:|/,,.^':';^:i;-'i^p^^ ■m/mmm^mi Class. Book._ Coipghtl^?_ '-'^ caazmiGHT DEPosm ^•.«>;*>-Xi> V .■^' \ X r^. NEW YORK BELTING & PACKING CO. 124-126 WEST LAKE STREET CHICAGO 1 NEW YORK BELTING & PACKING CO. 218-220 CHESTNUT STREET ST. LOI.TIS ^ Hliwj m ' I'V '' w i ^ ^^& '^^ 1 i ^ ''ji np Nl " ■ 1 V K ni:j , ,_| p " i 1 M i fi ■ m m ?'" ■M] .1 i i \ n 1 1 ;i "'■;! ■ 1 ^K^ Ir -1*^15' '1 1 'd k flUUMWift'- ' JI '\ . !■■. J Ins: h\ A MANUAL STEAM ENGINEERING COMPRISING Instructions, Suggestions and Illustrations FOR Progressive Steam Engineers, Concerning the Application to Modern Daily Practice of THE Approved Theory of Steam Engineering W. H. WAKEMAN AUTHOR OF "engineering practice and theory" "practical guide for firemen" AND numerous ARTICLES FOR THE MECHANICAL PRESS New York Belting & Packing Company 91-93 Chambers St., New York 124-126 West Lake St., Chicago 218-220 Chestnut St., St. Louis 821-823 Arch St., Philadelphia 519 Mission St., San Francisco 65 Pearl St., Boston 420 First A^e., Pittsburgh ^' \ Copyright, 1920 New York Belting anp Packing Company ^ i St? -B "^^ ©CI,A576279 f IL PREFACE Ca) ' I "^HE object sought in presenting this volume to steam engineers and others interested in steam engineering is to provide a convenient and reliable reference book, containing data wanted in every-day practice, arranged in con- venient form, with sufficient explana- tion to render the matter both interest- ing and instructive. It contains many tables, which are arranged for use in connection with the reading matter on the same subject, thus condensing information into con- venient space, and rendering it available for the busy workers. That the work will prove satisfactory to readers for whom it is intended is the sincere wish of THE AUTHOR DEDICATION 'npO the intelligent men who design, construct and operate the steam machinery of this country, keeping it in repair imder a great variety of con- ditions, and securing the best results in practice from every part of both compli- cated and simple plants, this book is respectfully dedicated by THE AUTHOR. SECTION 1 BOILERS STRENGTH OF STEAM BOILERS A N erroneous idea concerning the strength of steam boilers prevails among some of the men who are em- ployed in steam plants, which is well illustrated by their answers to the follow- ing question: "Suppose that two boilers are made of the same material, with riv- eted joints of equal strength, and are alike in every respect, except that one is 48 inches and the other 72 inches in di- ameter. On which of them will it be safe to carry the higher pressure?" Many of the men to whom this ques- tion is referred reply that the larger one will safely carry the higher pressure, and the reason for this is found in the fact that to those who have not intelli- gently studied the subject the larger a boiler is, the greater its strength appears to be, which is a mistake as the following lines fully explain. While pressure acts on every inch of the circumference of a boiler shell, it operates exactly as if it pressed upon a space equal to the diameter, therefore if the shell is 72 inches in diameter and the pressure is 100 pounds per square inch, 2 STEAM ENGINEERING the force which acts to rupture the shell is equal to the diameter multiplieq by the pressure and 72X100 = 7,200 pounds. If we draw a circle represent^ ing an end view of the shell, and the: draw a straight line dividing it into twd equal parts it will be plain that the strain is supported by the two sides of the shellJ therefore each must sustain a load equa] to 7,200 -=-2 =3,600 pounds. If the shell is but 48 inches in diam-i eter the total load is 48X100 = 4,80C[ pounds, or 2,400 pounds on each side! The pressure required to produce a loaq equal to that carried on each side of tha 72 inch shell is found by dividing 3,60(1 by one-half of the diameter of the boilei in question. In this case it is 3,600^-1 24 = 150 pounds, thus plainly demonJ strating that with 100 pounds on the 72 inch shell anl 150 on the 48 inch, thq loads are equal. The iron and steel plates of whicti boiler shells are made, vary in strength^ hence it becomes necessary to know ho-w much stress can be safely put on thd plates to be used. This can only be determined by pulling a sample of it apart in a testing machine and noting the strain in pounds that was required to break it. If the plate is .5 inch thick and we take a strip 1 inch wide, it might require 30,000 pounds or more to part it, and although it is quite possible to do this it is better to adopt a plan whereby much less strain will answer the same purpose. If a piece of this plate 1 inch wide is forged down until it is .3 inch thick, its area will be 1X.3 = .3 square inch, and if pulled apart the strain required to do it may be 16,611 pounds. Divid- ing the strain required by the area of the test piece where it fractured, gives the tensile strength of the plate in pounds per square inch of section. In this case it is 16,611 -^ .3 = 55,370 pounds. When calculating the strength of a boiler, it is necessary to take into ac- count the thickness of the shell, as its strength will vary directly with its thick- ness. For this calculation it is cus- tomary to take a strip of the shell 1 inch wide following the entire circumference, determine its strength and assume that all other parts are equally strong. In order to be on the safe side, it is necessary to take this strip from the most unfavorable location, as the strength of any structure is determined by the strain that can be safely carried by the weakest part. In some parts of the shell holes are cut for steam nozzles and other purposes, therefore if the strip found in or near the middle of such a place should be 4 STEAM ENGINEERING taken without qualification it would possess no strength at all, as it is cut in two, but in all well made boilers these places are strengthened by reinforcing rings, or by special flanging. The above explanation makes it plain that if a strip 1 inch wide is cut from a sheet .5 inch thick, with a tensile strength of 55,370 pounds, its ultimate strength is 55,370 X. 5 = 27,685 pounds. The riveted joint in the shell of a steam boiler can never be as strong as the solid plate, and as calculations for determining the comparative strength of joints require full explanation, it is here assumed that the design of joint gives .75 of the strength of the solid plate. Taking this into account we find that the strip 1 inch wide has strength equal to 55,370 X. 5 X. 75 =20,763 pounds. Again referring to the circle with a straight line drawn through the center of it, showing that the above calculation gives the strength of one side only, it is plain that we must calculate on one- half of the diameter. For a 72 inch boiler this is 36 inches, and 20,763^36 = 576 pounds, which is the pressure per square inch required to rupture this shell. As a large margin must be assumed for safety, a factor of 5 will be allowed, or in other words one- fifth of the bursting pressure will be taken as the safe working pressure, and 576-^5 = 115, showing that it is safe to carry 115 pounds on such a boiler. This explanation will make clear the following rule for determining the safe working pressure of steam boilers. Multiply the tensile strength of the plate in pounds per square inch, by its thickness in decimals of an inch, and by the comparative strength of the riveted joint. Divide by one-half of the diam- ater in inches, and the quotient is the bursting pressure. Divide this by the factor of safety (for which 5 is recom- mended), and the final quotient is the safe working pressure. This rule is fully explained in order that the reader may clearly understand the principles involved, and if results secured by it differ from other cases, the cause of difference may be plainly seen. The following table gives the safe working pressures of boilers from 42 to 84 inches in diameter, with plates of suitable thickness, the tensile strength of which is stated. The table is^based on the foregoing rule. STEAM ENGINEERING DIAMETER OF SHELL 42 INCHES FACTOR OF SAFETY 5 Tensile strength Tensile strength Tensile strength 50.000 pounds 55,000 pounds 60,000 pounds 1. k .•St tic 2i H^ C/3 O w a Ho C/3 O CO a Ho W o w a 25 .60 71 .25 60 78 .25 .60 85 8125 .60 89 .3125 .60 98 .3125 .60 107 375 .70 125 .375 70 137 .375 .70 150 4375 .75 156 .4375 .75 171 .4375 .75 187 5 .75 178 .5 .75 196 .5 .75 214 DIAMETER OF SHELL 48 INCHES FACTOR OF SAFETY 5 25 .60 61 .25 .60 69 .25 60 3125 .60 78 .3125 .60 86 .3125 .60 375 .70 109 .375 70 120 .375 70 4375 .75 136 .4375 .75 150 .4375 .75 5 .75 156 .5 .75 172 .5 .75 DIAMETER OF SHELL 54 INCHES FACTOR OF SAFETY 5 25 .60 56 ,25 .60 61 .25 60 3125 .60 69 .3125 .60 76 .3125 .60 375 .70 97 .375 .70 107 .375 .70 4375 .75 121 .4375 .75 134 .4375 .75 5 .75 139 .5 .75 153 .5 .75 DIAMETER OF SHELL 60 INCHES FACTOR OF SAFETY 5 .3125 .65 68 .3125 .65 74 .3125 .65 81 .375 .70 87 .375 .70 96 .375 .70 105 .4375 .75 109 .4375 .75 120 .4375 .75 130 ,5 .75 125 5 .75 137 .5 .75 150 .5625 .80 150 .5625 .80 165 .5625 .80 180 DIAMETER OF SHELL 66 INCHES FACTOR OF SAFETY 5 Tensile strength Tensile strength Tensile strength 50,000 pounds 55,000 pounds 60,000 pounds .5 a 1 ^1 2,^ tt 3 W o CO a H o CO O CO a Ho CO o CO a .3125 .65 61 .3125 .65 68 .3125 .65 74 .375 .70 79 .375 .70 87 .375 .70 95 .4375 .75 100 .4375 .75 109 .4375 .75 119 .6 .75 113 .5 .75 125 .5 .75 136 .5625 .SO 136 .5625 .80 150 .5625 .80 164 DIAMETER OF SHELL 72 INCHES FACTOR OF SAFETY 5 375 .70 73 .375 .70 80 .375 .70 4375 .70 85 .4375 .70 93 .4375 .70 5 .75 104 .5 .75 115 .5 .75 5625 .75 117 .5625 .75 129 .5625 .75 625 80 140 .625 .80 153 .625 .80 87 102 125 141 166 DIAMETER OF SHELL 78 INCHES. FACTOR OF SAFETY 5 375 .70 67 .375 70 74 .375 .70 4375 .70 78 .4375 .70 86 .4375 .70 5 .75 96 .5 .75 105 .5 .75 5625 .75 108 .5625 ,75 119 .5625 .75 625 .80 128 .625 .80 141 .625 .80 81 94 115 130 154 DIAMETER OF SHELL 84 INCHES .375 .4375 .5525 .625 FACTOR OF SAFETY 5 .70 62 .375 .70 68 .375 .70 .75 78 .4375 75 86 .4375 .75 ,75 89 5 .75 98 .5 .75 .80 107 5625 .80 118 .5625 .80 .85 126 625 .85 139 .625 .85 75 94 107 128 152 8 STEAM ENGINEERING As the thickness of boiler plates is frequently stated in sixteenths of an inch, the following table will enable the reader to convert it into decimal fractions without calculation. 146=. 0625 5^=. 125 3^6=. 1875 K=.25 %e=.3125 »A«=.5625 H=.375 %=.625 %e=. 43751 H/46=. 6875 ^=.5 %=.75 iS/ia=.8l26 ^=.875 i%o=.9375 1= 1000 RULES FOR USING DECIMAL FRACTIONS ADDITION Write down the numbers to be added SO that each decimal point (after the first) , will be directly tinder the preced- ing, and proceed to add as with whole numbers. Example. Proof. 17.87 .096 .096 41.69 3.7 17.87 41.69 3.7 63.356 63.356 If the same sum is obtained when the numbers to be added are located in dif- ferent positions, it is evidence that the result is correct. SUBTRACTION Set down the minuend, or larger number, and locate the subtrahend, or smaller number so that one decimal point will be directly under the other, and proceed as with whole numbers. Example. 107.8672 93.7526 14.1146 Proof. 93.7526 14.1146 107.8672 MULTIPLICATION Proceed as with whole numbers and point off as many decimals as there are in the multiplicand and multiplier, or the first and second numbers added together. Example. Proof. .375 .375).23250(.62 .62 2250 750 750 2250 750 .23250 DIVISION Divide the dividend by the divisor as with whole numbers, then point off as many decimals in the quotient or answer as those in the dividend exceed those in the divisor. Example. Proof. .235).43750(1.86 .235 235 1.86 2025 1410 1880 1880 1450 235 1410 40 40 .43750 A 10 STEAM ENGINEERING In all cases where there are not enough figures in the answer to provide the required number of decimal places, ciphers must be added at the left hand until enough are secured. Every cipher added at the left hand reduces the value of the fraction, but when added at the right hand for con- venience, they do not affect the result. THE UNITED STATES GOVERNMENT RULE FOR SAFE PRESSURES Many engineers prefer to use this rule especially where they desire to carry as much pressure on their boilers as they can find authority for, and this idea is correct provided the rule is used in an intelligent manner. This rule is as follows : Multiply one-sixth of the tensile strength by the thickness of plate and divide by one-half of the diameter, for single riveted seams. For double riv- eted seams add 20 per cent. A very common error when consider- ing this rule is to conclude that a factor of safety of 6 is used, but this is not the case, because one-sixth of the strength of the whole plate before it is punched, or drilled, is taken, and as the riveted seams are not as strong as the full plate the difference between the two operate 11 to reduce the factor of safety. For illustration of this point, see the follow- ing example: Selecting from the foregoing table a boiler 72 inches in diameter made of plates .5 inch thick whose tensile strength is 60,000 pounds, with a double riveted joint that has 75 per cent, of the strength of the solid plate, the safe pres- sure is 125 pounds. As the factor of safety is 5, the bursting pressure is 125 X5 = 625 pounds. Applying the U. S. Government rule to the above case gives the following result : (60,000 ^6) X.5 4- (72 ^2) =139, and adding 20 per cent, brings the result up to 166 pounds for a safe pressure. Dividing the bursting pressure by the latter, shows that the real factor of safety is 625 -f- 166 =3.76 although the apparent factor is 6. From the foregoing it will be plain that the U. S. Government rule does not take into consideration the varying strength of riveted joints of different designs, except that in all cases a double riveted joint is 20 per cent, stronger than the single riveted design. It is quite possible to design a single riveted joint that is stronger than another having two rows of rivets, but the U. S. Gov- ernment rule taken as a whole is not so 12 STEAM ENGINEERING short and simple as it appears, for it includes directions for making riveted joints that are strong and durable, there- fore the only mistake made along this line is when careless engineers or igno- rant steam users apply the rule to cases where infetior joints have been made by mcompetent boiler makers, but it was never intended for such applications. The following table has been prepared for the benefit of those who prefer this rule, but it should be remembered that every single riveted joint to which the table refers must contain 60 per cent, of the strength=of-the solid plate, and every double riveted joint must have 75 per cent, of it. Furthermore the factor of safety averages about 3.5. For these conditions the following safe pressures are allowed. DIAMETER OF SHELL 42 INCHES Tensile Tensile Tensile strength strength strength 50,000 lbs. 55,000 lbs. 60,000 lbs. i^ 'O «T3 ^.'^ S'O a,V. Ji-v :a5 If O > 3 > S > .s > Ho co-n «-C wn Q-C w-c P'C .25 99 119 109 131 119 143 .3125 124 148 136 163 148 178 .375 148 178 163 196 178 214 .4375 173 '^.07 191 229 208 249 .5 198 237 218 261 238 285 13 DIAMETER OF SHELL 48 INCHES Tensile Tensile Tensile strength strength strength ■ 50,000 lbs. 55,000 lbs. 60,000 lbs. k ^« o > c > o > c > O > Ho m-c Q-n co"c; Q-n w"n Q-n .25 87 . 104 95 114 104 125 .3125 108 130 119 143 130 156 .375 130 156 143 171 156 187 .4375 152 182 1H7 200 182 218 .5 173 207 191 229 208 249 DIAMETER OF SHELL 54 INCHES 25 77 92 85 102 92 3125 96 115 106 127 115 375 116 139 127 152 139 4375 135 162 148 177 ■ 162 5 154 184 169 202 185 111 138 167 194 222 DIAMETER OF SHELL 60 INCHES 3125 87 104 95 114 104 375 104 125 114 137 125 4375 120 145 133 159 146 5 139 166 153 183 166 5625 156 187 171 205 187 125 150 175 199 224 DIAMETER OF SHELL 66 INCHES 3125 79 95 87 104 95 375 95 114 104 125 113 4375 110 132 121 145 132 5 126 151 139 166 151 5625 142 170 156 187 170 114 136 158 181 204 DIAMETER OF SHELL 72 INCHES 375 87 104 95 114 104 4375 101 121 111 133 121 5 115 138 127 152 139 5625 130 156 143 171 156 625 144 173 159 190 173 125 145 166 187 207 DIAMETER OF SHELL 78 INCHES .375 80 96 88 106 96 115 .4375 93 111 103 123 112 134 .5 107 128 117 140 128 153 .5625 120 144 132 158 144 172 .625 133 159 147 176 160 192 14 STEAM ENGINEERING DIAMETER OF SHELL 84 INCHES Tensile Tensile Tensile strength strength strength 50,000 lbs. 55.000 lbs. 60,000 lbs. Eg -o 4)T3 V3 ■(u-d T3 (UT) "Sj^ 3 (U 1^ 3 q3 'i?, x^ O > •S > o > s > > H^ W-S q;c WC Q-C w'C Q-C .375 74 89 82 98 89 107 .4375 86 103 95 114 104 125 .5 99 119 109 130 119 142 .5625 111 133 122 146 134 160 .625 124 148 136 163 149 178 THE STRENGTH OF RIVETED JOINTS One of the most important problems- presented in connection with steam boilers is to calculate the strength of | riveted joints of various designs. As a general rule (or what may more prop- erly be called an estimate) , the strength of single riveted joints have 56 per cent. -: and double riveted joints 70 per cent, of the strength of the solid plate. However, it is not a good plan to as- sume this proportion of strength, for while some joints may greatly exceed it^ others will prove to be much weaker, hence the only safe plan is to calculate the strength of each joint separately when the safe working pressure of a boiler is to be determined. While studying this subject the prin- ciples involved should first receive at- BOILERS 15 tention, for if they are well understood it will assist the engineer not only in his efforts to learn the rules, but also in remembering them afterward. The comparative strength of the plate before and after it is punched or drilled for the rivets, is usually determined first. If we take a strip of boiler plate 3 inches wide as shown at 2 in Fig. 1, it represents 100 per cent, of strength, because none of it has been cut away for rivet holes. Proceeding to drill a %-inch hole in it, as shown at 3, it is plain that one-quarter of the metal has been cut away and it does not need any cal- culation to demonstrate it, but in order to fully illustrate the point the following may be considered. Having removed .75 inch of the metal there is 3 — .75 = 2.25 inches left, and dividing this by the original width shows the percentage remaining, or 3 — .75-^- 3=.75 of the strength of the solid plate hence the rule. 16 STEAM ENGINEERING From the pitch of the rivets subtract the diameter of one rivet, and divide the remainder by the pitch. The quotient is the percentage of the strength of the plate. As a formula it appears as follows: P= Pitch of rivets. D = Diameter of rivets. S = Percentage of strength. As the pitch of the rivets is used the strip appears with one-half of a rivet hole in each edge, but the result is not changed by it. See Fig. 2. The thick- ness of the plate is not considered in this connection as it is not necessary, and the use of it would make the calculation more complicated without correspond- ing benefit. The next point to be considered is the strength of [the rivets, and for conve- BOILERS . 17 nience of illustration it is assumed that the shearing strength of the rivets and the tensile strength of the plate are equal. While this is true in some cases it is not in others, therefore it cannot be laid down as a general rule. The area of a circle % inch in diam- eter is .44 square inch, and assuming that there are two rows of rivets, the area of two as illustrated in Fig. 3 is FiG_» .44X2 = .88 square inch. As this must be compared with the full area of the plate, its thickness must now be taken into consideration and for this purpose it is assumed to be .375 inch. Multiplying this by the pitch of rivets shows that the full area is .375X3 = 1.12 square inches. By dividing the area of rivets by the area of plate the strength of the rivets is found to be .88^-1.12 = .78 of the solid plate, hence the rule. 18 STEAM ENGINEERING Divide the area of one rivet multiplied by the number of rows, by the thickness of the plate multiplied by the pitch of the rivets. The quotient is the percen- tage of strength of the solid plate. As a formula it appears as follows: AXN_, T X P A = Area of one rivet. N = Number of rows, T = Thickness of plate. P = Pitch of rivets. S = Percentage of strength. In the above example the strength would be taken as .75, because the lower result must always be adopted in order to be on the safe side. This example seems to show that it is safe to call the strength of all double riveted joints .70 or more, but the defect in it is due to the fact that it only illustrates plates of a low tensile strength, and these are not fit for the construction of modern boilers. The Hartford Steam Boiler Inspec- tion and Insurance Co. have adopted 38,000 pounds per square ijich of sec- tional area as the shearing strength of rivets in single shear, and while it does not seem right to use an arbitrary rating for all joints, as rivets vary in strength, still if they are put into a joint in a work- BOILERS 19 manlike manner they will always be as strong as these figures indicate, and where they prove to be stronger, it ren- ders the boiler safer. Adopting this standard for the strength of rivets, and using plates with a tensile strength of 55,000 pounds, the result is much less, as follows: Pitch of rivets 3 inches. Diameter of rivets .75 inch. Number of rows 2. Thickness of plate .375 inch. 3-. 75 = .75 for the plates. .44X2X38,000 ^^ ^ = .54 for the rivets. .375X3X55,000 If the strength of this joint is taken at .70 it becomes dangerous because its real strength is only .54. It can be im- proved by reducing the pitch to 2.25 inches. 2.25 -.75 — — — — = .66 for the plates. 2.25 .44X2X38,000 .375X2.25X55,000 This increases the strength of joint to .66 when calculated on a very conserva- tive basis. = .72 for the rivets. 20 STEAM ENGINEERING For convenience in calculating the strength of rivets the following table gives the areas of circles from >^ to 1 inch inclusive. DIAMETER AND AREA OF RIVETS, Diameter Decimal of rivet equivalent ^ .5 .196 %6 .5625 .248 .625 .306 .6875 .371 M^' .75 .441 13A6 .8125 .518 Vi .875 .601 1%6 .9375 .690 1 1. .785 In some cases it is advisable to increase the pitch and add another row of rivets, making what is known as the triple riv- eted joint. The foregoing rules for strength of plate and rivets applies to such a joint and shows it to be efficient when well designed, but like others its actual efficiency should be calculated and not assumed. The following pro- portions will give good results. See Fig. 4. ~\^ o y-Y 21 Pitch of rivets 3.5 inches. Diameter of rivets 13/16 inch. Thickness of plate .375 inch. 3.5 -.8125 ^, , , , — — ' = .76 for the plates. 0.5 .518X3X38,000 .375X3.5X55,000 = .81 for the rivets. This demonstrates that the strength of such a joint may be taken at .76 of the strength of the solid plate. The same proportions may be used for a joint in plates of 60,000 pounds tensile strength, but owing to the increase in strength of the plates, the comparative strength of the rivets is less. .518X3X38,000 ^, , , . - = .75 for the rivets. .375X3.5X60,000 As the comparative strength of the plate, when punched or drilled ready for use, remains the same, or .76, the strength of the joint must be taken at ,75 which is practically the same as before. Using the same proportions of joint for plates of 50,000 pounds tensile strength raises the comparative strength of rivets. 518X3X38,000 • = 90 .375X3.5X50,000 22 STEAM ENGINEERING Therefore this joint may be taken at .75 for all plates mentioned in the fore- going tables, so far as their tensile strength is concerned. Modem practice in steam engineering, calling for high boiler pressures, has proved that every form of lap joint is unreliable, owing to the tendency to bend the plate as shown in Fig. 5. in and as this is repeated every time that pressure is raised and removed, it has caused disastrous failure in many cases. 23 To overcome this objection the double strap butt joint is used, a very simple form of which is shown in Fig. 6. Such a joint is very efficient even when only a single row of rivets is used, because the rivets are in double shear, or in other words they must be sheared in two places before they fail. If the strength in single shear is 38,000 pounds it is raised to 70,300 pounds for double shear if we consider double shear equal 1.85 single shear. For illustration of 24 STEAM ENGINEERING the Strength of this form of joint, the following proportions are taken. Pitch of rivets Diameter of rivets Number of rows Thickness of plate Tensile strength 3 inches. .375 50,000 pounds. 3 -.875 .70 for the plates. .601X1X70,300 •— - — - — Z7rz:z = -75 for the rivets. .375X3X50,000 The strength of this single riveted joint is thus shown to be .70 of the strength of the solid plates. - Increasing the pitch and adding an- other row of rivets makes a better joint, for which the following proportions are assumed : Pitch of rivets Diameter of rivets Number of rows Thickness of plate Tensile strength 3.5 inches. .375 " 60,000 pounds. 3.5— .75 3.5 = .78 for the plates. .44X2X70,300 .375X3.5X60,000' = .78 for the rivets. 25 In this case the strength of both plates and rivets equals .78 of the solid plates. Here the tensile strength is 60,000 pounds while in the preceding it is 50,000, but it may be taken at any less value in either case without bad effect on the joint, as such changes only raise the percentage of strength of the rivets. This joint may be still further im- proved by extending the inner strap as illustrated in Fig. 7, and adding an inner 26 STEAM ENGINEERING row of rivets as shown in Fig. 8 with double pitch. For illustration of the principles involved, the following pro- portions are assumed for this joint: j: B C HZ Pitch of outer rivets 3.5 inches. " " inner " 7 Diameter of rivets % " Thickness of plates .375 " Tensile strength 60,000 pounds. To determine the strength of this joint use the following rules: From the pitch of the inner row of rivets (or the 27 double pitch), subtract the area of one rivet and divide the' remainder by the double pitch. The quotient is the strength of the plates. =L o o o o o IT Multiply the combined area of all rivets in double shear by 70,300. Mul- tiply the combined area of all rivets in single shear by 38,000 and add the two products together. Divide the sum by the strength of the section of plate as found by multiplying the area of plate between centers of the rivets, by the ten- 28 STEAM ENGINEERING sile strength. The quotient is the per- centage of strength of the rivets. Stated as a formula these rules appear as follows: P = Double pitch, or pitch of the inner row. D = Diameter of rivet. S = Percentage of strength of plate. (A XR X70,300) + (E X V X38,000) TXPXH A = Area of one rivet in double shear. R = Number of rivets in double shear. E = Area of rivets in single shear. V = Number of rivets in single shear. T = Thickness of plate. P = Pitch of rivets. H = Tensile strength. S = Strength of rivets. Application of these formulas to the above example results as follows: 7 -.75 = .89 for the plates. (.44X4X70,300)-}-(.44XlX38,000) .375X7X60,000 ~ 140,448 ^ , , . = .89 for the nvets. 157,500 BOILERS 29 While it is not necessary to make the straps as thick as the plates, they must not be less than /^ of their thickness, therefore for /4 inch plates they should be .375 X. 625 = .234 inch or say, }4 inch thick. THE U. S. GOVERNMENT RULE FOR THE STRENGTH OF RIVETED JOINTS, IRON PLATES AND IRON RIVETS As these rules are similar to the fore- going they will be stated as formulas only. P = Pitch of rivets. D = Diameter of rivets. S = Strength of plates. T X P A = Area of rivet. R = Number of rows. T = Thickness of plates. P = Pitch of rivets. S = Strength of rivets. As neither the shearing strength of rivets, nor the tensile strength of plates are mentioned, it shows that they are equal for iron plates and iron rivets. 30 STEAM ENGINEERING The above formulas apply to single, double and triple riveted lap joints. STEEL PLATES AND STEEL RIVETS To determine the strength of plates at the joint proceed as for iron plates. The strength of rivets is determined by the following formula: AXRX.8 TXP This is the same as for iron rivets ex- cept that the constant .8 is added, because the shearing strength of steel rivets is taken as .8 of the tensile strength of the plate. In preceding rules and formulas the shearing strength of rivets is taken as a certain fixed value and while this may not seem to be correct for all cases, still it is the lowest value determined by several tests, hence a riveted joint that is made in a workmanlike manner should always show the value given and more in many cases. There is a difference between the di- ameter of a rivet and the diameter of the hole before the rivet is driven into place, but when the joint is finished the hole is or ought to be, entirely filled by the rivet, hence the diameter of the hole is used in these calculations. » BOILERS 31 JBLE BUTT-STRAP JOINTS WITH STEEL PLATES AND STEEL RIVETS I DOUBLE RIVETED The percentage of strength of plate lis found as in preceding examples. For strength of rivets the following formula ipplies: AXRX1.75X.8 TXP A = Area of rivets which are in double shear. R = Number of rows, which is 2 in this case. 1.75= A constant for rivets in double shear. This represents their strength compared with those in single shear. .8= A constant as above men- tioned. T = Thickness of plate. P = Pitch of rivets. S = Strength of rivets. TRIPLE RIVETED Strength of plates is determined by the above rule for other joints. The strength of rivets is determined by the preceding rule for double riveted joints, except that there are 2.5 rows instead of 2. This assumes that the inner row of rivets has a double pitch or else that 32 STEAM ENGINEERING the inside strap is long enough for three rows, and the inner strap for two rows of rivets. When designing riveted joints for steam boilers it is necessary to avoid very narrow pitches as they bring the rivet holes too near together for good results. Too wide pitches are also detri- mental, as the plate will spring be- tween the rivets, and the joint will not remain tight whe!n calked. It is sometimes claimed that all cal- culations give,n in books are applicable] to horizontal fire tube boilers only, but this is a mistaken idea, as they must be used in calculating the strength of all vertical fire tube boilers and many of| the water tube type contain steam and water drums that are shells carrying internal pressure, and are fitted with riveted joints the same as fire tube boilers. BRACING FLAT SURFACES All flat surfaces in steam boilers, ex- cept those of small area, require braces to support them under ordinary working pressures, therefore it becomes necessary to know how much pressure a given sur- face can safely carry. These surfaces are strong enough to carry a light pres- . sure without bracing, but this • fact is BOILERS 33 not generally taken into consideration when calculating the strength of these parts, because if there is an error in such a plan it is on the safe side, consequently it can do no harm. It is assumed that all of the pressure is carried by the braces, or stay bolts which are only short braces, therefore, the safe load for them must be known and not exceeded in practice. The following rule determines the safe working pressure for stay bolts and braces where the plates are not more than Jl6 inch thick: Multiply the area of the brace by 6,000 and divide the product by the horizontal multiplied by the vertical pitch in inches. The quotient is the safe working pressure. Analysis of this rule shows that braces are limited to a strain of 6,000 pounds per square inch of sectional area, which affords a liberal factor of safety as the tensile strength of such iron ought to be at least 45,000 pounds. Where this rule is applied to threaded stay bolts, the area must be calculated from the diameter at the base of the thread, as that represents the real strength of it. For illustration of this rule the following example is given: 34 STEAM ENGINEERING * Diameter of stay bolt .75 inch Area " " " .44 square inch Horizontal pitch 5 inches Vertical pitch 6 " .44X6,000 ^^ Then =88 pounds safe 5X6 working pressure. If any form of braces are located too far apart, the plate between them will bulge and finally cause leaks or perhaps a disastrous rupture, consequently the safe load for these plates must be deter- ■ mined and the actual working load kept below the safe limit. This may be de- termined by the following rule, for plates not more than Kq inch thick. Multiply 28,672 by the square of the thickness of the plate and divide the product by the horizontal multiplied by the vertical pitch. The quotient is the safe working pressure. For example, take the water leg of a locomotive boiler made in the following proportions : Thickness of plate .375 inch Horizontal pitch 6 inches Vertical " 6 " Then 28,672 X (.375 X .375 ) 6X6 pressure. 112 pounds safe h£^ BOILERS 35 Analysis of this rule shows that as the pitch increases, the safe pressure de- creases, which is logical. If the horizon- tal and vertical pitches were always equal the rule would read "square the pitch," but they sometimes differ in practice, hence the rule covers any differ- ence that is desired or required. Where the plates are more than % inch thick, the same rule applies if the safe pressure is based on the diameter and pitch of stay bolts, but larger bolts and greater pitches are adopted in order to be consistent with the increased thickness of plate, as the following ex- ample illustrates: Diameter of stay bolt 13^ inches. Area " " " 1.767 square in. Horizontal pitch 9.5 inches. Vertical " 9.5 " Then 1.767X6,000 — — = 117 pounds safe pressure. The following table of areas of circles from 1 to 2 inches in diameter is given for convenience in making calculations that are based on the foregoing rule: 36 STEAM ENGINEERING AREA OF CIRCLES FROM 1 TO 2 INCHES Diameter Decimal Area 1 1.0000 .785 iHe 1.0625 .886 IH 1.125 ,.994 l^ie 1.1875 1.107 IH 1.25 1.227 ma 1.3125 1.353 IH 1.375 1.484 ITie 1.4375 1.622 iy2 1.5 1.767 PAe 1.5625 1.917 1% 1.625 2.073 11^6 1.6875 2.236 IH 1.75 2.405 mia 1.8125 2.580 IH 1.875 2.761 li%a 1.9375 2.948 2 2.0000 3.141 Where the safe pressure is based on the thickness of the plate and the pitch of stay bolts, the following rule applies : Multiply 30,720 by the square of the thickness of the plate and divide the product by the horizontal multiplied by the vertical pitch. This rule contains a larger constant number than the former given for this purpose, which is the only difference between them. For illustration assume the following proportions ; Thickness of plate .625 inch Horizontal pitch 10 inches Vertical " 10 Then 30,720 X (.625 X. 625) ^„^ ^ . . ^^ = 120 pounds safe 10X10 pressure. i^^ BOILERS 37 The stay bolts for this case should not be less than 1^ inches in diameter, be- cause the strain to be supported is ; lOX lOX 120= 12,000 pounds and as the strain on stay bolts is limited to 6,000 pounds per square inch [of sectional area, these must have an area of at least 2 square inches, and the nearest to this according to the table is 1^ inches in diameter. The following table contains the safe loads for stay bolts and braces from % to 2 inches in diameter. The first col- umn gives the diameter, the second is the safe load at 6,000 pounds per square inch sectional area, which is the U. S. Government rule, but inasmuch as this affords a large factor of safety, the Hartford Steam Boiler Inspection and Insurance Co. allow 7,500 pounds and this is found in the third column. SAFE LOADS FOR STAY BOLTS AND BRACES Diameter Safe load Safe load in inches . 6,000 pounds 7,600 pounds \i 1,176 1,470 % 1,836 2,295 2.646 3,307 .^ 3,606 4,507 4,710 5,887 IH 5,964 7,355 7,362 9,202 1^ 8,904 11.130 1 j^ 10.602 13,252 1% il2,438 15,547 15^ 114.430 18,037 Wi 16,566 20.707 2 18.840 23,557 38 STEAM ENGINEERING SURFACE SUPPORTED BY STAY BOL AND BRACES Every stay bolt and brace occupies I more or less space on the plate that is to be supported, the amount varying with the diameter, and this space is covered, therefore it is not subjected to pressure. It is customary to ignore this fact when making these calculations, because if there is an error it is on the safe side, hence no harm can result. When braces contain toggle joints they should be well made, so that there will be no lost motion to be taken up when pressure is put on, and let out when it is removed, thus causing the plate to bend many times, the ulti- mate result of which is that the metal is weakened until it may fail under an ordinary working pressure, causing loss of life and property. The following table contains the num- ber of square inches on a fiat surface that stay bolts and braces will safely support, the diameter ranging from 3^ inch to 2 inches and the pressure from 80 to 120 pounds. The strain is limited BOILERS 39 to 6,000 pounds per square inch of sec- tional area. Following this • is another table which is the same except that the strain is* limited to 7,500 pounds per square inch of sectional area. To use these tables proceed as follows: Suppose that a space on the water leg of a locomotive boiler that is 24X56 inches, is to be made strong enough to carry 90 potmds pressure and stay bolts "J/g inch in diameter are to be used. How many will be required? The space con- tains 24X56 = 1,344 square inches. The first table, limiting the stress to 6,000 pounds, shows that each % inch stay bolt will support 40 square inches. under 90 pounds pressure. Then 1,344 ■T-40 = 33 with a remainder of 24 inches to be provided for, therefore it will require 34 stay bolts. If the strain is limited to 7,500 pounds ^ an examination of the next table shows that a J/g inch stay bolt will support 50 square inches under 90 pounds pressure. Then, 1,344^50 = 26 with a remain- der of 44 square inches, therefore 27 stay bolts will be required. 40 STEAM ENGINEERING SQUARE INCHES OF SURFACE SUPPORTED BY STAY BOLTS AND BRACES J_^ Strain Umited to 6,000 pounds «sl Boiler Pressure Q'SS 80 90 100 110 120 ^ 14.7 13.0 11.7 10 .,7 9.8 23.0 20.4 18.3 16.7 15.3 H 33.0 29.4 26.4 24.0 22.0 45.0 40.0 36.0 32.7 30.0 58.8 52.3 47.1 42.8 39.2 \yi 74.5 66.2 59.6 54.2 49.7 IH 92.0 81.8 73.6 66.9 61.3 ij^ 111.3 98.9 89.0 80.9 74.2 iH 132.5 117.8 106.0 96.3 88.3 1% 155.4 138.2 124.3 113.0 103.6 IM 180.3 160.3 144.3 131.1 120.2 lyi 207.0 184.0 165.6 150.6 138.0 2 235.5 209 3 188.4 171.3 157.0 SQUARE INCHES OF SURFACE SUPPORTED BY STAY BOLTS AND BRACES !r! « Strain Limited to 7,500 pounds "rt-S Boiler Pressure 80 90 100 110 120 H 18.3 16.3 14.7 13.3 12.2 H 28.7 25.5 22.9 20.8 19.1 41.3 36.7 33.0 30.0 27.5 t/^ 56.3 50.0 45.0 40.9 37.5 73.5 65.4 58.8 53.5 49.0 lyi 91.9 81.7 73.5 66.8 61.2 1 Ji 115.0 102.2 92.0 83.6 76.6 IH 139.1 123.6 111.3 101.1 92.7 1 ^ 165.6 147.2 132.5 120.4 110.4 1% 194.3 172.7 155.4 141.3 129.5 IH 225.4 200.4 180.3 163.9 150.2 IH 258.8 230.0 207.0 188.2 172.5 2 294.4 261.7 235.6 214.1 196.3 r BOILERS THE ANGULARITY OF BRACES 41 As a general rule, to which there may be a few exceptions, stay bolts are set at right angles to the plates, and all of the foregoing rules and directions are based on this condition, but braces must fre- quently be located at angles that are less than 90 degrees, and the effect of this is to put a greater load on the brace, although the same surface is supported and the same pressure carried. Fig. 9 illustrates a stay bolt in place at an angle of 90 degrees to the plate, therefore the pressure puts a strain on 42 STEAM ENGINEERING the brace that is represented by the sur- face of plate multiplied by the pressure per square inch. Fig. 10 shows a brace that is located at an angle of 45 degrees to the boiler head that it supports. The load on this FKS../0 brace is determined by the surface sup- ported in square inches, multiplied by the pressure per square inch, divided by the natural sine of the angle. Suppose that this brace is IM inches in diameter and the strain is limited to 6,000 pounds per square inch of section- al area. According to the table of safe loads this brace will carry 7,362 pounds which will be secured in accordance with the next table if it supports 73.6 square inches at 100 pounds pressure. The natural sine of an angle of 45 BOILERS 43 degrees is .7071, therefore the true load on this brace under these conditions is 7,362 -=-.7071. =10,411 pounds, which is an overload even if the limit is placed at 7,500 pounds per square inch of sec- tional area. To overcome this objection it becomes necessary to ascertain the .number of square inches that can be allowed with- out exceeding the safe limit. This is accomplished by multiplying the num- ber of square inches that could be sup- ported safely if the brace stood at an angle of 90 degrees as stated in the table, by the natural size of the angle. If this number is 73.6 and the brace stands at an angle of 45 degrees, the natural sine of which is .7071 then the surface that can safely be allowed to this brace is 73.6X.7071=52 square inches. While braces are not usually located at such an acute angle, this example illus- trates the effect of angularity and shows that it should not be neglected where accuracy is desired. If the angle is in- creased to 75 degrees, the space becomes 71 square inches. The following table contains the nat- ural sines of angles from 10 to 90 degrees which fully covers all that can be re- quired for use in connection with boiler bracing, and the use of the data given in it has already been fully explained. 44 STEAM ENGINEERING This is an important branch of the subject of boiler bracing, and is earn- estly recommended to those who have not heretofore given it due attention. NATURAL SINES OF ANGLES Angle Sine Angle Sine 10 .1736 51 .7771 11 .1908 52 .7880 12 2079 53 .7986 13 .2249 54 .8090 14 .2419 55 ,8191 15 .2588 56 .8290 16 .2756 57 .8386 17 .2923 58 .8480 18 .3090 59 .8571 19 3255 60 .8660 20 .3420 61 .8746 21 .3583 62 .8829 22 .3746 63 .8910 23 .3907 64 .8987 24 .4067 65 .9063 25 .4226 66 .9135 26 .4383 67 .9205 27 .4539 68 .9271 28 .4694 69 .9335 29 .4848 70 .9396 30 :5000 71 .9455 31 .5150 72 .9510 32 .5299 73 .9563 33 .5446 74 .9612 34 .5591 75 .9659 35 .5735 76, .9703 36 .5877 77 .9743 37 .6018 78 .9781 38 .6156 79 .9816 39 .6293 ^80 .9848 40 .6427 81 .9876 41 .6560 82 .9902 42 .6691 83 .9925 43 .6820 84 .9945 44 .6946 85 .9961 45 .7071 86 .9975 46 .7193 87 .9986 47 .7313 88 .9993 48 .7431 89 .9998 49 .7547 90 1.0000 50 .7660 BOILERS 45 BRACING THE HEADS OF TUBULAR BOILERS Every tube that is put into the head of a tubular boiler acts as a brace of more or less efficiency, and as a large portion of the head is removed in mak- ing places for these tubes, they are suf- ficient to hold what is left except a small space below them which usually requires two braces, and a larger space above them which assumes the form of a seg- ment of a circle. It is more difficult to compute the area of this space than to determine the number of square inches on the water leg of a locomotive boiler, or on any other part that can be put into the form of a square, as there are several points to be taken into consideration. These heads are usually about one- half inch thick, and taking this as a basis the head is self-supporting for 2 inches above the upper row of tubes, and for 3 inches from the shell, conse- quently if we take the head of a 72-inch boiler in which the upper tubes are 7 inches above the center line, the height of the segment to be braced is 24 inches, and it is part of a circle 72 -(3X2) =66 inches in diameter, as 6 inches must be subtracted for the self-supporting portion above mentioned. The chord 46 STEAM ENGINEERING or base is 63.375 inches long as shown by measurement on a full sized drawing. This is illustrated in Fig. 11. Boilers 47 rule for calculating the area of a segment of a circle Ascertain the area of a sector of the circle having the same arc as the seg- ment. Determine the area of the tri- angle formed by the chord of the seg- ment and the radii of the sector. Sub- tract the latter from the former and the remainder is the area of the segment. Fig. 12 represents a sector the upper part of which constitutes the segment. Applying this rule shows that the seg- ment in this case contains 1,125 square inches. It is assumed that the head is full 72 inches in diameter in order to 48 STEAM ENGINEERING agree with calculations made to deter- mine the bursting and safe working • pressure of boiler shells as the diameters given are determined by internal meas- urements. Fig. 13 illustrates another rule for determining the area of the segment to be braced, as it was laid out full size and divided into equal spaces 1 inch wide by ordinates, commencing at the center and working, both ways. The illustra- tion is reduced for convenience, but the correct proportions are retained. There are 63 ordinates and their total length is 1,127.7 inches, therefore the average height of this segment is 1,127.7 -^63 = 17.9 inches. As it is 63.375 inches long it contains 17.9X63.375 = 1,134 square inches. The rule on which this is based may be stated as follows: Draw a portion of a circle that is 6 inches smaller than the diameter of the boiler, to form the arc. Draw a hori- zontal line 2 inches above the upper row of tubes to form the chord. Begin at the center and lay off ordinates 1 inch apart, extending from the chord to the arc. Determine the length of each, add them together, divide by the number of ordinates and the quotient is the aver- age height. Multiply this by the length and the product is the number of square inches contained in the segment. 49 50 STEAM ENGINEERING It is difficult or impossible to secure exactly the same result by two different rules, but the difference is not sufficient to affect the number of braces required. EXPLANATION OF THE FOLLOWING TABLE This table contains the areas of seg- ments to be braced on tubular boiler heads from 42 to 84 inches in diameter. The distance from the center of the boiler to the top of the tubes is given, and it will be noted that this arrange- ment of tubes gives a very liberal steam space. If more tubes are put in the heating surface will be increased, but taken as a whole the boiler will not be benefited thereby. The columns ii' this table contain the following data: 1. Diameter of boiler head. 2. Diameter of circle on. which the ca' culation is based. 3. Distance from center of head to tci of tubes. 4. Distance from center of head d chord or base of segment. 5. Length of chord. 6. Greatest height of segment. 7. Average height of segment. 8. Area of segment. ^ 51 All measurements are stated in inches and areas in square inches. • tabLe of areas of segments determined by ordinates 1 2 3 4 5 6 7 8 42 36 4 6 34 20 12 8.61 294 48 42 4 6 40.20 15 10.86 436 54 48 5 7 46.00 17 12.36 568 60 54 5 7 52.-25 20 14.93 780 66 60 6 8 57.75 22 16.04 926 72 66 7 9 63.37 24 17.90 1,134 78 72 8 10 68.88 26 19.20 1,322 84 78 9 11 74.75 28 20.70 1,547 ANOTHER RULE A rule that is frequently used to de- termine the area of a segment of a circle, is expressed briefly in the following formula : H D XCXD2 = A H = Height of segment. ■ D = Diameter of circle. C = A constant taken from a table. A = Area of segment. As the height of segment and the di- ameter of circle are always known or easily determined, this constitutes a very simple formula, but a table of con- stants is required. 52 STEAM ENGINEERING The following table gives the area of segments previously mentioned in order that the reader may compare them with results obtained by the plan of laying them out by ordinates, which is here considere'd the standard. AREA OF SEGMENTS DETERMINED BY THE FOREGOING FORMULA Diam. Height Constant Diam. Area of head Diam. 42 12/36=. 333 .2288 1,296 296 48 i%2=.357 .2516 1,764 443 54 i%8=.354 .2488 2,304 573 60 20^4=.370 .2641 2,916 770 66 22/60=. 367 .2574 3,600 926 72 2%6=.363 .2622 4.356 1,142 78 26,^2=. 361 . 2555 5,184 1,324 84 28^8=. 359 .2535 6,084 1,642 The following table contains all of the constants that are required for ordinary cases along this line. The first column contains the quotients found by dividing the greatest height of segment by the diameter of the circle. The second column contains the corresponding con- stant. When the latter is multiplied by the square of the diameter of the circle, the product is the area of the segment. BOILERS TABLE OF CONSTANTS 53 Height Constant Height Constant Diametet Diameter .150 .0738 .198 .1102 .151 .0745 199 .1110 .152 .0753 .200 .1118 .153 .0760 .201 .1126 154 .0767 .202 . .1134 155 .0774 .203 .1142 .156 .0781 .204 .1150 157 .0789 205 .1158 158 .0796 .206 .1166 159 .0803 .207 .1174 160 .0811 .208 .1182 .161 .0818 .209 .1190 .162 .0825 .210 .1199 163' .0833 .211 .1207 .164 .0840 .212 .1215 .165 .0848 .213 .1223 .166 .0855 .214 .1231 .167 .0862 .215 .1239 .168 .0870 .216 .1248 .169 .0877 .217 .1256 .170 .0885 .218 .1264 .171 .0892 .219 .1272 .172 .0900 .220 .1281 .173 .0908 .221 .1289 174 .0915 .222 .1297 .175 .0923 .223 .1306 .176 .0930 .224 .1314 .177 .0938 .225 .1322 .178 .0946 .226 ,1331 .179 .0953 .227 .1339 .180 .0961 .228 .1347 .181 .0969 .229 .1356 .182 .0976 .230 .1364 .183 .0984 .231 .1373 .184 0992 .232 .1384 185 .1000 .233 .1390 .186 .1007 .234 .1398 .187 .1015 .235 .1406 .188 .1023 .236 .1415 .189 .1031 .237 .1423 .190 .1039 .238 .1432 .191 .1046 .239 .1440 .192 .1054 .240 .1449 .193 .1062 .241 .1458 .194 . 1070 .242 .1466 .195 .1078 .243 .1475 196 .1086 .244 .1483 .197 .1092 .245 .1492 54 STEAM ENGINEERING Table of Constants — Continued Height Height Diameter Constant Diameter Constant .246 .1500 .294 .1926 .247 .1509 .295 .1936 .248 .1518 .296 .1945 .249 .1526 .297 .1954 .250 .1535 .298 .1963 .251 .1544 .299 .1972 .252 .1552 .300 .1981 .253 .1561 .301 .1990 .254 .1570 .302 .2000 .255 .1578 .303 .2009 .256 .1587 .304 .2018 .257 .1596 .305 .2027 .258 .1605 .306 .2036 .259 .1613 .307 .2046 .260 ,1622 .308 .2053 .261 .1631 .309 .2064 .262 .1640 .310 .2073 .263 .1649 .311 .2083 .264 .1657 .312 .2092 .265 .1666 .313 .2101 .266 .1675 .314 .2110 .267 .1684 .315 .2120 .268 .1693 .316 .2129 .269 .1702 .317 .2138 .270 .1710 .318 .2148 .271 .1719 .319 .2157 .272 .1728 .320 .2166 .273 .1737 .321 .2176 .274 .1746 .322 .2185 .275 .1755 .323 .2194 .276 .1764 .324 .2204 .277 .1773 .325 .2213 .278 .1782 .326 .?.?.?.?. .279 .1791 .327 .2232 .280 .1800 .328 .2241 .281 .1809 .329 .2250 .282 .1818 .330 .2260 .283 .1827 .331 .2269 .284 .1836 .332 .2279 .285 .1845 .333 .2288 .286 .1854 .334 .2298 .287 .1863 .335 .2307 .288 .1872 .336 .2316 .289 .1881 ,337 .2326 .290 .1890 .338 ,2335 .291 .1899 .339 ,2345 ,292 .1906 .340 ,2364 .293 .1917 .341 .2364 55 Table of Constants — Continued Height Height Constant Constant Diameter Diameter .342 .2373 .390 .2835 .343 .2383 .391 .2845 .344 .2392 .392 .2855 .345 .2402 .393 .2865 .346 .2411 .394 .2875 .347 .2421 .395 .2884 .348 .2430 .396 .2894 .349 .2440 .397 .2904 .350 .2449 .398 .2914 .351 .2459 .399 .2923 .352 • .2468 .400 .2933 • .353 .2478 .401 .2943 .354 .2488 .402 .2953 .355 2497 .403 .2963 .356 .2507 .404 .2972 .357 .2516 .405 .2982 .358 .2526 .406 .2992 .359 .2535 .407 .3002 .360 .2545 .408 .3012 .361 .2555 .409 .3022 .362 .2564 .410 .3031 .363 .2574 .411 .3041 .364 .2583 .412 .3051 .365 .2593 .413 .3061 .366 .2603 .414 .3071 .367 .2612 415 .3081 .368 .2622 .416 .3091 .369 .2632 .417 .3100 .370 .2641 .418 .3110 .371 .2651 .419 .3120 .372 .2661 .420 .3130 .373 .2670 .421 .3140 .374 .2680 .422 .3150 .375 .2690 .423 .3160 .376 .2699 .424 .3169 .377 .2709 .425 .3179 378 .2719 .426 .3189 .379 .2728 .427 .3199 380 .2738 .428 .3209 .381 .2748 .429 .3219 .382 .2758 .430 .3229 .383 .2767 .431 .3239 .384 .2775 .432 .3249 .385 .2787 .433 .3259 .386 .2796 .434 .3268 .387 .2806 .435 .3278 .388 .2816 .436 .3288 .389 .2826 .437 .3298 56 STEAM ENGINEERING Table of Constants — Continued Height Height Diameter Constant Diameter Constant .438 .3308 .445 .3378 .439 .3318 .446 .3388 .440 .3328 .447 .3398 .441 .3338 .448 .3407 .442 .3348 .449 .3417 .443 .3358 .450 .3427 .444 .3368 To illustrate the operation of finding the area of a segment by the use of this table, suppose that on the head of an 84 inch boiler, there is a segment 28 inches high to be braced. As the circle is 84 — 6 = 78 inches in diameter, the height divided by the diameter is 28-4-78 = ,3-59 and when this number is found in the table, the constant opposite is ,2535. Squaring the diameter of the circle and multiplying by this constant shows that the area of this segment is 78X78X .2535= 1,542 square inches. DIRECTIONS FOR USING THE FOREGOING TABLES For illustration, suppose that ,on the head of a 72-inch boiler there is a seg- ment 24 inches high to be braced, to make it safe at 110 pounds pressure, and it is proposed to use round braces 1^ inches in diameter, or their equivalent in some other form. They are to be BOILERS 57 located at an angle of 65 degrees from the head. How many braces will be required? The table on page 51 shows that if the head of a 72-inch boiler has a segment 24 inches high its area is 1,134 square inches. The table of "Square Inches of Surface Supported by Stay Bolts and Braces, Strain Limited to 6,000 Pounds," shows that a brace 1}4 inches in diam- eter will support 66.9 square inches under 110 pounds pressure, if the brace is located at an angle of 90 degrees from the head. In this case it is at 65 de- grees, therefore as the table of "Natural Sines of Angles" shows that the sine of 65 is .9063 this brace will safely support 66.9 X. 9063 = 60.6 square inches. As the total area to be supported is 1,134 square inches, it will require 1,134 ^60.6 = 18.7 braces, or in practice it would be called 19. If a strain of 7,500 pounds per square inch of sectional area is allowed, each brace will support 83.6 square inches at 90 degrees under 110 poimds pressure as per table. Taking it at an angle^ of 65 degrees it will sup- port 83.6 X. 9063 = 75.7 square inches therefore it will require 1,134-7-75.7 = 15 braces under these conditions. These tables provide for the solution of any problem along this line that is found under ordinary working conditions. 58 STEAM ENGINEERING . It is not a difficult matter to adapt ' them to other conditions not mentioned directly, by the following plan. Under head of "Square Inches Supported by Stay Bolts and Braces. Strain Limited to 7,500 pounds," boiler pressures from 80 to 120 pounds are included, but if a brace will support 18.3 square inches under 80 pounds pressure, it will support 18.3 X 2 = 36.3 square inches under 40 pounds. If it will support 200.4 square inches under 90 pounds pressure, it will support 200.4^-2 = 100.2 square inches under 180 poimds pressure, and many other combinations can be secured from this table. The "Table of Areas of Segments" can be adapted to other sizes, as follows: Column 1 includes a boiler head 66 inches in diameter in which the distance from center of head to top of tubes is 6 inches. (See column 3.) The distance to the chord of this segment is 8 inches, the 'length of the chord is 57.75 inches, and the area is 926 square inches. Suppose that in another case the greatest height of segment is 21 inches or 1 inch less than given in column 6. As the chord in the table is 57.75 inches long, the area will be nearly 57.75 square inches less. If the segment is 1 inch higher or 23 inches, its area is about 57.75 square inches more. These results are BOILERS 59 practically correct for the calculations to which they belong, as the slight dif- ference due to approximate measure- ments will not change the number of braces required in a given case. BOILER FLUES SAFE PRESSURE FOR FLUES Flues in a shell boiler are subject to collapsing pressure, hence they must be treated in a different way from parts that resist bursting pressure. When calculating the safe internal pressure of the shell of a boiler it is not necessary to take the length of it into consideration, but experiments on flues show that when collapsing pressure is under considera- tion, the length becomes a factor. The following rule determines the safe pres- sure of flues: Multiply the square of the thickness of the iron by 806,300. Divide the product by the diameter multiplied by the length and by 3. The quotient is the safe pressure. For illustration take a flue made of iron 34 inch thick with riveted seams. It is 12 inches in diameter and 20 ft. long, .25 X. 25X806,300 = 70 pounds safe pres- 12X20X3 ^ ^ sure. 60 STEAM ENGINEERING THICKNESS OF FLUES The required thickness of flues for given conditions, is determined by the following rule: Multiply the diameter in inches, by the length in feet, by the steam pres- sure and by 3. Divide the final product by 806,300 and extract the square root of the quotient. The above mentioned example gives ^his result: V 20X12X70X3 =.25 inches thick. 806,300 DIAMETER OF FLUES To determine the proper diameter of a flue for given conditions the following rule applies: Multiply the square of the thickness by 806,300. Divide the product by the length in feet, multipled by the steam pressure and by 3. The quotient is the diameter in inches. Using the foregoing, example results as follows: .25 X. 25X806,300 . , = 12 mches diameter. 20X70X3 61 LENGTH OF FLUES As the length of a flue is a factor in determining the safe pressure, it becomes necessary in certain cases to determine how long a flue can be made without exceeding the safe limit. This point can be decided by the next rule. Multiply the square of the thickness by 806,300 and divide by the diameter multiplied by the safe pressure and by 3. The quotient is the length in feet. Applying this to the same example gives the following result: .25 X. 25X806,300 ■ =20 feet long. 12X70X3 In all the foregoing calculations con- cerning boiler flues, a factor of safety of 3 is used, which seems to have proved sufficient for all practical use in the judg- ment of Inspectors in the.U. S. Govern- ment service, but if a greater factor is desired it may be substituted, giving results in accordance with the change. The length of a flue, so far as its safe pressure is concerned is the distance be- tween supports. If it is a plain flue this means the extreme length, but if it is made in sections with flanged ends, each 62 STEAM ENGINEERING of these sections is called the length, and if re-inforcing rings are used, the distance between them is taken as the length in the above rules for safe pres- sure, etc. Furthermore, throughout this work a boiler flue is taken as being 43^^ inches or more in diameter while tubes are 4 inches or less. In accordance with this assumption, the foregoing rules are not recommended for anything less than 5 inches, and they probably give very conservative results in practice. There does not seem to be any really satisfactory data of a simple nature concerning the strength of boiler tubes, but fortunately they are strong enough to safely withstand much more pressure than is given for boiler shells of various diameters, consequently they are safer than other parts. The same reasoning applies to tubes for water tube boilers which are sub- jected to bursting pressure, hence they are properly termed "safety boilers" provided they do not include a large steam drum. As a general rule a water tube does comparatively little damage when .it bursts, but exceptions to this rule are not unknown. The next table contains the standard dimensions and weight per linear foot BOILERS '63 (Of boiler flues from 4*^ to 21 inclies' in diameter. When referring to the size of standard boiler flues and tubes it is well to remem- ber that when the diameter is men- tioned it is the outside diameter, conse- quently when ordering flue cleaners this fact must be taken into consideration. If the internal diameter is meant in any special case it should be plainly stated in order to avoid misunderstandings. Following this is a table of dimensions; of tubes fi:om 1 to 4 inches in diameter^ and this refers to the external diameter as above mentioned. SIZES OF STANDARD BOILER FLUES FROM 4H TO 21 INCHES Diameter Thick- Circumference Weight Ext. Int. ness Ext. Int. 4H 4.232 .134 14.137 13.295 6,17 5 4.704 .148 15.708 14.778 7.58 6 5.670 .165 18.850 17.813 10.16 7 6.670 .165 21.991 20.954 11.90 8 7,670 .165 25.133 .24.006 13.65 9 8.640 .180 28.274 27 . 143 16,76 10 9.594 .203 31.416 30.141 21.00 11 10.560 .220 34.558 33.175 25.00 12 11.542 .229 37.699 36.260 28.50 13 12.524 .238 40.841 39.345 32.06 14 13.504 .248 43.982 42.424 36.00 15 14.482 .259 47.124 45.497 40.60 {I 15.468 .271 50.266 48.563 45.20 16.432 .284 53.407 51.623 49.90 18 17.416 .292 56.549 54.714 54.82 19 18.400 .300 59.690 57.805 59.48 20 19.360 .320 62.832 60.821 66 77 21 20.320 .340 65.974 63.837 73.40 64 STEAM ENGINEERING SIZES OF STANDARD BOILER TUBES FROM 1 TO 4 INCHES Diameter Circumference Weight Ext. Int. Ext. Int. 1 .810 .095 3.142 2.545 .90 IH 1.060 .095 3.927 3.330 1.15 1/^ 1.310 .095 4.712 4.115 1.40 1% 1.360 .095 5.498 4.901 1.65 2 1.810 .095 6.283 5.686 1.91 2K 2.060 .095 7.069 6.472 2.16 2y2 2.282 .109 7.854 7.169 2.75 2% 2.532 .109 8.639 7.995 3.04 3 2.782 .109 9.425 8.740 3.33 3M 3.010 .120 10.210 9.456 3.96 3^ 3.260 .120 10.996 10.242 4.28 3M 3.510 .120 11.781 11.027 4.60 4 3.732 .134 12.566 11.724 5.47 EXTRA STRONG BOILER TUBES There are many cases where extra strong tubes are required for special purposes and they are made to meet this demand. As a thick tube will hold more than a thin one in the capacity of a brace ^ they are sometimes used near the center of large boiler heads on this account. They should be used in some of the horizontal water tube boilers now in the market, in order to make them more reliable, as more material is needed in a water tube than in a fire tube for the same pressure, as the former must support the weight of water from which the latter is free. However, the water tube is supported between the ends, BOILERS 65 while a fire tube cannot be so strength- ened. The next table gives dimensions of extra strong boiler tubes. SIZE OF EXTRA STRONG BOILER TUBES -w u u S *Thick- Inside "5 2.875 2.315 .280 .560 1.755 3 3.5 2.892 .304 .608 2.284 3H 4.0 3.358 .321 .642 2.716 4 4.5 3.818 341 .682 3.136 HEATING SURFACE OF STEAM ^OILERS The heating surface of a steam boiler consists of the parts that are in contact with the fire or the hot gases produced by it, on one side, and are covered by- water on the other. It may be possible to show an exception to this rule in the case of a vertical fire tube, boiler in which the tubes extend through the steam space to the upper head. For a com.pa.ratively short distance they are not covered by water but they tend to superheat the steam, or at least to evap- orate particles of water that are taken 66 STEAM ENGINEERING Up by the steam as it ascends from the water surface, hence the surface above the water level in such cases is of more or less value. The capacity of a boiler so far as the evaporation pf water is concerned, de- pends on the amount of heating surface it contains and the rapidity with which the water circulates through it. The number of square feet of heating surface is easily determined, but the efficiency of the circulation can only be determined by actual trial of various kinds of boilers. After it is once ascertained for a cer- tain design, all others of the same kind may be depended upon to show the same results, provided the conditions are alike. The amount of heating surface offers a suggestion concerning the power that a boiler can develop, but it should not be taken as definite information con- cerning what it can do or of what it actually is doing in practice. A boiler may have heating surface enough to develop 100 horse power ac- cording to standard rating for given conditions, but the actual conditions may be more favorable for evaporating water, hence it can be made to develop 150 horse power, although it would probably result in low efficiency so far as the amotmt of water evaporated per BOILERS 67 pound of coal is concerned, and repair bills may be large. On the other hand a boiler may have enough heating surface 'to warrant its rating at 100 horse power, yet owing to light demand for steam it may not devel- op more than 50 horse power, hence this must be taken into consideration when noting the amount of coal burned in different places. Some heating surface is much more efficient than others, but this is not con- sidered when the amount is stated, be- cause it is difficult or impossible to always tell just which is the most effi- cient, and to draw the line of separation between the two kinds. Where heat is travelling in one direction and water in the opposite, the best results are secured. When calculating the heating surface in the shell of a tubular boiler, or in the steam drum of one of the water tube type, multiply the circumference in feet by the length and divide the product by 2: In some cases the actual surface with which heat comes in contact may exceed the result secured by the above rule, because the brick work may be drawn in to touch the shell above the center line, thus increasing the surface by a few square feet. Where accuracy is required it is necessary to measure the exact distance from the wall on one 68 STEAM ENGINEERING side to a similar place on the other, fol- lowing the curve of the shell. This will give the width, and multiplying it by the length gives the square feet of heat- ing surface in the shell. The tubes seem to present a more complicated problem, but this can be greatly modified by modem methods. If we find the circumference of a tube in inches, then multiply it by the length in inches and divide the product by 144, the quotient will be the number of square feet in the tube, but it requires the use of many figures, and is therefore too long for convenience. The use of a table shortens the proc- ess, and thus proves satisfactory^ to the busy engineer. The following con- tains the required information, and further explanation follows it. Information in this table is classified as follows in the several columns: 1. External diameter in inches. 2. External area in square inches. 3. Internal " " " " 4. Length of tube required for one square foot of heating surface, inside measurement. 5. Length of tube required for one square foot of heating surface, out- side measurement. 69 Length of tube required for one square foot of heating surface, based on the mean diameter, or the exter- nal diameter less the thickness. BOILER TUBES 1 2 3 4 5 6 1 .785 .515 4.479 3.820 4.149 IM 1.227 .882 3.604 3.056 3.330 1.767 1.348 2.916 2.547 2.730 1 5^ 2.405 1.911 2.448 2.183 2.316 2 3.142 2.573 2.110 1.910 2.010 2H 3.976 3.333 1.854 1.698 1.770 2H 4.909 4.000 1.674 1,528 1.601 2H 5.940 5.035 1.508 1.389 1.449 3 7.069 6.079 1.373 1.273 1.329 SH 8.296 7.116 1.269 1.175 1.222 3H 9.621 8.347 1.172 1.091 i.l32 3M 11.045 9.676 1.088 1.019 1.054 4 12.566 10.939 1.024 .955 .990 Suppose that a fire tube or tubular boiler is fitted with 90 3-inch tubes, 16 feet long. How many square feet of heating surface are in the tubes ? The total length is 16X96 = 1,536 feet. As the fire can only come in contact with the internal surface of these tubes, the total length is to be divided by 1.373 because column 4 in the foregoing table shows that it requires 1.373 feet in length to make one square foot on the tube. The heating surface in this case is 1,536 -!- 1.373 =1,1 18 square feet. A water tube boiler contains 126 tubes 4 inches external diameter 20 feet long. 70 STEAM ENGINEERING How many square feet of heating sur- face do they contain? The total length is 20X126 = 2,520 feet. The fire comes in contact with the external surface of these tubes, hence it requires .955 feet in length to make one square foot. (See column 5 in the foregoing table.) Then 2,520-^.955 = 2,638 square feet in these tubes. If two-thirds of the heads in the above mentioned tubular boiler, minus the area of the tubes, is considered effective heat- ing surface, how many square feet do both heads contain? The area of a 66-inch circle is 66X66 X. 7854 = 3,421.19 square inches, two- thirds of which is 2,280.78. The exter- nal area of a 3-inch tube is 7.069 square inches. (See column 2 in the preceding table.) The combined area of 96 is then 7.069X96 = 678.62. Then 2,280.78- 678.62 = 1,602.16 square inches which is 15.83 square feet for each, or 31.66 for both heads. If it is claimed that only the internal area of the tubes should be subtracted, because the thickness of the metal ac- counts for the remainder, then the area of each tube is 6.079 square inches. (See column 3 in the table.) The combined BOILERS 71 area is 6.079X96=583.58 square inches and subtracting this from two-thirds of the area of the head leaves 2,280.78 - 583.58 = 1,697.20 square inches or 11.78 square feet, or 23.56 in both heads. These directions apply to all boiler heads and any number of tubes. The next table gives a list of boiler heads from 42 to 84 inches in diameter the area of each in square feet, the cir- cumference and one-half of the circum- ference of the shells of equal diameter in feet. It enables the reader to readily calcu- late the heating surface in any boiler head after accounting for the tubes. For illustration suppose that a boiler head 78 inches in diameter contains 120 three inch tubes, and the heating surface in it is to be determined, taking the whole head. The combined area of the tubes is 7.069X120^144 = 5.89 square feet. The table shows that this head con- tains 33.18 square feet and 33.18 — 5.89 = 27.29 square feet. This table may also be used for deter- mining the heating surface in boiler shells. The circumference of each is given in feet, and it follows that this is 72 STEAM ENGINEERING the number of square feet of heating surface for each foot in length of the boiler. For illustration suppose that a boiler 84 inches in diameter is 20 feet long. How many square feet of heating surface are in the shell? The table shows that there are 21.99 for each foot or 21.99X20 = 439.8 in the whole sheU. If only one-half of the shell is taken the table shows that there are 10.99 square feet for each foot in length, or 219.8 square feet for one-half of the shell. In the case of a vertical fire tube boiler, the shell cannot be counted as heating surface because the fire does not touch it, but the furnace contains some that is very effective. Suppose that in a given case the circular furnace is 60 inches in diameter. The foregoing table shows that the circumference of this furnace is 15.70 feet, or in other words there are 15.70 square feet for each foot in height, therefore, if it is 4 feet high above the grates there are 15.70X4 = 60.28 square feet in this part. The surface in the lower head may be determined by the rule already explained. 73 TABLE OP AREAS OF BOILER READS In Sqtiare Feet, the Circumference, and One -half the Circumference in Feet Diameter Area in Circum- One-half Circtim- in inches square ft. ference in feet ference in feet 42 9.62 10.99 5.49 44 10.55 11.51 5.75 46 11.54 12.04 6.02 48 12.56 12.56 6.28 50 13.63 13.09 6.54 52 14.74 13.61 6.80 54 15.90 ' 14.13 7.06 56 17.10 14.66 7.33 58 18.34 15.18 7.59 60 19.63 15.70 7.85 62 20.96 16.23 8.11 64 22.34 16.75 8.37 66 23.75 17.27 8.63 68 25.22 17.80 8.90 70 26.72 18.32 9.16 72 28.27 18.84 9.42 74 29.86 19.37 9.68 76 31.50 19.89 9.94 78 33.18 20.42 10.21 80 34.90 20.94 10.47 82 36.67 21.46 10.73 84 38.48 21.99 10.99 The heating surface in a vertical fire tube boiler consists of the furnace and the tubes. In a horizontal tubular boiler it includes the shell, tubes and heads. The locomotive type utilises the sides of the furnace, also the crown sheet, the heads and the tubes. The water tube kind takes all of the tubes, the headers and the lower half of the steam drum. Flue boilers include about two-thirds of the shell, all of the flues and what is left of the heads. The 74 STEAM ENGINEERING cylinder only has about two-thirds of the shell and the same proportion of the heads. When the total heating surface in either or all of the above types has been ascertained in accordance with these rules, tables and suggestions, it forms a basis on which to make an estimate of what a certain kind and size of a boiler will do un'der fair conditions. The following figures show what pan be secured along this line. They indi- cate the number of square feet that will develop one horse power. HEATING SURFACE PER HORSE POWER Vertical 18 square feet Horizontal 15 " " Locomotive 15 " " Water tube 12 " " Flue 10 " " Cylinder 8 " " Vertical boilers are usually designed to include a large amount of heating sur- face in a comparatively small shell, but the vertical portion of the tubes render them slightly less effective than when in a horizontal position, as they are found in the common tubular and loco- motive boilers. The water tube type is more efficient in evaporating water per square foot of BOILERS 75 heating surface, hence the number re- quired per horse power is less. The flue boiler is efficient in this respect, but owing to its design the heating surface that can be secured with a shell of given diameter is less than with others above mentioned. The cylinder boiler is cred- ited with developing a horse power with less than any of the preceding kinds, but the square feet of surface secured in a given boiler is very small, hence a much larger shell is required for a given power. The author is aware that a horse power has been developed in numerous cases with much less heating surface than these figures represent, but the natural tendency of steam users to load their machinery to the extreme limit, and the ambition of faithful engineers to meet every responsbility put upon them needs no encouragement here. On the contrary there is more need of conservative advice now than ever be- fore, and to this end it is earnestly recommended that boilers never be loaded beyond what these figures in- dicate. The worst case that has come to our notice in detail is where a horse power was actually developed for every three square feet of heating surface that the toiler contained, but the conditions 76 STEAM ENGINEERING showed an utter disregard of the danger to human life, and indifference to the cost of maintenance and repairs. ACTUAL HORSE POWER OF BOILERS When men who are interested in steam engineering consider the subject of the power of a boiler, they seem to naturally divide themselves into three classes. First, those who claim that there is no such thing as the horse power of a boiler. Second, those who admit that a boiler does develop power, but think that the present way of determining it is illog- ical and wrong, hence wish to have a different standard adopted. Third, those who admit that the pres- ent practice along this Une is apparently not up-to-date, but cannot understand how any standard can be devised which will suit even a majority of the cases in common practice, and so long as this is true now and liable to be for a long time to come, it is useless to introduce a decid- edly disturbing element into the theory of steam engineering, which cannot be of sufficient advantage to recompense for the trouble and expense of changing set rules in thousands of volumes on this important subject. BOILERS 77 In reply to the first it is proper to call attention to the fact that all standards of this or any other kind are simply the result of the deliberations of one man that subsequently were adopted by men in council, or they were accepted by bodies of men congregated for the purpose, hence have become laws on the various subjects to which they apply. It is just as logical and proper to de- cide on what shall be known as one horse power in a boiler, as it is to decide that 5,280 feet shall constitute a mile. Concerning the objections of the sec- ond class, it is only necessary to say that the present standard was adopted many years ago when the average boiler pres- sure was much lower than it is at the present time. However, even at that time there were many boilers that were operated imder much lower pressure than the standard calls for, while others carried higher pressures. Now the only difference between con- ditions at that time and at the present is that some boilers are carrying much higher pressure than ever before. On the other hand thousands of boilers are operated every day under less pressure than the standard calls for, but this standard can be appHed to every boiler in use, without regard to the conditions 78 STEAM ENGINEERING I under which it is operated. Could any other standard do more? The third class are a conservative body of men who are willing to accept anything that is decidedly better than what has been, or is now in use, but they insist on being convinced that old stand- ards are defective, and that new ones are free from defects before they discard the former and adopt the latter. Sure- ly this is safe ground on which to stand, and without this element the whole superstructure of steam engineering would become unstable and imreliable so far as theoretical standards are con- cerned, and this means almost every branch of the subject. The foregoing remarks refer to what is known as the Centennial rating of the power of steam boilers, as follows: The evaporation of 30 pounds of water per hotu, from feed water at 100 degrees Fah. into steam at 70 pounds gauge pres- sure, or its equivalent under other con- ditions, constitutes one horse power. If boilers were always nm under these conditions, it would only be necessary to divide the weight of water evaporated per hoiu- by 30 and the quotient would be the power developed. In practice it becomes necessary to reduce the actual results seciu-ed, to terms of the above rating in order to make it agree, and this A BOILERS 79 proves a stumbling block to the working engineer and the owners of boilers who have not given the subject due atten- . tion. The matter will be clear to all who study the following statements: THE OBJECT OF A BOILER TEST The object sought in conducting a boiler test is to accurately determine the amount of water evaporated into dry steam, in order to calculate the power developed, and to find the weight of coal actually burned in order to ascertain the efficiency of the boiler. The foregoing seem to be self-evident facts, but past experience shows that they are not, for numerous so-called tests have been reported which neither tell how much water was evaporated nor the weight of coal burned to evaporate it. Where these points are not settled, the whole proves tinreliable and unsat- isfactory. Reports of conditions that can have no effect on the results will not be intro- duced for the purpose of making the matter appear more complicated, as the object is to simplify the process and retain accuracy. 80 STEAM ENGINEERING STARTING A TEST Before a test is started the water level • ' should be brought to the point where it is considered advisable to carrv' it which will be at about two gauges usually. Tie a string around the gauge glass at this point, maintain the same water level as closely as possible throughout the test, and bring it to exactly the same place at the conclusion of it. As a further precaution the steam pressure should be the same at the beginning and the end of the test. If these directions are followed there will be no error on account of more or less water in the boiler than there should be. Care should be taken to know that none of the water pumped in is lost through a leaky blow off valve, or at any other point below the water line. It is very convenient to use a water meter to determine the amount deliv- ered to the boiler, and there is no good reason why this method should not be used. If a water meter does not cor- rectly indicate the amount of water pas- sing through it, and its indications are accepted without correction, the final ^ BOILERS 81 result will not be correct, but it is not so difficult to calibrate, or prove a meter as it appears. Set a barrel on a pair of platform scales and note its exact weight. Let water pass through the meter into the barrel until the meter indicates that say, 4 cubic feet have passed. Put a ther- mometer into this water and note its temperature, which is assumed to be 68 degrees. By referring to a table of the proper- ties of water the weight per cubic foot at 68 degrees is found to be 62.33 poimds, therefore 4 cubic feet weighs 62.33X4 = 249.32 pounds. Suppose that the water in the barrel actually weighs 244.25 pounds. In that case the water actually delivered to the boiler is 244.25 H- 249.32 = .98 of what the meter in- dicates, consequently when the meter is read at the end of the test, the result must be multipHed by .98 to ascertain the true quantity in cubic feet. Suppose that the water actually weighed 253 pounds, then the indica- tions of the meter would "have to be multiplied by 253-^249.32 = 1.015 in order to determine the actual quantity used. 82 STEAM ENGINEERING WEIGHING THE WATER Water for testing an ordinary boiler may be weighed by means of three bar- rels as shown in Fig. 14. Two of them are mounted on a platform and are fitted with outlet pipes 2 inches in diameter, both of which discharge into another barrel under them. Valves are pro- vided to shut off either one at pleasure. Before the lower barrel is placed in position and connected to the pump, both of the upper ones should be filled BOILERS 83 with water and each of them drained separately into a barrel on a pair of scales, thus determining the exact weight of water that each holds. The third barrel is then placed in posi- tion and connected as shown, so that during the test water may be drawn continuously from the lower barrel as it is fed from each of the others alternate- ly. By keeping a record of the number of times these barrels are filled and emptied, the exact weight of water* used may be known without further calcu- lation. QUALITY OF STEAM PRODUCED A boiler test made without determin- ing the quality of the steam produced, is of no value, because much of the water pumped into the boiler may not be evap- orated, but pass away with the steam in the form of hot water. This water may be raised to a temper- ature equal to the steam with which it mingles, and the boiler should be cred- ited with this heat, but the latent heat of evaporation has not passed into it, and as this is much greater than the sen- sible heat, it cannot be ignored. A sample of the steam to be tested should be taken from a vertical pipe if possible, by means of a small perforated 84 STEAM ENGINEERING pipe screwed into it as shown in Fig. 15. It should always be arranged so as to prevent taking steam from the inner FKS.I5 surface of the large pipe, as water may trickle down on this surface, thus not giving a true sample of the steam. If it is necessary to take the sample from a horizontal pipe, special care should be taken to avoid the water which alwa3^s runs along the bottom of such a pipe. Having property connected this pipe the steam may be tested by blowing a BOILERS 85 portion of it into a certain weight of cold water, as illustrated in Fig. 16. A tee should be put on the end of this pipe to prevent the steam from interfering with correct weighing of the whole. The temperature of this water should be raised to not less than 110, nor more than 150 degrees Fah. The former ought to be secured in order to give _^ 86 STEAM ENGINEERING sufficient rise in temperature to lessen the possibility of error, and it is a good idea not to exceed the latter, as the dan- ger of loss of heat increases with the temperature. It should be thoroughly- stirred to make the temperature even throughout the whole of it. It is not necessary to use any given weight of cold water (provided the cor- rect weight is known), but from 300 to 400 pounds is suggested, because more reliable results are usually secured with a large quantity. An ordinary oil bar- rel will hold 320 pounds without being too full for convenience, and as one of them is usually available around a steam plant it can be cleaned and used for this purpose, therefore a uniform weight of 320 pounds is recommended for these tests. The percentage of moisture in the steam tested may be determined by the following formula: ^X(H-C)-(T-H) o r=» W = Weight of cold water used. S = « « steam condensed. H = Total heat of one pound of the heated water. C = Total heat of one pound of the cold water. BOILERS 87 T = Total heat of one pound of the water at a temperature cor- responding to the pressure of steam used. L = Latent heat of the steam, Q= Quality of the steam tested, taking dry steam at unity or I. The weight of steam condensed is found by subtracting the weight of the cold water from the weight of the heated water. In all cases where there is moisture in the steam tested, the value of Q is less than one, as it represents the compara- tive value of the steam, as for illustra- tion, if the formula is applied to a given case and the value of Q is .95 the steam is .95 dry or I -Q= I -.95 = .05 moist, or in other words it is 95 per cent, dry and there is 5 per cent, of moisture in it. For illustration, suppose that 320 pounds of water are put into the barrel at a temperature of 65 degrees Fah., the total heat of which is 33.01. Steam is blown into this water until it weighs 340 pounds or 340-320 = 20 pounds more and the temperature is raised to 125 degrees Fah., the total heat of which is 93.17. Pressure is maintained at 95 pounds absolute, or 80 by the gauge. The total heat of the water under this pres- 66 STEAM ENGINEERING i r sure is 295.1 and the latent heat of the It steam is 885.6. An application of the formula results as follows: 320 X (93.17 - 33.1) - (295.1-93.17) = (16X60.07 -201.93) X. 0011.= .83 885 .6 Therefore .83 of the mixture coming from the boiler is dry steam and 1.00 — .83 = .17 of it is water. If it only re- quired 19 pounds of condensed steam to secure the same temperature in the bar- rel, then the quality of the steam would be .89 and if 18 pounds were sufficient it would be raised to .94. As 17.5 pounds will raise it to .98 it illustrates the neces- sity of taking great care to secure cor- rect weights for every experiment. In case that only 17 pounds of con- densed steam gives the required rise in temperature imdef the same conditions the final result is 1.02 and as this is more than I, further explanation is necessary. It denotes that the steam is superheated slightly. It now becomes necessary to proceed as follows, in order to determine the de- grees of superheat. From the quality BOILERS 89 of the steam subtract 1 and multiply the remainder by 2.0833. In this case it is 1.02-1X2.0833 = .04 degree, showing that the steam is practically dry. Suppose that it required only 5 pounds of water to secure the same rise in temperature, then there would be 6 degrees of superheat present. The tem- perature of this steam as it comes from the boiler would be 6 degrees higher than the temperature of saturated or dry steam at the same pressure. THERMOMETERS In order to make the necessary cal- culations after testing the steam, a table of the properties of water is re- quired, and it follows this explanation. The temperatures are given from the freezing to the boiling point on the Fahrenheit, Centigrade and Reaumur thermometers, to enable the reader to easily use the kind that is preferred. It should be remembered, however, that zero on the Fahrenheit scale is 32 degrees below the freezing point, while the boiling point under atmospheric pressure at sea level is 212. Zero and the freezing point are the same on the Centigrade scale and the boiling point is foimd at 100, while the Reaumur takes the freezing 90 STEAM ENGINEERING point at zero and places the boiling point: at 80 degrees above it. For temperatures higher than the table contains the following rules may- be used to convert the value of one scale into a corresponding value on another. TO CHANGE FAHRENHEIT TO CENTIGRADE Subtract 32, multiply the remainder by 5 and divide the quotient by 9. Ex- ample: A barrel contains 320 pounds of water at 110 degrees Fahrenheit. What is its temperature by the Centi- grade scale? 110-32X5^9 = 43.3 degrees. TO CHANGE FAHRENHEIT TO REAUMUR Subtract 32, multiply the remainder by 4 and divide the quotient by 9. In the foregoing example what is the temperature of the water by the Reau- , mur scale? 110-32X4^-9=347 degrees. TO CHANGE CENTIGRADE TO FAHRENHEIT Multiply by 9, divide the product by 5 and add 32 to the quotient. Exam- ple: A barrel contains 320 pounds of BOILERS 91 water at 70 degrees Centigrade. What is its temperature by the Fahrenheit scale? 70X9 -^5+32 = 158 degrees. TO CHANGE CENTIGRADE TO REAUMUR Multiply by 4 and divide the product by 5. In the preceding example what is the temperature of the water by the Reau- mur scale? 70X4^5 = 56 degrees. TO CHANGE REAUMUR TO CENTIGRADE Multiply by 5 and divide the product by 4. Example: A barrel contains 320 pounds of water at 60 degrees Reau- mur. What is its temperature on the Centigrade scale? 60X5-^4 = 75 degrees. TO CHANGE REAUMUR TO FAHRENHEIT Multiply by 9, divide the product by 4 and add 32 to the quotient. In the pre- ceding example what is the temperature of the water on the Fahrenheit scale? 60X9-^4^-32 = 167 degrees. These rules may be applied to any case with correct results. 92 STEAM ENGINEERING PROPERTIES OF WATER Temperature Heat Weight per F c R units cubic foot 32 62.42 33 0.6 0.4 1 62.42 34 1.1 0.9 2 62.42 35 1.7 1.3 3 62.42 36 2.2 1.8 4 62.42 37 2.8 2.2 5 62.42 38 3.3 2.7 6 62.42 39 3.9 3.1 7 62.42 40 4.4 3.6 8 62.42 41 5.0 4.0 9 62.42 42 5.6 4.4 10 62.42 43 6.1 4.9 11 62.42 44 6.7 5.3 12 62.42 45 7.2 5.8 13 62.42 46 7.8 6.2 14 62.42 47 8.3 6.7 15 62.42 48 8.9 7.1 16 62.41 49 9.4 7.6 17 62.41 50 10.0 8.0 18 62.41 51 10.6 8.4 19 62.41 52 11.1 8.9 20 62.40 53 11.7 9.3 20.01 62.40 54 12.2 9.8 22.01 62.40 55 12.8 10.2 23.01 62.39 56 13.3 10.7 24.01 62.39 57 13.9 11.1 25.01 62.39 58 14.4 11.6 26.01 62.38 59 15.0 12.0 27.01 62.38 60 15.6 12.4 28.01 62.37 61 16.1 12.9 29.01 62.37 62 16.7 13.3 30.01 62.36 63 17.2 13.8 31.01 62.36 64 17.8 14.2 32.01 62.35 65 18.3 14.7 33.01 62.34 66 18.9 15.1 34.02 62.34 67 19.4 15.6 35.02 62.33 68 20.0 16.0 36.02 62.33 69 20.6 16.4 37.02 62.32 70 21.1 16.9 38.02 62.31 71 21.7 17.3 39.02 62.31 72 22.2 17.8 40.02 62.30 73 22.8 18.2 41.02 62.29 74 23.3 18.7 42.03 62.28 75 23.9 19.1 43.03 62.28 76 24.4 19.6 44.03 62.27 93 Properties of Water — Continued Temperature Heat Weight per F C R units cubic foot 77 25.0 20.0 45.03 62.26 78 25.6 20.4 46.03 62.25 79 26.1 20.9 47.03 62.24 80 26.7 21.3 48.04 62.23 81 27.2 21.8 49.04 62.22 82 27.8 22.2 50.04 62,21 83 28.3 22.7 51.04 62.20 84 28.9 23.1 52.04 62.19 85 29.4 23.6 53.05 62.18 86 30.0 24.0 54.05 62.17 87 30.6 24.4. 55.05 62.16 88 31.1 24.9 56.05 62.15 89 31.7 25.3 57.05 62.14 90 32.2 25.8 58.06 62.13 91 32.8 26.2 59.06 62.12 d2 33.3 26.7 60.06 62.11 93 33.9 27.1, 61.06 62.10 94 34.4 27.6 62.06 62.09 95 35.0 28.0 63.07 62.08 96 35.6 28.4 64.07 62.07 97 36.1 28.9 65.07 62.06 98 36.7 29.3 66.07 62.05 99 37.2 29.8 67.08 62.03 100 37.8 30.2 68.08 62.02 101 38.3 30.7 69.08 62.01 102 38.9 31.1 70.09 62.00 103 39.4 31.6 71.09 61.99 . 104 40.0 32.0 72.09 61.97 105 40.6 32.4 73.10 61.96 106 41.1 32.9 74.10 61.95 107 41.7 33.3 75.10 61.93 108 42.-2 33.8 76.10 61.92 109 42.8 34.2 77.11 61.91 110 43.3 34.7 78.11 61.89 111 43.9 35.1 79.11 61.88 112 44.4 35.6 80.12 61.86 113 45.0 36.0 81.12 61.85 114 45.6 36.4 82.13 61.83 115 46.1 36.9 83.13 61.82 116 46.7 37.3 > 84.13 61.80 117 47.2 37.8 85.14 61.78 118 47.8 38.2 86.14 61.77 119 48.3 38.7 87.15 61.75 120 48.9 39.1 88.15 61.74 121 49.4 39.6 89.15 61.72 122 50.0 40.0 90.16 61.70 04 STEAM ENGINEERING Properties of Water — Continued Temperature Heat units Weight per F C R cubic foot 123 50.6 40.4 91.16 61.68 124 51.1 40.9 92.17 61.67 125 51.7 41.3 93.17 61.65 126 52.2 41.8 94.17 61.63 127 52.8 42.2 95.18 61.61 128 53.3 42.7 96.18 61.60 129 53. « 43.1 97.19 61.58 130 64.4 43.6 98.19 61.66 131 55.0 44.0 99.20 61.54 132 65.6 44.4 100.20 61.62 133 66.1 44.9 101.21 61.51 134 56.7 45.3 102.21 61.49 135 57.2 45.8 103.22 61.47 136 67.8 46.2 104.22 61.45 137 68.3 46.7 105.23 61.43 138 58.9 47.1 106.23 61.41 139 59.4 47.6 107.24 61.39 140 60.0 48.0 108.25 61.37 141 60.6 48.4 109.25 61.36 142 61.1 48.9 110.26 61.34 143 61.7 49.3 111.26 61.32 144 62.2 49.8 112.27 61.30 145 62.8 60.2 113.28 61.28 146 63.3 60.7 114.28 61.26 147 63.9 61.1 115.29 61.24 148 64.4 51.6 116.29 61.22 149 65.0 52.0 117.30 61.20 150 65.6 52.4 118.31 61.18 151 66.1 62.9 119.31 61.16 152 66.7 53.3 120.32 61.14 153 67.2 53.8 121.33 61.12 154 67.8 64.2 122.33 61.10 155 68.3 64.7 123.34 61.08 156 68.9 55.1 124.35 61.06 157 69.4 65.6 125.35 61.04 158 70.0 66.0 126.36 61.02 159 70.6 56.4 127.37 61.00 160 71.1 56.9 128.37 60.98 161 71.7 57.3 129.38 60.96 162 72.2 57.8 130.39 60.94 163 72.8 58.2 131.40 60 92 164 73.3 68.7 132.41 60.90 165 73.9 59.1 133.41 60.87 166 74.4 59.6 134.42 60.85 167 75.0 60.0 135.43 60.83 BOILERS 95 Properties of Water — Continued Temperature Heat Weight per F C R units cubic foot 168 75 6 60.4 136 44 60.81 169 76 1 60 9 137.45 60.79 170 76 7 61 3 138.45 60.77 171 77 2 61 8 139 46 60.75 172 77 8 62,2 140 47 60.73 173 78.3 62.7 141 48 60.70 174 78.9 63.1 142 49 60.68 175 79 4 63.6 143.50 60.66 176 80.0 64.0 144 51 60.64 177 80.6 64 4 145.52 60.62 i 178 81 1 64 9 146.52 60.59 179 81 7 65.3 147.53 60.57 . 180 82 2 65.8 148.54 60.55 181 82.8 66.2 149.55 60.53 182 83.3 66.7 150 56 60.52 183 83.9 67 1 151.57 60.48 184 84.4 67 6 152 58 60.46 185 85 68.0 153 50 60.44 • 186 85 6 68 4 154.60 60.41 187 86 1 68 9 155 61 60.39 188 86.7 69 3 156.62 60.37 189 87 2 69.8 157 63 60.34 190 87 8 70 2 158.64 60.32 191 88 3 70 7 159 65 60.29 192 88 9 71 1 160.67 60.27 193 89 4 71.6 161.68 60.25 194 90 72 162 69 60.22 195 90 6 72.4 163 70 60.20 196 91 1 72.9 164.71 60.17 197 91 7 73.3 165 72 60.15 198 92 2 73.8 166 73 60.12 199 92 8 74 2 167. 74 60.10 200 93.3 74 7 168.75 60.07 201 93 9 75 1 169.77 60.05 202 94 4 75.6 170. 78 60 02 203 95.0 76.0 171 79 60.00 204 95.6 76 4 172.80 59.97 205 96.1 76 9 173.81 59.95 206 96 7 77.3 174.83 59.92 207 97 2 77.8 175.85 59.89 208 97 8 78.2 176.85 59.87 209 98 3 78 7 177.86 59.84 210 98.9 79 1 178 87 59.82 211 99.4 79 6 179.89 59.79 212 100.0 80 180.90 59.76 96 STEAM ENGINEERING The foregoing tables show that as the temperature of water is increased it ex- pands, hence if a cubic foot at 40 de-' grees Fah. or at any higher temperature 1 is still further heated, it will occupy more than a cubic foot of space, and it follows that if the volume is kept con- stant the weight must decrease. The difference is so small that it doc ; not appear in the table because the fif ures are given to two decimal place, only, until the temperature is raised to 48 degrees or more. If it is raised from 32 to 39 degrees it contracts slightly, thus occupying less space, but the differ- ence is very small. Maximum density is attained at 39.1 degrees Fahrenheit, 3.9 Centigrade or 3.1 Reaumur. It is useless for engineers, under even the best working conditions, to attempt to prove these figures, on account of dif- ficulty of measuring out exactly a cubic foot, and of obtaining a sample of per- fectly pure water. SATURATED STEAM This name does not always seem to be appropriate, as it suggests to the average working engineer, steam that is saturated with water, whereas it is in- tended for dry steam, as otherwise it could not constitute a standard for com- BOILERS 97 parisori, for as soon as steam becomes mixed with water, or when there is water suspended in the steam, its quaHty be- comes variable with the amount of water present, hence it could not be used with profit for comparison. Saturated steam is therefore the dividing quality between wet and superheated steam. In order to solve probleras that have already been presented, as well as some of those that follow, it is necessary to know something of the properties of sat- urated steam. These are given in the next table which will be explained here in order that the working engineer who has not enjoyed the advantages of a technical education may understand them, also for firemen who wish to be advanced to engineers, and all others interested in this important subject. Absolute pressures are used because all pressure must be reckoned from a perfect vacuum in this work, as other- wise there would be no standard for a base of operations. For all practical pur- poses it may be taken at 15 pounds above the gauge pressure, for steam gauges indicate the unbalanced pressure, and safety valves are designed to operate on the same principle. To ascertain the 98 STEAM ENGINEERING gauge pressures, subtract 15 from those given in the table. Temperatures are stated in the Fah- renheit scale in which zero is 32 degrees below the freezing point. It is not con- venient or practicable to state the heat units in water above zero, because the amount of heat required to raise the temperatures through a given range below 32 on this scale is less than to raise it through the same range above 32 degrees. It is therefore better to base all such calculations in which heat units are factors, on the freezing point, as it saves confusion and trouble. It is claimed that the temperature of water and of steam in a boiler is the same, and this is true after the water has been in the boiler under working conditions long enough to attain its maximum temperature, but it does not immediately flash into steam, because it lacks the latent heat of evaporation. This is a wise provision as otherwise we could not operate steam boilers as we do at present. When the heat units in a pound of water and the latent heat of evaporation are added, the sum is the total heat of steam at given pressure. We are sometimes told that the total 1 heat of steam is the same for all pres- sures, but this is not true, hence should not be accepted. The latent heat decreases as the tem- perature or sensible heat increases, but not in the same proportion as the total for 15 pounds, absolute pressure, is' 1,146.9 while for 200 pounds it is, 1,198.3 a difference of 51.4 heat units, or more than 4 per cent. It is necessary to know the weight of steam under various pressures when calculating the weight of a given volume and this is stated in the table. PROPERTIES OF SATURATED STEAM P= Absolute pressure in pounds per square inch, or 15 pounds above gauge pressure. T = Temperature of steam under the given pressure. W = Heat units in a pound of water under pressure that corresponds to the temperature. L= Latent heat, or the number of heat imits required to convert one pound of water at a given tem- perature and pressure into steam. S = Total heat of steam per pound above 32 degrees Fah. C= Weight of one cubic foot of steam at stated pressure. 100 STEAM ENGINEERING PROPERTIES OF SATURATED STEAM p T W L S C 14.7 212.0 180. £ 965.71 1.146.6 .03794 15 213.0 181. c 965.0 1,146.9 .03868 16 216.3 185. S 962.7 1,147.9 .04110 17 219.4 188.4 960.5 1,148.9 .04352 18 222.4 191.4 958.3 1,149.8 .04592 19 225.2 194.3 956.3 1,150.6 .04831 20 227.9 197. C 954.4 1,151.5 .0507C 21 230.5 199.7 952.6 1,152.2 .05308 22 233.0 202.2 950.8 1,153.0 .05545 23 235.4 204.7 949.1 1,153.7 .05782 24 237.8 207. C 947.4 1,154.5 .06018 25 240.0 209.3 945.8 1,155.1 .06253 26 242.2 211.5 944.3 1,155.8 .06487 27 244.3 213.7 942.8 1,156.4 .06721 28 246.3 215.7 941.3 1,157.1 .06955 29 248.3 217.8 939.9 1,157.7 .07188 30 250.2 219.7 938.9 1.158.3 .07420 31 252.1 221.6 937.2 1,158.8 .07652 32 254.0 223.5 935.9 1,159.4 .07884 33 255.7 225.3 934.6 1,159.9 .08115 34 257.5 227.1 933.4 1,160.5 .08346 35 259.2 22'8.8 932.2 1,161.0 .08576 36 260.8 230.5 931.0 1,161.5 .08806 37 262.5 232.1 929.8 1,162.0 .09035 38 264.0 233.8 928.7 1,162.5 .09264 39 265.6 235.4 927.6 1,162.9 .09493 40 267.1 236.9 926.5 1,163.4 .09721 41 268.6 238.5 925.4 1,163.9 .09949 42 270.1 240.0 924.4 1,164.3 .1018 43 271.5 241.4 923.3 1,164.7 .1040 44 272.9 242.9 922.3 1,165.2 .1063 45 274.3 244.3 921.3 1,165.6 .1086 46 275.7 245.7 920.4 1,166.0 .1108 47 277.0 247.0 919.4 1,166.4 .1131 48 278.3 248.4 918.5 1,166.8 .1153 49 279.6 249.7 917.5 1,167.2 .1176 50 280.9 251.0 916.6 1,167.6 .1198 51 282.1 252.2 915.71 1,168.0 .1221 52 283.3 253.5 914.9 1,168.4 .1243 53 284.5 254.7 914.0 1,168.7 .1266 54 285.7 256.0 913.1 1,169.1 .1288 55 286.9 257.2 912.3 1,169.4 .1311 56 288.1 258.3 911.5 1,169.8 .1333 57 289.1 259.5 910.6 1,170.1 .1355 58. 290. a 260.7 909.8 1,170.5 .1377 59 291.4 261.8 909.0 1,170.8 ..1400 60 292.5 262.9 908.2 1,171.2 .1422 101 Properties of Saturated Steam — Continued ! p T W L s C 61 293.6 264.0 907.5 1,171.5 .1444 62 294.7 265.1 906.7 1,171.8 .1466 63 295.7 266.2 905.9 1,172.1 .1488 64 296.8 267.2 905.2 1,172.4 .1511 65 297.8 268.3 904.5 1,172.8 .1533 66 298.8 269.3 903.7 1,173.1 .1555 67 299.8 270.4 903.0 1,173.4 .1577 68 300.8 271.4 902.3 1,173.7 .1599 69 301.8 272.4 901.6 1,174.0 .162] 70 302.7 273.4 900.9 1,174.3 .1643 71 303.7 274.4 900.2 1,174.6 .1665 72 304.6 275.3 899.5 1,174.8 .1687 73 305.6 276.3 898.9 1,175.1 .1709 74 306.5 277.2 898.2 1,175.4 .1731 75 307.4 278.2 897.5 1,175.7 .1753 76 308.3 279.1 896.9 1,176.0 .1775 77 309.2 280.0 896.2 1,176.2 .1797 78 310.1 280.9 895.6 1,176.5 .1819 79 310.9 281.8 895.0 1,176.8 .1840 80 311.8 282.7 894.3 1,177.0 .1862 81 312.7 283.6 893.7 1,177.3 .1884 82 313.5 284.5 893.1 1,177.6 .1906 83 314.4 285.3 892.5 1.177.8 .1928 84 315.2 286.2 891.9 1,178.1 .1950 85 316.0 287.0 891.3 1,178.3 .1971 86 316.8 287.9 890.7 1,178.6 .1993 87 317.7 288.7 890.1 1,178.8 .2015 88 318.5 289.5 889.5 1,179.1 .2036 89 319.3 290.4 888.9 1,179.3 .2058 90 320.0 291.2 888.4 1,179.6 .2080 91 320.8 292.0 887.8 1,179.8 .2102 92 321.6 292.8 887.2 1,180.0 .2123 93 322.4 293.6 886.7 1,180.3 .2145 94 323.1 294.4 886.1 1,180.5 .2166 95 323.9 295.1 885.6 1,180.7 .2188 96 324.6 295.9 885.0 1,181.0 .2210 97 325.4 296.7 884.5 1,181.2 .2231 98 326.1 297.4 884.0 1,181.4 .2253 99 326.8 298.2 883.4 1.181.6 .2274 100 327.6 298.9 882.9 1,181.8 .2296 101 328.3 299.7 882.4 1,182.1 .2317 102 329.0 300.4 881.9 1,182.3 .2339 103 329.7 301.1 881.4 1,182.5 .2360 104 330.4 301.9 1,182.7 .2382 105 331.1 302.6 88013 1,182.9 .2403 106 331.8 303.3 879.8 1,183.1 .2425 102 STEAM ENGINEERING Properties of Saturated Steam — Continued p T W L S C 107 332.5 304.0 879.3 1,183.4 .2446 108 333.2 304.7 878.8 1,183.6 .2467 109 333.9 305.4 878.3 1,183.8 .2489 110 334.5 306.1 877.9 1,184.0 .2510 111 335.2 306.8 877.4 1,184.2 .2531 112 335.9 307.5 876.9 1,184.4 .2553 113 336.5 308.2 876.4 1,184.6 .2574 114 337.2 308.8 875.9 1,184.8 .2596 115 337.8 309.5 875.5 1,185.0 i,185.2 .2617 116 338.5 310.2 875.0 .2638 117 339.1 310.8 874.5 1,185.4 .2660 118 33.9.7 311.5 874.1 1,185.6 .2681 119 340.4 312.1 873.6 1,185.8 .2703 120 341.0 312.8 873.2 1,185.9 .2724- 121 341.6 313.4 872.7 1,186.1 .2745 122 342.2 314.1 872.3 1,186.3 .2766 123 342.9 314.7 871.8 1,186.5 .2788 ,124 343.5 315.3 871.4 1,186.7 .2809 125- 344.1 316.0 870.9 1.186.9 .2830 126 344.7 316.6 870.5 1,187.1 .2851 127 345.3 317.2 870.0 1,187.3 .2872 128 345.9 317.8 869.6 1,187.4 .2894 129 346.5 318.4 869.2 1,187.6 .2915 130 347.1 319.1 868.7 1,187.8 .2936 131 347.6 319.7 868.3 1,188.0 .2957 132 348.2 320.3 867.9 1,188.2 .2978 133 348.8 320.8 867.5 1,188.3 .3000 134 349.4 321.5 867.0 1,188.5 .3021 135 350.0 322.1 868.6 1,188.7 .3042 136 350.5 322.6 866.2 1,188.9 .3063 137 351.1 323.2 865.8 1,189.0 .3084 138 351.8 323.8 865.4 1,189.2 .3105 139 352.2 324.4 865.0 1,189.4 .3126 140 352.8 325.0 864.6 1,189.5 .3147 141 353.3 325.5 864.2 1,189.7 .3169 142 353.9 326.1 863.8 1,189.9 .3190 143 354.4 326.7 863.4 1,190.0 .3211 144 355.0 327.2 863.0 1,190.2 .3232 145 355.5 327.8 862.6 1,190.4 .3253 146 356.0 328.4 862.2 1,190.5 .3274 147 356.6 328.9 861.8 1,190.7 .3295 148 357.1 329.5 861.4 1,190.9 .3316 149 357.6 330.0 861.0 1,191.0 .3337 150 358.2 330.6 860.6 1,191.2 .3358 151 358.7 331.1 860.2 1,191.3 .3379 152 359.2 331.6 859.9 1,191.5 .3400 153 359.7 332.2 859.5 1,191.7 .3421 BOILERS 103 Properties of Saturated Steam — Continued p T W L s C 154 360.2 332.7 859.1 1,191.8 .3442 155 360.7 333.2 868.7 1,192.0 .3463 156 361,3 333.8 858.4 1,192.1 .3483 157 361.8 334.3 858.0 1,192.3 .3504 158 362.3 334.8 857.6 1,192.4 .3525 159 362.8 335.3 857.2 1,192.6 .3546 160 363.3 335.9 856.9 1,192.7 .3567 161 363.8 336.4 856.5 1,192.9 .3588 162 364.3 336.9 856.1 1,193.0 .3609 163 364.8 337.4 855.8 1,193.2 .3630 164 365.3 337.9 855.4 1,193.3 .3650 165 365.7 338.4 855.1 1,193.5 .3671 166 366.2 338.9 854.7 1,193.6 .3692 167 366.7 339.4 854.4 1,193.B .3713 168 367.2 339.9 854.0 1,193.9 .3731 169 367.7 340.4 853.6 1,194.1 .3754 170 368.2 340.9 853.3 1,194.2 .3775 171 368.6 341.4 852.9 1,194.4 .3796 172 369.1 341.9 852.6 1,194.5 .3817 173 369.6 342.4 852.3 1,194.7 .3838 174 370.0 342.9 851.9 1.194.8 .3858 175 370.5 343.4 851.6 1,194.9 .3879 176 371.0 343.9 851.2 1,195.1 .3900 177 371.4 344.3 850.9 1,195.2 .3921 178 371.9 344.8 850.5 1,195.4 .3942 179 372.4 345.3 850.2 1,195.5 .3962 180 372.8 345.8 849.9 1,195.7 .3983 181 373.3 346.3 849.5 1,195.8 .4004 182 373.7 346.7 849.2 1,195.9 .4025 183 374.2 347.2 848.9 1,196.1 .4046 184 374.6 347.7 848.5 1,196.2 .4066 185 375.1 348.1 848.2 1,196.3 .4087 186 375.5 348.6 847.9 1,196.5 .4108 187 375.9 349.1 847.6 1,196.6 .4129 188 376.4 349.5 847.2 1,196.7 ,4150 189 376.9 350.0 846.9 1,196.9 .4170 190 377.3 350.4 846.6 1,197.0 .4190 191 377.7 350.9 846.3 1.197.1 .4212 192 378.2 351.3 845.9 1,197.3 .4233 193 378.6 351.8 845.6 1,197.4 .4254 194 379.0 352.2 845.3 1,197.5 .4275 195 379.5 352.7 845.0 1,197.7 .4296 196 380.0 353.1 844.7 1,197.8 .4317 197 380.3 353.6 844.4 1,197.9 .4337 198 380.7 354.0 844.1 1.198.1 .4358 199 381.2 354.4 ^ 843.7 1,198.2 .4379 200 381.6 354.9 843.4 1,198.3 .4400 104 STEAM ENGINEERING WATER EVAPORATED UNDER WORKING CONDITIONS When water that is used in conducting a boiler test is measured in barrels, it is only necessary to multiply the number of barrel fulls by the weight of each to secure the total weight, but if a meter is used, the quantity that has passed through it is indicated in cubic feet. Care must be taken to note the temper- ature as that determines the weight per cubic foot. Suppose that during a test lasting 10 hours, the meter indicates that 658 cubic feet have passed, or 65.8 per hour, and calibration of the meter according to directions already given shows that .98 of its indications are the true quan- tity. Then 65.8 X. 98 =64.484 cubic feet. Taking the temperature at 65 de- grees, the weight per cubic foot is 62.34 pounds, or 64.484X62.34 = 4,019.93 pounds per hour. For a simple illustration it is assumed that after the feed water passes through the meter at 65 degrees it goes to a heat- er where its temperature is raised to 100 degrees Fah., and it is then forced into the boiler which carries 70 pounds pres- sure by the gauge or 85 pounds absolute. The atmospheric pressure is 14.7 pounds or less, but inasmuch as our ordinary BOILERS 105 steam gauges do not designate fractions of a pound it is not necessary to take them into account in this calculation. Under these conditions every 30 pounds of water pumped into the boiler represents one horse power, therefore this boiler developed 4,019.93-^30 = 134 horse power. Particular attention is called to the fact that no mention is made of the pur- pose for which this steam is used, be- cause it makes no difference in the cal- culations. Some of it may be used to run an engine, another portion to oper- ate pumps, and the remainder to heat dry kilns, or for any other purpose for which steam is required, but this has no effect on the power developed by the boiler. This does not necessarily mean that it wiU supply enough steam to run an engine and develop 134 horse power, because it might require 50 pounds of steam per hour for each horse power developed. This steam would then fur- nish 4,019.93^50 = 80.4 horse power. On the other hand, it might be used to run a high grade engine requiring only 15 pounds of steam per hour for each horse power developed. Under this 106 STEAM ENGINEERING condition the boiler would supply-:* 4,019.93 -^15 =268 horse power. These two examples clearly illustrate the injustice of rating a boiler by the power developed in an engine. In the former case the engine might be rated at 134 horse power, still the boiler could not supply the steam required to run it, although it might be forced much be- yond its rated capacity in an effort to keep the engine in operation. On this basis the boiler would be condemned, although developing more power than it was designed for. In the latter case the engine might be rated at 134 hbrse power and the boiler might be highly commended because it supplies the required steam with a slow fire in the furnace and a small amount of coal per hour, but this would not be a fair decision, because the boiler would be supplying only 134X15-^30 = 67 horse power which fully explains its easy performance. ACCOUNTING FOR MOISTURE IN STEAM Frequently there is moisture in steam supplied by a boiler, therefore, it be- comes necessary to take this into ac- BOILERS 107 count in order that the boiler may be given credit for its exact performance. In this case 4,019.93 pounds of water were pumped into the boiler. If the calorimeter test shows that 3 per cent, of this water is not evaporated, but passes out as hot water mixed with the steam, it must be subtracted from the total weight used. Then 4,019.93- (4,019.93 X .03) = 4,019.93 - 120.59 = 3,899.34 pounds. This water went into the boiler at a temperature of 100 degrees and passed out at 85 pounds absolute pressure, the corresponding temperature of which is 316 degrees F^h. and this heat must be accounted for. Water at 100 degrees contains 68.08 heat units per pound, which is increased to 287 at 85 pounds absolute pressure, therefore 287—68.08 = 218.92 heat units were put into each pound of it, or 120.59X218.92=26,- 399.56 heat units for the whole. In order to reduce this to proper terms it is necessary to ascertain how many pounds of water this amount of heat will evaporate under given conditions. The total heat of steam at 85 pounds absolute pressure is 1,178.3. (See table.) It already contains 68.08 heat units per 108 STEAM ENGINEERING pound, therefore, it requires 1,178.3 — : 68.08 = 1,110.22 heat units. Then 26,399.56 will evaporate 26,399.56^ 1,110.22=23.78 pounds of water, if it was utilized for this purpose. Adding this to the amount actually evaporated shows that if all of the heat accounted for had been used to convert water into steam, the amount would have been 3,899.34+23.78 = 3,923.12 pounds. Dividing this by » 30 shows under these conditions the boiler would develop 130.77 horse power. EQUIVALENT HORSE POWER The above title is used because it ex- presses concisely the meaning of this paragraph when fully explained. Boil- ers are seldom operated under the exact conditions laid down for standard tests when the horse power developed is to be determined, but fortunately it is not necessary to comply with these condi- tions so far as steam pressure carried and temperature of feed water are con- cerned, as it is not difficult to reduce the results secured under any given conditions to terms that will admit of comparison on a common basis with the BOILERS 109 standard, which is the evaporation of 30 pounds of water per hour, when carrying 70 pouaids gauge, or 85 pounds absolute pressure, with feed water at 100 degrees Fah. ^ Every pound (in weight) of steam at this pressure contains 1,178.3 heat units, and every pound of feed water at 100 degrees contains 68.08 heat units, there- fore heat from the furnace must supply 1,178.3-68.08 = 1,110.22 heat units. This demonstrates that the generation and application to water in a boiler of enough heat to evaporate 30 pounds in one hour where each pound requires 1,110.22 heat units, constitutes a boiler horse power. It naturally follows that if steam is generated under conditions that require less heat per pound, a greater weight of water will be evaporated by the same amount of heat. Consequently if con- ditions are such that more heat is re- quired per pound of steam, less water will be evaporated by the same quantity of heat. The quantity of water required per hour to constitute one horse power under different conditions can be deter- mined by the following formula: 110 STEAM ENGINEERING 1,110.22 -^-^X30 = W. T = Total heat of steam at given pressure. F=Heat units in the feed water above 32 degrees, at given temperature. W= Weight of water in pounds. For an illustration of the application of this formula, suppose that a boiler evaporates into dry steam 4,019.93 pounds of water per hour, under 165 pounds absolute pressure, with feed water at 210 degrees Fah. How much water constitutes one horse power under these conditions and how much power is developed? The total heat of steam at 165 abso- lute, or 150 pounds gauge pressure is 1,193.5 and water at 210 degrees con- tains 178.87 heat units 1,110.22 X30 = 32.826 pounds of 1,193.5-178.87 ^ water required to constitute one horse power. 4,019.92^32,826 = 122.46 horse power developed. As the evaporation of the same weight of water under less favorable conditions BOILERS 111 developed 134 horse power, the im- proved conditions, consisting of heating the feed water to a higher temperature, reduced the load by 11.54 horse power. This reduction of load results in a corresponding saving in fuel, calling at- tention to great benefits derived from heating the feed water by exhaust steam which is frequently a waste product. The next table gives the weight, in pounds, of water that must be evapor- ated per hour to constitute one horse power under different conditions. It is based on the foregoing formula, and will be very useful to engineers and others who wish to know at a glance how much water is required for one horse power under conditions found in their respective plants. For illustration, suppose that a certain boiler is operated under 125 pounds gauge pressure and the feed water enters at 210 degrees after passing through any kind of a heater that utilizes exhaust steam. Following the column under 140 pounds absolute pressure (which is equal to 125 by the gauge) until it in- tersects with the line beginning with 210 it shows that 32.95 pounds are re- quired under these conditions. 112 STEAM ENGINEERING POUNDS OP WATER PER HORSE POWER Absolute Boiler Pressure 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 212 28.74 28.97 29.23 29.48 29.75 30.02 30.29 30.57 30.85 31.14 31.44 31.74 32.05 32.36 32.68 33.01 33.34 33.69 33.75 28.56 28.80 29.05 29.31 29.57 29.84 30.11 30.39 30 30.95 31.24 31.54 31.84 32.15 32.46 32.79 33.12 33.46 33 33.53133 28.37 28.61 28.86 29.12 29.37 29.63 29.90 30.17 30.45 30.73 31.02 31.32 31.61 31.92 32.23 32.55 32.87 33.21 33.27 POUNDS OF WATER PER HORSE POWER Absolute Boiler Pressure 40 50 60 70 80 90 100 110 "120 130 140 150 160 170 180 190 200 210 212 28.08 28.32 28.56 28.80 29.08 29.31 29.57 29.84 30.11 30.39 30.67 30.96 31.25 31.55 31.85 32.16 32.48 32.80 32.87 BOILERS 113 BENEFITS OF FEED WATER HEATERS Although the saving in fuel is more than enough benefit to pay for the in- stallation of a good feed water heater, it is not the only advantage gained by its use, and under some conditions the saving of unnecessary strains on the boiler is a greater compensation than the saving in fuel. This is especially true of locomotive boilers or any other type that is fitted with a water leg into which the cool feed water is discharged. The Hartford Steam Boiler Inspection & Insurance Co. made experiments some time ago which demonstrated that cool water coming in contact with a heated boiler plate causes it to contract, and as such a plate is rigidly connected to others, a very great strain on these parts is the sure result. While it is difficult or impossible to calculate with even a reasonable degree of accuracy what these strains amount to, it is a well known fact that they cause cracks in the plates which greatly weaken them, and if such cracks are not given intelligent attention, the result may be disastrous explosions. As plates contract directly in propor- tion to the difference between the tem- perature of the feed water striking directly against them, and that of the steam or hot water in contact with ad- 114 STEAM ENGINEERING jacent parts, anything that reduces this difference cannot fail to be beneficial. The girth seams of horizontal boilers frequently leak from the same cause. The percentage of fuel saved by the installation of a good feed water heater that utilizes exhaust steam, or by an economizer that takes heat from waste gases on their way to the chimney, can be determined by the following rule. From the total heat, or heat units in the heated water, subtract the heat units in the cold water. Divide the re- mainder by the total heat of steam at the pressure carried, minus the heat units in the cold water. Multiply the quotient by 100. When written as a formula it appears as follows: |^^X100 = P, H = Total heat in the heated water. C = Total heat in the cold water. S = Total heat in the steam at the pressure carried, P = Percentage of gain, or the por- tion of fuel saved by heating the feed water. For illustration, suppose that a boiler carries 140 pounds absolute pressure and uses water from the street main at a temperature of 50 degrees Fah. What percentage of the fuel now burned will be BOILERS 115 saved by the installation of an exhaust steam feed water heater that will raise the temperature of it to 211 degrees Fah., assuming that the exhaust steam is not utilized for any other purpose? Applying the formula to this case results as follows: 179.89-18 X 100 = 13.8 per cent. 1,189.5-18 It is not a difficult matter to determine the saving that will result under any conditions that can be found in practice by the foregoing rule and formula, using tables of properties of water and steam that are found on preceding pages, but for the convenience of readers the next table contains the results of calculation to determine these values. The initial temperatures refer to the temperature of water as it enters the heater. This is given from 40 to 100 degrees Fah. as this range will be sufficient to cover alT ordinary cases. For lower or higher temperatures use the formula. The table includes cases where, the water is heated to 180, 190, 200, and 210 degrees Fah., as a heater that will not deliver water at the former temperature is of little value, and the latter is seldom exceeded without back pressure on the engine. The pressures are absolute, therefore 15 must be subtracted from 116 STEAM ENGINEERING them to secure gauge pressures. The re- sults given are the percentage of saving on all fuel burned where water is forced into boilers at the initial temperatures. o 11.85 11.10 10.33 9.56 8.77 7.96 7.14 § 11.86 11.11 10.34 9.57 8.78 7.97 7.15 g 11.87 11.12 10.35 9.58 8.79 7.98 7.16 o 11.89 11.14 10.38 9.59 8.80 7.99 7.17 Pi t3 "-^ 11.91 11.16 10.39 9.61 8.82 8.00 7.18 11.93 11.18 10.41 9.63 8.83 8.02 7.19 Pi o 11.95 11.19 10.42 9.64 8.84 8.03 7.20 oi w h4 s 11.97 11.21 10.44 9.66 8.86 8.05 7.22 g i § 11.99 11.24 10.46 9.67 8.88 8.06 7.24 § •-H CO 03 O O 00 o O IM Tt 03 O (N drHddododt>l o 12.05 11.29 10.51 9.73 8.92 8.10 7.27 s 12 08 11.32 10.54 9.75 8.95 8.13 7.29 g 12.12 11.35 10.58 9.78 8.97 8.15 7.31 ^ 12.16 11.39 10.61 9.82 9.01 8.18 7.35 5g8g§§S (Nr-lr-lO03 00 00 rH t>. r-( rt< CD CD iO r^qc^Tiiqoqo im" r-5 .-5 d d 00 00 (N --I rH O 05 00 00 ;qqq I y c4(NrHddo6o6 I Ph 00 tJ< 00 .-I rH C . _. , p t^OC030 ; w co r- Oi »H I pu, (NNi-nddodoo I J C<1(M r-( O 03 00 00 (N00 00 KNr-iOOlOOOO N(N I-H 00 03 00 C3 q oj eoc rt>Ui ;::<;:; ;;HrHi.H ■* CO COCCOOCOOOOO ■* >; 05(N -"l^ CO -^-eoNdt-Hdc = JO Oi- j ^COCONt-iOOS OCONrHOOS a «3 ;qN"5t^q Z. ^ TticOCONrHdcJ S P$ COtNOO '-H'^'OCO •g fq ioooqcoiqt-;q - d ■^coco i>. ^ P5 40oqrHco"5i>q o la '^Mco(N-'-5dd ^ f:' (M 00 CO CO 00 05 OS ^^ tD ;O00rHC0»Ot>;O5 ^ h4 -^'cococQj^dd > W t> rH CO Oi -"-I --H P* pq qqi-HcoqooQ •a -q(Nn 00 00 00 t- q (N '^ CO 00 q ■* CO CO -i O O EQUIVALENT EVAPORATION When a certain weight of water is evaporated in a steam boiler at a known 118 STEAM ENGINEERING pressure, it forms a basis for computing the power developed, as before explained, also for comparing results secured with other boilers, but for convenience and accuracy it is customary to reduce all of them to a common level. Boilers are fed with water whose tem- perature varies through a wide range, and steam is generated under many different pressures, but when it is as- sumed that the feed water is heated to 212 degrees Fah. and that steam is gen- erated under atmospheric pressure at a temperature of 212 degrees Fah. and all results are reduced to these standards, comparisons can be intelligently made at short notice. As the feed water and the steam gen- erated have the same temperature, it demonstrates that only the latent heat of steam at atmospheric pressure is put into the water after it enters the boiler. This amounts to 965.7 heat units per pound above 32 degrees Fah., and this result is obtained by subtracting the heat units in a pound of the feed water at this temperature, from the total heat of steam at this pressure, and 1,146.6 — 180.9 = 965.7. If water at 100 degrees is pumped into a boiler carrying 85 pounds absolute pressure, each pound of it requires 1,178.3-68.08 = 1,110.22 heat units to evaporate it into dry steam. BOILERS 119 Thus it becomes plain that the numbers 965.7 and 1,110.22 are used for compari- sons along this line. The evaporation of 30 pounds of water in one hour, where each pound of it re- quires 1,110.22 heat imits, takes 33,306.6 heat units. Under other conditions the evaporation of one pound of water requires 965.7 heat units, therefore the total just mentioned will evaporate 33,306.6-^965.7 = 34.489 pounds of water, which is called 34.5 for conve- nience in calculating results. Thus the evaporation of 34.5 pounds of water in one hour from and at 212 degrees con- stitutes one boiler horse power, as it is equivalent to the standard explained on foregoing pages. Another way in which this can be used is to show how much water would have been evaporated in any given case found in practice, provided the feed water was at a temperature of 212 degrees and there was no pressure by the gauge. Such a problem is solved by the fol- lowing rule: Multiply the weight of water actually evaporated into dry steam, by the num- ber of heat units required to evaporate one pound and divide the product by 965.7. The quotient is the weight that would be evaporated under assumed conditions. 120 STEAM ENGINEERING For example, suppose that a boiler evaporates into dry steam 4,019.93 pounds of water in one hour, from feed water at 100 degrees, into steam at 70 pounds gauge pressure. How much would have been evaporated from and at 212 degrees? How much power would have been developed? 4,019.93 X (1,178.3 - 68.08) -^ 965.7 = 4,621.5 pounds. When this is divided by 34.5 it shows that 134 horse power was developed. COAL REQUIRED TO EVAPORATE WATER Owners of steam plants and superin- tendents of mills, shops and factories fre- quently say that if two kinds of coal are to be tested it is only necessary to com- pare the weight used to run the machin- ery one week, with what is required to operate it another week, and that comparison decides the comparative value of two kinds of coal. To a certain limited extent this con- clusion is correct, because the weight of coal burned, in connection with the price per ton determines the cost of fuel for a given time, but it is unjust and unfair to base an opinion concerning the real merit of any kind of fuel on the result of such a so-called test, which is BOILERS 121 SO crude and unsatisfactory that it is not worthy to be called a test at all. When discussing the merits of such a transaction the steam user always claims that the same amount of machinery was operated during the time mentioned, but while such a claim may seem rea- sonable from his point of view, it really is not, because an engine will seldom or never develop just the same power for many days in succession, even if the machines operated are engaged on a class of work that apparently does not vary, and for some other kinds the variation is great from day to day. Where live steam is used in varying quantities there is much more chance for a difference in actual results. The quality of the steam produced may not change, but this is not known defin- itely unless careful tests are made of it in accordance with instructions fo\ind on foregoing pages of this work. The actual weight of coal consumed may not have been correctly reported, because some kinds contain much more moisture than others, and water in the furnace should not be counted as coal. When a boiler test is to be made, a fair sample of the coal should be selected, carefully dried and the percentage of moisture it contains accurately deter- mined. It is usually convenient to take 122 STEAM ENGINEERING a small wooden box, fill it with a sample of the coal, then place it on the boiler setting to dry. Unless the box has just been kiln dried it is sure to contain moisture, and as this evaporates when the coal is dried, it makes enough differ- ence to spoil the effort to fairly rate the coal used in making the boiler test. In a certain case the small box used for this purpose weighed one-half pound less after it had been thoroughly dried, and the moisture actually evaporated in drying the sample of coal was .7 pound. If the moisture coming out of the box had been credited to the coal, and the whole pile had been judged by the sample, the entire test would have been worthless. If the sample, as taken from the pile, weighed 18.25 pounds and after being thoroughly dried it weighed 17.5 pounds it shows that 18.25- 17.5 -^ 18.25 X 100=4.1 per cent, of the weight of ma- terial brought from the coal yard was water and 95.9 per cent, was coal. By courtesy the whole weight is called coal, and what is left after the weight of moisture is subtracted is called dry coal. Assuming that 4,019.93 pounds of water were pumped into the boiler in one hour, and that there was 3 per cent, of moisture in the steam produced, the BOILERS 123 total weight evaporated is 3,899.34 pounds, and the heat used in raising the temperature of this moisture is equiva- lent to the evaporation of 23.78 pounds, then the final weight accounted for is 3,923.12 pounds. If 448 pounds of coal were required and it contained 4.1 per cent, of moisture which is 18.36 pounds, the actual weight of dry coal is 448 - 18.36 = 429.64 pounds. The actual evaporation is therefore 3,923.12-^429.64=9.13 pounds of water per pound of dry coal. A rule has already been given and explained for determining the weight of water that would have been evapor- ated with feed water at 212 degrees and steam at zero by the gauge. In that case the total weight of water evaporated per hour was taken, but in this case it is the weight evaporated per pound of coal that is to be compared with the given standard. Then 9.13 X (1,178.3 - 68.08) ^ 965.7 = 10.5 pounds from and at 212 degrees. WATER EVAPORATED PER POUND OF COMBUSTIBLE UNDER GIVEN CONDITIONS Another point to be taken into con- sideration in this connection is that after a boiler test is finished, so far as the 124 STEAM ENGINEERING burning of coal is concerned, there is more or less ash left which cannot be burned. When we consider that this varies greatly with different kinds of coal, the injustice of charging it to the boiler as actually burned, is at once plain, therefore it must be taken from the weight of dry coal burned. Examination of several reports of boiler tests shows that the ashes remain- ing ranged from 6.4 to 26.2 per cent, of the entire weight of dry coal fed into the furnace. This shows that it is neces- sary in every case to determine the weight of dry ashes remaining at the conclusion of a test. Suppose that in this case there were 62.75 pounds of ashes left, for each hour covered by the test. This would be 429.64-62.75-^429.64 X 100 = 85.3 per cent, of combustible, and as the entire weight is represented by 100 the ash amounts to 100 — 85.3 = 14.7 per cent. Subtracting 62.75 pounds from 429.64 shows that the weight of combustible is 366.89 pounds and as this evaporated 3,923.12 pounds of water, it demon- strates that 3,923.12 -=-366.89 = 10.7 pounds were evaporated for each pound of combustible burned under given con- ditions. BOILERS 125 WATER EVAPORATED PER POUND OF COMBUSTIBLE FROM AND AT 212 DEGREES FAH. While the foregoing example seems to be complete, there is another point to be disposed of in order to cover the whole process. This consists of demon- strating the weight of water that would- be evaporated per pound of combust- ible from and at 212 degrees Fah. As 10.7 pounds were evaporated under given conditions which required, 1,110.22 heat units for each pound of water, then each pound of coal yielded 1,110.22 X 10.7 = 11,879.35 heat units. As it requires 965.7 to evaporate one pound "from and at 212 degrees," this is equiv- alent to the evaporation of 12.3 pounds under the assumed conditions, accord- ing to a rule given and explained on previous pages. This forms a correct and equitable standard for comparison, and it is the only one worthy of serious consideration where accuracy is desired, as anything else that is worked out with less care is of less value, and in many cases the results secured by incorrect methods are worse than useless. Where the actual results secured from several tests made on different boilers, to determine their efficiency in 126 STEAM ENGINEERING service, and these results have all been reduced to this common standard, it is not necessary to study all of the reports as the weight of water evaporated into dry steam per pound of combustible, "from and at 212 degrees," enables the engineer to compare them intelligently at short notice. THE EFFICIENCY OF STEAM BOILERS Steam users are frequently asked to buy appliances that will save coal, and in hundreds of plants there are oppor- tunities to do all that salesmen guaran- tee for their goods, but in some cases the conditions have not been thoroughly investigated, causing enthusiastic ad- vocates of certain inventions to make extravagant claims for them which can- not be realized in practice. These remarks do not apply to cases where it is proposed to save steam and thus save coal indirectly, as this is not the proper place to treat them, but only to plants where it is expected to save coal directly by some appliance for the furnace. Efforts are made in some of these cases to convince steam users that only 10 or 15 per cent, of the coal burned in a boiler furnace is taken up by the water when it is converted into steam. If BOILERS 127 this was true there would be a good opportunity to save a portion of such a great loss, but unfortunately for these enthusiasts, and fortunately for the steam user, these claims are not true, as the following example demonstrates. The report of a test made on a verti- cal fire tube boiler of the most simple kind, shows that for each pound of coal burned in the furnace, 11.34 pounds of water were evaporated into dry steam "from and at 212 degrees." As it re- quires 965.7 heat unit's to evaporate one pound under these conditions, to evap- orate 11.34 pounds it is necessary to use 10,951 heat units. The number of heat units in the brand of coal used is not stated, but much of our ordinary steam coal does not con- tain more than 13,000 heat units per pound, in which case the efficiency of this boiler under ordinary working con- ditions is 10,951 -r- 13,000X100 = 84 per cent. Assuming that the coal con- tains 13,500 heat units, the efficiency is 81 per cent, and for 14,000 heat unfts it is 78 per cent. This should show every reader that it is impossible to save from 25 to 50 per cent, which has been claimed in some cases. The vertical fire tube boiler apparent- ly affords an excellent chance for heat to ascend in the tubes and escape to the 128 STEAM ENGINEERING stack, but this is more apparent than real j provided the boiler is well proportioned. , During the above mentioned test, the'' temperature of the escaping gases was 427 degrees. The steam pressure was 60 pounds absolute, the temperature of which' is 292.5 degrees, and it was super- heated 18 degrees by the tubes passing through the steam space, therefore the final temperature was 310.5 degrees. As the escaping gases were only 116.5 degrees above this, there cannot be much improvement made at this point, because there must be more heat in the gases than there is in the steam, or else heat will escape from the latter to the former, thus lowering the efficiency of the boiler. This is the principal source of loss from a well set boiler and an ordinary furnace, but measures should be taken to prevent radiation of heat from all other parts, and all holes in brick setting around cast iron fronts, in connection with stacks, and in all other places where cold air can be drawn in to cool the heated surfaces, should be carefully closed, as each one represents loss of drawing power on the fire, or of heat from the coal consumed. This is an im- portant point, for when cold air is drawn inward the defect is not noticed as quickly as when heat comes outward , BOILERS 129 yet all such imperfections are a direct source of loss. THE LOAD AND THE STEAM PRESSURE The load on a steam boiler is frequently estimated by the pressure carried on it in everyday service, as men who are not well informed on the subject of steam engineering conclude that when a boiler carries a high pressure there must neces- sarily be a heavy load on it, but while this may be true, and it frequently is, still it cannot be laid down as a principle because there are many boilers in use carrying a low pressure for heating pur- poses, yet the load on them is heavy. The load on a boiler is determined by the weight of water evaporated into dry steam in a given time, and if 20 pounds gauge pressure is enough for a certain place, that does not prevent conditions from demanding a rapid rate of evap- oration. On the other hand the nature of the business for which another boiler supplies steam may be such that while a gauge pressure of 200 pounds or more may be re- quired, only a comparatively small quan- tity of steam is used, hence the load is light. Nobody would allow a boiler used under such conditions to be run without a fireman or an engineer in constant 130 STEAM ENGINEERING attendance, yet we are sometimes asked if steam cannot be left on a building all night, without anybody in attendance on the boiler, because there is not a very high pressure on, consequently there can be no danger. Suppose a boiler should be left alone all night, and soon after the fireman has departed the gauge glass should break. What would be the consequence by the time that he returned in the morning? What would become of a fire if left without attention for 10 or 12 hours? Boilers are frequently run all day, the fires banked at night, while the pressure is but little lower than is required during the day, and when the fireman returns the next morning he finds a working pressure of steam on. This does not prove that steam could be used during the night without loss, as some managers seem to think, for if heat is taken from the boilers after the fires are banked there is just so much less left for use in the morning. What- ever remains at night after a day's run, is not lost as it is only stored for future use. Coal that is used for banking a fire is either there for use when a bright fire is wanted or else a portion of it is burned and the resulting heat has kept the boil- er just so much nearer ready for use when wanted at short notice. SECTION 2 BOILER FEEDERS REMARKS ON BOILER FEEDERS When a boiler feeder is to be selected for a steam plant, there are several points to be considered, which are ap- parently not always remembered, judg- ing by the illogical selections made in some cases. This does not include the efficiency of the boiler feeder as a ma- chine, for that will be considered sepa- rately, because its importance warrants it, but to other conditions which make a certain kind suitable for some places and unsuitable for others. For illustration, take a plant where the nearest revolving shaft from which power can be obtained is perhaps 100 feet distant from the boiler room. A power pump is not suitable for such a plant because the fireman will have to leave his boilers too many times in order to attend to the pump and regulate the supply of feed water delivered, thus not only diverting his attention from duties in front of his boilers which require con- stant care and labor, but also causing much useless walking, and furthermore such practice results in his being absent from the boiler room without good rea- 132 STEAM ENGINEERING sons whenever he feels so inclined, to the detriment of good service. If more or less of the feed water is warm before it passes through a heater it is not a good idea to use an injector, as it is not reliable under such conditions. Many of them will take warm or even hot water when new and in perfect order, but after they have been used long enough to cause slight wear in the tubes they "kick" especially if the water is warmer than usual, for in all cases the incoming water must be cool enough to condense the steam used to operate the injector. It will pay to install a good feed water heater in practically every case, but where this valuable feature must be omitted for any cause, an injector should always be used as it delivers hot water to the boilers, thus preventing the great strains on plates, due to feeding cold water. In electric power and lighting plants where current is always available a power pump driven by a motor is con- sidered an up-to-date machine. As it is practicable to vary the speed of such a motor to meet the requirements of one or more boilers, and as it may be located in the most convenient place without regard to the nearest shaft or the most BOILER FEEDERS 133 available steam pipe, it forms a very desirable combination for feeding boilers. THE EFFICIENCY OF BOILER FEEDERS The mechanical efficiency of a boiler feeder is found by dividing the power actually used in forcing water through' pipes and valves into boilers against the pressure carried, by the power required to operate the machine. In the form of a formula it appears as follows : A ' — =M.E. P A = Actual power required to force water into boilers. P = Power required to operate the machine. M E = Mechanical efficiency. For example, suppose that 4.8 horse power are actually used in forcing water into a battery of boilers, and it requires 6 horse power to operate the machine. The mechanical efficiency is therefore 4.8 — =.80 6 From this example it will be plain that the mechanical efficiency of a boiler feeder (or any other machine), is always a fraction, because it requires a perfect machine in which there is absolutely no 134 STEAM ENGINEERING power lost, to equal unity, or 1, and it is impossible to devise and construct such a machine. If a pump is used for this purpose and the pistons are packed very tightly, the value of P will be large, consequently the fraction resulting from an applica- tion of the formula is small, or in other words the mechanical efficiency is low. Where it is desired to express the efficiency in the form of a percentage of the whole power used the formula be- comes — X100 = M. E. The thermal efficiency of a boiler feed- er is the amount of heat used in forcing water into the boilers, divided by the heat put into the machine to operate it. It is found in accordance with the above explanation relating to mechanical efficiency. POWER PUMPS When selecting a boiler feeder the mechanical efficiency of all kinds taken into consideration should be noted, but a certain kind may show high mechan- ical efficiency when taken as a machine designed for this purpose, and when used in connection with some other appliance the combination may give excellent BOILER FEEDERS 135 results, but when the boiler feeder is considered alone it may be wasteful and unsatisfactory. The improved up-to-date power pump is a good illustration of this principle because when in good repair its mechan- ical" efficiency is high. Furthermore, the quantity of steam required to oper- ate it is small, as the power needed is developed in the main engine which is generally economical in the use of steam. Still it would be very poor practice to use a power pump to force water into, one or more boilers without using a heat- er to raise the temperature as high as possible. This combination gives ex- cellent satisfaction in practice, provided the pump can be conveniently located near a shaft used for other purposes, so that but little power will be used in oper- ating the transmission devices, what- ever they may be, between the main engine and the pump. Fig. 17 illustrates a single acting ! power pump fitted with o^e cylinder. Water is drawn in on the upward stroke ; an^ forced out on the downward stroke of the plunger. It is a very simple ! pump, but its capacity is small and its mechanical efficiency is comparatively low, as there is but one effective stroke 1 for each revolution of the shaft. 136 STEAM ENGINEERING FI&./.7 When a pump of this kind is fitted with two cylinders, its capacity is doubled and its mechanical efficiency is BOILER FEEDERS 137 higher, because the friction is not in- creased in proportion to the increase in capacity. As there are two effective strokes for each revolution, the flow of water is nearly continuous, although its speed is not constant. When fitted with three cylinders this is known as the FIG. /a A 138 STEAM ENGINEERING single acting triplex pump. It delivers ; a nearly constant stream of water. Fig. 18 illustrates a double acting ' power pump fitted with one cylinder. As it draws in water and expels it at each stroke, it gives fair results in prac- tice. FIG, /? Ita BOILER FEEDERS 139 When this kind of a pump is fitted with two cylinders, and the driving cranks are set at an angle of 90 degrees, the flow of water is practically continu- ous, and the mechanical efficiency is satisfactory. These pumps are sometimes fitted with three cylinders, and as the pistons are double acting, an even and contin- uous flow of water is secured, when the driving cranks are set at an angle of 120 degrees. Fig. 19 illustrates the arrangement of valves in this machine, which is known as the double acting triplex pump. HORSE POWER REQUIRED BY PUMPS The first part of the next table gives the power required to operate Gourd's single acting triplex pumps, when forc- ing water against columns of water of stated height, or in other words the given head in feet, which gives corre- sponding pressure. The head includes the height from the point where water is lifted to the highest part of the delivery pipe. The second part applies to double ing triplex pumps at given capacities. 140 STEAM ENGINEERING When comparing the power required by these two kinds of pumps, the capacity must be considered in connection with the size of pump. For illustration, a 7X8 inch single act- ing pump when working against 108 pounds pressure requires 15 horse power for the given capacity. A 7X8 inch double acting pump would require 30 horse power at the same rate, but the capacity of the * latter is not twice as much as the former, therefore when the table states that 28 horse power will be required, it is a logical con- clusion. The first column contains the diam- eter and stroke of the pump under the heading "D, & S." The second gives the usual capacity, or the number of gallons that each will deliver at normal speed under the heading of "Capacity." Succeeding columns give first the head or height of the column of water, and under it the pressure due to this height of water. This represents boiler pres- sure where the pump is used to feed boilers instead of raising the water to the given height. Figures under these headings are the horse power required for stated conditions. BOILER FEEDERS 141 CO 8 CO ^^ G a- "o "o h 8 1 d — WOO (X h § a On CO CO -1 (M. O (N. t^ i-O lOO 00 00 O CO lO r-i(MC0C0^«300O(NiOt^r>.-50iooiooooooio rHl^^(^>cocoo^.C5|^co'Oloa)-^co O 00 lO t^ O'OO (N lO t^ O t^ I> O CSI lO '-i'riiMC^JCOTtOOiOiO lOtOt^OOC^JOOiOiOCOOlMOCOOO rH,-(lM(NC0CO-*TtiiOiO0'0OOOt-,I>00 142 STEAM ENGINEERING o o o CO o CO c u ,■">- cr— a ^o . cl a o w oa Q l>0000O(N>0000>i-lC0'*C0t»00'-lTl 0(N0000e3(N(N(N<©o>-ioNwco-<*"> BOILER FEEDERS 143 i^ 4) CD O r-i CO 00 O 005f-I-^CD05 lO I> 03 t-l CO CO CO»Ol^OOO(N ^COrt*iOiO (35 00 O M OS N- O COfO»0»0«3t*000(N(N-*OiOO 8§888888888§88 00C<>(NOk0 « t^ 23.00 27.00 34.00 41.60 45.60 61.70 63.40 77.60 91.60 85.00 101.00 77.10 111.00 140.00 8§S8g888§88288 00 ^ 00 CO CO o o (M CO r- o »-i 00 o .-lN(MCOfO'*»OCOt>COOOCOOO'-l 8g88g§8g8S8^88 coioo-*coaicoTiC^^|O00j^gjHC.tr^O00^ 1 a 6 346 411 533 612 684 776 952 1,164 1,368 1,276 1,531 1,170 1,700 2,117 CO OOC5^ 6 .42 100 ' 150 85 ' 125 6M ly, 5 6 .51 100 ' 150 100 ' 150 7 7H 41^ 10 .69 75 ' 125 100 ' 170 ^n p 5M 10 .93 75 * 125 135 ' 230 734 10 6 10 1.22 75 ' 125 180 ' 300 834 10 7 10 1.66 75 ' 125 245 ' 410 9Ji 12 7 10 1.66 75 ' 125 245 ' 410 9J^ 14 7 10 1.66 75 ' 125 245 ' 410 9^8 12 8H 10 2.45 75 ' 125 365 ' 610 12 14 8H 10. 2.45 75 ' 125 365 ' 610 12 16 8^ 10 2.45 75 ' 125'365 ' 610 12 181^ 8i^ 10 2.45 75 • 125 365 ' 610 12 20 8H 10 2.45 75 ' 125 365 ' 610 12 12 10 K 10 3.57 75 * - 125 530 ' 890 14Ji 14 10^ 10 3.57 75 ' 125 530 ' 890 14^ 16 10 1^ 10 3.57 75 * 125 530 ' 890 14M 18J^ ioji 14 12 10 4.89 75 * 125 730 '1220 17 16 12 10 4.89 75 ' 125 730 '1220 17 COMPQUNB' STEAM PUMPS Where fuel is expensive and the ex- haust steam from a pump cannot be used for other purposes, the compound pump, either single or duplex is recom- mended, as it will save about 30 per cent, of fuel over what a single pump requires to do the same work. The principle involved in the use of steam in these two kinds of pumps is that in. the single pump (which may be 172 STEAM ENGINEERING either single or duplex), steam, is admit- ted for the whole length of every stroke, and then exhausted at practically the same pressure that it had at the begin- ning of the stroke, hence there is great waste of heat. In the compound pump (which may be either single or duplex), steam is ad- mitted to the high pressure cyHnder and after its work is completed here, it is exhausted into the low pressure cylin- der (which is much larger than the high pressure), where it is expanded to a comparatively low terminal pressure. As work is done during the expanding process the results so far as the consump- tion of fuel is concerned, are satisfac- tory. Fig. 23 illustrates this type of pump, and examination of it shows that it is not a complicated machine, as it can be cared for by anybody who is competent to take care of a single pump to do the same work. The use of steam in the second cylin- der causes back pressure in the first, and this l,e;ssens the economy that would be secured if this back pressure could be eliminated, but owing to the fact that it opposes the progress of a small piston and assists a much larger one, there is a material gain by the process. BOILER FEEDERS 173 174 STEAM ENGINEERING The next table contains the dimen- sions and capacity of compound steam pumps to which the following explana- tion applies: H P = Diameter of high pressure cylinder. L P = Diameter of low pressure cyl- inder. W C = Diameter of water cylinder. S = Stroke in inches. G = Gallons per stroke. N = Number of strokes per minute for a single pump that can be secured in every day prac- tice without excessive wear. The number will be doubled in case of a duplex pump. C = Capacity in pounds per minute for a single pump, at given speed. D = Capacity in pounds per minute for a duplex pump giving full strokes, at given speed. Attention is called to the fact that the capacity of each is high because the pis- ton speed is high, although the number of strokes per minute is comparatively low. These desirable features are se- cured by adopting a long stroke. BOILER FEEDERS 175 SIZE AND CAPACITY OF qOMPOUND PUMPS HP LP WC S G N c D 4 7 4 10 .55 100 456 912 5y2 8 4 10 .55 100 456 912 6 10 4 10 .55 100 . 456 912 7 12 4 10 .55 100 456 912 5H 8 5 10 .85 100 705 1,410 6 10 5 10 .85 100 705 1,410 7 . 12 5 10 .85 100 705 1.410 8 12 5 10 .85 100 705 1.410 6 10 6 10 1.22 100 1,012 2,024 7 12 6 10 1.22 100 1,012 2.024 8 12 6 10 1.22 100 1,012 2,024 9 14. 6 12 1.47 100 1,220 2,440 10 16 6 12 1.47 100 1,220 2,440 12 18 6 12 1.47 100 l,220i 2,440 7 12 7 10 1.66 100 1,377 2,754 8 12 10 1.66 100 1,377 2.754 9 14 7 10 1.66 100 1,377 2.754 10 16 7 12 2.00 100 1,660 3,320 12 18 7 12 2.00 100 1,660 3,320 14 20 7 ■12 2.00 100 1.6601 3,620 8 12 S 12 2.61 100 2,16614,332 9 14 8 12 2.61 100 2,16614,332 10 16 8 12 2.61 100 2,166 4,332 12 18 8 12 2.61 100 2,166 4,332 14 20 8 12 2.61 100 2,166 4,332 9 14 9 12 3.30 100 2.739 5.478 10 16 9 12 3.30 100 2,739 5,478 12 18 9 12 3.30 100 2,739 5,478 14 20. 9 12 3.30 100 2,739 5,478 16 24 9 12 3.30 100 2,739 5,478 10 16 10 12 4.08 100 3,386 6,772 12 IS 10 12 4.08 100 3.386 6,772 14 20 10 12 4.08 100 3,386 6,772 16 24 10 12 4.08 100 3,386 6,772 10 16 10 14 4.75 80 3,154 6.308 12 18 10 14 4.75 80 3,154 6,308 14 20 10 14 4.75 80 3,154 0,308 16 24 10 14 4.75 so 3,154 6,308 10 16 10 20 6.80 80 4,515 9,030 12 18 10 20 6.80 80 4,515 9,030 14 ■ 20 10 20 6.80 80 4.515 9,030 16 24 10 20 6.80 so 4,515 9,030 12 IS 12 14 6.85 80 4,548 9,096 14 20 12 14 6.85 80 4,548 9,096 16 24 12 .14 6.85 80 4.548 9,096 12 18 12 24 11.75 50 4,872 9,744 14 20 12 24 11.75 50 4,872 9.744 16 24 12 24 11.75 50 4,872 9.744 18 30 12 24 11.75 50 4,8721 9.744 176 STEAM ENGINEERING THE SPEED OF STEAM PUMPS The most difficult point to decide when ordering a steam pump, is the speed at which it will give the best re- sults when everything is considered. The purchaser does not want to buy a pump that is too large for the service required, as that means, extra expense, hence he is inclined to take the maker's statement of the speed at which it can be run in case of emergency, for what will give good results in practice; but this is a mistaken idea because excessive speed wears a pump more than it would be 'worn if it were run at a slow speed for a much longer time. Furthermore, it greatly increases the danger of failure on account 'of severe shocks and jars. It is claimed that a piston speed of 100 feet per minute is the highest limit that can be allowed for a pump, and it is quite safe to say that it should never be exceeded for boiler feeding purposes, and that in many cases the limit ought to be placed at 50 feet. It is a self-evident truth, although it may not always be remembered, that a high piston speed never damages a pump while the piston is swiftly moving in one direction, but when its motion is quick- ly reversed the resulting concussion BOILER FEEDERS 177 causes rapid wear and loosening of the joints. The lesson to be leagied from these observations, and practical experience along the same line is that a pump should always be designed with a long stroke. It is not practicable to lay down a cast iron rule for the length of stroke, but it should be from 2 to 3 times the diameter of the water cylinder. Some pumps are designed with a stroke longer than this indicates, as it is 4 or even 5 times the diameter of the water cylinder, but they are designated as a special kind. There is no good reason why the stroke of boiler feeders should not be made much longer than it now is in many cases. The following, dimensions are taken from the catalogue of a prominent firm who have long been engaged in the manufacture of pumps of many kinds. They would make first class boiler feeders. LONG STROKE PUMPS Diameter of Diameter of Length steam cylinder water cylinder of stroke 10 5 25 10 6 25 12 7 25 14 9 33 16 10 H 33 18 12 38 -178 STEAM ENGINEERING The next table contains the nuniber of strokes that pumps must make to attain speeds from 50 to 125 feet per minute, with strokes ranging from 3 to 18 inches in length. It not only gives valuable information along this line, but it enables the reader to make comparisons readily which show that a statement of the piston speed of a pump does not always give an intelli- gent idea of its operation. For illustration, a pump with an 18 inch stroke will attain a piston speed of 100 feet per minute by making 67 strokes, while another with a stroke of 5 inches must make 240 strokes to attain the same speed. A pump with a 4-inch stroke at- tains a speed of only 50 feet per minute when making 150 strokes, but when a pump with a 10-inch stroke makes 150 strokes it has a pi^ston speed of 125 feet. NUMBER OF STROKES REQUIRED ro ATTAIN A GIVEN PISTON SPEED u Stroke in inches ll 3 4 5 6 1 7 1 8 10 1 12 1 15 1 18 c^E Number per minute 50 200 150 120 100 86i 75 60 50 40 33 55 220 165 132 110 94 82.5 66 55 44 37 60 240 180 144 120 103 90 72 60 48 40 65 260 195 156 130 111 97.5 78 65 52 43 70 280 210 168 140 120 105 84 70 56 47 75 300 225 180 150 128 112.5 90 75 60 50 80 320 240 192 160 137 120 96 80 64 53 85 340 255 204 170 146 127.5 102 85 68 57 90 360 270 216 180 154 135 108 90 72 60 95 380 285 228 190 163 142.5 114 95 76 63 100 400 300 240 200 171 150 120 100 80 67 105 420 315 252 210 180 157.5 126 105 84 70 110 440 330 264 220 188 165 132 110 88 73 115 460 345 276 230 197 172.5 138 115 92 77 120 480 360 288 240 206 180 144 120 96 80 125 500 375 300 250 214 187.5 150 125 100 83 BOILER FEEDERS 179 ::^;^ :^:^;^ :i^:s;§^ :5t^:?^ :it-^;^ 180 STEAM ENGINEERING g^gg8^^2S^§^2§g§gS§ 183 215 249 286 326 368 413 460 510 562 617 734 861 999 1.147 1,305 1.652 B c 1 u O. c S .2 o o oc(roa>»o>-it>.-^c^oooo«oiot-'0»oo> 146 172 199 229 261 294 330 368 408 449 493 587 689 799 918 1,044 1.321 § S^S;i?8^^??§S3j:?t2Sf2§§i: § OOtHOOWOOOOOCD-^OOOOOO iOOOiCDOiCOCC'OTj-t^'Oioo50»oro t^ir>:)cot^coooiO(M(£>r^to.-Hco C<10050iMCO'-it^>0-*iO>-i(MOC— i(M c \M \c-» \N s^ <-fv «DtOr^t^0000O5OSrH.-l.-i.-.r-.rHr-l.-..-( 1^ BOILER FEEDERS 181 EXPLANATION OF THE PRECEDING TABLES An explanation of the practical opera- tion of the two foregoing tables will assist the reader in making ready appli- cation of them and point out interesting features that otherwise might be over- looked. Suppose that in a certain case 160 gallons of water are wanted per minute, and the proper size of pump is required. The piston speed is limited to 50 feet per minute for ordinary use, which is to be doubled in case of emergency. Taking the table of "Capacities of Pumps in Gallons," finding the column under 50 feet per minute and following it down we find that the next quantity above 160 is 165.24 which will answer the pur- pose, as the quantity delivered should never be less than the requirements. In the column headed "Diameter in inches," opposite the quantity delivered as above stated is a figure 9 indicating that the water piston must (or at least ought to) be 9 inches in diameter. Referring to the table entitled "Ntim- ber of Strokes Required to Attain a Given Piston Speed," we find that if a stroke of 15 inches is adopted it will only be necessary to make 40 strokes per minute^to attain a piston speed of 50 182 STEAM ENGINEERING feet, thus securing conditions that result;: in ease of operation, and durability of ;i the machinery, as we will have a 9X15,! inch pump running 40 strokes per minute. Again suppose that 280 gallons of water are wanted per minute and it is to be secured with a pump that does not ; make more than 50 strokes per minute, and the piston speed is limited to 70 feet. What is the proper size? Following down the column under 70 until 285.60 gallons are noted we find that a piston 10 inches in diameter will give the desired quantity. In the other table we find 70 in the column entitled "Speed per minute," and opposite this the only number below 50 is 47 strokes per minute, and by following this col- umn up to the top we find that the proper stroke is 18 inches, therefore the pump should be 10X18 inches. It may be necessary to determine the capacity of a pump that is available for a certain place, provided it is large enough. Suppose that the water cylin- der of this pump is 4 inches in diameter with a stroke of 8 inches and it is con- sidered safe to operate it at 120 strokes per minute for maximum speed. What is the capacity of this pump? Under 8 in the proper column we find 120 and by following the line to the left BOILER FEEDERS 183 the piston speed is found to be 80 feet per minute, which is not excessive for a maximum speed. In the other table we find 80 and by following it down until it intersects the line where 4 is located at the left hand, the capacity is found to be 52.22 gallons per minute. A pump with a water cylinder 4 inches in diameter and a stroke of 4 inches, delivers 60 gallons of water per minute when running 300 strokes, but this speed is excessive, causing unecessary wear and much trouble. How fast will a 6 X 8 inch pump run if used to ! supply the same quantity of water? I In the column entitled "Diameter in inches," we find 6 and following out that line until we find 73.44 gallons, which is i the next number above 60, Following this coliunn upward shows that in order to deliver this quantity of water the piston speed will be 50 feet per minute. P-ef erring to the other table we find that if a pump with a stroke of 8 inches is run 50 feet per minute it will make 75 strokes giving satisfactory service, therefore if the 4X4 inch pump is replaced by a 6X8 inch, the number of strokes will be reduced from 300 to less than 75, for the same amount of water, or if it makes 75 strokes it will deliver more water than the other did at 300. 184 STEAM ENGINEERING STEAM AND WATER CYLINDERS Attempts hav.e been made to use pumps for boiler feeding that were not properly proportioned for this service, hence all efforts to make them work failed because the available force acting on the steam piston was not sufficient to overcome the resistance opposing the water piston. As this was due to igno- rance on the subject, or carelessness in failing to ascertain the relative diam- eters of the steam and water pistons, attention is called to it here in order that readers may not make the same mistake. Fig. 24 is a pimip piston rod with a steam piston 10 inches, and a water piston 6 inches in diameter on it. As- suming that a steam pressure of 100 pounds to the square inch is realized, the total pressure on the steam piston is 7,854 pounds, but with the same pres- sure per square inch opposing the water piston, the total is 2,827 pounds, or a difference of 5,027 pounds. BOILER FEEDERS 185 This is graphically illustrated by Fig. 25 which shows the two pistons together. If both of these pistons were the same diameter the pump would not work because the total resistance would be greater than the total force acting on the steam piston, for if there is 100 poimds pressure on a boiler it will usu- lally be necessary to pump against at least 110 pounds. However, it is neither advisable nor practicable to use full boiler pressure in the steam cylinder of a pump, hence the piston must be larger accordingly. With 50 pounds pressure on the steam piston, the total is 3,927 pounds, and if the water piston works against 110 pounds the total is 3,109 pounds, leav- ing a difference of 818 pounds, which is enough to cause the pump to run as de- sired. This comparison demonstrates 186 STEAM ENGINEERING that much less than boiler pressure will drive such a pump, and it also shows that the steam piston must always be larger than the water piston. The next table gives the height to which pumps with given steam and water pistons or cylinders will elevate water. As it is impossible to determine the friction that will result from forcing water through a system of pipes until all conditions are known, or a trial made in practice, no attempt is made to in- clude it in this table, therefore, the fig- ures where the horizontal and the ver- tical lines intersect represent the height in feet of a colufnn of water acting on the water piston that will balance a pressure of 50 pounds to the square inch on the steam piston. This height may be re- duced to pounds by multiplying it by .43. For illustration, take a steam piston 12 inches and a water piston 7 inches in diameter. By following the horizontal line on a level with 12 imtil it inter- sects the vertical line under 7, we find that the column of water must be 220 feet high, or 220 X. 43 =94.6 pounds will balance 50 pounds on the steam piston. It will be noted that wherever the diam- eter of the steam piston is twice the diameter of the water piston, the col- umn of water is 300 feet high. BOILER FEEDERS 187 2 u "o 1 Q (M CO (N O lOC^ ^ (N 00 co'*'or^O'*coo O i-*oo.-iiooor^(Ncoo ?0Tt(CDI>O^Oxt C0u:l05l0Tt^C0lMC0OO co-*iot>05cooocoor^ r-lr-l(MCOCO 00 (Nt>.ioiot>o>oooa>oi I-H r-l CM OO CO ■<1< I> 00»OiOOO-*COOO(NOO CO»Ot^a2CMiOCMOOTC20 «o Ttoxfioo:i .-i.-lrHCMC0-*ir3CD00 >o I>00>OOOI>C<1COO(MOOCMCOJ •* T-lrHC>^COCO^OCJ CO iOTtCM^ 1>COIOC^OTJ CO CO '^ to 00 CO CM '^ 05 O 00 CO >0 CO ocoooocot^co .-H r-1 CM CO '^ "O CO 00 g§8§||g C^ CM CO-* CO C5 .2 c O rt o w a CO-^iOtOt^OOCTJOCMTjHcOOOO 188 STEAM ENGINEERING ORDERING STEAM PUMPS Having decided ojn the proper size of pump for the maximum quantity of water wanted, the engineer should take into consideration the following condi- tions, and inform the parties of whom the pump is to be purchased, concerning them, that there may be no misunder- standing. Whether the water to be pumped is hot or cold, or each kind alternately. If only cold water is to be used, how high must it be lifted by suction, and how long is the suction pipe? Is the water pure or does it contain impurities that must be prevented from passing the pump? The available steam pressure must be considered, also the pressure against which water is to be forced. This in- cludes consideration of the length of the discharge pipe, also the number of short turns and valves in it. It should be known whether the pump is to exhaust into a condenser, the atmos- phere, or a heating system of any kind, as these conditions effect the back pres- sure on the steam piston, or in other words they make a difference in the total load on the pump. When ordering parts for repairs give the shop number of the pump, also the BOILER FEEDERS 189 size and serial number if there is one provided. The parts wanted are usu- ally illustrated in the manufacturer's catalogue, therefore one of them should be kept on hand for use in an emergency. Reading and studying these catalogues enables an engineer to thoroughly under- stand the machines that he uses. DIRECTIONS FOR SETTING AND OPERATING STEAM PUMPS Having selected a place for the pump to be set, have a brick foimdation built for it in order to hold it firmly in posi- tion. Do not bolt it to a light wooden floor that will not be stiff enough to pre- vent vibration when new, and that will soon rot and become useless. Where a pump is to take water under pressure from a street main, the suction pipe may be made smaller than the suc- tion opening calls for, but where water is to be lifted from a well, pond or brook, it should never be reduced even for a low lift, and for a high lift or a long suc- tion pipe, it should be made one size larger. Always make the suction as short and straight as conditions will admit, as short ells and globe valves add much to the necessary friction of water flowing through pipes. The highest part of a 190 STEAM ENGINEERING long suction pipe should always be at the pump, and the grade should be con- tinually downward to the water. If it is raised and lowered to suit the ground on which it is located, air will collect in the high places or air pockets, and cause trouble. Where it is to be laid under ground, cast iron flanged pipe is recommended as durable and satisfactory. Special care should be taken to keep sand, stones, and other foreign matter out of the pipe while it is being laid, as but a small quantity will cause much trouble and annoyance. Where it is necessary to locate a valve in the straight part of a suction pipe, it should be a gate valve in order to create as little friction as possible. If there is a convenient turn in the pipe, an angle valve may be 'used instead of an ell. If the suction pipe is long, a foot valve should be located on the end of it, then by providing a small priming pipe, water can be admitted to the suction pipe, from an overhead tank, or a street main, thus filling the suction pipe and insuring prompt operation of the pump when steam is turned on. If this suction pipe is exposed, provision must be made for draining the water out of it when the pump is stopped in cold weather. Frost plugs in the water cylinder should BOILER FEEDERS 191 be removed to allow all water to drain out. A large air chamber should be located on the suction pipe in addition to one provided on the pump in some cases as the latter provides a cushion for the dis- charge pipe only. Fig. 26 illustrates Fig. ^6 ^ 192 STEAM ENGINEERING the proper location of the air chamber, for either one or two suction pipes. If two suction pipes are provided; the water coming in through them will move slowly and quietly. The discharge pipe should be of ample size to allow water to move at a comparatively slow speed when the pump is operated at its full capacity. When locating the steam pipe, make due allowance for expansion when it is heated by steam. Put a globe valve near the pump and a good double con- nection sight feed lubricator above it. Before admitting steam to the pump, blow out the pipes thoroughly under full pressure in order to remove red lead, iron chips, and dirt, thus preventing such foreign matter from injuring the steam cylinder. Keep the stuffing boxes well filled with first-class packing and do not let it remain in use long enough to become hard, as it will score the rods, making it impossible to keep them from leaking steam and water. Use as good oil on all pump bearings as you would on the best kind of an en- gine, and only first-class cylinder oil in the steam cylinder. If the pump is to remain idle for several days, use an extra quantity of cylinder oil during the last five minutes that it is run, in order BOILER FEEDERS 193 to keep it from rusting when standing still. The advantage gained by the use of pipes of ample size for both the suction and discharge of pumps will be made plain by studying the next table, which treats pipes from 1 to 6 inches in diam- eter. G = Gallons discharged per minute. V = Velocity of water in feet per . second. F = Friction of water in pounds per square inch for each 100 feet of clean iron pipe, or the pres- sure required to overcome friction. It will be noted that as the velocity is increased, the friction increases very fast, therefore, a constant loss results from the use of pipes that are too small for the required service, hence while the first cost of them is less, they are ulti- mately very expensive. For illustration, suppose that 20 gal- lons of water per minute are forced through a 13^ in. pipe, causing a friction loss of 1.66 pounds. If the amount of water is doubled the loss is increased to 6.52 pounds. If 35 gallons are forced through 1 inch pipe the loss is 37 pounds, but 13^ inch pipe will convey the same amount with 5.05 pounds loss. 194 STEAM ENGINEERING FRICTION IN POUNDS PRESSURE PER SQUARE INCH For each 100 feet of clean iron pipe. G. A. .a CO c .c c .c c :^ c S3 i 1 b Ellis. C. E. «0 O »HC0t^O»fl^{0| O ^ t^(NCO»OCO00O> 6 6 dddddodi > 1.13 1.70 2.27 2.84 3^40 3.97 4.54 5.11 5.67 'fu 0.09 0.33 0.69 1.22 1.89 2.66 3.65 4.73 6.01 7.43 > 1.28 2.55 3.83 5.11 6.39 7.66 8.94 10.20 11.50 12.80 fo 0.10 0.35 0.74 1.31 1.99 2.85 3.85 5.02 7.76 11.20 15.20 19.50 25.00 30.80 > 1.13 2.27 3.40 4.54 5.67 6.81 7.94 9.08 11.30 13.60 15.90 18.20 20.40 22.70 fu d d'-o>(NoJod > 1.63 3.26 4.90 6.53 8.16 9.80 11.40 13.10 16.30 19.60 fo 0.12 0.42 0.91 1.60 2.44 5.32 9.46 14.90 21.20 28.10 37.50 > 1.02 2.04 3.06 4.09 5.11 7.66 10.20 12.80 15.30 17.10 20.40 (i< -t^CO(NiO»0COcOt^OiO.-iO-*0 ddd-H (Nco^ocdoodNoi 1-HWCO > 0.81 1.82 2.73 3.63 4.54 5.45 6.36 7.26 8.17 9.08 13.60 18.20 iu 0.31 1.05 2.38 4.07 6.40 9.15 12.04 16.10 20.20 24.90 56.10 > 1.31 2.61 3.92 5.22 6.53 7.84 9.14 10.40 11.70 13.10 19.60 > dcocDddi^i^'oo 2.04 4.08 6.13 8.17 10.20 12.30 14.30 16.30 O lO O "5 O >0 O "O O U5 O IC O lO o o o o o o o o o .-^ 49.873 197.93 10 M 31.809 80.516 16 50.265 201.06 10 K 32.201 82.516 16>^ 50.658 204.22 i 10 H 32.594 84.541 IQK 51.051 207.39 1 101^ 32.987 86.590 16H 51.444 210.60 , 10 H 33.379 88.664 163^ 51.836 213.82 10^ 33.772 90.763 16H 52.229 217.08 i 10 Vi 34.165 92.886 16% 52.622 220.35 11 34.558 95.033 16^ 53.014 223.65 ll>i 34.950 97.205 17 53.407 226.98 11^ 35.343 99.402 17 M 53 ..800 230.33 IIH 35.736 101.62 17 M 54.192 233.71 UVi 36.128 103.87 17 H 54.585 237.10 IIH 36.521 106.14 17 M 54.978 240.53 IIM 36.914 108.43 17 H 55.371 243.98 11^ 37.306 110.75 17 H 55.763 247.45 12 37.699 113.10 nvi 56.156 250.95 12^ 38.092 115.47 18 56.549 25*. 47 12 >i 38.485 117.86 18 H 56.941 258.02 12^ 38.877 120.28 18% 57.334 261.59 12 >^ 39.270 122.72 181^ 57.727 265.18 125^ 39.663 125.19 18^ 58.119 268.80 125^ 40.055 127.68 18 H 58.512 272.45 STEAM ENGINES 241 Xircumferences and Areas of Circles — Continued Diaxn. Circmn. Area Diam. Circum. Area 18M 58.905 276.12 24 H 77.362 476.26 18?^ 59.298 279.81 24^ 77.754 481.11 19 59.690 283.53 24 4 78.147 485.98 19 >^ 60.083 287.27 25 78.540 490.87 19 H 60.476 291.04 25 H 78.933 495.79 19 H 60.868 294.831 25 H 79.325 500.74 19^ 61.261 298.651 25 H 79.718 505.71 191^ 61.654 302.49 2514 80.111 510.71 19^ 62.046 306.35 25 SA 80.503 515.72 19^ 62.439 310.24 25 M 80.896 520.77 20 62.832 314.16 25 7A 81.289 525.84 20H 63.225 318.10 26 81.681 530.93 20 M 63.617 322.06 26 H 82.074 536.05 20 H 64.010 326.05 26 M 82.467 541.19 201^ 64.403 330.06 26 H 82.860 546.35 20 H 64.795 334.10 26 >i 83.252 551.55 20 M 65.188 338.16 26H 83.645 556.76 20 H 65.581 342.25 26^ 84.038 562.00 21 65.973 346.36 262^ 84.430 567.27 21K 66.366 350.50 27 84.823 572.56 21>i 66.759 354.66 27 M 85.216 577.87 21^ 67.152 358.84 21 K 85.608 583.21 21H 67.544 363.05 27 H 86.001 588.57 21H 67.937 367.28 27 J^ 86.394 593.96 21?i 68.330 371.54 27^ 86.786 599.37 21^ 68.722 375.83 27 M 87.179 604.81 22 69.115 380.13 27^ 87.572 610.27 22 H 69.508 384.46 28 87.965 615.75 22 M 69.900 388.82 283^ 88.357 621.26 22 H 70.293 393.20 28 M 88.750 626.80 22 H 70.686 397.61 28 H 89.143 632.36 22^ 71.079 402.04 28 M 89.535 637.94 22 H 71.471 406.49 28 H 89.928 643.55 22^ 71.864 410.97 28 M 90.321 649.18 23 72.257 415.48 28 J^ 90.713 654.84 23 H 72.649 420.00 29 91.106 660.52 iS 73.042 424.56 29 H 91.499 666.23 73.435 429.13 29 K 91.892 671.96 231^ 73.827 433.74 29 H 92.284 677.71 23 H 74.220 438.36 29 H 92.677 683.49 23^ 74.613 443.01 29^ 93.070 689.30 & 75.006 447.69 29 5i 93.462 695.13 54 H 75.398 452.39 29 J^ 93.855 700.98 75.791 457.11 30 94.248 706.86 24 >i 76.184 461.86 30 M 94.640 712.76 24 H 76.576 466.64 30 Ji 95.033 718.69 24 H 76.969 471.44 30H 1 95.426 724.64 242 STEAM ENGINEERING Circumferences and Areas of Circles — Continued Diam. Circum. Area Diam. Circum. Area 30 J^ 95.819 730.62 36H 114.275 1039.2 30 5^ 96.211 736.62 36^ 114.668 1046.3 30 5i 96.604 742.64 36H 115.061 1053.5 30?^ 96.997 748.69 365^ 115.454 1060.7 31 97.389 754.77 36^ 115.846 1068.0 ^X'A 97.782 760.87 37 116.239 1075.2 31K 98.175 766.99 37 H 116.632 1082.5 31H 98.567 773.14 31 y^ 117.024 1089.8 311^ 98.960 779.31 31 H 117.417 1097.1 31H 99.353 785.51 31 Yi 117.810 1104.5 SIH 99.746 791.73 37 H 118.202 1111.8 ZIM 100.138 797.98 37 M 118.596 1119.2 32 100.531 804.25 3nA 118.988 1126.7 32 J^ 100.924 810.54 38 119.381 1134.1 32 H 101.316 816.86 3%H 119.773 1141.0 32 H 101.709 823.21 38>i 120.106 1149.1 32yi 102.102 829.58 38J^ 120.559 1156.6 32 H 102.494 835.97 38 H 120.951 1164.2 32^ 102.887 842.39 38H 121.344 1171.7 32 H 103.280 848.83 38 M 121.737 1179.3 33 103.673 855.30 38^ 122.129 1186.9 33 H 104.065 861.79 39 122.522 1194.6 33 K 104.458 868.31 39 H 122.915 1202.3 33 H 104.851 874.85 39 J^ 123.308 1210.0 33 H 105.243 881.41 3^H 123.700 1217.7 33 H 105.636 888.00 39 H 124.093 1225.4 33^ 106.029 894.62 39 H 124.486 1233.2 33 J^ 106.421 901.26 39^ 124.878 1241.0 34 106.814 907.92 39 J^ 125.271 1248.8 34 H 107.207 914.61 40 125.664 1256.6 34 }i 107.600 921.32 40H 126.056 1264.5 34 H 107.992 928.06 40 >i 126.449 1272.4 34 H 108.385 934.82 40 H 126.842 1280.3 34 H 108.778 941.61 40 H 127.235 1288.2 345^ 109.170 948.42 40H 127.627 1296.2 34^ 109.563 955.25 40 5^ 128.020 1304.2 35 106.956 962.11 40^ 128.413 1312.2 35 H 110.348 969.00 41 128.805 1320. a 35 >^ 110.741 975.91 41H 129.198 1328.3 35 5^ 111.134 982.84 41 >i 129.591 1336.4 35 H 111.527 989.80 41J^ 129.983 1344.5 35 H 111.919 99rt.78 41 H 130.376 1352.7 35 M 112.312 1003.8 415^ 130.769 1360.8 35 3^ 112.705 1010.8 41?^ 131.161 1369.0 36 113.097 1017.9 41H 131.554 1377.2 36^ 113.490 1025.0 42 131.947 1385.4 36 K 113.883 1032.1 42 H 132.340 1393.7 STEAM ENGINES 243 Circumferences and Area? of Circles — 'Continued Diam.jCircum. Area Diam. Circum. Area 42 M 132.732 1402.0 485^ 151.189 1819.0 A2H 133.125 1410.3 48 >i 151.582 1828.5 421^ 133.518 1418.6 48 H 151.975 1837.9 42 s^ 133.910 1427.0 48H 152.367 1847.5 425^ 134.303 1435.4 48 H 152.760 1857.0 42 ^i 134.696 1443.8 483^ 153.153 1866.5 43 135.088 1452.2 48 5^ 153.545 1876.1 tn 135.481 1460.7 49- 153.938 1885.7 135.874 1469.1 495/8 154.331 1895.4 A.ZH 136.267 1477.6 49 M 154.723 1905.0 43 H 136.659 1486.2 49?^ 155.116 1914.7 43 H 137.052 1494.7 49 H 155.509 1924.4 43 M 137.445 1503.3 49 H 155.902 1934.2 43^ 137.837 1511.9 49 M 156.294 1943.9 44 138.230 1520.5 49 >| 156.687 1953.7 44 H 138.623 1529.2 50 157.080 1963.5 44 >i 139.015 1537.9 50 H 157.472 1973.3 44^ 139.408 1546.6 50 M 157.865 1983.2 44 H 139.801 1555.3 50 K 158.258 1993.1 44 H 140 . 194 1564.0 503^ 158.650 2003.0 44 K 140.586 1572.8 50 H 159.043 2012.9 44 ?i 140.979 1581.6 50 5i 159.436 2022.8 45 141.372 1590.4 50^ 159.829 2032.8 45 H 141.764 1599.3 51 160.221 2042.8 45 >i 142.157 1608.2 51M 160.614 2052.8 45^ 142.550 1617.0 51 M 161.007 2062.9 45 J^ 142.942 1626.0 5iy& 161.399 2073. a 45 M 143.335 • 1634.9 51^ 161.792 2083.1 45 M 143.728 1643.9 51H 162.185 2093. 2-. 45^ 144.121 1652.9 51^ 162.577 2103.3 46 144.513 1661.9 5VA 162.970 2113.5. 46 H 144.906 1670.9 52 163.363 2123.7 46 K 145.299 1680.0 52 H 163.756 2133.^ 46 H 145.691 1689.1 52 M 164. 148 2144.2 46 H 146.084 1698.2 52 H 164.541 2154.5 46 H 146.477 1707.4 52}^ 164.934 2164. S 46 Ji 146.869 1716.5 52 H 165.326 2175.1 46 H 147.262 1725.7 52^ 165.719 2185.4 47 147.655 1734.9 52^ 166.112 2195.8 47 H 148.048 1744.2 53 166.504 2206.2 47^ 148.440 1753.5 53 H 166.897 2216.6 47 fi 148.833 1762.7 53 >i 167.290 2227.0 47 >^ 149.226 1772.1 53^ 167.683 2237.5 47 H 149.618 1781.4 53 H 168.075 2248.0 47% 150.011 1790.8 53H 168.468 2258.5 47 Ji 150.404 1800.1 53% 168.861 2269.1 48 150.796 1809.6 53?^ 169.253 2279.6 244 STEAM ENGINEERING Circumferences and Areas of Circles — Continued Diam. Circum. Area Diam. Circum. Area 54 169.646 2290.2 59^ 187.710 2803.9 54H 170.039 2300.8 59;^ 188.103 2815.7 54 M 170,431 2311.5 60 188.496 2827.4 54 H 170.824 2322.1 60H 188.888 2839.2 54 H 171.217 2332.8 &0}4 189.281 2851.0 54 H 171.609 2343.5 QOH 189.674 2862.9 54 M 172.002 2354.3 60 H 190.066 2874.8 54: pi 172.395 2365.0 60 H 190.459 2886.6 55 172.788 2375.8 60^ 190.852 2898.6 55 K 173.180 2386.6 60 2^ 191.244 2910.5 55 J^ 173.573 2397.5 61 191.637 2922.5 55 H 173.966 2408.3 Qiys 192.030 2934.5 55 M 174.358 2419.2 61M 192.423 2946.5 55 H 174.751 2430.1 61 H 192.815 2958.5 55 3^ 175.144 2441.1 61M 193.208 2970.6 55?^ 175.536 2452.0 61 H 193.601 2982.7 56 175.929 2463.0 61 M 193.993 2994.8 56 H 176.322 2474.0 6114 194.386 3006.9 56 >i 176.715 2485.0 62 194.779 3019.1 561^ 177.107 2496.1 62 M 195.171 3031.3 56 K 177.500 2507.2 62 M 195.564 3043.5 56 H 177.893 2518.3 62 H 195.957 3055.7 56 M 178.285 2529.4 62 M 196.350 3068.0 56 2^ 178.678 2540.6 62^ 196.742 3080.3 57 179.071 2551.8 62 M 197.135 3092.6 57 H 179.463 2563.0 62 J^ 197.528 3104.9 57 >i 179.856 2574.2 63 197.920 3117.2 57 fi 180.249 2585.4 63^ 198.313 3129.6 57 H 180.642 2596.7 63 >i 198.706 3142.0 57 ys 181.034 2608.0 63 H 199.098 3154.5 57 H 181.427 2619.4 62, Vi 199.491 3166.9 57 H 181.820 2630.7 63 H 199.884 3179.4 58 182.212 2642.1 63 M 200.277 3191.9 58 >i 182.605 2653.5 63^8 200.669 3204.4 58 M 182.998 2664.9 64 201.062 3217.0 58 H 183.390 2676.4 64^ 201.455 3229.6 58 V^ 183.783 2687.8 64 M 201.847 3242.2 58 H 184.176 2699.3 64 H 202.240 3254.8 585^ 184.569 2710.9 64 J^ 202.633 3267.5 58 J^ 184.961 2722.4 64S/i 203.025 3280.1 59 185.354 2734.0 64 M 203.418 3292.8 595^ 185.747 2745.6 64H 203.811 3305.6 59 K 186.139 2757.2 65 204.204 3318.3 59^ 186.532 2768.8 65 H 204.596 3331.1 591^ 186.925 2780.5 65 H 204.989 3343.9 59 H 187.317 2792.2 6b H 205.382 3356.7 STEAM ENGINES 245 Circumferences and Areas of Circles — Continued Diam. Circum. Area Diam. Circum, Area 65 H 205.774 3369.6 71 H 224.231 4001.1 65 H 206.167 3382.4 71H 224.624 4015.2 65 M 206.560 3395.3 71^ 225.017 4029.2 65^8 206.952 3408.2 71H 225.409 4043.3 66 207.345 3421.2 71V& 225.802 4057.4 66M 207.738 3434.2 72 226.195 4071.5 66 H 208.131 3447.2 72 H 226.587 4085.7 66 H 208.523 3460.2 72 M 226.980 4099.8 66 Ji 208.916 3473.2 72 H 227.373 4114.0 66^ 209.309 3486.3 72 >^ 227.765 4128.2 66 M 209.701 3499.4 72 H 228.158 4142.5 66?^ 210.094 3512.5 72 M 228.551 4156.8 67 210.487 3525.7 72^ 228.944 4171.1 67 H 210.879 3538.8 73 229.336 4185.4 67 M 211.272 3552.0 73^ 229.729 4199.7 67 H 211.665 3565.2 73 >^ 230.122 4214.1 673^ 212.058 3578.5 73 H 230.514 4228.5 67 H 212.450 3591.7 73 J^ 230.907 4242.9 67 % 212.843 3605.0 73 H 231.300 4257.4 67^ 213.236 3618.3 73 M 231.692 4271.8 68 213.628 3631.7 73^ 232.085 4286.3 68 H 214.021 3645.0 74 232.478 4300.8 68 M 214.414 3658.4 74 Vs 232.871 4315.4 68 H 214.806 3671.8 74 3I 233.263 4329.9 683^ 215.199 3685.3 74 H 233.656 4344.5 68 H 215.592 3698.7 741^ 234.049 4359.2 68 34 215.984 3712.2 74 H 234.441 4373.8 683^8 216.377 3725.7 7434 234.834 4388.5 69 216.770 3739.3 74?^ 235.227 4403.1 69 K 217.163 3752.8 75 235.619 4417.9 69 M 217.555 3766.4 75^8 75 M 236.012 4432.6 69^ 217.948 3780.0 236.405 4447.4 691^ 218.341 3793.7 75 H 236.798 4462.2 69 H 218.733 3807.3 751^ 237.190 4477.0 69 M 219.126 3821.0 75 H 237.583 4491.8 69^ 219.519 3834.7 75 M 237.976 4506.7 70 219.911 3848.5 7bVi 238.368 4521.5 70 H 220.304 3862.2 76 238.761 4536.5 70^ 220.697 3876.0 76% 239.154 4551.4 70^ 221.090 3889.8 76 M 239.546 4566.4 70 J^ 221.482 3903.6 76 H 239.939 4581.3 70 H 221.875 3917.5 76^ 240.332 4596.3 70^ 222.268 3931.4 76 H 240.725 4611.4 70^ 222.660 3945.3 763^ 241.117 4626.4 71 223.053 3959.2 76?^ 241.510 4641.5 71^ 223.446 3973.1 77 241.903 4656.6 71M 223.838 3987.1 77% 242.295 4671.8 246 STEAM ENGINEERING Circumferences and Areas of Circles — Continued ' Diam. Circum. Area Diam. Circum. Area 77 K 242.688 4686.9 83 Vs 261.145 5426.9 77 H 243.081 4702.1 83 M 261.538 5443.3 77 Yi 243.473 4717.3 83 H 261.930 5459.6 77 H 243.866 4732.5 83 H 262.323 5476.0 77 M 244.259 4747.8 83^8 262.716 5492.4 77^ 244.652 4763 . 1 83 H 263.108 5508.8 •78 245.044 4778.4 83 ys 263.501 5525.3 78% 245.437 4793.7 84 263.894 5541.8 783^ 245.830 4809.0 84 Vs 264.286 5558.3 783/i 246.222 4824.4 84: H 264.679 5574.8 783^ 246.615 4839.8 84: H 265.072 5591.4 78^ 247.008 4855.2 84y2 265.465 5607.9 78 M 247.400 4870.7 84 H 265.857 5624.5 78 H 247.793 4886.2 84 M 266 . 250 5641.2 79 248.186 4901.7 84 J^ 266.643 5657.8 79 Vs 79 M 248.579 4917.2 85 267.035 5674.5 248.971 4932.7 85 Vs 267.428 5691.2 79 H 249.364 4948.3 85 S 267.821 5707.9 79 H 249.757 4963.9 85^ 268.213 5724.7 79 H 250 . 149 4979.5 85 H 268.606 5741.5 79 M 250.542 4995.2 85 s^ 268.999 5758.3 79 >i 250.935 5010.9 85 3^ 269.392 5775.1 80 251.327 5026.5 85 >g 269.784 5791.9 80 Vs 251.720 5042.3 86 270.177 5808.8 80K 252.113 5058.0 86% 270.570 5825.7 80H 252.506 5073.8 86 M 270 . 962 5842.6 80 >^ 252.898 5089.6 86 H 271.355 5859.6 80 H 253.291 5105.4 86 Vi 271.746 5876.5 «0M 253.684 5121.2 86 H 272.140 5893.5 80^ 254.076 5137.1 86^ 272.533 5910.6 81 254.469 5153.0 86^ 272.926 5927.6 81% 254.862 5168.9 87 273.319 5944.7 81^ 255.254 5184.9 87 Vs 273.711 5961.8 81 H 255.647 5200.8 87 M 274.104 5978.9 81^ 256.040 5216.8 87 H 274.497 5996.0 81 H 256.433 5232.8 87 Yi 274 . 889 6013.2 81 M 256.825 5248.9 87 H 275.282 6030.4 81J^ 257.218 5264.9 87 3^ 275 . 675 6047.6 .82 257.611 5281.0 87?/8 276.067 6064.9 82 Vs 258.003 5297 . 1 88 276.460 6082.1 82 M 258.396 5313.3 88% 276.853 6099.4 82^ 258.789 5329.4 88 >| 277.246 6116.7 821^ 259.181 5345 . 6 88?^ 277.638 6134.1 82 H 259.574 5361.8 881^ 278.031 6151.4 82 M 259.967 5378.1 88 H 278.424 6168.8 82^ 260 . 359 5394.3 88 M 278.618 6186.2 83 260.752 5410.6 88 >i 279.209 6203.7 STEAM ENGINES 247 ,Cii6umferences and Areas of Circles — Continued Diam. Circum. Area Diam. Circum. Area 89 279.602 6221.1 94 H 298.059 7069.6 89% 89 k 279.994 6238.6 95 298.451 7088.2 280.387 6256.1 95% 298.844 7106.9 89 H 280.780 6273.7 95% 299.237 7125.6 89 H 89 k 281.173 6291.2 95 H 299 . 629 7144.3 281.565 6308.8 95y2 300.022 7163.0 89 M 281.958 6326.4 9b SA 300.415 7181.8 89?^ 282.351 6344.1 95% 300.807 7200.6 60 282.743 6361.7 95^ 301.200 7219.4 ^^ 283.136 6379.4 96 301.593 7238.2 283.529 6397.1 96% 301.986 7257 . 1 90 ys 283.921 .6414.9 96% 302.378 7276.0 90H 284.314 6432.6 96^ 302.771 7294.9 90 H 284.707 6450.4 961^ 303.164 7313.8 9^M 285 . 100 6468.2 96^ 303.556 7332.8 285.492 6486.0 96% 303.949 7351.8 91 285.885 6503.9 96^ 304.342 7370.8 tm 286.278 6521.8 97 304.734 7389.8 286.670 6539.7 97% 305.127 7408.9 91H 287.063 6557 . 6 97% 305.520 7428.0 91 H 287.456 6575.5 97 H 305.913 7447.1 91H 287.848 6593.5 97 H 306.305 7466.2 91% 288.241 6611.5 91 H 306.698 7485.3 91?^ 288.634 6629.6 97% 307.091 7504.5 92- 289.027 6647.6 97 Vi 307.483 7523.7 i^ 289.419 6665.7 98 - 307.876 7543.0 289.812 6683.8 98% 308.269 7562.2 92 H 290.205 6701.9 98% 308.661 7581.5 921^ 290.597 6720.1 98 H 309.054 7600.8 92 H 290.990 6738.2 9sy2 309.447 7620.1 928^ 291.383 6756.4 98 H 309.840 7639.5 92?^ 291.775 6774.7 98% 310.232 7658.9- 93 292.168 6792.9 98^4 310.625 7678.3 93% 292.561 6811.2 99 311.018 7697.7 93)^ 292.954 6829.5 99% 311.410 7717.1 93 H 293.346 6847.8 99% 311.803 7736.6 931^ 293.739 6866.1 99^ 312.196 7756.1 93 H 294.132 6884.5 99 H 312.588 7775.6 93% 294.524 6902.9 99 H 312.981 7795.2 93^ 294.917 6921.3 99 H 313.374 7814.8 94 295.310 6939.8 99 ys 313.767 7834.4 MV& 295.702 6958.2 100 314.159 7854.0 94: H 296.095 6976.7 94^ 296.488 6995.3 nn 296.881 7013.8 297.273 7032.4 94% 297.666 705 rro 248 STEAM ENGINEERING DETERMINING THE MEAN EFFECTIVE PRESSURE There are many cases in which it be- comes necessary to determine the mean effective pressure that will result from given conditions in advance of the in- stallation of the engine, or in other words before an indicator diagram can be se- cured. As this is an important matter it will be explained in detail. The terms "average pressure" and "mean effective pressure" are used indiscriminately, not only by engineers in daily practice, but in mechanical books and papers by men who in some cases do not understand the difference, and in others are too careless to properly separate them. The effect in either case on the student is precisely the same, as it gives him a wrong idea of the whole subject. The average pressure acting on the piston of a steam engine is found by taking into consideration the initial pressure, or pressure at the beginning of the stroke in connection with the pres- sure realized at short succeeding inter- vals until the end is reached. When the average of them is found it consti- tutes the average pressure for those conditions, and this must necessarily be the pressure above a perfect vacuum in all cases. STEAM ENGINES 249 Special attention is called to the fact that the back pressure is not considered, as it can have no effect on the average <}> pressure, because they act on opposite sides of the piston. Fig. 38 is a theoretical indicator dia- gram in which the full lines only are used to determine the average pressure. The 250 STEAM ENGINEERING dotted lines are inserted to make the diagram complete, but they have no other use here. This 'diagram was orig- inally laid out accurately by a No. 40 scale, showing an initial pressure of 120 pounds absolute with the point of cut-off at one-quarter stroke. While it is nec- essary to reduce the size of this diagram for use here, the correct proportions are preserved, but it is not practicable to measure it with a No. 40 scale now. When the ordinates are laid out as shown their total length in inches ascertained and divided by the number used, the quotient is the average height of the diagram. Multiply this by the scale adopted (which is No, 40 in this case), and the product is the average pressure acting on the engine piston. These ordinates are the exact length to be measured in order to make the matter as plain as possible. The atmospheric line is shown at AA and the perfect vacuimi line at VV. While a diagram clearly illustrates the principle involved, the same result can be secured with less trouble by calcula- tion, using the following rule: Ascertain the ratio of expansion and find the corresponding hyperbolic logar- ithm in a table prepared for this pur- pose. Add 1, multiply the sum by the ini- tial pressure absolute, and divide by the STEAM ENGINES 251 ratio of expansion. The quotient is the average pressure for stated conditions. When given as a formula it appears as follows: (HypLog+l)XP_. R -^- Hyp Log = Hyperbolic logarithm of the ratio of expansion. P = Initial pressure absolute. R= Ratio of expansion. A = Average pressure. For illustration and explanation take a plant carrying 110 pounds pressure by the gauge, or 125 pounds absolute, with an initial pressure of 120 pounds in the cylinder, cutting off steam at one-quar- ter or .25 of the stroke. Under these conditions the ratio of expansion is 4 the hyperbolic logarithm of which is 1.3863 and when due appli- cation is made of the formula it gives the following result: (1.3863+1) X120 ^^ ^^ 4 pounds average pressure. Fig. 39 illustrates the proper method for finding the mean effective pressure from an indicator diagram. It is a reproduction of Fig. 38, except that there are no dotted lines, and the ordi- nates are shortened to show the exact 252 STEAM ENGINEERING measurements required When the total length of these ordinates in inches is found and divided by the number used, the quotient is the mean effective height of the diagram, and when this is multiplied by the scale used, the pro- duct is the mean effective pressure. As these ordinates are shorter than STEAM ENGINES 253 before, the effect is to cat off or subtract the back pressure. No stated number of ordinates is required, as the desired result is found by dividing the total length by the number adopted. Examination of the two preceding diagrams illustrates the fact that when the rule for finding the average pressure on the piston of an engine is stated, it is only necessary to add another clause and it becomes a rule for calculating the mean effective pressure as follows: Ascertain the ratio of expansion and find the corresponding hyperbolic logar- ithm in a table prepared for this purpose. Add 1, multiply the sum by the initial pressure absolute, divide by the ratio of expansion, and subtract the back pres- sure. The remainder is the mean effec- tive pressure for stated conditions. When given as a formula it appears as follows: (HypLog+l)XP _^^^^p Hyp Log = Hyperbolic logarithm of the ratio of expansion. P = Initial pressure absolute. R = Ratio of expansion. B = Back pressure above a vacuum. M E P = Mean effective pressure for given conditions, 254 STEAM ENGINEERING Applying this formula to a case where the initial pressure is 120 pounds abso- lute, the ratio of expansion 4 and the back pressure 16 pounds gives the fol- lowing result: (1.3863 + l)Xl20_^g^^^^^g 4 pounds mean effective pressure. When calculating the size of an engine that would be required to develop 300 horse power, the mean effective pressure was assumed to be 50 pounds. As the above result is more than the required pressure, the point of cut off would be a trifle shorter than at one- quarter stroke, which is satisfactory, as it will give a lower terminal pressure. THE RATIO OF EXPANSION AND THE BACK PRESSURE When the cut-off valve on an auto- matic, or any other kind of an engine, closes, the piston has travelled a certain part of the stroke, and the relation that this part bears to the whole stroke is the ratio of expansion. For illustration, suppose that the cut-off valve closes when the piston has travelled one-quar- ter or .25 of the stroke. Taking the whole stroke as unity or 1 and dividing STEAM ENGINES 255 it by .25 gives the ratio of expansion. Then 1-=-. 25 = 4. For estimating the mean effective pressure the clearance is not taken into account, as it makes the calculation more complicated for what is not in- tended to be an accurate computation. If greate accuracy is required, the clear- ance should be stated as the percentage of the whole stroke. It is then added to unity or 1 which represents the whole stroke, also to the fraction which represents the point of cut off and the former is divided by the latter as before. Suppose that the clearance is 5 per cent, or .05 of the whole stroke, and the cut off takes place at one-quarter stroke. The ratio of expansion is then: l + -°^- = 3.5 .25 + .05 The next table gives the actual ratios of expansion taking clearance from 1 to 10 per cent, into consideration. The first column gives the point of cut off as a fraction of the whole stroke. The second gives the ratio of expansion with- out clearance, and succeeding columns give the ratio with the amount of clear- ance given for each as a per cent, of the whole stroke. 256 STEAM ENGINEERING J ACTUAL RATIOS OF EXPANSION. ij Per cent, of Clearance. :i PofO 1 2 3 4 ': .01 100.00 50.5 34.0 25.75 20.8 .02 50.00 33.67 25.50 20.60 17.33, .03 33.33 25.25 20.40 17.16 14.86 .04 25.00 20.20 17.00 14.71 13.00 .05 20.00 16.83 14.57 12.87 11.55 .06 16.67 14.43 .12.75 11.44 10.40 .07 14.28 12.62 11.33 10.30 9.46 .08 12.60 11.22 10.2 9.36 8.67 .09 11.11 10.10 9.27 8.58 8.00 .10 10.00 9.18 8.50 7.92 7.43 .11 9.09 8.42 7.84 7.36 6.93 .12 8.33 7.78 7.25 6.86 6.50 .14 7.14 6.73 6.37 6.06 5.78 .16 6.25 5.94 5.67 5.42 5.20 .20 5.00 4.81 4.64 4.48 4.33 .25 4.00 3.88 3.77 3.68 3.58 .30 3.33 3.26 3.19 3.12 3.06 .40. 2.50 2.46 2.43 2.40 2.36 .50 2.00 1.98 1.96 1.94 1.92 .60 1.67 1.66 1.65 1.64 1.63 .70 1;43 1.42 1.42 1.41 1.41 .80 1.25 1.25 1.244 1.241 1.238 .90 1.111 1.11 1.109 1.108 1.106 1.00 1.00 1.00 1,000 1.000 1.000 ACTUAL RATIOS OF EXPANSION. Per cent, of 'Clearance. Pof C 5 6 7 8 9 10 .01 17.5 |15.14 13.38 12.00 '0.9 10. .02 15.00 1 13.25 11.89 10.80 9.91 8.17 .03 13.12 11.78 ]0.70 9.82 9.08 8.46 .04 11.66 10.60 9.73 9.00 8.39 7.86 .05 10.50 9.64 8.92 8.31 7.79 7.33 .06 9.55 8.33 8.23 7.71 7.27 6.88 .07 8.75 8.15 7.64 7.20 6.81 6.47 .08 8.08 7.57 7.13 6.75 6.41 6.11 .09 7.50 7.07 6.69 6.35 6.06 5.79 .10 7.00 6.62 6.30 6.00 5.74 5.50 .11 6.56 6.24 5.94 5.68 5.45 5.24 STEAM ENGINES 257 Actual Ratios of Expansion — Continued Per cent, of Clearance PofC 5 6 7 8 9 10 .12 6.18 5.89 5.63 5.40 5.19 5.00 .14 5.53 5.30 5.10 4.91 4.74 4.58 .16 5.00 4.82 4.65 4.50 4.36 4.23 .20 4.20 4.08 3.96 3.86 3.76 3.61 .25 3.50 3.42 3.34 3.27 3.21 3.14 .30 3.00 2.94 2.90 2.84 2.80 2 75 .40 2.33 2.30 2.28 2.25 2.22 2^20 .50 1.90 1.89 1.88 1.86 1.85 1.83 .60 1.615 1.606 1.597 1.588 1.580 1.571 .70 1.400 1.395 1.390 1.385 1.380 1.375 .80 1.235 1.233 1.230 1.227 1.224 1.222 .90 1.105 1.104 1.103 1.102 1.101 1.100 1.00 1.000 1.000 1.000 1.000 1.000 1.000 Having determined the assumed or the actual ratio of expansion, it becomes necessary to find the corresponding hyperbolic logarithm in a table, and add one to it in each case. The reason for this is because the work done by the steam from the beginning of the stroke to the point of cut off is represented by unity or 1 and the work performed after the cut off has taken place, or during expansion of the steam, is shown com- paratively by the hyperbolic logarithm of the ratio of expansion. As these must be added in order to get the total work done during the whole stroke it appears in the rules and formulas given , to make the process complete. This is illustrated in Fig. 40 which shows a -cut off at one-quarter stroke 258 STEAM ENGINEERING which makes the expansion rate 4 as previously explained. The vertical line extends from the point of cut off to the vacuum line, and the space to the right of it represents work done by steam direct from the boiler, and this is unity or 1. The space to the left shows work ^ b STEAM ENGINES 259 done by expansion of the steam, and it is represented by the hyperbolic logarithm of 4, which is 1.3863. When these two factors are added the sum is the total work done during the complete stroke. These measurements are taken to the vacuum line, because it is necessary in order to include the whole. The counter pressure line and the atmospheric line are shown in dotted form to make the diagram complete, but their only prac- tical use in this connection is to show how the total work is divided, as they cannot make it either more or less. Where an engine is located at or near the sea level, and is run non-condensing, the back pressure should be estimated at not less than 16 pounds, as the atmos- phere causes nearly 15 and the remain- der is allowed for friction in exhaust passages and pipes, as the steam travels to the outer air. If a condenser is to be used under good conditions, the back pressure may be taken at 3 pounds, as that represents good practice. The following table contains hyper- bolic logarithms of numbers from 1.01 to 20 to be used in connection with rules and formulas for determining the aver- age and the mean effective pressures. When the ratio of expansion is deter- mined, find the nxmiber in this table and the corresponding hyperbolic logarithm 260 STEAM ENGINEERING will be found in the next column, and this is to be used as directed. ; HYPERBOLIC LOGARITHMS OF NUMBERS | from 1.01 to 20.00. No.- Log No. Log. No. Log. 1.01 .0099 1.43 .3577 1.85 .6152 1.02 .0198 1.44 .3646 1.86 .6206 1.03 .0296 1.45 .3716 1.87 .6259 1.04 .0392 1.46 .3784 1,88 .6313 1.05 .0488 1.47 .3853 1.89 .6336 1.06 .0583 1.48 .3920 1.90 .6419 1.07 .0677 1.49 .3988 1.91 .6471 1.08 .0770 1.50 .4055 1.92 .6523 ! 1.09 .0862 1.51 .4121 1.93 .6575 i 1.10 .0953 1.52 .4187 1.94 .6627 1.11 .1044 1.53 .4253 1.95 .6678 1.12 .1133 1.54 .4318 1.96 .6729 1.13 .1222 1.65 .4383 1.97 .6780 ! 1.14 .1310 1.56 .4447 1.98 .6831 ! .6881 1.15 .1398 1.57 .4511 1.99 1.16 .1484 1.58 .4574 2.00 .6931 1.17 .1570 1.59 .4637 2.01 .6981 1.18 .1655 1.60 .4700 2.02 .7031 1.19 .1740 1.61 .4762 2.03 .7080- 1.20 .1823 1.62 .4824 2.04 .7129 1.21 .1906 1.63 .4886 2.05 .7178 ' 1.22 .1988 1.64 .4947 2.06 .7227 1.23 .2070 1.65 .5008 2.07 .7275 1.24 .2151 1.66 .5068 2.08 .7324 1.25 .2231 1.67 .5128 2.09 .7372 1.26 .2311 1.68 .5188 2.10 .7419 1.27 .2390 1.69 .5247 2.11 .7467 1.28 .2469 1.70 .5306 2.12 .7514 1.29 .2546 1.71 .5365 2.13 .7561 1.30 .2624 1.72 .5423 2.14 .7608 1.31 .2700 1.73 .5481 2.15 .7655 1.32 .2776 1.74 .5539 2.16 .7701 1.33 .2852 1.75 .5596 2.17 .7747 1.34 .2927 1.76 .5653 2.18 .7793 1.35 .3001 1.77 5710 2.19 .7839 1.36 .3075 1.78 •5766 2.20 .7885 1.37 .3148 1.79 •5822 2.21 .7930 1.38 .3221 1.80 •5878 2.22 .7975 1.39 .3293 1.81 •5933 2.23 .8020 1.40 .3365 1.82 •5988 2.24 .8065 1.41 .3436 1.83 •6043 2.25 .8109 1.42 .3507 1.84 •6098 2.26 .8154 STEAM ENGINES 261 Hyperbolic Logarithms of Numbers — Continued No. Log. No.^ Log. No. Log. 2.27 .8198 2.74 1.0080 3.21 1.1663 2.28 .8242 2.75 1.0116 3.22 1.1694 2.29 .8286 2.76 1.0152 3.23 1.1725 2.30 .8329 2.77 1.0188 3.24 1.1756 2.31 .8372 2.78 1.0225 3.25 1.1787 2.32 .8416 2.79 1.0260 3.26 1.1817 2.33 .8458 2.80 1.0296 3.27 1 . 1848 2.34 .8502 2.81 1.0332 3.28 1.1878 2.35 .8544 2.82 1.0367 3.29 1.1909 2.36 .8587 2.83 1.0403 3.30 1.1939 2.37 .8629 2.84 1.0438 3.31 1.1969 2.38 .8671 2.85 1.0473 3.32 1.1999 2.39 .8713 2.86 1.0508 3.33 1.2030 2.40 .8755 2.87 1.0543 3.34 1.2060 2.41 .8796 2.88 1.0578 3.35 1.2090 2.42 .8838 2.89 1.0613 3.36 1.2119 2.43 .8879 2.90 1.0647 3.37 1.2149 2.44 .8920 2.91 1.0682 3.38 1.2179 2.45 .8961 2.92 1.0716 3.39 1.2208 2.46 .9002 2.93 1.0750 3.40 1.2238 2.47 .9042 2.94 1.0784 3.41 1.2267 2.48 .9083 2.95 1.0813 3.42 1.2296 2.49 .9123 .2,96 1.0852 3.43 1.2326 2.50 .9163 2.97 1.0886 3.44 1.2355 2.51 .9203 2.98 1.0919 3.45 1.2384 2.52 .9243 2.99 1.0953 3.46 1.2413 2.53 .9282 3.00 1.0986 3.47 1.2442 2.54 .9322 3.01 1.0009 3.48 1.2470 2.55 .9361 3.02 .1.1053 3.49 1.2499 2.56 .9400 3.03 1 . 1086 3.50 1.2528 2.57 .9439 3.04 1.1119 3.51 1.2556 2.58 .9478 3.05 1.1151 3.52 1.2585 2.59 .9517 3.06 1.1184 3.53 1.2613 2.60 .9555 3.07 1.1217 3.54 1.2641 2.61 .9594 3.08 1.1249 3.55 1.2669 2.62 .9632 3.09 1.1282 3.56 1.2698 2.63 .9670 3.10 1.1314 3.57 1.2726 2.64 .9708 3.11 1 . 1346 3.58 1.2754 2.65. .9746 3.12 1.1378 3.59 1.2782 2.66 .9783 3.13 1.1410 3.60 1.2809 2.67 .9821 3.14 1.1442 3.61 1.2837 2.68 .9858 3.15 1.1474 3.62 1.2865 2.69 .9895 3.16 1.1506 3.63 1 . 2892 2.70 .9933 3.17 1.1537 3.64 1.2920 2.71 .9969 3.18 1 . 1569 3.65 1.2947 2.72 1.0006 3.19 1.1600 3.66 1.2975 2.73 1.0043 3.20 1.1632 3.67 1.3002 262 STEAM ENGINEERING Hyperbolic Logarithms of Numbers — Continued No. Log. No. Log. No. Log. 3.68 1.3029 4.13 1.4183 4.58 1.5217 3.69 1.3056 4.14 1.4207 4.59 1.5239 3.70 1.3083 4.15 1.4231 4.60 1.5261 3.71 1.3110 4.16 1.4255 4.61 1.5282 3.72 1.3137 4.17 1.4279 4.62 1.5304 3.73 1.3164 4.18 1.4303 4.63 1.5326 3.74 1.3191 4.19 1.4327 4.64 1.5347 3.75 1.3218 4.20 1.4351 4.65 1.5369 3.76 1.3244 4.21 1.4375 4.66 1.5390 3.77 1.3271 4.22 1.4398 4.67 1.5412 3.78 1.3297 4.23 1.4422 4.68 1.5433 3.79 1.3324 4.24 1.4446 4.69 1.5454 3.80 1.3350 4.25 1.4469 4.70 1.5476 3.81 1.3376 4.26 1.4493 4.71 1.5497 3.82 1.3403 4.27 1.4516 4.72 1.5518 3.83 1.3429 4.28 1.4540 4.73 1.5539 3.84 1.3455 4.29 1.4563 4.74 1.5560 3.85 1.3481 4.30 1.4586 4.75 1.5581 3.86 1.3507 4.31 1.4609 4.76 1.5602 3.87 1.3533 4.32 1.4633 4.77 1.5623 3.88 1.3558 4.33 1.4656 4.78 1.5644 3.89 1.3584 4.34 1.4679 4.79 1.5665 3.90 1.3610 4.35 1.4702 4.80 1.5686 3.91 1.3635 4.36 1.4725 4.81 1.5707 3.92 1.3661 4.37 1.4748 4.82 1.5728 3.93 1.3686 4.38 1.4770 4.83 1.5748 3.94 1.3712 4.39 1.4793 4.84 1.5769 3.95 1.3737 4.40 1.4816 4.85 1.5790 3.96 1.3762 4.41 1.4839 4.86 1.5810 3.97 1.3788 4.42 1.4861 4.87 1.5831 3.98 1.3813 4.43 1.4884 4.88 1.5851 3.99 1.3838 4.44 1.4907 4.89 1.5872 4.00 1.3863 4.45 1.4929 4.90 1.5892 4.01 1.3888 4.46 1.4951 4.91 1.5913 4.02 1.3913 4.47 1.4974 4.92 1.5933 4.03 1.3938 4.48 1.4996 4.93 1.5953 4.04 1.3962 4.49 1.5019 4.94 1.5974 4.05 1.3987 4.50 1.5041 4.95 1.5994 4.06 1.4012 4.51 1.5063 4.96 1.6014 4.07 1.4036 4.52 1.5085 4.97 1.6034 4.08 1.4061 4.53 1.5107 4.98 1.6054 4.09 1.4085 4.54 1.5129 4.99 1.6074 4.10 1.4110 4.55 1.5151 5.00 1.6094 4.11 1.4134 4.56 1.5173 5.01 1.6114 4.12 1.4159 4.57 1.5195 5 02 1.6134 STEAM ENGINES 263 Hyperbolic Logarithms of Numbers — Continued No. Log. No. Log. No. Log. 5.03 1.6154 5.49 1.7029 5.95 1.7834 5.04 1.6174 5.50 1.7047 5.96 1.7851 5.05 1.6194 5.51 1.7066 5.97 1.7867 5.06 1.6214 5.52 1.7084 5.98 1.7884 5.07 1.6233 5.53 1.7102 5.99 1.7901 5.08 1.6253 5.54 1.7120 6.00 1.7918 5.09 1.6273 5.55 1.7138 6.01 1.7934 5.10 1.6292 5.56 1.7156 6.02 1.7951 5.11 1.6312 5.57 1.7174 6.03 1.7967 5.12 1.6332 5.58 1.7192 6.04 1.7984 5.13 1.6351 5.59 1.7210 6.05 1.8001 5.14 1.6371 5.60 1.7228 6.06 1.8017 5.15 1.6390 5.61 1.7246 6.07 1.8034 5.16 1 . 6409 5.62 1.7263 6.08 1.8050 5.17 1.6429 5.63 1.7281 6.09 1.8066 5.18 1.6448 5.64 1.7299 6.10 1.83 5.19 1.6467 5.65 1.7317 6.11 1.8099 5.20 1.6487 5.66 1.7334 6.12 1.8116 5.21 1.6506 5.67 1.7352 6.13 1.8132 5.22 1.6525 5.68 1.7370 6.14 1.8148 5.23 1.6544 5.69 1.7387 6.15 1.8165 5.24 1 . 6563 5.70 1.7405 6.16 1.8181 5.25 1.6582 5.71 1.7422 6.17 1.8197 5.26 1.6601 5.72 1.7440 6.18 1.8213 5.27 1 . 6620 5.73 1.7457 6.19 1.8229 5.28 1.6639 5.74 1.7475 6.20 1.8245 5.29 1.6658 5.75 1.7492 6.21 1.8262 5.30 1.6677 5.76 1.7509 6.22 1.8278 5.31 1.6696 5.77 1.7527 6.23 1.8294 5.32 1.6715 5.78 1.7544 6.24 1.8310 5.33 1.6734 5.79 1.7561 6.25 1.8326 5.34 1.6752 5.80 1.7579 6.26 1.8342 5.35 1.6771 5.81 1.7596 6.27 1.8358 5.36 1.6790 5.82 1.7613 6.28 1.8374 5.37 1.6808 5.83 1.7630 6.29 1.8390 5.38 1.6827 5.84 1.7647 6.30 1.8405 5.39 1.6845 5.85 1.7664 6.31 1.8421 5.40 1.6864 5.86 1.7681 6.32 1.8437 5.41 1.6882 5.87 1.7699 6.33 1.8453 5.42 1.6901 5.88 1.7716 6.34 1.8469 5.43 1.6919 5.89 1.7733 6.35 1.8485 5.44 1.6938 5.90 1.7750 6.36 1.8500 5.45 1.6956 5.91 1.7760 6.37 1.8516 5.46 1.6974 5.92 1.7783 6.38 1.8532 5.47 1.6993 5.93 1.7800 6.39 l.«547 5.48 1.7011 5.94 1.7817 6.40 1.8563 264 STEAM ENGINEERING Hyperbolic Logarithms of Numbers — Continued. No. Log. No. Log. No. Log 6.41 1.8579 6.87 1.9272 7.33 1.9920 6.42 1.8594 6.88 1.9286 7.34 1.9933 6.43 1.8610 6.89 1.9301 7.35 1.9947 6.44 1.8625 6.90 1.9315 7.36 1.9961 6.45 1.8641 6.91 1.9330 7.37 1.9974 6.46 1.8656 6.92 1.9344 7.38 1.9988 6.47 1.8672 6.93 1.9359 7.39 2.0001 6.48 1.8687 6.94 1.9373 7.40 2.0015 6.49 1.8703 6.95 1.9387 7.41 2.0028 6.50 1.8718 6.96 1.9402 7.42 2.0042 6.51 1.8733 6.97 1.9416 7.43 2.0055 6.52 1.8749 6.98 1.9430 7.44 2.0069 6.53 1.8764 6.99 1.9445 7.45 2.0082/ 6.54 1.8779 7.00 1.9459 7.46 2.0096 6.55 1.8795 7.01 1.9473 7.47 2.0109 6.56 1.8810 7.02 1.9488 7.48 2.0122 6.57 1.8825 7.03 1.9502 7.49 2.0136 6.58 1.8840 7.04 1.9516 7.50 2.0149 6.59 1.8856 7.05 1.9530 7.51 2.0162 6.60 1.8871 7.06 1.9544 7.52 2.0176 6.61 1.8886 7.07 1.9559 7.53 2.0189 6.62 1.8901 7.08 1.9573 7.54 2.0202 6.63 1.8916 7.09 1.9587 7.55 2.0215 6.64 1.8931 7.10 1.9601 7.56 2.0229 6.65 1.8946 7.11 1.9615 7.57 2.0242/ 6.66 1.8961 7.12 1.9629 7.58 2.0255' 2.0268 6.67 1.8976 7.13 1.9643 7.59 6.68 1.8991 7.14 1.9657 7.60 2.0281 6.69 1.9006 7.15 1.9671. 7.61 2.0295 6.70 1.9021 7.16 1.9685 7.62 2.0308 6.71 1.9036 7.17 1.9699 7.63 2.0321 6.72 1.9051 7.18 1.9713 7.64 2.0334 6.73 1.9066 7.19 1.9727 7.65 2.0347 6.74 1.9081 7.20 1.9741 7.66 2.0360 6.75 1.9095 7.21 1.9755 7.67 2.0373 6.76 1.9110 7.22 1.9769 7.68 2.0386/ 6.77 1.9125 7.23 1.9782 7.69 2.0399' 6.78 1.9140 7.24 1.9796 7.70 2.0412 6.79 1.9155 7.25 1.9810 7.71 2.0425 6.80 1.9169 7.26 1.9824 7.72 2.0438 6.81 1.9184 7.27 1.9838 7.73 2.0451 6.82 1.9199 7.28 1.9851 7.74 2.0464 6.83 1.9213 7.29 1.9865 7.75 2.0477 6.84 1.9228 7.30 1,9879 7.76 2.0490 6.85 1.9242 7.31 1.9892 7.77 2.0503 6.86 1.9257 7.32 1.9906 7.78 2.0516 STEAM ENGINES 265 Hyperljolic Loganthms of Numbers — Continued No. Log. No. Log. No. Log. 7.79 2.0528 8.25 2.1102 8.71 2.1645 7.80 2.0541 8.26 2.1114 8.72 2.1656 7.81 2.0554 8.27 2.1126 8.73 2.1668 7.82 2.0567 8.28 2.1138 8.74 2.1679 7.83 2.0580 8.29 2.1150 8.75 2.1691 7.84 2.0592 8.30 2.1163 8.76 2.1702 7.85 2.0605 8.31 2.1175 8.77 2.1713 7.86 2.0618 8.32 2.1187 8.78 2.1725 7.87 2.0631 8.33 2.1199 8.79 2.1736 7.88 2.0643 8.34 2.1211 8.80 2.1748 7.89 2.0656 8.35 2.1223 8.81 2.1759 7.90 2.0669 8.36 2.1235 8.82 2.1770 7.91 2.0681 8.37 2.1247 8.83 2.1782 7.92 2.0694 8.38 2.1258 8.84 2.1793 7.93 2.0707 8.39 2.1270 8.85 2.1804 7.94 2.0719 8.40 2.1282 8.86 2.1815 7.95 2.0732 8.41 2.1294 8.87 2.1827 7.96 2.0744 8.42 2.1306 8.88 2.1838, 7.97 2.0757 8.43 2.1318 8.89 2.1849 7.98 2.0769 8.44 2.1330 8.90 2.1861 7.99 2.0782 8.45 2.1342 8.91 2.1872 8.00 2.0794 8.46 2.1353 8.92 2.1883 8.01 2.0807 8.47 2.1365 8.93 2.1894 8.02 2.0819 8.48 2.1377 8.94 2.1905 8.03 2.0832 8.49 2.1389 8.95 2.1917 8.04 2.0844 8.50 2.1401 8.96 2.1928 8.05 2.0857 8.51 2.1412 8.97 2.1939 8.06 2.0869 8.52 2.1424 8.98 2.1950 8.07 2.0882 8.53 2.1436 8.99 2.1961 8.08 2.0894 8.54 2.1448 9.00 2.1972 8.09 2.0906 8.65 2.1459 9.01 2.1983 8.10 2.0919 8.56 2.1471 9.02 2.1994 8.11 2.0931 8.57 2,1483 9.03 2.2006 8.12 2.0943 8.58 2.1494 9.04 2.2017 8.13 2.0956 8.59 2.1506 9.05 2.2028 8.14 2.0968 8.60 2.1518 9.06 2.2039 8.15 2.0980 8.61 2.1529 9.07 2.2050 8.16 2.0992 8.62 2.1541 9.08 2.2061 8.17 2.1005 8.63 2.1552 9.09 2.2072 8.18 2.1017 8.64 2.1564 9.10 2.2083 8.19 2.1029 8.65 2.1576 9.11 2.2094 8.20 2.1041 8.66 2.1587 9.12 2.2105 8.21 "2.1054 8.67 2.1599 9.13 2.2116 8.22 2.1066 8.68 2.1610 9.14 2.2127 8.23 2.1078 8.69 2.1622 9.15 2.2138 8.24 2.1090 8.70 2.1633 9.16 2.2148 ^ 266 STEAM ENGINEERING Hyperbolic Logarithms of Numbers — Continued^ i No. Log. No. Log. No. Log. ; 9.17 2.2159 9.55 2.2565 9.93 2.2956 9.18 2.2170 9.56 2.2576 9.94 2.2966 9.19 2.2181 9.57 2.2586 9.95 2.2976 9.20 2.2192 9.58 2.2597 9.96 2.29SJ 9.21 2.2203 9.59 2.2607 9.97 2.2996 9.22 2.2214 9.60 2.2618 9.98 2.3006 9.23 2.2225 9.61 2.2628 9.99 2.3016: 9.24 2.2235 9.62 2.2638 10.00 2.3026 9.25 2.2246 9.63 2.2649 10.25 2.3279: 9.26 2.2257 9.64 2.2659 10.50 2.3513 i 9.27 2.2268 9.65 2.2670 10.75 2.3749 1 9.28 2.2279 9.66 2.2680 11.00 2.3979 9.29 2.2289 9.67 2.2690 11.25 2.4201 : 9.30 2.2300 9.68 2.2701 11.50 2.4430 9.31 2.2311 9.69 2.2711 11.75 2.4636 9.32 2.2322 9.70 2.2721 12.00 2.4849 9.33 2.2332 9.71 2.2732 12.25 2.5052 1 9.34 2.2343 9.72 2.2742 12.50 2.5262 9.35 2.2354 9.73 2.2752 12.75 2.5455 9.36 2.2364 9.74 2.2762 13.00 2.5649 9.37 2.2375 9.75 2.2773 13.25 2.5840 9.38 2.2386 9.76 2.2783 13.50 2.6027 9.39 2.2396 9.77 2.2793 13.75 2.6211 9.40 2.2407 9.78 2.2803 14.00 2.6391 9.41 2.2418 9.79 2.2814 14.25 2.6567 9.42 2.2428 9.80 2.2824 14.50 2.6740 9.43 2.2439 9.81 2.2834 14.75 2.6913 9.44 2.2450 9.82 2.2844 15.00 2.7081 9.45 2.2460 9.83 2.2854 15.50 2.7408 9.46 2.2471 9.84 2.2865 16.00 2.7726 9.47 2.2481 9.85 2.2875 16.50 2.8034 9.48 2.2492 9. 86 2.2885 17.00 2.8332 9.49 2.2502 9.87 2.2895 17.50 2.8621 9.50 2.2513 9.88 2.2905 18.00 2.8904 9.51 2.2523 9.89 2.2915 18.50 2.9173 9.52 2.2534 9.90 2.2925 19.00 2.9444 9.53 2.2544 9.91 2.2935 19.50 2.9703 9.54 2.2555 9.92 2.2946 20.00 2.9957 In order to save the trouble of applying a rule or a formula for the purpose of determining the mean effective pressure for stated conditions, the next table is STEAM ENGINES 267 given, but the following explanation must be carefully noted, as otherwise correct results will not be secured from it. The first horizontal line contains the various points at which steam is cut off from the cylinder, ranging from 1/10 to 9/10 of the stroke. The second line is the corresponding ratio of expansion, pro- vided that clearance is not taken into accoimt. The first column contains initial pressures from 10 to 200 pounds, all absolute or above a perfect vacuum, therefore, when taking gauge pressure for an example in practice at or near the sea level, 15 pounds should be added to it, and the resulting number found in the first column. Gauge pressure might have been used in place of absolute pressures, but in that case it would only apply to places where the atmosphere weighs nearly 15 pounds to the square inch, whereas the plan adopted makes it available for all conditions. For the same reason the back pressure was not subtracted, as there is no universal rule to follow. To fully illustrate the use of this table of "Average Pressure of Steam" suppose that the initial pressure as shown by 268 STEAM ENGINEERING measuring upward from the atmos- ;[ pheric line of an indicator diagram, is 105 pounds, the atmospheric pressure is practically 15 pounds, and the point of cut off is at M stroke. The engine is run non-condensing. What is the mean \ effective pressure? The absolute pressure is 105+15 = 120 poimds. Finding 120 in the first col- umn and following the line to the right hand to the sixth column under 3^ we find that the average pressure is 71.58 pounds. Subtracting 15 for the atmos- phere and one for friction of steam, or 16 pounds back pressure, shows that under these conditions the mean effec- tive pressure is 55.58 pounds. This agrees with the result secured by calcu- lation as demonstrated on preceding pages. Assuming that a condensing engine is run under conditions that agree with the preceding example, except that while the load is increased enough to maintain the cut off at 3^ stroke, the back pres- sure is reduced to 3 pounds. What is the mean effective pressure? We have demonstrated that the aver- age pressure is 71.58 pounds, therefore STEAM ENGINES 269 the mean effective pressure is 71.58 — 3 = 68.58 pounds. Assuming that the non-condensing engine has 7 per cent, of clearance, what is the mean effective pressure, pro- vided the clearance is taken into consid- eration? Referring to the table entitled "Actual Ratios of Expansion," and following down the first column under P of C until .25 is found (meaning that the point of cut off is at ]4: or .25 of the stroke), then taking the horizontal line until the col- umn under 7 per cent, is reached, we find that the actual ratio of expansion is 3.34. In the table of "Average Pressure of Steam" the nearest ratio of expansion is 3.33 which practically agrees with the conditions above mentioned. In this column on the horizontal line beginning with 120 poimds pressure we learn that the average pressure is 79.31 pounds from which must be subtracted the back pressure of 16 pounds, therefore the mean effective pressure is 63.31 pounds. Suppose that a condenser is added to this engine, and more machinery is in- stalled in the mill or shop, causing the cut off to take place at 1/5 or .20 of the 270 STEAM ENGINEERING Stroke, the clearance remaining at 7 per cent., what is the mean effective pres- sure? Following the directions above given the actual ratio of expansion is 3.96, which is 4 for all practical purposes. With 120 pounds initial pressure, and 4 expansions, or a ratio of expansion of 4, the average pressure is 71.58 pounds and the mean effective pressure is 71.58—3 = 68.58 pounds. The following explanation of the next table is given in condensed form for the convenience of application: Cut off = The proportion of the stroke completed by the piston when the cut off valve closes. R of E = Ratio of expansion, or 1 divided by the "cut off" as above described. I P = Initial pressure absolute, or the pressure at the beginning of the stroke above a vacuum, which is maintained until the cut off valve closes. STEAM ENGINES 271 AVERAGE PRESSURE OF STEAM Cut-off Vio H Va \^ M R.ofE. 10 8 6 5 4 I. P. Average Pressure 3.30 4.94 6.60 8.25 9.90 11.56 13.21 14.86 16.51 18.16 19.81 21.46 23.10 24.77 26.42 28.07 29.73 31.37 33.03 34.68 36.38 37.98 39.64 41.28 42.92 44.59 46.23 47.89 49.54 51.19 52.84 54.49 56.15 57.80 59.45 61.10 62.75 64.40 66.06 3.84 5 77 1.-' 9.62 11.54 13.47 15.39 17.32 19.24 21.16 23.09 25.01 26.94 28.86 30.79 32.71 34.64 35.56 38.48 40.41 42.34 44.26 46.18 48.10 50.03 51.95 53.88 55.80 57.73 59.65 61.58 63.50 65.42 67.35 69.27 71.20 73.12 75.05 76.97 4.64 6.98 9.29 11.63 13.96 16.28 18.59 20.94 23.26 25.59 27.92 30.24 32.55 34.90 37.21 39.55 41.88 44.20 46.51 48.56 51.17 53.51 55.84 58.16 60.47 62.82 65.13 67.47 69.80 72.13 74.45 76.78 79.10 81.43 83.76 86.08 88.41 90.74 93.05 5 21 7 82 10 43 13 04 15 65 18 26 20 87 23 48 26 09 28 69 31 31 33 91 36 53 39 13 41 74 44.351 46 96| 49 57 52 18 54 78 57 40 60 00 62 62 65 22 67 83 70 40 73 05 75 66 78 27 80 87 83 48 86 09 88.701 91 31 93 771 96 53 99 14 101 7 104 4 5.96 8.94 11.93 14.91 17.90 20.87 23.86 26.84 29.82 32.80 35.79 38.77 41.75 44.73 47.72 50.57 53.68 56.66 59.65 62.63 65.61 68.59 71.58 74.56 77.54 80.52 83.51 86.49 89.47 92.45 95.44 98.42 101.4 103.3 107.3 110.3 113.3 116.3 119.3 r 1 272 STEAM ENGINEERING AVERAGE PRESSURE OF STEAM Cut-off %o Vs %o ^ %o % R.ofE. 3.33 3 2.5 2 1.66 1.5 LP. Average Pressure. 10 6.60 6.98 7.66 8.46 9.03 9.36 15 9.91 10.49 11.49 12.69 13.55 14.05 20 13.21 13.98 15.32 16.93 18.07 18.73 25 16,52 17.48 19.16 21.16 22.59 23.41 30 19.82 20.99 22.99 25.39 27.11 28.10. 35- 23.13 24.48 26.82 29.64 31.62 32.78 40 26.43 27.98 30.65 33.86 36.15 37.43 45 29.74 31.48 34.38 38.09 40.66 42.14 50 33.04 34.96 38.32 42.32 45.18 46.82 55 36.38 38.48 42.15 46.55 49.93 51.51 60 39.65 41.98 45.98 50.79 54.22 56.20 65 44.00 45.47 49.81 55.02 59.00 60.88 70 46.26 48.96 53.65 59.25 63.26 65.56 75 49.61 52.47 57.48 63.48 68.08 70.25 80 52.87 55.96 61.31 67.72 72.30 74.86 85 56.23 59.47 65.14 71.95 77.16 79.61 90 59.48 62.97 68.97 76.18 81.34 84.28 .95 62.84 66.46 72.80 80.41 86.24 88.98 100 66.08 69.92 76.64 84.65 90.36 93.64 105 69.46 73.46 80.47 88.88 95.32 98.35 110 72.70 76.94 84.30 93.11 99.40 103.0 115 76.07 80.46 88.13 97.34 104.4 107.7 120 79.31 83.96 91.96 95.80 101.6 108.4 112.4 125 82.69 87.45 105.8 113.4 117.0 130 85.91 90.92 99.63 110.0 117.5 121.7 135 89.31 94.45 103.4 114.2 122.5 126.0 140 92.52 97.94 107.3 118.5 126.5 131.1 145 95.92 101.4 111.1 122.7 131.6 135.8 150 99.13 104.9 114.9 126.9 135.5 140.5 155 102.5 108.4 118.7 131.2 140.7 145.5 160 105.8 111.9 122.6 135.4 145.2 149.9 165 109.1 115.4 126.4 139.6 149.7 154.5 170 112.4 118.9 130.2 143.9 154.3 159.2 175 115.7 122.6 134.1 148.1 158.9 163.9 180 119.0 125.9 137.9 152.3 163.4 168.6 185 122.3 129.4 141.7 156.6 167.9 173.2 190 125.6 132.9 145.6 160.8 172.4 177.3 195 129.0 136.4 149.4 165.0 177.0 182.6 200 132.3 139.9 153.3 169.3 180.7 187.3 STEAM ENGINES 273 AVERAGE PRESSURE OF STEAM Cut-off %o H «/io H %o R.ofE. 1.43 1.33 1.25 1.14 1.11 LP. Average Pressure 10 9.48 9.65 9.78 9.92 9.94 15 12.23 14.48 14.67 14.88 14.92 20 18,98 19.30 19.56 19.84 19.89 25 23.72 24.13 24.46 24.80 24.86 30 28.46 28.96 29.35 29.76 29.84 35 33.21 33.79 34.24 34.72 34.81 40 37.95 38.61 39.13 39,68 39.78 45 42.70 43.44 44.02 44,64 44.75 50 47.44 48.27 48.92 49.60 49.73 55 52.19 53.09 53.81 54.56 54.70 60 56.93 57.92 58.70 59.52 59.67 65 61.68 62.75 63.59 64.48 64.64 70 66.42 67.57 68.48 69.44 69.62 75 71.17 72.40 73.38 74.40 74.59 80 75.91 77.23 78.27 79.37 79.56 85 80.66 82.06 83.16 84,32 84.54 90 85.40 86.88 88.05 89.28 89.50 95 90.15 91.71 92.94 94.25 94.48 100 94.89 96.54 97.84 99.21 99.46 105 99.63 101.3 102.7 104.1 104.4 110 104.4 106.2 107.6 109.1 109.4 115 109.1 111.0 112.5 114.0 114.3 120 113.8 115.8 117.4 119.0 119.3 125 118.6 120.6 122.3 124.0 124.3 130 123.3 125.5 127.2 128.9 129.3 135 128.1 130.3 132.0 133.9 134.2 140 132.8 135.1 136.9 138.8 139.2 145 137.5 139.9 141.8 143.8 144.2 150 142.3 144.8 146.7 148.8 149.2 155 147.0 149.6 151.6 153.7 154.1 160 151.8 154,4 156.5 158.7 159.1 165 156.5 159.2 161.4 163.6 164.1 170 161.3 164.1 166.3 168.6 169.0 175 166.0 168.9 171.2 173.6 174.0 180, 170.8 173.7 176.1 178.5 179.0 185 175.5 178.6 181.0 183,5 184.0 190 180.3 183,4 185.9 188.5 188.9 195 185.0 188.2 192.3 193.4 193.9 200 189.8 193.0 195.6 198.4 198.9 274 STEAM ENGINEERING CAUTION Do not attempt to use the foregoing table until you have carefully read the explanation of it which precedes the table, as otherwise correct results may not be obtained owing to misapplication of the figures given. As a further illustration of its value take the case of an engine located on very high ground where the atmosphere pressure is only about two-thirds of what we find it at sea level, or say 10 pounds, for convenience. If the steam gauge indicates 110 pounds and the initial pressure is 5 pounds less, the initial pres* sure absolute is 110—5 + 10 = 115 pounds. Assuming that the steam is cut off at 3^ stroke and ignoring the clearance, the table indicates that the average pressure is 68.59 pounds. If this engine is operated without a condensei the mean effective pressure is 68.5ti — 16 = 52.59 pounds. If the condensei is used it is 68.59 — 3=65.59 pounds. REMARKS ON CALCULATING THE HORSE POWER OF STEAM ENGINES Preceding calculations on this impor- tant subject relate to simple double acting engines, which constitute a ma- jority of the engines now in use, but STEAM ENGINES 275 there are others in service, and as the proper way to determine the power they develop may not be plain to the young engineer, explanations are herewith ' given that will prove useful in such cases. Where a single acting engine is in use the effective piston speed is only one- half of what it is for a double acting engine, therefore the indicated horse power will be but one-half of that ob- tained by preceding rules and formulas. Where there are two single acting cylinders the engine is to be treated as if it were a double acting engine with one cylinder. When calculating the power developed by these engines, the piston speed is taken while steam is acting on the piston. If this principle is always applied, correct results will be obtained. When treating a double acting engine, the total piston speed is to be used, but the mean effective pressure for two dia- grams should not be added together and the result used in making the calculation, as that gives twice as much power as really is developed. It is proper to add them but the sum must be divided by 2. A double engine is to be treated as if it consisted of two separate engines located in different parts of the works .where machinery is used. The power of each is to be computed, in accordance with 276 STEAM ENGINEERING rules given in this book, and the results added together. Where great accuracy is required it becomes necessary to make allowance for the space occupied by the piston rod on the area of the piston, because steam pressure cannot act on this space. In the case of a single acting engine with two cylinders, no allowance is to be made for the rod as steam only acts on the head end, where there is no rod to reduce the area. With a double acting engine (not fitted with a tail rod), it is proper to sub- tract one-half of the area of the piston rod, and call the remainder the effective area of the piston. The piston rod occupies space on one side of the piston, while the other side is clear, therefore if one-half of it is assumed to be on each side of it, the result is correct. For example, take a 20= inch piston with a piston rod S'J/g inches in diameter. The area of a 20= inch circle is 314.16 square inches, and the area of a 3J^ circle is 11.793 square inches. Then (314.16 - 11.793) -f 314.16 -v- 2 = 308.26 square inches. The area of the piston rod is 11.793 square inches, one-half of which is 5.896; then 314.16-5.896 = 308.26 square inches as before. Large horizontal engines are fitted with heavy pistons that rest on the bot- STEAM ENGINES 277 torn of the cylinders and cause much friction. Unless superior lubrication is provided, the wear is excessive, and in order to improve these conditions, a tail rod is added which is illustrated in Fig. 41. The piston rod is continued through the cylinder head on the head end, which is fitted with a stuffing box sim- ilar to the crank end cylinder head. The outer end of this piston rod is carried by a second crosshead that travels on a lower guide, and as this is always in sight, it can be properly lubricated, thus preventing imdue wear on the piston and the cylinder. When calculating the power of such engines the whole area of the rod should be subtracted from the area of the piston. For a 20-inch piston with a rod 3J^ inches in diameter the effective area is 314.16-11.793=302.36 square inches. Where several pounds back pressure are added to an engine in order to use the exhaust steam for heating a mill or shop, or for any other purpose, it in- creases the load and makes it necessary to bum more coal. As this change makes no difference in the indicated horse power, it does not seem to be con- sistent to some engineers, but it admits of a perfectly logical explanation. The indicated horse power of an engine is represented by the area of the indicator 278 STEAM ENGINEERING STEAM ENGINES 279 diagram taken from it, and while this varies with changes made in the ma- chinery driven by this engine, it is not affected by changes in the back pressure. How then is the apparent change in the load accounted for? Careful study of the following state- ments will make this clear. Taking for standard conditions an engine in which there is no back pressure above the atmos- phere, the steam and expansion lines average a certain number of inches above the vacuum line, and this height represents the total load on the engine. If back pressure is added to the piston by forcing exhaust steam around the shop until the back pressure line is raised a certain part of an inch, the average height of the steam and expansion lines will be raised the same fraction of an inch, showing that the total load has been increased. On the other hand, if a condenser is added and the back pressure line is lowered a certain fraction of an inch by it, the average height of the steam and the expansion lines will be lowered the same fraction of an inch, showing that the total load has been decreased, and the coal required to generate steam to operate the same machinery is less. Under all of the foregoing changes it is assumed that the same amount of power 280 STEAM ENGINEERING is required to drive the works, as any ; change in this respect will prevent proper comparison of the effects of the above mentioned difference in back pressure. HORSE POWER CONSTANTS It is frequently necessary to deter- mine the power that an engine is devel- oping under varying conditions, which cause changes in the mean effective pressure. As the speed is assumed to be constant under these changes (and it is practically so with an up-to-date engine), the mean effective pressure is the only factor that changes, hence it follows that if a constant is determined which represents the power developed for one pound mean effective pressure, it is only necessary to multiply this constant by the mean effective pressure to determine the power developed. This constant is found by use of the following rule. Multiply the area of the piston by the piston speed in feet per minute, and divide by 33,000. The quotient is the horse power constant for that engine under given conditions. For illustration suppose that an en- gine is fitted with a piston 20 inches in diameter, the area of which is 314.16 square inches. The stroke is 42 inches and the speed 90 revolutions per minute, STEAM ENGINES 281 giving a piston speed of 630 feet. Then 314.16X630^-33,000 = 5.9976 which is the horse power constant. If the mean effective pressure is 50 pounds to the square inch, it develops 5.9976X50 = 299.88 horse power. The next table gives the horse power constants for cylinders from 4 to 60 inches in diameter, with piston speed from 10 to 900 feet per minute. To illus- trate its practical application, suppose that a 24X48 inch engine, at 100 revo- lutions per minute shows a mean effec- tive pressure of 56 pounds; what power is developed? The piston speed is 8 feet per revolu- tion, or 800 feet per minute. Finding the column under 800 and following it downward until the horizontal line opposite 24 is found, the horse power constant is 10.967. Then 10.967X56 = 614.15 horse power developed under these conditions. Suppose that an 18X36 inch engine revolves 80 times per minute, and indi- cator diagrams from it show 47 pounds mean effective pressure; what power is developed? The piston speed is 6 feet per revolu- tion, or 480 feet per minute. In the column under 400 and on the horizontal line opposite 18 the horse power constant 282 STEAM ENGINEERING is 3.0845. On the same line under 80 I the constant is .6169. These two con- ' St ants are to be added together to ac- count for 480 feet per minute, and 3.0845 + .6169 = 3.7014. Multiplying this by 47 shows that 173.96 horse power was developed when the diagrams were taken. HORSE POWER CONSTANTS Piston speed per minute. s .2 o 10 20 30 40 50 60 4 .0038 .0076 .0119 .0114 .0152 .0190 .0228 5 .0059 .0178 .0238 .0297 .0357 6 .0085 .0171 .0257 .0342 .0428 .0514 7 .0116 .0233 .0349 .0466 .0583 .0699 8 .0152 .0304 .0457 .0609 .0761 .0913 9 .0192 .0385 .0578 .0771 .0963 .1156 10 .0238 .0476 .0714 .0952 .1190 .1428 11 .0288 .0576 .0863 .1151 .1439 .1729 12 .0342 .0685 .1028 .1370 .1713 .2056 13 .0402 .0804 .1206 .1608 .2011 .2413 14 .0466 .0933 .1399 .1865 .2332 .2798 15 .0535 .1071 .1606 .2142 .2677 .3213 16 .0609 .1218 .1827 -.2437 .3046 .3655 17 .0687 .1275 .1963 .2651 .3339 .4026 18 .0771 .1542 .2313 .3084 .3855 .4626 19 .0859 .1718 .2577 .3436 ;4295 .5155 20 .0952 .1904 .2856 .3808 .4760 .5712 21 .1049 .2099 .3148 .4198 .5247 .6297 22 .1151 .2303 .3455 .4607 .5759 .6911 23 .1259 .2518 .3777 .5036 .6295 .7554 24 .1370 .2741 .4112 .5483 .6854 .8225 25 .1487 .2975 .4462 .5950 .7437 .8925 26 .1608 .3217 .4826 .6435 .8044 .9653 27 .1735 .3470 .5205 .6940 .8675 1.0410 28 .1865 .3731 .5597 .7463 .9329 1.1196 29 .2001 .4003 .6004 .8006 1.0008 1.2009 30 .2142 .4284 .6426 .8568 1.0710 1.2852 31 .2287 .4574 .6861 .9148 1.143.6 1 .3723 32 .2437 .4874 .7311 .9748 1.2186 1.4623 33 .2591 .5183 .7775 1.0367 1.2959 1.5551 34 .2751 .5502 .8253 1.1005 1.3766 1.6508 STEAM ENGINES 283 Horse Power Constants — Continued. Piston speed per minute. .1 10 20 30 40 50 60 85 .2915 .5831 .8746 1.1662 1.4578 1.7493 36 ,3084 .6169 .9253 1.2338 1.5422 1.8507 87 .8258 .6516 .9774 1.3033 1.6291 1.9549 8S .8486 .6873 1.0310 1.3747 1.7184 2.0620 89 .3620 .7240 1.0860 1.4480 1.8100 2.1720 40 .8808 .7616 1.1424 1.5232 1.9040 2.2848 41 .4000 .8001 1.2002 1.6003 2.0004 2.4005 42 .4198 .8386 1.2585 1.6783 2.0982 2.5180 48 .4400 .8801 1.3202 1.7602 2.2003 2.6404 44 .4607 .9215 1.3823 1.8431 2.3038 2.7646 45 .4819 .9639 1.4459 1.9278 2.4098 2.8917 46 .50.86 1.0072 1.5108 2.0144 2.5180 3.0216 47 .5257 1.0515 1.5772 2.1030 2.6287 3 . 1545 48 .548.8 1.0967 1.6451 2.1934 2.7418 3.2901 49 .5714 1 . 1429 1.7143 2.2858 2.8572 3.4286 50 .5950 1.1900 1.7850 2.3800 2.9750 3.5700 51 .6190 1.2381 1.8571 2.4762 3.0952 3.7142 52 . 6485 1.2871 1.9307 2.5742 3.2178 3.8613 58 .6685 1.3371 2.0036 2.6742 3.3427 4.0113 54 .6940 1.3880 2.0820 2.7760 3.4700 4.1640 55 .7199 1.4399 2.1599 2.8798 3.5998 4.3197 56 .7463 1.4927 2.2391 2.9855 3.7318 4.4782 57 .7782 1.5465 2.3198 3.0930 3.8663 4.6396 58 .8006 1.6013 2.4019 3.2025 4.0032 4.8038 59 .8284 1.6570 2.4854 3.3139 4 . 1424 4.9709 60 .8568 1.7136 2.5704 3.4272 4.2840 5.1408 Piston speed per minute. i 70 80 90 100 200 300 4 .0266 .0304 .0342 .0381 .0762 .1142 5 .0416 .0476 .0535 .0595 .1190 .1785 6 .0599 .0685 .0771 .0857 .1714 .2570 7 .0816 .0933 .1049 .1166 .2332 .3499 8 .1066 .1218 .1370 .1523 .3046 .4570 9 .1849 .1542 .1735 .1928 .3856 .5783 10 .1666 .1904 .2142 .2380 .4760 .7140 11 .2015 .2303 .2581 .2880 .5760 .8639 12 .2899 .2741 .3084 .3427 .6854 1.0282 18 .2815 .3217 .3620 .4022 .8044 1.2067 14 .3265 .3731 .4198 .4665 .9330 1.3994 15- .3748 .4284 .4819 .5355 1.0710 1.6065 284 STEAM ENGINEERING Horse Power Constants — Continued. Piston speed per minute. 5 70 80 90 100 200 300 16 .4265 .4874, .5483 .6093!l.2186 1.8278 17 .4614 .5402 .6190 .6878 1.2756 1.9635 18 .5397 .6169 .6940 .7711 1.5422 2.3134 19 .6014 .6873 .7732 .8592 1.7184 2.5775 20 .6664 .7616 .8568 .9520 1.904012.8560 21 .7347 .8396 .9446 1.0496 2.099213.1488 22 .8063 .9215 1.0367 1.1519 2.3038 3.4558 23 .8813 1.0072 1.1331 1.2590 2.5180 3.7771 24 .9516 1.0967 1.2338 1.3709 2.7418 4.1126 25 1.0413 1.1900 1.3388 1.4875 2.9750 4.4625 26 1.1262 1.2871 1.4480 1 . 6089 3.217814.8266 27 1.2145 1.3880 1.5615 1.7350 3.4700l5.2051 28 1.3061 1.4927 1.6793 1.8659 3.731815.5978 29 1.4011 1.6013 1.8014 2.0016 4.0032 6.0047 30 1.4994 1,7136 1.9278 2.142014.2840 6.4260 31 1.6010 1.8297 2.0585 2.2872 4.5744 6.8615 32 1.7060 1.4497 2.1934 2.4371 4.8742 7.3114 33 1.8143 2.0735 2.3326 2.5918 5.1836 7.7755 34 1.9259 2.2010 2.4762 2.7513 5.5026 8.2538 35 2.0409 2.3324 2.6240 2.9155 5.8310 8.7465 36 2.1591 2.467612.7760 3.0845 6.1690 9.2534 37 2.2808 2.6066 2.9324 3.2582 6.5164 9.7747 38 2.4057 2.7494 3.0930 3.4367 6.8734 10.310 39 2.5340 2.8960 3.2580 3.6200 7.2400 10.860 40 2.6656 3.0464 3.4272 3.8080 7.6160 11.424 41 2.8005 3.2006 3.6007 4.0008 8.0016 12.002 42 2.9378 3.3577 3.7775 4.1983 8.3866 12.585 43 3.0804 3.5205 3.9606 4.4006 8.8012 13.202 44 3.2254 3.6861 4.1469 4.6077 9.2154 13.823 45 3.3737 3.8556 4.3376 4.8195 9.6390 14.459 46 3.5253 4.0289 4.5325 5.0361 10.0721 15. 108 47 3.6802 4.2059 4.7317 5.2574 10.515 15.772 48 3.8385 4.3868 4.9352 5.4835 10.967 16.451 49 4.0001 4.5715 5.1429 5.7144 11.429 17.143 50 4.1650 4.7600 5.3550 5.9500 11.900 17.850, 51 4.3333 4.9523 5.5713|6.1904 12.381 18.571" 52 4.5049 5.1484 5.7920 6.4355 12.871 19.307 53 4.6790 5.3483 6.0169 6.6854 13.371 20.056 54 4.8581 5.5521 6.2461 6.9401 13.880 20.820 55 5.0397 5.7596 6.4796 7.1995 14.399 21.599 56 5.2246 5.9709 6.71737.4637 14.297 22.391 57 5.4128 6.1861 6.9584 7.7326 15.465 23.198 58 5 . 6044 6.4051 7.205718.0063 16.013 24.019 59 5.7993 6.6278 7. 4563!8. 2849 16.570 24.854 60 5.9976 8. 854417. 7112|8. 5680 17.136 25.704 STBAM ENGINES 285 Horse Power Constants— Ccw/tn«*(i Piston speed per minute. 1 a 400 500 600 700 800 900 4 .15231 .1904 .2285 .2666 .3046 .3427 5 .2380 .2975 .3570 .4165 .4760 .5355 6 .3427 .4284 .5141 .5998 .6854 .7711 7 .4665 .5831 .6997 .8163 .9330 1.049S 8 .6093 .7616 .9139 1.0662 1.2186 1.3709 9 .7711 .9639 1.1567 1.3495 1.5422 1.7350 10 .9520 1.1900 1.4280 1.6660 1.9040 2.1420 11 1.1519 1.4399 1.7279'2.0159 2.3038 2.5818 12 1.3709 1.7136 2.0563 2.3990 2.7418 3.0845 13 1.6089 2.0111 2.4133 2.8155 3.2178 3.6200 14 1.8659 2.3324 2.7989 3.2654 3.7318 4.1983 15 2.1420 2.6775 3.2130 3.7485 4.2840 4.8195 IG 2.4371 3.0464 3.6557 4.2650 4.8742 5.4835 17 2.6513 3.3391 4.0269 4.6147 5.4026 6.1904 18 3.0845 3.8556 4 . 6267 5.3978 6.1690 6.9401 19 3.4367 4.2959 5.1551 6.0143 6.8734 7.7326 20 3.8080 4.7600 5.7120 6.6640 7.6160 8.5680 21 4.1983 5.2479 6.2975 7.3471 8.3966 9.4462 22 4.6077 5.7596 6.9115 8.0634 9.2154 10.367 23 5.0361 6.2951 7.5541 8.8131 10.072 11.331 24 5.4835 6.8544 8.2253 9.5962 10.967 12.338 25 5.9500 7.4375 8.9250 10.413 11.900 13.388 26 6.4355 8.0444 9.6534 11.262 12.871 14.480 27 6.9401 8.6751 10.410 12.145,13.880 15.615 28 7.4637 9.3296 11.196 13. 061114. 927 16.793 29 8.0063 10.008 12.009 14.011 16.013 18.014 30 8.5680 10.710 12.852 14.994 17.136 19.278 31 9.1487 11.436 13.723 16.010 18.297 20.585 32 9.7485 12.186 14.623 17.060 19.497 21.934 33 10.367 12.959 15.551 18.143 20.735 23.326 34 11.005 13.756 16.508 19.259 22.010 24.762 35 11.662 14.578 17.493 20.409 23.324126.240 36 12.338 15.422 18.507 21.591 24.676127.760 37 13.033 16.291 19.549 22.808 26.066,29.324 38 13.747 17.184 20.620 24.057 27. 494130. 930 39 14.480 18.100 21.720 25.340 28. 960132. 580 40 15.232 19.040 22.848 26.656 30.464 34.272 41 16.003 20.004 24.005 28.005 32.006 36.007 42 16.783 20.982 25.180 29.378 33.577| 37.775 43 17.602 22.003 26.404 30.804 35.205 39.606 44 18.431 23.038 27.646 32.254 36.861 41.469 45 19.278 24,098 28.917 33.737 38.556 43.376 46 20.144 25.180 30.216 35.253 40.289145.325 i 286 STEAM ENGINEERING Horse Power Constants — Continued Piston speed per minute. i 400 500 600 700 800 900 47 21.030 26.287 31.545 36.802 42.059147.317 48 21.934 27.418 32.901 38.385 43.868 49.352 49 22.858 28.572 34.286 40.001 45.715'51.429 .50 23.800 29.750 35.700 41.650 47.600 53.550 ,51 24.762 30.952 37.142 43.333 49.523 55.713 52 25.742 32.178 38-. 613 45.049 51.484 57.920 .53 26.742 33.427 40.113 46.798 53.483 60.169 ,54 27.760 34.700 41.640 48.581 55.521 62.461 ,5.5 28.798 35.998 43.197 50.397 57.596 64.796 ,56 29.855 37.318 44.782 52.246 59.709 67.173 .57 30.930 38.663 46.396 54.128 61.861 69.594 ,58 32.025 40.032 48.038 56.044 64.051 72.057 ,59 33.139 41.424 49.709 57.993 66.278 74.563 60 34.272 42.840 51.408 59.976 68.544 77.112 FLY WHEELS When the speed of an engine is to be determined there are several points that ought to be considered, one of which is the safe speed for the fly wheel. This cannot be stated in revolutions per min- ute alone, but must be taken in connec- tion with the diameter of the wheel. For illustration of this point we cannot say that a fly wheel should never be run more than 300 revolutions per minute, because the safe limit for a large wheel is much less and for a small one it may be a great deal more. The safe limit of any wheel is the num- ber of feet that the rim or the face of the STEAM ENGINES 287 wheel can travel in a minute without danger of disruption by centrifugal force. The rim speed of a fly wheel may be determined by the following rule. Multiply the diameter in feet by 3.1416 and by the number of revolutions per minute. The product is the speed in feet per minute. Now the safe speed of cast iron fly wheels was formerly taken at 5,000 feet per minute (which is about one mile), but as higher speeds are imperatively demanded in modern practice, the limit has been raised to 100 feet per second or 6,000 feet per minute. Even this allows Si large factor of safety, provided the iron is of fair quality, and the casting is free from defects, but these desirable quali- ties cannot be guaranteed in every case. All the parts of a fly wheel should be designed with a large factor of safety to iwithstand even greater strain than it is subjected to under ordinary working iconditions, especially in view of the fact that if a governor does not control the ■speed perfectly, allowing it to increase above normal conditions, the strain may [be greatly increased before the vspeed can be reduced. 288 STEAM ENGINEERING When the rim of a fly wheel is made thicker than usual it is not a guarantee of greater safety, because centrifugal force increases with the weight, hence the strain is much greater on a thick rim than on a thin one, when both are run at the same speed, and the danger of hid- den flaws in cast iron increases with the size of the casting, therefore after a cer- tain thickness is secured, based on the shape of rim, number of arms supporting the same, etc., it is useless to make it thicker. , The number of revolutions per minute that can safely be allowed for well de- signed cast iron wheels, free from defec- tive castings, is determined by the fol- lowing rule: Divide 6,000 by the diameter multi- plied by 3.1416. The quotient is the safe number of revolutions per minute. For illustration take a wheel 10 feet in diameter. Then 6,000-j- (10X3.1416) = 191 revolutions. The next table gives the safe speed of wheels from 4 to 30 feet in diameter based on a rim speed of 6,000 feet per minute. For well designed and constructed wooden fly wheels, it is probably safe to add 25 per cent, to the figures given in the table. STEAM ENGINES 289 SAFE SPEED OF FLY WHEELS Diameter Revolutions Diameter Revolutions in feet per minute in feet per minute 3 636 17 112 4 477 18 106 6 381 19 100 6 318 20 95 7 272 21 91 8 -238 22 86 9 212 23 83 10 191 24 79 11 173 25 76 12 159 26 73 13 146 27 70 14 136 28 68 15 127 29 66 16 119 30 63 MORE ABOUT HORSE POWER Men who are not engineers and who have not given the matter much atten- tion^ seem to think that if an engineer is told the horse power of an engine that he has never seen, he should know at once the size of it, or in other words the diameter of cyHnder and length of stroke. It is impossible to do this because a given horse power may be secured from a great variety of sizes, and on the other hand a given size may represent a wide range of power developed under differ- ent conditions. In order to fully illustrate this matter several tables will be given which repre- sent good practice at the present time 290 STEAM ENGINEERING as they are published by up-to-date engine builders as representing their product to prospective customers. For the benefit of the reader who is seeking practical information along this line, they will prove valuable as showing combinations of sizes that will give sat- isfaction in service. The first of these tables shows the wide range of power that can be obtained from each engine of given size, beginning with a small one with a 10X24 inch cyl- inder rated at 38 horse power, and end- ing with a 34X60 inch cylinder rated at 647 horse power. There are four ratings given for each engine although only one speed is included in each case, and the , boiler pressure is 80 pounds by the gauge, in all cases mentioned in the table, the columns of which contain the following information : D = Diameter of cyhnder in inches. S = Stroke in inches. R = Revolutions per minute. P = Piston speed in feet per minute. V= Variation in power without seri- ously affecting economy. M = Maximum power that can be secured under given condi- tions. B = Power developed with best economy. STEAM ENGINES 291 HORSE POWER WITH 80 LBS. PRESSURE D S R P V M B 10 24 110 440 33 to 43 56 38 12 28 95 443 48 " 59 76 53 14 32 85 453 68 ' 83 109 75 16 30 90 450 90 ' 109 142 100 16 38 85 538 106 ' 128 170 117 16 42 85 595 119 ' 144 188 131 18 36 90 540 135 ' 151 213 143 18 42 85 595 149 ' 181 234 165 20 42 80 560 174 ' 211 275 192 20 48 75 600 186 ' 227 300 205 22 42 75 525 197 ' 240 313 218 22 48 75 600 225 * 274 360 250 22 52 75 649 244 • 296 390 270 24 42 82 560 257 ' 312 398 284 24 48 75 600 270 ' 326 429 295 24 56 70 653 294 ' 350 465 322 26 48 75 600 315 • 383 503 350 26 54 70 630 331 • 400 528 367 26 60 65 660 344 • 416 545 380 28 54 67 603 367 • 444 584 405 28 60 65 650 400 ' 483 632 440 30 60 65 650 459 • 556 726 507 32 48 80 640 510 * 619 809 564 32 60 65 650 520 ' 633 826 576 34 60 65 650 585 ' 710 932 647 The indicated horse power of an en- gine varies directly with the speed, pro- vided this is not excessive, for it was probably designed to run at a given rate and if the number of revolutions is in- creased, the mean effective pressure may not be as high as it was with a lower speed, although the boiler pressure re- mains unchanged. While the preceding table gives various ratings at SO pounds boiler pressure, the next states the indi- cated horse power that can be realized with higher boiler pressures. Both relate to simple, non-condensing engines 292 STEAM ENGINEERING The several colurflns contain the follow- ing information. D= Diameter of cylinder in inches S = Stroke in inches. R = Revolutions per minute. There are two columns under 90 pounds, the first giving the builder^s rating when steam is cut off at Vs stroke, and the second when the point of cut off is lengthened to j^ stroke, which is not unreasonable. The next two columns give the ratings with the same points of cut off, provided the boiler pressure is increased to 100 pounds, while the next two give ratings based on the same points of cut off, with a boiler pressure of 110 pounds by the gauge. INDICATED HORSE POWER— LOW SPEED S R 90 100 110 D \k H \% H hi H 11 24 110 50 79 55 65 61 72 12 30 90 62 54 69 83 77 92 12 36 85 70 84 78 94 87 105 14 36 85 95 114 107 128 121 142 16 36 82 120 144 135 162 151 180 16 42 78 133 159 150 179 168 200 18 36 80 148 177 166 199 186 222 18 42 78 168 202 189 227 212 253 18 48 75 195 222 208 249 234 271 20 42 75 200 240 225 270 252 300 20 48 72 219 263 246 296 275 330 22 42 75 242 290 271 326 303 364 22 48 72 265 318 298 358 333 400 24 48 70 307 368 345 414 386 460 26 48 70 360 432 405 486 454 541 28 48 68 406 487 457 548 514 595 30 48 68 444 526 507 694 590 683 STEAM ENGINES 293 LOW AND HIGH SPEED When the speed of an engine is men- tioned, it usually refers to revolutions of the crank shaft, but it may mean the piston speed in feet per minute. How- ever, the latter may be the same for two engines where the former differs widely. For illustration, take a 12x36 inch en- gine at 90 revolutions, giving a piston speed of 540 per minute. If a 12X12 inch engine revolves three times as fast, making 270 revolutions, the piston speed will be 540 feet as in the preced- ing case, but the former is generally called a low speed engine, while the latter is known as a high speed machine. With the same initial pressure, and cut- ting off at equal points in the stroke, the indicated horse power is alike, therefore the difference between them is not so great as it appears at first. If power is to be transmitted by belt from the engine to a shaft in a mill, shop or factory, the low speed engine with a long stroke is appropriate, because it will prove much more durable owing to the fact that the valve gear reverses its motion only 180 times per minute, and it is the reversing process that causes wear and tear in an engine. If a comparative high speed must be obtained at once, making it necessary to connect the en- 294 STEAM ENGINEERING gine directly to the machine to be driven as in the case of a dynamo or generator, the high speed engine with a short stroke must be used, but the valve gear is of a very different type, as a general rule, for its direction of travel must be reversed 540 times per minute, therefore, any form of cut off in which a moving part engages a part that is at rest (as with the Corliss valve gear) is impracticable and cannot be used successfully. The following table gives the indicated horse power of high speed engines under various conditions. The sizes given refer to the diameter of cylinder and length of stroke. The speed mentioned is the number of revolutions per minute. Three rates are given for each engine, showing the range of speed for which it is adapted. Boiler pressures from 80 to 120 pounds are included with cut off at 3^, H and }4 stroke. The former should not be exceeded in general service, but if a heavy load is thrown on occasion- ally, the longer points of cut off may be utilized for the emergency. When selecting an engine of this class it should always be large enough to carry the esti- mated load, when running at the lowest speed given, and cutting off steam at the shortest point mentioned. STEAM ENGINES 295 1 o § 05.-|^occo(Nooococ5l^o^•lOO^o o 8 Ot>-00M«-'5t0'-iC0C0O-*00r000(M § rf#'*iCiO § 1 a fa o 1 1 t^ 00 era "O t>. 00 CO CD CT) Tj< t^ O 00 crj t^ r-lrH,-^(N(MIMOOCOMTfl'J-hI>C^CDCn § -4(NfOCOt^OO-00'HN § CO«Ot^l^OOOOOiO>Ot>.OOOOOSOO § SfoSSnS^JSSSS^J^JSoS .•8 1 ?2^§§g§|2g88§||g o CO C-( 00 OS 05 O !-< ^ 8 gsg?:§sss;|?:sS8g| § SgS§^?:§§-g§f2?^S§8§ § t^ r-l lO 00 CO 00 O CO (M 00 ■* O O 00 lO Tl* lO »0 <0 CO CD t^ t>. 00 «5 CO tN. t>. t^ 00 :5 1 S S CO t^ t^ 00 00 OS OS OX^ 00 CJ> OS o o o U5 CO CO CO t>. 00 00 00 OS CO t^ 00 00 OS OS I g;s§S5?2^§goSS^^g§ § Tl<^U51OlOCOCOI>t>.lOCDCOCOt^00 S OS N lO 00 (N CO 00 CO 00 00 CO 00 00 rj< O co<<^nH>*ioioiococD'*ic»»oiocot>. OT OiOOOiOOOiOOOLOOOiOO OlMiOO0 CO CO CO CO CO CO CO CO CO (N (M CO -00?OiOt>-«300005'-iCO 8 '-^air-iiMiot>.>-nO'-icoor^ O•-^(N(NC0lO'-^(^^C0(^0T}^CDl0r>•00 § ^23HBS^S§2§S3SS 1 1 i o i-l 1-1 i-H rH T-l r-l rHT-li-li-li-trHrHr-tC^ 8 sSS§2S3S§SSI§l§ § ^g2^g5i^8:::?5^g5^:J3S S •<*! . CO CO T»< »o 0>(N o 000>00>0-iOOOSOOr-((N'-tcOTl< O 3 o 1-1 sSSBSSSSsSSssSS o ^sSSSSsSSSSSSSS 8 0500t-'^ioiOMrO'*05<-icccookO 00 05 O O rH (M 03 O ^ O !M coo? '^ lO o a3t^iOO:|iM^(M.-^^t^0000ooa3G>0'-iooa5oaiO'-H'-t(Nco § OJcOfOr-^aJt^iMooicio^oooio '^OOcO'-IO^-C>OTt N(M(NrHeO(M050lOOCCH>CDt^OC 0> rH CT) •* Oi 00 1> t^05'-not>0}t^O(MOCSlu:)(M»000 § T}<,-IOOt>^rHaJCDCOOi.-HO-JrHI>(M lot^oocoior^iot^osb-oc^ocqio eS o o 1 000000C000 i-HC0C005'-IC0'-HTl^t>.TtOI>'--i(M(N(M(NlM(MCO3r- 05 CO CO 00 CO 00 t>. o t^ Oi -H lO t^ 05 1^ cr> CO O (M lO (N lO 00 « rtrtC<,^,H,-(,-(,-((NcJCOCOCO(N § t*eccoc.ioi>05t^oco 1 eS o 1 § o rH05t>.C0'-H0SC0Tt<-*r^OC0OI>C0 1 rHr-Hi-li-li-liHi-HT-lrHiHi-ICO'-ICOC^) 2 05 CO t* »0 C75 CO 1> CO Oi 00 1^ Oi o ^ CvJ'*lO>-IC1-^cO-*fOTj(CO00COCT>i-l S S§§2SSS§SS§s§Ss lOOiOOiOOOiOOOiOOOiOO 1 Ttt «o CO to eo k: : x: : x: : x; : x: ; iO -^ >0 CO !> STEAM ENGINES 299 o 1 Tl< CO (M C3J M t-- tC lO lO fO lO lO CD 00 (M t^ 00 rt< O NNMCqC^COCgcOCOCOfOTTiMCOCO g (M(NCa5l>.CDOOTjHCDOO^a3CD-*(M t^O(M03(NiOlMiOOO'*00^(MiOOO rH(N(M-<(N(M(M(N(M(Mr-H>r-HOOlOO)'*CT>Tt<^lOOO N cq CO (N CO CO CO CO (^^ CO CO •* CO CO CO o s ->-i-*00'# (N>O00iO00(N00(MCD-^if3O00^»O (N(N(M00iMCDiO05(N (N(M. 1 lO O lO lO O lO lO O lO »0 O lO o o o en 00 00 "^ °o <=> '><::'x;:'x::'«::*»<:: CO t* 00 OJ « 300 STEAM ENGINEERING Pi o K Q » i Q IS 1 la P o OOiOOTtHt^i-it^t^t^t^NtOMOO 05COOOCOCO-*t^0005'*03COO>'<*0> O to O lO to -* CO lO O T}< 00 00 00 00 CO t* »0 O ■* 0> -^ 05 CO 05 Tj< o •<* 00 -"l* 0> CO 00 ■<1< ■* CO ^l* 'i^ ■* ■* »o ■<*< Tj< •* ■* TJHO 8 rHrHi-ir^.-llO(MIN'-IOO»Or-tTt to O TJH O Tt< 00 C0CO-<*00-*-*CO-*'*00-* to o 00 r* to to Q ''Jt o to U5 ■* O ■* t^ CO •* CO CO 00 ■<* t^ t* t>i 8 00 N lO tH lO CS rj< 0> CO CO lO O lO 0> 00 cocoeococooococo'!}o.-(ioooo5cq-<*icokooo c^cooococooocooococococoooooco 8 00 rH c:> 00 00 0> CO t^ r-l to 1-1 1^ .-( o> t^ 5 o § 00 -^ O ^ Q O CO N. CO 1-1 ■* t^ CO 00 lO o CO U5 00 CO 00 •«* O rH CO .-1 1-1 ,-H rH rj( to 8 t* CO to 00 to 00 c:5 to CO .-1 00 >o 00 00 00 00 to C» to 05 CO 00 CO to t^ 05 CO 05 CO >o cqcqcococoooc CO •* CO CO t^ CT> CO .-llO OS lO CO 00 i-HCOCOC0tDO3lO00C^-<*tO00tOC3Si-l CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO g -d<00rHiOOtOtDTt. T-tCOCOCOCOCOCOCOCOCOCOCOCOCON §|8|g|||8|||||| (0 19x20 20x20 21x20 20x22 21x22 STEAM-ENGINES 301 INDICATED HORSE POWER— HIGH SPEED Speed Cut off at H stroke Size 80 90 100 110 120 22x22 150 255 291 328 363 399 165 281 320 361 400 439 " IHO 30« 349 393 436 479 23x22 150 280 319 359 398 437 165 308 351 395 438 481 180 336 383 431 478 525 Speed Cut off at H stroke Size 80 90 100 110 120 22x22 150 309 352 394 437 480 " 165 340 387 434 481 527 •' 180 371 422 473 524 575 23x22 150 338 386 433 479 526 "• 165 372 424 475 527 578 180 406 462 518 574 630 Speed Cut off at H stroke Size 80 90 100 110 120 22x22 150 348 396 444 492 540 '* 165 383 435 488 542 594 *' 180 418 475 533 591 648 23x22 150 381 434 487 540 592 165 420 478 536 594 652 180 457 521 585 648 711 ^ 302 STEAM ENGINEERING COMPOUND ENGINES Many steam engineers seem to believe that the principal object in adopting a compound engine is to secure more power than could be developed in any other kind occupying the same space. This idea is probably based on the well known fact that two cylinders are used and as they are supposed to develop more power than could be secured from one, it constitutes conclusive proof in their estimation. It follows as a nat- ural consequence that if pressure in the receiver between the two cylinders is light, the second cylinder is considered of little or no value, because, it is claimed that the small piston does all of the work, and in addition to this, it must drive the large piston. It is possible to find a few places where this state of affairs exists, but they are not so common as engineers who are not well educated along this line seem to beheve. One reason for this belief is found in the following statement of facts: A small piston driven by high steam pressure may operate against a com- paratively high back pressure, therefore, the net power available for driving ma- chinery is not as great as the initial pres- sure indicates when considered alone. On the other hand a large piston may be ( STEAM ENGINES 303 driven by a low steam pressure, but it operates against a very low back pres- sure, consequently the net power avail- able for useful work is nearly or quite equal to that secured in the high pres- sure cylinder. If a simple engine is overloaded until it cannot maintain the required speed, when a superior cylinder oil is used to lubricate its internal parts, and the valves are properly set, the best way to secure more power is to remove the old machine and put in another simple en- gine with a cylinder large enough to do the work easily, provided economy in the use of steam is not of great impor- tance. If a simple engine is run under conditions that prove wasteful of steam, the remedy is to install a compound engine that is well adapted to the neces- sary load. Where the exhaust steam can be used profitably, it should be run non-condensing, but otherwise a con- denser should be added to remove back pressure from the large piston. From this it will be plain that the real object in installing a compound engine is to develop power with the least pos- sible amount of steam. This is consistent because this type makes it practicable to actually use steam at high pressure by expanding it to the greatest profit- able extent, and at the same time cylin- 304 STEAM ENGINEERING der condensation is reduced to a lower point than can be secured when expand- ing steam to a low pressure in a single cylinder. If a very high pressure is used in a simple engine carrying a light load, the terminal pressure will be low, and the temperature of the cylinder at the end of each stroke will be low, consequently when another charge of steam is admit- ted, some of it will be condensed in raising the temperature of the cylinder, thus causing a loss of heat. With a compound engine this difference is divided between two cylinders, hence it is less for each, resulting in economical use of the steam. DESIGNING COMPOUND ENGINES A very good method of designing a simple engine, assuming that 300 horse power would be required, has been illus- trated on previous pages, and in order to show the economy of the compound engine it becomes necessary to design one for a load of 300 horse power, and compare the results. It is assumed that this engine is run non-condensing. Modern practice with these engines has demonstrated that within certain reasonable limits the pressure, total ratio of expansion, and comparative size of STEAM ENGINES 305 cylinders must follow general rules in order to secure good results, and these have been observed in the example given. Data to be used as a basis for the calculations may be stated as follows : Gauge pressure at the boiler, 130 pounds Atmospheric pressure, 15 " Initial pressure absolute, 140 " Ratio of expansion, high • pressure cylinder, 3 Ratio of expansion, low pres- sure cylinder, 2.5 Total ratio of expansion, 7.5 TO DEVELOP 300 HORSE POWER In order to make an intelligent com- parison that can be easily imderstood and appreciated, the stroke of this engine is assumed to be 42 inches and the speed 90 revolutions, making the piston speed 630 feet per minute, to correspond with the simple engine above mentioned. The first point in the problem is to determine the mean effective pressure that will result from these conditions, using the following formula. SZPi±S±i22' 200 308 346 383 418 455 493 a7&28x20^ 160 310 348 385 420 458 495 180 349 391 433 473 515 558 200 387 434 481 525 572 619 17&28x22 150 320 359 397 433 472 510 165 352 394 437 477 520 563 " 180 383 429 476 520 567 613 19&32x22 150 408 459 508 554 604 654 165 449 504 558 612 665 720 " 180 490 550 609 675 725 784 STEAM ENGINES 319 HIGH SPEED COMPOUND NON-CON- DENSING ENGINES Cut off at % Stroke Size T3 Initial pressure 100 110 120 13a 140 150 7&11X10 . 300 53 59 65 72 78 84 325 57 64 71 79 84 91 ' ' 350 62 69 76 83 91 98 8«S:13xlO 300 72 80 89 97 106 114 325 78 87 96 105 114 124 " 350 83 94 104 113 123 133 8&;L3x12 250 72 80 89 97 106 114 275 79 88 98 107 116 126 •' 300 86 96 107 116 127 137 9&16xl2 250 100 113 125 137 149 161 275 111 124 138 150 164 177 •' 300 121 136 150 164 178 183 9&16xl4 225 105 118 131 143 156 169 «* 250 117 132 146 159 173 187 275 129 145 160 175 190 206 9&18xl4 225 144 161 178 194 210 229 250 .160 179 198 216 235 254 " 275 175 197 218 237 258 279 ll&18xl6' 200 146 164 181 198 215 232 225 164 184 204 222 241 261 250 182 204 227 247 269 291 12&20xl6 200 177 198 220 240 260 282 225 199 223 247 270 293 318 250 221 248 275 300 326 353 1 12&20xl8 175 174 196 216 236 257 278 '■ 200 199 224 248 270 294 318 *• ■225 224 251 27 S 304 330 357 I 14&23xl8 175 233 262 290 316 343 372 200 267 300 332 362 393 426 I " 225 300 336 373 407 442 479 ! 15&25x20 160 279 313 346 378 411 445 '! 180 314 352 390 426 462 501 200 349 392 434 473 514 556 : 17&28x20 160 351 393 436 476 516 559 ' 180 395 442 490 534 582 629 " 200 438 492 544 594 645 699 : 17&28x22 150 362 405 450 491 532 576 165 398 446 495 539 587 634 «• 180 433 487 538 587 638 691 19&32x22 150 461 520 576 628 682 738 i *' 165 509 571 632 690 750 813 i . " 180 555 623 690 753 818 886 320 STEAM ENGINEERING LOW SPEED COMPOUND CONDENSING ENGINES [ea| As a general rule it is not a good id to expand steam until the terminal pres- sure is lower than the back pressure, and while this rule limits the total ratio of expansion in a non-condensing compoimd engine to a point that will make the ter- minal pressure about 15 pounds absolute under ordinary conditions, and other considerations may raise it several poimds, the addition of a condenser to the plans and specifications for an en- gine to develop a given power, makes it possible to expand the steam much lower, as the terminal pressure may be as low as 6 pounds where the back pres- sure is about 3 pounds, both absolute or above a vacuum. This is accomplished by using a larger low pressure cylinder and cutting off steam earlier in the high pressure. When designing compound engines the same rules can be used for both con- densing and non-condensing service, but inasmuch as there is more than one method for this work, a better illustra- tion of the whole process (or a larger part of it), will result from using a STEAM ENGINES 321 somewhat different plan here than was adopted for the non-condensing & engine. In order to make a complete and logi- cal comparison later on, it is assumed that 300 horse power is wanted, and that the stroke of the engine is 42 inches with a piston speed of 630 feet per minute. When the other data is added the whole appears as follows,- giving an intelligent j basis for designing the cylinders. Gauge pressure at the boiler = 140 pounds. Atmospheric pressure . . . = 15 " Initial pressure absolute = 150 " Terminal " " = 7.5 '' Total ratio of expansion = 20 " Ratio of cylinders = 1 to 4 Stroke = 42 inches. ■ Speed =90 revolutions. Piston speed per minute = 630 feet. To develop 300 horse power. The first point is to determine the ratio of expansion for the high pressure cylinder. According to a rule previously given, this is found by dividing the total ratio of expansion by the ratio of cylin- ders. In this case it is 20-5-4=5. The 322 STEAM ENGINEERING ratio of expansion for the high pressure cylinder is 5, therefore steam is cut ofif in this cylinder at yi or .20 of the stroke, as clearance is ignored in these estimates. There is a drop in pressure between the two cylinders, especially in the case of a cross compound engine due to free ex- pansion in the receiver, but inasmuch as this would seldom be the same in two or more engines in practice, no attempt is made to account for it when estimating cylinders for a compound engine. The terminal pressure in the high pres- sure cylinder is 150-7-5=30 pounds. This is also the back pressure in the same cylinder, and the initial for the low pressure, all absolute. The mean effec- tive pressure for the high pressure cylin- der is therefore — (1.6094+1) X 150 ■^^ —^ 30 = 48.3 pounds. One-half of the total of 300 horse power, or 150, is to be developed in this cylinder, therefore the required area is — 150X33,000 ,^„^ — — - — — — - =162.6 square mches, 48.3X630 ^ which is a circle 14.4 inches in diameter, STEAM ENGINES 323 but would be called U inches in order to avoid impracticable fractions. The area is 153.93 square inches, as this cyl- inder is 14X42 inches. The given ratio of cylinders is 1 to 4, therefore, the area of the low pressure cylinder is 153.93x4 = 615.7 square inches, corresponding to a circle 28 inches in diameter. As the initial pressure in this cylinder is 30 pounds and the ratio of expansion is 4 with a back pressure of 3 pounds, which is in accordance with ordinary practice in condensing engines, the mean effective pressure is — 03863+1) X30 ^ ^ ^^ gg p^^^^3^ 4 Under these conditions the high pres- sure cylinder will develop— • 153.93 X48.3X630 _^,,^ ^^^^^ p^^^,. 33,000 The low pressure will develop— 615.7X14.89X630 _^^, ^^^^^ p^^^,. 33,000 The complete engine will develop 141.9+175 = 316.9 horse power, which 324 STEAM ENGINEERING is about 5 per cent, more than is wanted but it is not always practicable (although it may be possible), to design cylinders under given conditions so that exactly the desired amount of power will be developed, but the automatic cut oflF device on the high pressure cylinder will respond to the demand for power and give desired results. The power developed in these cylin- ders is not equal, but these conditions show the necessity of providing an auto- matic cut off for the low pressure cylin- der, which can be adjusted by the engi- neer, then by lengthening the comparative range of the governor he can lengthen the point of cut ofif in the low pressure cylinder, thus throwing some of the load from the low to the high pressure cylin- der, and make them nearer equal in this respect, for in these estimates it is as- sumed that the cut off in the low pres- sure cylinder corresponds to the ratio of areas between the two cylinders. In this case the ratio is 4, therefore the cut off in the low pressure cylinder is as* sumed to be at 34 or .25 of the stroke. A COMPARISON OF RESULTS Here are three engines designed to develop approximately 300 horse power STEAM ENGINES 326 all having the same stroke, and as they revolve 90 times per minute the piston speed is alike, therefore, it is practicable to illustrate their relative economy by determining the weight of steam required per horse power hour by each, and com- paring the results. The weight of steam used is found by the following rule. Multiply the area of piston in square inches, by the distance in inches travelled by the piston at the point of cut off, and by the number of strokes per hour, and divide by 1,728. Multiply the quotient by the weight of steam per cubic foot at given pressure. Divide by the horse power developed, and the quotient is the weight of steam used per horse power hour. If it is desired to take clearance into account, multiply the above result by the given per cent, of clearance and add it to the amount. The following data applies to the first engine to be considered: Size of cylinder = 20 X 42 inches. Area " " =314.16 square inches. Ratio of expan- sion =4 Distance to point of cut off = 42 -^4 = 10.5 inches. 326 STEAM ENGINEERING Strokes per hour = 90X2X60 = 10,800 Absolute pressure = 120 pounds Weight per cubic foot = .2724 pounds. Horse power de- veloped =299.88 Then 314.16X10.5X10,800 ^ 1,728 = 20,616 cubic feet per hour, the weight of which is .2724 pound per cubic foot, therefore the total weight used per hour is 20,616 X. 2724 = 5,615.798 pounds. Then 5,615.798 -^ 299.88 = 18.72 pounds per horse power hour. Assuming that the clearance is 3 per cent, of the whole volume of the cylinder will raise this to 18.72+ (18.72 X. 03) = 19.28 pounds per horse power hour. Adding 30 per cent, to this increases it to 25.06 pounds, and the reason for this addition is found in the following lines. The weight of steam accounted for by the above calculation which is based on theoretical conditions, does not repre- sent the weight of water pumped into the boilers, and furthermore it is not in- tended for this purpose, as the only reliable process is to either measure or weigh the water as it goes into the boilers after which some of it will be used to run STEAM ENGINES 327 the engine forming a part of the plant, a portion will be used for operating pumps and other machines, and the remainder will be lost through leaky joints, or disappear as the result of radi- ation. These factors are seldom or never the same in two different plants, therefore it is not practicable to make a fixed allowance that will apply to all cases, and no attempt is made to do so here. However, if 30 per cent, is added to the results secured by these calcula- tions, the sum will represent what can be realized under first-class conditions, but whether it is secured or not, can only be determined by direct experiment in each test, as it is made from time to time. As 30 per cent, is added in all cases mentioned here for comparison, the results bear the same relation to each other that existed previously, but the final amount in each case is reasonable, hence is an improvement over the rate secured by the necessarily crude and unfinished calculation previously se- cured. The following data applies to the sec- ond engine to be considered, which is of the compound non-condensing type: 328 STEAM ENGINEERING Size of cylinders. =14 and 22X42 inches. Area of high pres- sure cyHnder. . . =153.93 square inches. Ratio of expansion for this cylinder = 3 Distance to point of cut off =42 -^3 = 14 inches. Strokes per hour. =90X2X60 = 10,800 Absolute pressure = 140 pounds. Weight per cubic foot = .3147 pound. Horse power devel- oped =301.2 Then 153.93 X 14 X 10,800 4- 1,728 = 13,468 cubic feet per hour, the weight of which is .3147 pound per cubic foot, therefore the total weight used per hour is 13,468 X. 3147 = 4,238.379 pounds. Then 4,238.379-7-301.2 = 14.07 pounds per horse power hour. Adding 3 per cent, for clearance raises this to 14.49 pounds and adding 30 per cent, as before gives a total of 18.83 pounds per horse power hour. The following data applies to the third engine to be considered which is of the compound condensing type: STEAM ENGINES 329 Size of cylinders = 14 and 28 X42 inches. Area of high pres- sure cylinder = 153.93 square inches. Ratio of expansion for this cylinder = 5 Distance to point of cut off = 42 -T- 5 = 8.4 inches. Strokes per hour = 90 X 2 X 60 = 10,800 •Absolute pressure = 150 pounds. Weight per cubic foot = .3358 pound. Horse power de- veloped =316.9. Then 153.93 X 8.4 X 10,800 -r- 1,728 = 8,081 cubic feet per hour, the weight of which is .3358 pound per cubic foot, therefore the total weight used per hour is 8,081 X .3358=2,713.6 pounds. Then 2713.6 4-316.9 = 8.55 pounds per horse power hour. Adding 3 per cent, for clearance raises this to 8.8 pounds, and adding 30 per cent, as before gives a total of 11.44 pounds per horse power hour. The difference between results that can be secured by use of these engines does not seem large as here stated ac- cording to common practice, but when it is multiplied by the power developed in a given case, and this goes on from 10 to 24 hours per day according to the service in which an engine is used, the economy of securing a first-class engine 330 STEAM ENGINEERING and of placing a competent engineer in charge of it, will be very plain. The next four tables give sizes of com- pound condensing engines that will ren- der satisfactory service under given conditions. The first contains engines suitable for 125 poimds boiler pressure, when the load causes about 14 expansions and consideration of this matter calls for explanation of what constitutes unrea- sonable conditions. The fact that a com- pound engine must run under conditions which give a low terminal pressure if economical results are desired, has been made plain on previous pages, but the prospective customer, or the superin- tendent or the owner of a plant where one or more of these engines are to be used, frequently forget that a low ter- minal pressure means a comparatively light load. Now, if a very heavy load is put on a compound engine, resulting in a high terminal pressure in the second cylinder, this improved kind of an en- gine will be almost as wasteful as a sim- ple engine, when used under similar conditions. When the manufacturer of a com- pound engine is asked to state the amount of power that it will develop in an emergency, he usually answers the question just as it is stated, although he knows that while carrying the maximum STEAM ENGINES. 331 load it is wasteful of steam. If a steam user proceed? to put this load on his engine for 10 hours or more per day, and the result is very unsatisfactory, as the wear and tear is excessive, and the coal bill proves to be very large, he ought to blame nobody but himself. He should ask the engine builder to state the power that it will develop on an economical basis, and then keep within the limits so determined. The second table contains sizes of low speed engines where the ratio of cylin- ders is 1 to 4. This means that the area of the low pressure is four times as much as the high pressure. The ratio of diam- eter is 1 to 2 in all such cases, as stated in the list given. These engines are suit- able for 150 pounds pressure by the gauge. The third table contains the proper sizes for given loads where the pressure is 120 pounds, and the speed is high. The ratio of cylinders is about 1 to 3.5 although it varies with the larger sizes given. The fourth table contains sizes of cylinders with a ratio of 1 to 4, to carry 150 pounds pressure. In this and in the ^preceding table three different speeds are given with power developed accord- ingly. If the speed of an engine is in- creased it will develop more power with out changing it from an economical to a 332 STEAM ENGINEERING wasteful machine, provided that the boiler pressure and the point of cut off remain constant. Excessive speed will cause rapid wear, and better lubrication will be necessary, but these details can Usually be dealt with properly if an in- telligent engineer is in charge and his . recommendations are adopted. The speeds given in these tables are not ex- cessive, and there is no good reason why a well made engine should give trouble of any kind while developing power as stated in them. Good judgment should be shown in the selection of a superior cylinder oil for all engines working under high pressure. The cost per galloii" should be a secondary consideration, J)rovided it does satisfactory work. COMPOUND CONDENSING ENGINES. Long stroke. Low speed. About 14 Expansions . Ratio of Cylinders Approximately 1 to 3Vi. Fo] ■ 125 pounds boiler pressure. Size 'X3 t Size 73 (U 1 a o a 03 pL, w Oi 9&16x30 100 96, 22&40x54 70 750 10& 18x30 100 122 23&42x60 65 864 ll&20x36 90 163 24&44x60 65 948 12&22X36 90 190 25&46x60 65 1,036 13&24x36 90 234 26&48x66 55 1,050 14&26x42 80 285 28&50x66 55 1,140 16&28x42 80 330 29&52x66 55 1,233 I7&30x42 80 380 30&54x72 50 1,319 18&32X48 75 463 31&56x72 50 1,411 19&34x48 75 523 32&58x72 50 1,620 20&36x54 70 615 34&62x72 50 1.739 21&38x54 70 678 36&64x72 50 1,858 STEAM ENGINES 333 COMPOUND CONDENSING ENGINES. Long stroke. Low speed. 16 Expansions. Ratio of cylinders 1 to 4. For 150 pounds boiler pressure. Size ♦a 1 Size a 1 w a, w 0^ 8&16x30 inn 99 20&40x54 70 784 9&18x30 100 12G 21&42x60 65 891 .0&20x36 90 168 22&44x60 65 978 :.l&22x36 90 203 23&46x60 65 1,069 .2&24x36 90 242 24&48x66 55 1.084 13&26X42 80 294 25&50x66 55 1,176 14&28x42 80 341 26&52x66 55 1,272 15&30x42 80 392 27&54x72 50 1,360 16&32X48 7.5 478 28&56x72 50 1,463 17&34x48 75 539 29&58x72 50 1,569 18&36x54 70 634 31&62x72 50 1,793 19&38x54 70 707 32&64x72. 50 1,900 COMPOUND CONDENSING ENGINES. Short stroke. High speed. About 14 Expansions. . Ratio of Cylinders approximately 1 to 3.5. For 120 pound s boiler pressure. •d u •a V TS S3 Size ^ ^ ^ n^ % o w fu w &i CO Oh 7&llxl0 300 45 325 49 350 53 8&13xl0 300 61 325 66 350 71 8&13xl2 250 61 275 67 300 73 9&16xl2 250 84 275 93 300 101 9&16xl4 225 89 250 98 275 108 U&18xl4 225 122 250 136 275 149 ll&18xl6 200 124 225 1.39 250 155 12&20X16 200 150 225 169 250 187 12&20X18 175 148 200 169 225 190 14&23X18 175 198 200 227 225 255 15&25x20 160 236 180 266 200 295 17&28x20 160 298 180 335 200 372 17&28x22 150 308 165 337 180 368 19&32x22 150 391 165 432 180 470 334 STEAM ENGINEERING COMPOUND CONDENSING ENGINES Short stroke. High speed. 16 Expansions Ratio of cylinders 1 to 4. For 150 pounds boiler pressure •a u -0 u 13 u Size 1 1 I o 1 1 w cu w CLi W D^ SJ^&llxlO 300 42 325 45 350 49 6}^&13xl0 300 58 325 63 350 68 6i^&13xl2 250 58 275 64 300 70 8 &16xl2 250 88 275 97 300 106 8 &16xl4 225 93 250 103 275 113 9 &18xl4 225 117 250 130 275 143 9 &l8xl6 200 119 225 134 250 149 10 &20xl6 200 147 225 165 250 184 10 &20xl8 175 145 200 166 225 186 12 &24xl8 175 199 200 228 225 256 12J^&25x20 160 240 180 270 200 300 14 &28x20 160 288 180 324 200 360 14 &28x22 150 297 165 326 180 356 16 &32x22 150 387 165 427 180 465 PROVIDING FOR INCREASE OF POWER WHEN INSTALLING A COMPOUND ENGINE When a steam plant is to be designed constructed and installed, .the serviced of a competent designing engineer should be secured to draw the specifications and superintend the work, as it is im- possible to lay down rules for such cases that will cover every contingency that may arise without making them too cumbersome for practical use. It is pos- sible and practicable, however, to make a few suggestions and give rules that STEAM ENGINES 335 apply to this work, that will prove valu- able to both engineer in charge, and owner of the plant, as they either give clear directions, or point out the neces- sity for investigation along these lines. Suppose that a cross compound con- densing engine is preferred, and for one or two years the load is to be very light after which it will be greatly increased. This engine is illustrated in Fig. 42, but while the load is light the low pressure connecting rod may be disconnected from the crank pin, and the eccentric straps taken off, thus leaving it a sim- ple non-condensing engine. In order to illustrate the matter, assume that a single diagram taken from this engine under these conditions appears like Fig. 43. It is now working under economical conditions as the terminal pressure is not enough above the atmosphere to denote serious waste, yet it is sufficient to pre- vent excessive cylinder condensation. This engine was designed for 150 pounds boiler pressure by the gauge, but only 100 is carried now, as no more is needed, and it is useless to carry a high boiler pres- sure unless it can actually be used to good advantage. Fig. 44 is another diagram from the same engine while carrying 100 pounds boiler pressure, but the load is much heavier than before. This is a wasteful 336 STEAM ENGINEERING FiG>.4 2 FiS.A-b STEAM ENGINES 337 r i ii'— T^ ■=^^=w^ 1 \ F\e^A^^ 338 STEAM ENGINEERING condition of affairs, therefore, the boiler pressure is raised to 150 pounds and the diagram Fig, 45 is taken. The in- creased boiler pressure has shortened the point of cut off and lowered the ter- minal pressure until economical condi- tions are again secured. However, the load is again increased until it produces a diagram similar to 46. The limit of boiler pressure is shown by the diagram, therefore, the next move is to connect the low pressure connecting rod, adjust the eccentric straps, make proper steam connections, put the condenser into ser- vice and run the engine as it was origi- nally intended to be used. A diagram STEAM ENGINES 339 from the high pressure cyHnder as now running, is shown in Fig, 47, and one from|the low pressure cylinder appears in Fig. 48. 340 STEAM ENGINEERING The flexibility of an engine of this j kind is well illustrated by this example, and there are other points that are ; FIG. ^8 worthy of special attention. The com- plete engine should be installed at first, and such parts as are not wanted for j immediate use can be held in reserve until needed. While this is the best plan that can be devised, it is objected to by some engineers and owners, as j they believe that only the high pressure side should be installed at first, as the low pressure side can be added when wanted, thus saving interest on the in- vestment, etc. This plan is earnestly objected to for. the following reason: My observation and experience teaches that although a plant may be started in an unfinished condition, it will be run that way as long as possible. The engine may be overloaded until the speed is much less than it ought to STEAM ENGINES 341 be, and the terminal pressure is so high that a large quantity of heat is thrown away every day, but so long as the plant continues to run without an absolute stop, there is no time to shut down for improvements, money cannot be spared for that purpose, etc., and matters usual- ly remain in that condition until enough money has been wasted to more than pay the cost of needed improvements, after which they are made, resulting in marked economy of operation causing the owner to wonder why he did not do it before. Other reasons why the low pressure side of this engine ought to be installed complete when the plant is first erected, are that if it is not done then, the firm who build these engines may go out of business, their works may burn down, or they may be so busy when the extra parts are wanted that it will be necessary to wait a year for the work to be com- pleted. ■ On the other hand if the low pressure side is completed, it may be put into service at a few hours' notice, thus saving serious loss due to shutting down the plant for several weeks, for such ma- chinery is sometimes wanted when least 342 STEAM ENGINEERING expected. Suppose that the piston rod on the high pressure side should break, allowing the piston to be forced out through the cylinder head, taking pieces F«e|. of the cylinder with it, thus making it necessary to build a new cylinder, piston and piston rod. The high pressure con- necting rod could then be disconnected, and the eccentric straps taken off. The STEAM ENGINES 343 piping might be quickly changed to deliver steam directly to the low pres- sure cylinder, the boiler pressure reduced to 30 or 40 pounds and in a few hours the plant could be in full operation, which might easily be continued indefi- nitely, or until repairs were completed. This would also make it unnecessary to work overtime on the job, thus saving 344 STEAM ENGINEERING heavy expense, as overtime must be paid for extra, although the work cannot be carried on to good advantage at night with ordinary lighting facilities, by men who are taxed beyond their strength in working from 24 to 48 hours without rest. Another advantage of this plan is that it does not include expensive changes in the engine in order to secure the full power, no additions are required, and the speed is not increased, therefore it is not necessary to provide a new and larger main pulley on the jack shaft to keep the machinery speed ' constant while the engine speed is changed, and the main belt does not have to be length- ened to meet new conditions. Fig. 49 illustrates a double tandem • compoimd condensing engine that is a very fiejyble unit. If only a small por- tion of the full load is to be carried at first, one side can be laid up, and a light boiler pressure will be sufficient for the other. After six months have elapsed the other side can be started and each run alternately, thus keeping one side in reserve, ready for use in case of acci- dent to the other. As the load is in- creased, the boiler pressure can be ;r frame type CROSS COMPOUND HARRIS-CORLISS ENGINE, STANDARD GIRDER FRAME TYPE STEAM ENGINES 345 raised, and when it is no longer econom- ical to run with one side they can both be used with a low boiler pressure, then as more load is added it can be raised imtil the full power of the complete engine is utilized. While the highest efficiency cannot be expected imder all of these varying con- ditions, it will be realized imder some of them, hence the total difference is small when compared with the benefits secured. SECTION 4 PRACTICAL POINTERS FOR PRO- GRESSIVE POWER PLANT OPERATORS PACKING A MAN-HOLE COVER Putting in a man- hole cover is a rough job, yet it requires a certain amoimt of care in order to make it successful, for if the gasket is cut in tv/o by coming into contact with a sharp corner it will cause a bad leak, and where a tubular gasket is used, it is necessary to clamp both ends of it in proper place, or else it will be necessary to empty the boiler and make a new joint. While this is very unpleasant to all concerned, when there is plenty of time to repack the joint, it is much worse to dis- cover such a mistake about an hour be- fore it is time to start the engine, because every self-respecting engineer wishes to start his plant on time, as failure to do so, even when there is apparently a good reason for it, injures his reputation and causes his employer to lose confidence in him. On this account it is always a good idea to raise pressure on a boiler after it has been cleaned and inspected, before it is wanted for actual service, then if it becomes necessary to cool it off and PRACTICAL POINTERS 347 repack one or more joints it will cause but little expense and no delay to the plant. FAILURE OF MAN-HOLE GASKETS Sometimes a man-hole or a hand-hole gasket will blow out under pressure, but such accidents are always due to bad design of the parts, carelessness in mak- ing the joints, or failure to properly care for them. The surfaces to be packed may be roughened by corrosion, or made winding by abuse of the boiler. It may be necessary in such a case to use two flat gaskets, but tjiis should be avoided as long as possible, because the extra thickness of gasket makes it more liable to blow out. When a boiler is filled with cold water and one of these joints leaks, it is a great temptation to seize a long wrench and screw the nut as far down as possible. Of course this is proper to a limited extent, but if exces- sive leverage is applied the cast iron dog which spans the hole may be broken. It is well to have an extra one on hand for such emergencies. PACKING A HAND-HOLE COVER Horizontal return tubular boilers are frequently made without a hand hole in the rear head. As long as the boiler is 348 STEAM ENGINEERING in service, there is no need of a hand hole here, but when it is laid off to be cleaned it is very convenient to have a place where at least a little fresh air can be secured, also an opening through which tools can be passed. It is difficult in some cases and impossible in others to properly care for a hand-hole cover ow- ing to its location. When packed with a rubber gasket and the nut is screwed down firmly, the joint may be tight, but when steam is raised the heat softens the gasket, and pressure acting on the back of the cover settles it down into place until the nut is quite loose. If it is made tight again before all pressure is taken off, it will probably make a good joint until it is time to remove the cover again, but if there is no chance to do this for several days or weeks, and the steam pressure goes down to zero, it will prob- ably leak, and water coming through the imperfect joint will cause corrosion that in course of time will waste away the head until a tight joint cannot be secured. FITTING A HAND-HOLE COVER Before attempting to pack a hand- hole cover for the first time, on either an old or a new boiler, the engineer should put the cover in place without packing PRACTICAL POINTERS 349 and be sure that the hole is large enough to allow the cover to rest firmly on the head without binding on the edges as otherwise the gasket may not be clamped firmly, and when subjected to pressure it may be blown out. After a tight joint is secured, and all lost motion due to shrinking of the gasket has been taken up, if the bolt projects through the nut, another should be screwed on to protect the end of it, then the dog, nuts and bolt should be covered with asbestos to pro- tect them from the fierce heat. RUBBER AND METAL GASKETS As a general rule, to which there may be a few exceptions, a rubber man-hole gasket can be used several times, provid- ed there is a broad surface in contact to afford a good bearing. If it is desired to use a gasket more than once, the side put next to the cover should not contain anything to prevent it from sticking to the metal, but the other side ought to be coated with Dixon's graphite, ground ■fine and mixed with cylinder oil to the consistency of a thick paste. This will prevent the rubber from sticking to the head, and if care is taken to clean pieces of scale, etc., off from the surfaces to be packed, and the cover is put back in exactly the place from which it was re- 350 STEAM ENGINEERING moved, it should make a tight joint. '■] This cannot be done with some of the modern boilers where the head is simply- flanged inward and planed off to receive the cover, as the surface is too narrow to admit of it. The metal cuts into the gasket until it is practically metal to metal, with only enough rubber between them to fill the places that would other- wise be vacant, therefore, such a joint will not readily fail under pressure. Lead gaskets are sometimes adopted for this service, and they would be used much more if it was possible to put them back after cleaning and inspecting boil- ers, and secure tight joints with little trouble, but as a rule this is not practi- cable owing to the difficulty of getting them back exactly in their former posi- tions. LOCATING FUSIBLE PLUGS The fusible plug in a horizontal tubu- lar boiler should be located in the rear head, three inches above the upper tubes. As such a boiler ought to be one inch lower at the rear than at the front, in order to have all water drain to the blow- off pipe, this will leave but two inches of water above the highest part of the tubes when the fusible plug is uncovered, and this is no more than enough to insure safety. PRACTICAL POINTERS 351 In a locomotive boiler it should be in the highest part of the crown sheet, and in every other kind it ought to be located where it will melt and give emphatic notice of the condition of affairs, before any part of the boiler is injured through lack of water. LEVELLING BOILERS The upper row of tubes in a tubular boiler, should be set level crosswise of the boiler, causing the water to cover them evenly, then if the dome or the steam nozzles do not stand plumb, the defect may be counteracted by using pipe flanges that are thicker on one edge than the other. HEAVILY LOADED BOILERS Boilers are frequently made to devel- op more power in practice than their builders intended, and there are engi- neers who claim that it is a good idea to secure as much power as possible from a boiler, and then put it in the junk pile. One reason why this plan should not be followed is that such boilers will not be put into the junk pile soon enough, but will be used long after they become unsafe, as it is an expensive job to shut down a plant, remove old boilers and install new ones. 352 STEAM ENGINEERING SMOKE CONSUMERS AND PREVENTERS A good smoke consuming device is a valuable apparatus, but a smoke pre- venter is much better. A very good device for this purpose is a large furnace, and plenty of boiler power, enabling the fireman to run comparatively slow fires, and thus consume the coal properly, leaving no valuable carbon to go up the chimney. It naturally follows that a good fireman will be necessary in order to secure the full advantage of furnaces and boilers that are well proportioned for the service that they were intended to perform. A boiler should be high enough above the grates to permit proper combustion of the coal, before the flames come into direct contact with the metal, because this contact lowers the temperature, which must be very high in order to se- cure good results. Under these condi- tions a fire may be carried 8 or 10 inches thick, and if coal is supplied frequently and in small quantities, with a suitable amount of air admitted above the fire, it is possible to run a plant without having much black smoke come out of the chimney. A certain plant with which the writer is somewhat familiar, sends large quan- tities of very black smoke out of its PRACTICAL POINTERS 353 chimneys. One reason for this is that although the boilers are rated fully as high as they ought to be, still they are caused to develop 50 per cent, more power than they were built for. This leaves the fireman no chance to manage his fires to prevent smoke by firing in front and allowing the smoke producing elements to be consumed by passing over the rest of the fire, as he must man- age his fires to produce the greatest pos- sible amount of steam without regard to good appearance or economy of fuel. FORCED DRAFT When forced draft is mentioned it may mean that boilers under which it is used are worked beyond their rated capacity, but it may be used to force air through a bed of very small coal, that could not be used with ordinary natural draft. In the latter case it is not wise to claim that the forced draft is ruining the boilers of a plant, because no more air passes through such a furnace, and the temperature is no higher in it than would be secured by burning large coal with good natural draft. TEMPERATURE OF GASES Whether a boiler is overloaded or not can usually be determined by observing 354 STEAM ENGINEERING i the temperature of the products of com- ; bustion as they pass to the stack. If , they are less than 100 degrees higher than the temperature of steam at the pressure carried, the boiler cannot be seriously overloaded, but if they are 200 or 300 degrees higher, it indicates that more power is demanded than the boiler can supply at an economical rate. This conclusion is based on the fact that if the grate and the heating surface are properly proportioned, all heat generated on the grate will be absorbed by the heating surface, except enough to cause good draft. This applies to ordinary power plants, and if an exception can be found to this general rule it denotes special conditions. THROTTLING VS. AUTOMATIC ENGINES Suppose that a certain engine, fitted with a D slide valve and a throttling governor, is running with no cut off, or in other words it takes steam constantly throughout every stroke, and the load calls for a mean effective pressure of 40 pounds. Under these conditions there will be 40 pounds pressure by the gauge at the beginning of each stroke, and this will be continued to the end. Sup- pose that the size of this engine and the speed at which it runs are such that it PRACTICAL POINTERS 355 now develops 100 horse power. The boiler pressure is 80 pounds by the gauge and the reduction is made by the throt- tling governor with which it is fitted. The cylinder and governor are re- moved, and another cylinder of the same size is substituted, but it is fitted with an automatic cut off valve gear. The speed remains the same, and as the load is not changed it requires 40 pounds mean effective pressure to drive it. With a boiler pressure of 80 pounds arid the cut off taking place at yi stroke, the desired result is secured provided all conditions are favorable. In the first case the cylinder was filled with steam flowing directly from the boiler through the full stroke. In the second case the flow of steam is cut off at ]/i stroke and no more enters during that stroke. Do we get the same power by taking from the boiler one-quarter of the amount taken before, thus saving 75 per cent, of the coal bill? No, decidedly not. Provided there were no leaks in the former case, the change will result in saving about 25 per cent, of fuel. Why is not a greater saving realized? The following explanation will make this clear: When one pound of water at its great- est density is turned into steam, it makes 284.5 cubic feet at 80 pounds gauge pres- 356 STEAM ENGINEERING i sure. When this steam passes the ' throtthng governor its pressure in this case is reduced to 40 pounds. The same weight of steam now fills 475.9 cubic feet of space, therefore, it fills the cylinder nearly twice as many times as it would at 80 pounds. Furthermore, the throt- tling process slightly superheats the steam, thus making it more valuable than before. As the pressure remains the same throughout the stroke, there is no change of temperature to cause cylin- der condensation, and this condition prevents much loss of heat. The automatic engine takes enough steam at 80 pounds gauge pressure to fill the cylinder one-quarter full (which would fill it nearly one-half full at the lower pressure) at each stroke, and as the supply is then cut off it begins to expand, and as the pressure is lowered the temperature becomes less until the stroke is completed. As soon as the crank has passed the center at that end, the cylinder receives another charge of steam at nearly boiler pressure, but more or less of it is condensed by raising the temperature of the cylinder and this is a direct loss that is repeated at every stroke. These facts are sufficient to explain why the automatic cut off en- gine is not more economical than it real- ly is in practice. A saving of 25 per PRACTICAL POINTERS 357 cent, is sufficient to warrant its use, but it appears to the casual observer as if it should be more. DRAINING THE STEAM PIPE When it is nearly time to start an en- gine, do not forget to open the small drip valve with which every engine is, or ought to be fitted, for the purpose of allowing all water to drain out of the steam pipe. Everybody knows that this ought to be done, but when something happens to interfere with the regular routine usually observed in starting the plant, it may be forgotten, and if the throttle valve is opened when the steam pipe above it is full of cold water, some- thing interesting may happen. It may not amount to more than a heavy, sharp pound in the pipe that an engineer does not readily forget after he has heard it once, or a gasket may be blown out of a packed joint. It is quite possible for a valve to be burst in this way, causing the plant to be shut down until a new one is put in. Some of these drip pipes are too large, therefore if the valve in one of them is opened wide it will cause water hammer in the main pipe. A one- half inch drip pipe is large enough for a 358 STEAM ENGINEERING 12 inch main steam pipe, then there will not be much danger of trouble on this account, even if the valve is opened wide. WARMING THE CYLINDER. After all water is removed from the main steam pipe, the cylinder ought to be gradually warmed by admitting steam to it, taking care not to admit enough at first to start the engine before it is time to set the machinery in motion. If the engine is fitted with a detachable valve gear, this feature can be utilized to admit steam to alternate ends of the cylinder, but as soon as it is well heated, the valve gear should be hooked in and steam enough admitted to start the en- gine slowly. The practice of rocking the valve gear of an engine back and forth when starting it, does not tend to free the cylinder of water, but on the contrary it closes the exhaust valves before they would be otherwise, hence water is pre- vented from escaping freely. Some engine builders now make their valve gears so that they cannot be unhooked, as they desire to compel the engineer to start his engine without giving it the shocks and jars so frequently resulting from the reversing process. It is claimed that fly wheels are sometimes i loosened on the crank shaft by it. PRACTICAL POINTERS 359 RUNNING AN ENGINE "OVER" When you write to an engine builder or a firm that was organized for the pur- pose of building engines of various sizes, and ask them if their horizontal engines will run "under" as well as "over" you must always expect a reply in the affirm- ative. There are a few engines that were made to run "over" and they can- not be reversed, but with these excep- tions all others are advertised to run as well in one direction as the other. It is a well known fact that when an engine runs "over" (or in other words, when the top of the fly wheel travels from the cylinder), the crosshead is held down on the guides, hence it is only nec- essary to adjust it to the proper height to bring it into line, as it is not necessary to make fine adjustments to prevent it from being lifted. On the other hand if an engine runs "imder" and is carrying a load that equals one-half of its rated capacity or more, the crosshead will be lifted at every stroke unless it is held firmly in place. ADJUSTING THE CROSSHEAD I once had charge of a Corliss engine that nm "under" for 132 hours per week. When it was comparatively cold I would 360 STEAM ENGINEERING carefully adjust the crosshead between • the upper and lower guides until it was a ■ perfect fit. After it had run for an hour the vertical space between the guides near the cylinder, would be greater than it was before, hence the crosshead would . lift and cause a pound at every revolu- tion which was much worse on Saturday than it was on Monday, but the best engineer in the world could not stop it, because he could not keep the guides parallel vertically, when one end was hot and the other cool. If that fly wheel had revolved in the opposite direction, the crosshead could have been run for months without adjustment, and if there wa^ room enough between the top of it and the upper guide to move a piece of thick writing paper, there would have been no pound, as it would still have run quietly. SHUTTING DOWN AN ENGINE When an engine is to be shut down for 1 a month or two, do not simply close the throttle valve and let it stand without further attention, until it is wanted again, as rust and corrosion will damage it much more than it would be worn while in use under fair conditions for a year, and perhaps for double that time. The valve or valves should be taken out PRACTICAL POINTERS 361 after all packing has been removed from the stems, thoroughly inspected, and if repairs are needed, now is a very good time to have them made. If these parts are in good order, cover them with cylin- der oil and put them in place ready for use, but do not repack the stems imtil they are wanted for service. PREVENTING CORROSION Remove all packing from the piston rod stuffing box, clean all parts and cover them with cylinder oil, taking care to have a good coat of it between the gland and the rod. Take off the cylin- der head, remove the follower bolts, the plate, and every part of the piston. Carefully inspect them for defects, and if springs are worn, studs corroded or jam nuts loose, have such defects re- paired or the parts renewed while there is plenty of time for the work. Measure the cylinder and if it is worn much larg- er in one or more places than in others, it should be re-bored and new packing rings put into the piston. If this is not necessary, put the piston rod exactly in the center of the cylinder, replace every part of the piston ready for use, taking care to cover them all with cylinder oil at the proper time, also every square inch of the internal surface of the cylin- 362 STEAM ENGINEERING der, in order to prevent it from rusting, and replace the cylinder head ready for use. STARTING AN ENGINE. When an engine is to be started after remaining idle for several months, the work necessary to be done depends on how the several parts were cared for when the machine was put out of com- mission. If the preceding directions concerning this important matte;- were intelligently followed, then it is only necessary to repack the valve stems and the piston rod, turn on the steam and start the engine. USING A STOP MOTION. On evjery Corliss engine, and on sev- eral other kinds there is or can be, some kind of a "stop motion," which is a device for preventing the engine from becoming a wreck in case the governor belt breaks or runs off from the pulleys. A certain class of engineers appreciate the value of such a device, keep it in good order and frequently test it to know that it will do the work for which it was installed. Another class seem to resent the idea that any such safeguard is necessary on a machine of which they have charge, consequently it is either PRACTICAL POINTERS 363 removed altogether, or disabled and rendered worthless. This is a serious mistake, because an engineer n^ever knows when a hidden flaw will cause one of his governor pul- leys to collapse, neither can he tell when the governor belt will fail or come off, thus admitting the full force of steam to the cylinder, increasing the speed of the fly wheel in a few seconds until the safe limit is exceeded, and unless steam is quickly shut off a bad wreck will result. The cautious engineer will always take advantage of every possible precaution and keep his plant ready for a test by interested parties at any time. SPEED OF A GOVERNOR Do not forget that the governor on vour engine was built to revolve at a lertain speed, which is the standard for your case. This applies to a fly ball governor without springs, or adjustable weights. If you expect to increase the speed of your engine by changing the diameter of the governor pulley, or the other one, do not state that you intend to run your governor faster in order to secure the desired result, because the speed of it will not be changed. When making calculations to determine the diameter of a pulley required to change 364 STEAM ENGINEERING the speed of an engine, just assume that the governor is the prime mover and that its speed does not change. This will prevent making statements that are not wise, and facilitate the actual work re- quired by the contemplated change. TROUBLE WITH A CRANK PIN If the crank pin of an engine heats when lubricated with good oil, it should be thoroughly examined for defects in the pin and its boxes. If none are found .the engine ought to be indicated without delay, as the sole cause of trouble may be located at the valves, for if they are not set to admit, exhaust and compress steam properly, the effect may appear in connection with the crank pin, al- though it is as far away as possible. LINING AN ENGINE Your engine may have been' in line when it was erected ten years ago, but that does not prove it to be so now, as it is quite possible for it to be changed a great deal, by taking up lost motion and making other adjustments from time to time, consequently if it pounds now more than it did when new, take out the piston and remove all other parts neces- sary, then draw a line exactly through PRACTICAL POINTERS 365 the center of the cylinder and see if the crosshead travels parallel' to it, also if the crank shaft stands at right angles. You may be surprised at the result of your investigations. FILING CRANK PIN BRASSES We occasionally find an engineer who believes that every time his crank pin boxes are keyed up to take out lost mo- tion, they must be filed so that they will come together nicely at both top and bottom, but this is not necessary. On locomotives it is advisable to do this, but it is not required on stationary work, for if they are open 1/16 inch at these points it can do no harm, and it is much more convenient to put a pair of boxes on a planer and take off enough to answer for a year or two, than to file it off every time that lost motion must be taken up. AVERAGE PRESSURE OF STEAM The average presstue of steam acting on the piston of an engine is never used when calculating the indicated horse power of it, although it is so stated in ' some of the rules given for this purpose. The average pressure is always taken above a perfect vacuum and the back pressure can have no effect on it, be- 366 STEAM ENGINEERING cause the two pressures are acting on opposite sides of the piston. The aver- age pressure shows the total force acting on the face of a piston to propel it for- ward, but gives no clue whatever to the division of the opposing force. When calculating this pressure it makes no difference whether a condenser is used or not, as only the initial pressure and point of cut off (including clearance), are taken into consideration. Of course, there are times when we want to know how much back pressure opposes the advance of an engine piston, also how much of it is above atmospheric pres- sure and other partictilars, but this only occurs when we wish to determine the mean effective pressure, and when this is known it is used in calculating the indicated horse power developed by an engine. KEEPING AN ENGINE CLEAN When a certain engine is correctly adjusted and properly lubricated, it will give good results, whether the cylin- der head is kept bright or allowed to "become dingy and dirty. There is, however, a connection between the out- ward appearance and the inward condi- tion of an engine, that is well understood by engineers and steam users, for as a PRACTICAL POINTERS 367 general rule to which there may be a very few exceptions, when an engine is rusty and dirty on the outside, the inside of it will not bear careful inspection. The outward surfaces can be kept clean and bright when the machinery is in operation, consequently if a in an will not attend to this during working hours, he will probably not spend any more time taking care of the internal parts, while the machinery is shut down and other employes are enjoying themselves, than will barely keep them in operation. THE STRIKING POINTS To ascertain what may be called the "striking points" of an engine, disconnect the connecting rod from the crosshead, move the piston as far as it will go in one direction and put a mark on the guides at one end of the crosshead. Now move the piston as far as it will go in the op- posite direction and mark the guide in the same way. This reads very smooth- ly, and it will work in the same way, provided you take the packing rings out before the piston is moved further than it moves in regular service. If you fail to do this and one of them is caught in a port, it may cause more or less trouble to get it out. When the connecting rod and the packing rings have been put in 368 STEAM ENGINEERING again, place the crank on each center alternately and mark the extreme travel of the crosshead as before. The differ- ence between these two marks at each end represents what is sometimes called the clearance. This is correct so far as the travel of the piston is concerned, but it does not include the waste space in ports, etc. An engine may be' so de- signed that it will wear unevenly, hence the piston may be drawn gradually towards one of the cylinder heads, as lost motion is taken up, but so long as the crosshead does not reach these marks on the guides, known as the "striking points," there is no danger of the piston striking either cylinder head. SMALL REPAIR JOBS Do not attempt to do a job of piping, or a small repair job on the engine during the noon hour, as it will probably take longer than you expect, hence when it is time to start the machinery for the after- noon you will not be ready, the other employes will be imable to work, and you will heartily wish that you had postponed it until evening, when there was plenty of time to do it without in- terfering with the regular work. STEAM ENGINEERING 369 N. 1-t I>. CO 00 CO 00 00 1>» - C0rJ»t*"00-o »o Nk00>C.O o '-' ciinch $.03 1 14 inch $.09 H " .04 13^ " .12 H " .04 2 .18 H " .05 2H " .24 1 " .06 3 .33 NEW YORK BELTING & PACKING CO. STEAM ENGINEERING 409 THE VULCANITE EMERY WHEEL IT can be safely said, to-day, that there is hardly a plant of any kind that does not use an Emery Wheel for some purpose; if for nothing else, to sharpen the tools of the workmen. Where Emery Wheels are used, the vexatious question arises, "Which is the safest Wheel to use?" The Vulcanite is universally conceded to be the strongest and best Emery Wheel made. By our process, the Emery is thoroughly and evenly mixed with best Para rubber, then forced into moulds and vulcanized under great pressure. The result is a Wheel of extraordinary strength and uniform consistency — one that is absolutely safe — will cut fast — stand up well on the corners and is easy to operate. VULCANITE EMERY WHEELS FOR ALL PURPOSES Malleable Iron Castings Grey Iron Castings Steel Castings Wrought Iron Machine Shop Work Stove Castings Car Wheels Dental Purposes Twist Drills Brass Castings Rough Work in General Plow Points Drop Forgings Car Couplings Tool Work Agricultural Implements Gumming and Sharpening Saws And many other purposes NEW YORK BELTING & PACKING CO. STEAM ENGINEERING RUBBER HOSE MADE in our three well known '^* brands "1846 Para," "Double Diamond " and " Carbon," also " Inde- structible " brand. The latter is made with a special woven inner jacket, manufactured under our patent, and protected by rubber cover of high quality. We manufacture a complete line of Fire, Water, Steam, Brewers' Suction, Air Brake, Tender, Acid, Garden, Oil, Air drill, Pneumatic tool. Chemical and other hose, and are prepared to make any special hose for any specific pur- pose our trade may desire. NEW YORK BELTING & PACKING CO. STEAM ENGINEERING 411 GOODS THAT WE MANUFACTURE Pneumatic Tool Hose Vacuum Cleaning Hose Water Hose Steam Hose Brewers' Hose Mill Hose Fire Hose Suction Hose Air Brake Hose Tubing (Pure, Machine and Cloth Inserted) Garden Hose Packings Gaskets and Rings Valves Dredging Sleeves Mats and Matting Rubber Belting Bradley Hammer Cushions Oil Well Packers Rubber Covered Rolls Fire Department Supplies Molded Goods Interlocking RubberTiling Etc., Etc NEW YORK BELTING & PACKING CO. J, 1'^)^-^ ^^^M : :»^I«f '^ LIBRARY OF CONGRESS 021 213 192 1