an d Q — av 
 
 1 + 54 d 
 
 where v=the velocity in feet per second, 
 
 d = the inside diameter of the tile in feet, 
 
 h = the head, or difference in elevation between the outlet and 
 
 the upper end, in feet, 
 l=length of the drain considered, in feet, 
 a = the area of the cross-section of the flow in square feet, 
 Q=the flow in cubic feet per second. 
 
 In order to give consideration to some other factors Mr. Elliott 
 suggested three modifications of Poncelet's formula, each of the four 
 to be used under certain conditions. He first introduced a factor "k." 
 or fractional part of "k." This factor represents the depth of earth 
 over the upper end of the drain. If the soil is loose and becomes sat- 
 urated the water therein was taken as creating an additional "head" 
 which would increase the flow through the drain. In loose soil he 
 recommended that "dh" be increased by J / 2 "k." 
 
 Another factor which he considered as increasing the capacity of 
 the drain is the increase in velocity which may be caused by the num- 
 ber and grades of the submains. In order to take this into account 
 further modification is suggested by replacing "h" by "the quantity." 
 
51 
 
 h + - 
 
 n 
 in which h = the head, in Poncelet's formula, 
 
 b == the sum of the amounts of the excess head in the sub- 
 mains, 
 
 n = the number of submains. 
 
 The amount of excess head in each submain is the difference be- 
 tween the head on it and that for a like length of the main. 
 
 Mr. Elliott recommends the uses of these four formulas as follows : 
 
 Poncelet's formula: 
 
 v = 48 V 
 
 / dh 
 
 for use in small systems in close soil and, 
 
 l-(-54d as a general rule, for outlet mains. 
 Elliott's modifications 
 
 v = 48 V 
 
 /dh + y 2 k 
 l+54d 
 
 for use in systems where soil is open. 
 
 / b 
 
 /d(h+-) 
 48 V n 
 
 for use in large systems in close soil. 
 
 l + 54d 
 
 and v 
 
 / b 
 
 /d(h+-)+/ 2 k 
 48 V n for use in large systems in open soil. 
 
 l+54d 
 
 Trawtwine's "Engineer's Pocket Book" recommends that for 
 pipes larger than 12 inches in diameter the following numbers be 
 used instead of the constant 48: 
 
 For 18 inch pipe, coefficient, 53 
 
 24 ' 
 
 ia t 
 
 57 
 
 30 ' 
 
 ( n i 
 
 60 
 
 36 ' 
 
 ( (t c 
 
 62 
 
 42 ' 
 
 I 11 I 
 
 64 
 
 48 ' 
 
 ( (C t 
 
 66 
 
 60 ' 
 
 its I 
 
 68 
 
 Use of "Elliott's" Formula: The use of either of these formulas may 
 be simplified by the preparation of tables or diagrams showing the 
 
52 
 
 discharge in cubic feet per second, or the acres served at a given rate 
 of runoff, by various sizes of drains at different grades. A separate 
 discharge table must be prepared for each formula. A separate "acres- 
 drained" table must be prepared for each formula and each rate of 
 runoff used. 
 
 The general discussions as to the use of Kutter's formula apply 
 equally when either of these formulas is used. 
 
 33. Advantages of Each of the Two Formulas: Hydrologists 
 quite generally consider Kutter's formula more accurate than Ponce- 
 let's for calculating the flow through pipes. Authorities on sewer de- 
 sign generally consider that the flow through a sewer is given more 
 accurately by Kutter's formula than by Poncelet's ; practically all texts 
 on sewer design recommend the use of either Kutter's formula, with a 
 value of .015 for "n" for pipe sewers, or of some form of exponential 
 formula which has been especially adapted to sewer design. 
 
 The accuracy of Elliott's modifications of Poncelet's formula is 
 often questioned on the ground that they are based on unsound prem- 
 ises. It is probably true that under certain extreme conditions, the 
 soil above the drain may become so saturated that the water in this 
 soil would tend to increase the head on the drain. This condition 
 would not obtain, however, if the drains had the capacity to remove 
 the water as rapidly as it passed through the soil to them. No water 
 which is flowing has any actual head upon it unless the drain is sur- 
 charged ; up to the capacity of the drain, all static head is converted 
 into velocity head or used in overcoming frictional resistance. In other 
 words, it would seem that the premise on which Elliott's first modi- 
 fication is based could be true only when the water is moving through 
 the soil to the drain more rapidly than it can flow away through the 
 drain. 
 
 Elliott's second modification is made to care for an increase in 
 velocity due to the fact that the submains have a steeper grade than 
 the main. This case is very similar to that just discussed except that, 
 when the velocity in the submain is greater than through the main, 
 this excess in velocity is converted into static head when the flow 
 passes into the main. The extra head so created would, however, be 
 small, and it is difficult to see how the velocity in the main will be 
 increased materially by that of the submains so long as the main has 
 sufficient capacity to care for all the flow entering it without backing 
 water up in the submains. 
 
 The use of tables and diagrams makes these two formulas (Kut- 
 ter's and Poncelet's) equally easy to use. Familiarity with the tables 
 or diagrams of either enables the engineer to use either speedily and 
 accurately. It is obvious that if the capacities are to be determined 
 by solving the complete formula in each calculation, either of Elliott's 
 formulas can be used with much less tedious labor than Kutter's. 
 
 For small tile Elliott's basic formula (Poncelet's) gives larger 
 capacities than Kutter's ; the difference in the results by the two 
 
53 
 
 formulas decreases as the size of tile increases so that for 20 inch or 
 24 inch tile they give very approximately the same result; for the 
 larger sizes there is little difference, comparatively, though Kutter's 
 formula gives the slightly larger capacities. The fact that Elliott's 
 formulas allow the use of smaller sizes of tile, within the range of 
 sizes common to farm tile systems, than Kutter's is an argument 
 against them as the sizes used in such systems are too small much 
 more often than they are too large. 
 
 VII. RESULTS OF UNDERDRAINAGE. 
 
 The results, or effects, of underdrainage may be divided into the 
 three classes ; financial, physical and general. However, any such 
 classification must be quite elastic, as the financial and general results 
 are due either directly or indirectly, to the physical changes brought 
 about by the construction and operation of the underdrainage system. 
 On the other hand, the resulting financial gain or loss is usually the 
 most apparent result of the prosecution of the drainage work. 
 
 34. Financial Results : The financial returns from any drainage 
 improvement work will usually be taken as a measure of the success 
 of the work. Probably the only exception to this is found in the com- 
 paratively rare cases where the drainage is resorted to as a means of 
 protecting the health of the community and for no other purposed 
 Even in such cases, the probable value of the reclaimed land is usually 
 given serious consideration before the work is started. 
 
 When a drainage improvement is proposed the owner of each 
 parcel of land to be affected by the proposed drain will ask himself 
 the question, "How and to what extent will this drain benefit me?" 
 The direct results of the construction of the drainage system will be 
 changes in the physical condition of the lands drained. Certain of 
 these physical changes will afford the landowner a financial gain. 
 
 The removal of the surplus water from a piece of wet lartd will 
 change this tract from an unproductive to a productive area. By rea- 
 son of this change the actual sale value of this land will be increased 
 in proportion to its increase in productiveness. 
 
 This increased productiveness will make possible a direct financial 
 gain in the greater value of the crops raised. Proper drainage will 
 make the cultivation less difficult, thus making the cost of producing 
 the large crop less than that of raising the small crop. 
 
 Another, though smaller, financial gain from proper drainage re- 
 sults from the lessened cost of transporting the farm produce to a 
 market or shipping point. It is a well proven fact that good and 
 economical highway construction must be preceded by drainage. The 
 removal of the surface water by open ditches is no more important 
 in this respect than the removal of the surplus ground water so as to 
 provide a firm foundation for the roadway. The cost of hauling the 
 farm crops over a good highway is much less than that of hauling 
 
54 
 
 this same crop over a poorly constructed and poorly maintained road. 
 If improper drainage works are constructed, the financial results 
 will be smaller or may even constitute a loss. If the conditions are 
 not improved by the construction of the drain or drains, the cost of 
 the work and the loss of the benefits which would have resulted had 
 the work been properly designed and constructed will constitute no 
 small loss. 
 
 35. Physical Results: The direct effects of underdrainage are 
 the physical changes which are due to the operation of the drains. 
 The most important of these physical changes are those which take 
 place within the soil, the character and mechanical composition of an 
 ever-wet or water logged soil being completely changed by under- 
 drainage. It is significant that all the physical changes resulting from 
 underdrainage are classed as benefits by agriculturists and that many 
 of these are due wholly or in part to actions which take place when 
 the surplus soil moisture is removed. 
 
 The following short discussion of the effects of underdrainage is 
 but a recapitulation and application of the discussions given in the 
 earlier sections of this bulletin. 
 
 1. Improves the Physical Character or Mechanical Composition of 
 the Soil: Underdrainage aids greatly in the formation of soil granules. 
 The granular structure is particularly desirable in fine grained soils, 
 as they then have the desirable properties of coarser grained soil in 
 permitting of the rapid passage of moisture and air. One of the im- 
 portant factors in soil granulation is alternate wetting and drying. 
 
 When a soil is saturated the soil grains are held apart, and partially 
 floated, by the water. In addition to this, the water acts as a lubri- 
 cant so that the soil will not support the weights necessary in culti- 
 vation. When the soil is saturated continually the soil granules are 
 broken down and the smaller grains move into the spaces between 
 the larger ones. In this condition the soil becomes almost a compact 
 mass and is termed puddled. Underdrainage prevents puddling. 
 
 These actions and conditions are often expressed by saying that 
 underdrainage makes the soil more loose, more open or more mellow, 
 and that standing water, or saturation, packs it. These are but dif- 
 ferent methods of expressing the conditions discussed above. 
 
 2. Improves the Aeration: Many agriculturists hold that the physi- 
 cal changes which cause a more rapid and greater passage of air 
 through the soil is the largest single benefit of underdrainage in that 
 thorough aeration is one of the most important factors in crop pro- 
 duction, in so far as this depends upon the condition of the soil. Un- 
 derdrainage improves the aeration in two ways ; it removes the sur- 
 plus, or gravitational moisture, thus leaving the soil pores open for the 
 passage of air; and promotes soil granulation, thus providing larger 
 channels for the circulation of air. 
 
55 
 
 3. Increases the Supply of Available Plant Food and Moisture: This 
 is probably the most important effect of underdrainage upon the soil, 
 but it was not taken up till now because of its dependence upon (1) 
 and (2). This effect is due to several actions, all resulting- from the 
 drainage, the most important of which will be mentioned. 
 
 It has been explained that plant roots take up food that is in solu- 
 tion in soil moisture ; that they can take up this moisture only when 
 it occurs in the soil as capillary moisture ; and that the capillary mois- 
 ture is present only after the surplus, or gravitational, moisture has 
 been removed. This chain of facts makes it at once apparent how 
 underdrainage may increase the available supply of plant food. Un- 
 derdrainage lowers the plane of saturation, thus making available the 
 food supply of a larger volume of soil. 
 
 By causing the formation of granules, the underdrainage increases 
 the amount of capillary moisture and thus increases the food supply. 
 
 Underdrainage improves aeration which in turn causes the forma- 
 tion of additional plant food in the soil. 
 
 Underdrainage promotes the growth of the desirable forms of soil 
 organisms and retards the growth of the undesirable forms. If the 
 soil is saturated, the products of these organisms are held in the soil 
 causing the destruction of all organisms. These desirable organisms 
 increase the amount of plant food in the soil. 
 
 Underdrainage increases the supply of plant food through chemical 
 changes which are dependent upon this moisture condition. 
 
 It has already been explained that underdrainage causes certain 
 changes in the physical character of the soil and thus increases the 
 maximum content of available or capillary moisture. This explains 
 why crops in a thoroughly drained field withstand drouth better than 
 those in a similar undrained field. Underdrainage increases the sup- 
 ply of available plant moisture by removing the injurious surplus 
 gravitational moisture from a wet soil and by causing physical changes 
 in the soil that result in the storage of an increased supply of avail- 
 able moisture in the soil after this surplus has been removed. 
 
 The benefits of underdrainage in increasing the supply of plant 
 food and moisture are well illustrated by Fig. 9. The measurements 
 from which this diagram was prepared were taken at the foot of a 
 slope where possibly seep water was present. It will be noticed that 
 the stalks of corn grew much stronger directly over the lines of tile 
 where the drainage was most thorough. 
 
 4. Raises the Average Temperature: The specific heat of water is 
 much higher than that of soil. The greater the proportion of water a 
 soil contains the more heat is required to raise the temperature of the 
 sample a given amount. The continual evaporation from the surface 
 of a wet soil reduces the temperature or retards the increase in tem- 
 perature. The heat applied to a given soil area is fairly constant, so 
 that if this heat must be used up in evaporating water the temperature 
 of the soil body is not raised. 
 
56 
 
 Drainage removes the excess water from the soil, reducing- the heat 
 required for evaporation and causing the soil body to warm up more 
 readily. As a result of this, a drained soil warms up much earlier in 
 the spring, and so lengthens the growing season. This enables the 
 farmer to start his spring work earlier, which is especially valuable 
 
 Fig. 9. Diagram Showing the Effects of Drainage Upon the Height of Corn at 
 Hanford, Cerro Gordo County, Iowa, October, 1910. 
 
 in a so-called "backward" spring. The growth of the crop upon 
 drained land is greatly benefited by the high temperature that pre- 
 vails here in the spring and fall. Investigators have found that at a 
 depth of seven or eight inches a drained soil is from 12° to 15° warmer 
 than an undrained soil of the same nature and in the same climate. 
 
 5. Reduces Heaving: It is often noted that posts have been raised 
 out of the ground during the winter. This heaving is due to the freez- 
 ing of a wet soil. When water freezes it expands one-eleventh of its 
 volume and in a saturated soil this expansion must be upward, the 
 amount of the heaving depending upon the amount of water in the 
 soil and the depth to which it is frozen. This same action tends to 
 raise the roots of certain crops out of the ground, as the soil settles 
 back after thawing, more rapidly than the plant root. This heaving 
 also breaks many of the small roots. 
 
 6. Reduces Erosion: In an undrained area all of the rainfall must 
 either be absorbed by the soil or pass away over the surface. In a 
 continued rainy season the soil soon becomes saturated after which 
 all the rainfall must flow away over the surface. The particles of the 
 saturated soil are easily displaced and carried away by the water. 
 
 In an underdrained area the soil has a greater water capacity and 
 allows of a continual removal of the surplus water by the drains. 
 This greatly reduces the amount of water which must pass away 
 over the surface and thus reduces erosion. Underdrainage of slopes 
 will often prove a profitable investment if installed for no purpose 
 other than reducing or preventing erosion. 
 
 36. General Results: Those results of the physical changes 
 brought about by drainage, to which cannot be readily assigned a 
 
57 
 
 monetary value, are termed general benefits. In the well drained 
 section the better highways allow of more, easier, and more rapid 
 travel. The benefits of this in a social way are no small matter. The 
 rural mail service demands better highways than are usually possible 
 without both open channels and underdrainage in many sections. The 
 consolidated school depends upon the possibility of transporting the 
 children to and from school, and this in turn depends upon good roads. 
 The appearances and generally better financial condition in the well 
 drained territory add to the value of the farm. The sanitary condition 
 in wet or swamp areas are bettered materially by both open ditches 
 and underdrainage. 
 
LIBRARY OF CONGRESS 
 
 000 936 716 
 
 The College 
 
 The Iowa State College of Agriculture and Mechanic Arts con- 
 ducts its work along five major lines : 
 
 Agriculture 
 
 Engineering 
 
 Home Economics 
 
 Industrial Science 
 
 Veterinary Medicine 
 
 The Graduate Division conducts advanced research and in- 
 struction in all these five lines. 
 
 Four, five and six-year collegiate courses are offered in differ- 
 ent divisions of the College. Non-collegiate courses are offered 
 in agriculture, engineering and home economics. Summer Ses- 
 sions include graduate, collegiate and non-collegiate work. Short 
 courses are offered in the winter. 
 
 Extension courses are conducted at various points throughout 
 the state. 
 
 Research work is conducted in the Agricultural and Engi- 
 neering Experiment Stations and in the Veterinary Research 
 Laboratory. 
 
 Special announcements of the different branches of the work 
 are supplied, free of charge, on application. The general cata- 
 logue will be sent on request. 
 
 Address The Registrar, 
 
 Ames, Iowa.