UNIVERSITY OF CALIFORNIA 
 AT LOS ANGELES
 
 SCLLIVflN'S 
 
 NEW HYDRAULICS 
 
 Consisting of 
 
 New Hydraulic Formulas 
 
 and 
 
 The Rational Law of Variation of 
 Coefficients 
 
 Plow and Resistance to Flow in all Classes of Rivers, Canals, 
 Flumes, Aqueducts, Sewers, Pipes, Fire Hose. Hy- 
 draulic Giants, Power Mains, Nozzles, 
 Reducers, etc. with Extensive Ta- 
 bles and Data of Cost of Pipes 
 and Trenching and Pipe 
 Line Construction. 
 
 MARVIN E. SULLIVAN, B. PH., L.L.B, 
 Hydraulic Engineer. 
 
 DENVER 
 
 MINING REPORTER 
 1900
 
 COPYRIGHT, 19OO 
 
 BY 
 MARVIN E. SULLIVAN
 
 C. 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 Page 36 Under table of channels, add the following: 
 Divisor : quotient :: Dividend : quotient squared. 
 
 P : r :: a : r 8 
 or r : r 8 :: p : a, in any possible case, 
 
 Page 40 9th line from bottom. "If the value of the co- 
 efficient etc." This should be corrected so as to read: 
 As the loss of effective head or slope is inversely as v/d 3 
 or i/r 3 for any constant head,it is evident that a change in 
 the value of d or r cannot affect the value of the coeffi- 
 cient n, for as the loss of head per foot length, S", de- 
 creases directly as -\/d 3 or -y/r 3 increases, the effective 
 head or slope will increase as /d 3 or ^/r 3 and this will re- 
 sult in a like increase of v 2 . As n is the ratio of 
 SVd 8 
 
 , and as S" varies inversely with v/d s , it is evi- 
 
 dent that v s varies directly with v/d s or yr 3 . Hence 
 
 the ratio of 5- n, will be constant for all diameters 
 v 2 
 
 and all slopeu and velocities, and will not be affected by 
 anything except a change in roughness of perimeter. A 
 similar correction should be applied to similar errors oc- 
 curring from page 40 to page 51. See for a general cor- 
 rection of such errors, pages 237 to 241. 
 
 42 /_ L= / ^ should be C= '-L 
 V m vS-i/r 3 A m 
 
 ' C =4^T_ 
 
 Page 42 v=Cf/r 3 y<S should be v=C t/r 3 Xi/S 
 Page42 9th line from bottom, "Varies with {/r 3 " should be 
 
 7,,
 
 SULLIVAN'S NEW HYDRAULICS. 
 "Varies inversely with $/r 8 . But see pages 237 241. 
 
 Page 45 18th line from top. "His n might be made & o" 
 should be "His C might be made to vary &c. 
 
 Page 46 Bottom line, v 3 should be v 8 . 
 
 Page 48 9th line from top. S/r 2 should be S/r 8 . 
 
 Page 52 Equation (18) should be m= s '+ Sv Xy/r 8 
 
 Page 85 River Elbe. C=49.80 should be 0=32.51, and C= 
 52 should be 0=38.40. 
 
 Page 86 Top line. 1885 should be 1855. 
 
 Page 109, 110 Remark. Add the following: As large cast 
 iron pipes are full of swellings and contractions, a 48 inch 
 pipe is not really 48 inches diameter. As the effective 
 value of any constant head or slope varies directly with 
 the actual value of ;/d 3 , if we credit the pipe as being 48 
 inches, when in fact it is not, the result is to make the 
 value of Sv/d 3 , apparently too large for the correspond- 
 ing value of v a . Hence m will be too large or C will be 
 too small for a pipe which is really 48 inches diameter 
 throughout. The irregularity of diameter in large cast 
 iron pipes reduces the value of C by from 3 to 5 per cenf 
 for diameters greater than 36 inches. It is not the fault 
 of the formula, nor is it a peculiarity in the law of flow. 
 It is simply the fault in casting pipes of large diameters. 
 
 Page 114 4th line from bottom. ACXt/d 3 -3- should 
 
 be A CXt/d 3 = -5L 
 
 Page 148-d=U/ gMgOBXq* 2632^^- shouM be
 
 PREFACE 
 
 |_|YDRAULICIANS and engineers have long been aware 
 * that there is some element or law governing the flow 
 and resistance to flow of water which is not provided for in 
 any of the formulas presented up to this time. This is made 
 evident by the fact that the results as computed by formula 
 do not agree with actual results, and by the further fact that 
 no two formulas will give the same result for like conditions. 
 Nearly all writers give one theory of flow and resistance to 
 flow in pipes and closed channels, and an entirely different 
 theory and formula for flow in open channels. The usual 
 formulas for flow in pipes give results too high for all diam- 
 eters smaller than about fourteen inches, and too low for 
 all greater diameters. 
 
 The loss of head or pressure by resistance as computed 
 by the ordinary formulas is much too small in small pipes and 
 greatly in excess of the truth in large pipes. The reason of 
 these erroneous results is that the coefficients were deter- 
 mined for pipes of medium diameter and do not vary correctly 
 so as to meet the requirements of varying diameters. Hence 
 the greater the diameter varies from the medium, either be- 
 low or above, the greater will be the error in the computed 
 result. The usual formulas for flow in open channels are 
 equally faulty, but not in the same way. 
 
 The acknowledged fault in all the formulas so far pre- 
 sented is due to the failure of hydraulicians to discover the 
 rational law of variation of the coefficient. This law has 
 been sought in vain since the beginning of the sixteenth cen- 
 tury, at which time Galileo discovered the law of gravity and 
 undertook to formulate rules for flow in rivers. The failure 
 to discover the true law of variation of the coefficient has 
 been generally conceded by all, and the possibility of its dis- 
 covery has been denied by macy. Ganguillet and Kutter ob-
 
 4 SULLIVAN'S NEW HYDRAULICS. 
 
 serve that "more than a century ago, Michelotti and Bossut 
 established the true principle that the formulae for the move- 
 ment of water must be ascertained from the results of observa- 
 tion, and not by abstract reasoning." In the Translator's 
 preface (Hering& Trautwine) to the work of Ganguillet and 
 Kutter the following observation occurs: 
 
 "As V=C i/RS will most likely remain the fundamental 
 expression for such formulae, the attention of hydraulicians 
 will be turned chiefly to the more accurate determination of 
 the variable coefficient C. A number of authors have en- 
 deavored to establish laws for its variation, and among them 
 Ganguillet and Kutter appear so far to have been the most 
 successful." Ganguillet and Kutter, however, do not claim to 
 have discovered the true law of variation, as many unthink- 
 ing persons have supposed, but on the contrary they announce 
 the belief that it cannot be discovered by abstract reasoning, 
 and in default of its discovery they propose a formula which 
 is entirely empirical. They observe (page 105): "The form- 
 ula (Kutter's) rests only upon actual guagings. * * * Be- 
 an empirical formula, it is confined to the limits occurring in 
 nature and makes no claim whatever to absolute perfection. 
 In spite of the large number of available guagings, it cannot 
 be denied that our knowledge of the elements and laws of the 
 motion of water still need extension and correction." 
 
 Webster's definition of the word empirical is, "used and 
 applied without science." The Ganguillet and Kutter formula 
 does not claim to be scientific or rational, and yet it is a con- 
 siderable improvement on some of the older formulas, but is 
 quite complicated and not simple and easy of application. In 
 the search for the true law of variation of the coefficient 
 the greatest mistake has been made in assuming that V= 
 C^/RS is the fundamental expression for the formula. The 
 I/ S is the factor which expresses the unimpeded and con- 
 stant effect of gravity, while R is an expression for a factor 
 which modifies the effect of gravity. The constant effect of 
 gravity should be expressed separately and should not be con- 
 fused in the same expression with other factors which are
 
 SULLIVAN'S NEW HYDRAULICS. 6 
 
 variable and which impede or modify the effect of gravity. 
 All the variable factors should be included in the coefficient 
 formula for C, and then all elements which" affect or modify 
 the law of gravity will be included in the value of C, and the 
 fundamental form of the formula then becomes simply V= 
 
 (V~s. 
 
 This is evidently true, because the value of B or D ha& 
 no connection with the law of gravity, which is constant. 
 The value of R or D has to do directly with the law of resist- 
 ance, and as R or D varies the resistance to flow varies. C is 
 supposed to include this resistance, and hence the value of R 
 or D should be included in the formula for C. If there were 
 no resistance_to flow whatever, then the velocity would be di- 
 rectly as i/ "S~ regardless of the value of R or D.But as the re- 
 sistance to flow does vary with the value of R or D, it is evi- 
 dent that C must vary with R or D, and if we write V=Cy ~S~ 
 simply, we thereby have all modifying factors included in 
 the value of C, while the constant law of gravity is expressed 
 by i/S. Thus we prevent confusing the opposing laws of 
 gravity and of resistance in one combined factor, and clear 
 the way for ascertaining the true law which governs the var- 
 iation of the value of C. 
 
 By the law of gravity we know that if there were no re- 
 sistance whatever the velocity would be equal in all diame- 
 ters, regardless of dimensions, where the values of ^/ S 
 were equal. But by experiment we tind that the smaller the 
 diameter becomes, the smaller the velocity becomes for equal 
 values of |/ S . It is therefore evident that the resistance 
 to flow must vary with some function of the diameter or of 
 the hydraulic mean radius. As the resistance to flow is the 
 variable factor, and is separate and distinct from and direct- 
 ly opposed to, the acceleration of gravity which is a con- 
 stant, we know that -\/ S has nothing to do with the value 
 or variation of C. We therefore narrow the field of investiga- 
 tion by writing V=C^ S, and then searching for the law of 
 variation in C, which we know is some function of the diam- 
 eter or hydraulic radius. After years of diligent experiment
 
 6 SULLIVAN'S NEW HYDRAULICS. 
 
 and observation the writer discovered that for any constant 
 degree of roughness of wetted perimeter, either in pipes or 
 open channels, the value of C varied asi/R 3 or as f/D 3 
 In other words, if K is a constant which represents the given 
 degree_p roughness of perimeter, then C=KX t/R 3 ,and V 
 = GI/S. But if we confuse the element of resistance,D or R 
 with the element of acceleration |/~S7by writing V=Cv/RS 
 then we find C varies as f/R~ simply, and if K represents 
 the degree of roughness, and we write V=Ci/BS, then we 
 have C=KXf / T^andV=<VRS. 
 
 As all hydraulic formulas are necessarily based on the 
 laws of gravity and of friction, the correctness of such formu- 
 las must depend upon their accordance with these laws. If 
 our present understanding and acceptance of these laws is 
 correct, then any formula which violates either of these laws 
 must necessarily be incorrect. It is the object of thie vol- 
 ume to present the rational law of variation of the coefficient 
 in accordance with our present understanding of the laws of 
 gravity and friction. If those laws are yet unknown it must 
 remain for some future investigator to supply a theoretically 
 correct hydraulic formula. The discussion in the following 
 pages is based on the assumption that those laws are cor- 
 rectly known, or nearly so. 
 
 In the case of open channels and rivers of irregular cross 
 section, and where the banks alternately diverge and con- 
 verge, and the perimeter varies in roughness at different 
 depths of flow, the correct application of any formula will be 
 difficult. In sections 13 and 83 methods are pointed out for 
 ascertaining the value of C in such cases. 
 
 The law of resistance in nozzles and convergent pipes, as 
 herein stated has been very thoroughly tested and its cor- 
 rectness established by hundreds of experiments. This law 
 will be found cf great service to hydraulic miners and fire- 
 men and also in determining the coefficient for flow in con- 
 verging reaches of rivers and other channels. 
 
 In the course of experiments of the writer which has 
 extended over a period of six years, it was discovered that the
 
 SULLIVAN'S NEW HYDRAULICS. 7 
 
 discharges over weirs and through orifices, as computed by 
 the usual formulas, and with the tabulated direct coefficient 
 were frequently erroneous, especially if the weir used did not 
 correspond exactly in breadth and depth with that from 
 which the coefficient was determined. Interpolation for in- 
 termediate conditions was certain to result in error. On in- 
 vestigation it was found that the difficulty lay in the fact that 
 the law of variation of the c;efficient of contraction has never 
 been discovered. In order to avoid this difficulty until the 
 law of contraction shall be understood, an appendix has 
 been added to this volume in which the difficulties are 
 pointed out and the suggestion made that the position of the 
 weir be reversed in order to prevent contraction from taking 
 place at all. New weir and orifice formulas are proposed and 
 the writer hopes that other experimentalists will perfect the 
 theories there suggested. It is proper that attention should 
 here be called to the fact that our coefficient m or C, as used 
 for determining the flow in pipes includes all resistances to 
 flow, including the resistance to entry into the pipe. No sep- 
 arate provision was made in the formula for the resistance 
 to entry because it is a matter of no practical consequence 
 under ordinary circumstances, or in any case except for high 
 velocities in very short pipes. (See remarks under Group No. 
 1, 14.) The writer hopes that the theory of coefficients and 
 the law of their variation as herein presented may contribute 
 something new and valuable to hydraulics as a science. 
 
 For each degree of roughness of perimeter there is a unit 
 value of the coefficient from which unit value the coefficient 
 varies as f/Rs", or as f/D^when V=Cy~S; or C varies as 
 t/~R~or f/ D~if we write V=CyRS. At section 20 the var- 
 ious methods of writing the formula are given. As the old 
 theories and formulas are generally admitted to be erroneous 
 they have been given no space in this volume except in a few 
 instances, where the defects in the best of them have been 
 pointed out in the course of demonstrating the new princi- 
 ples herein presented. 
 
 Perhaps the great variety of theories of variation of the
 
 8 SULLIVAN'S NEW HYDRAULICS. 
 
 coefficient, and of formulas for flow will beet exhibit the pres- 
 ent confuBed and uncertain knowledge of hydraulics. A few 
 of the leading formulas for flow in pipes, and a few of the 
 leading formulas for flow in open channels are here given in 
 order to illustrate the general confusion with which every 
 student of hydraulics has met. It will be noted that all, or 
 nearly all, these formulas may be reduced to the form V^Cv/KS. 
 Hence the main difference in them lies in the different theor- 
 ies of the variation of C. We find in most cases the same 
 author gives a different law of variation in C for pipes from 
 that given for open channels, as though the law depended 
 upon'the form of the channel, and changed with the change 
 in form of channel. Others adopt a constant unit value of C 
 for all classes and degrees of roughness of both open channels 
 and pipes, and make C vary with ^/TTonly. Hence the same 
 value of i/RS will give the same result by such formulas for open 
 channels as for pipes, and for rough as for smooth perimeter. 
 If, in the following formulas, the cofficient formula for C be 
 separated from the formula for V, the various theories for 
 variation in C at once appear, and we at once see why it is 
 that scarcely any two formulas will give like results for 
 the same conditions. It is evident, therefore, that if one is 
 right all the others are wrong. 
 
 for pipes (Fanning) 
 
 .000077^+ 
 
 RS 
 
 00000162 for Pips' 3 (D'Arcy)
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 V=105.926 (RS)H for pipes (Saint Vennant) 
 
 V=(9579 RS + .00813) * 0.0902 for pipes 
 
 (D'Aubuisson) 
 
 V=47.913 ^Sd^for pipes (Black well) 
 
 V=100 ^RS for pipes (Leslie) 
 
 V =/(! 1703.95 RS + .01698) 01308 for pipes ....... 
 
 ..................................... (Eytelwein) 
 
 til 
 
 for pipes ........... (Hawkeslej ) 
 
 /+54d 
 
 V=v/ (9978.76 RS + .02375) 0.15412 for pipes ...... 
 
 ................... ..................... (Prony) 
 
 V=J _ _ for pi pet- ...... (Neville) 
 
 A/.0234 R + 0001085 I 
 
 1.811 .00281 
 
 //R/ 
 channels ............................... (Kutter) 
 
 In the Kutter formula n represents the degree of rough- 
 ness, and 
 
 In the formula for n 
 1=1.811; C=-5L=; B = 
 
 It is to be observed in regard to the variation of Ganguil- 
 
 let and Kutter's C that 
 
 First In all cases of pipes or open channels, where the hy- 
 draulic mean radius (R) is less than 3.281 feet, an in- 
 crease in slope (S) will increase the value of C. 
 
 Second In all cases of pipes or open channels where R is 
 greater than 3.281 feet, an increase in S will cause C 
 to decrease.
 
 10 SULLIVAN'S NEW HYDRAULICS. 
 
 Third Where R=3.28l feet exactly, the value of C will be 
 
 1 fil 1 
 
 constant for all slopes and will equal 
 
 n 
 
 At page 106 of Ganguillet and Kutters work (Hering 
 and Trautwine'stranslation)an unsatisfactory attempt 
 is made to explain this reverse variation of the coeffi- 
 cient. In the translator's preface it is pertinently 
 stated "that the laws of flowing water must be the 
 same whether the channel is large or small, slightly 
 inclined or precipitous." In this remark the writer 
 fully concurs. The above variations of C would lead 
 to the conclusion that the law of gravity reversed it- 
 self at the point where R=3 281 feet. Such variation 
 is clearly erroneous and is unsupported by any sound 
 theory or facts. 
 
 In order that the various theories of flow in open channels 
 may be compared with the theories of flow in pipes, and their 
 differences noted, a collection of the most prominent formu- 
 las for flow in open channels will here be given: 
 
 l/T = Af R~Xt/~S~ (Gauckler.) 
 
 In Gauckler's formula A is supposed to be constant for 
 any given roughness, and the coefficient varies as tf~R. 
 
 V=92.20 t/RS (Brahms & Eytelwein) . 
 
 In Brahm's formula the coefficient varies only as -^ R 
 
 V=4.9 R e/~S~for small streams (Hagen.) 
 
 Here the coefficient varies directly with R. 
 V=3.34 y~R X e/S~ for large streams. . .(Hagen) 
 
 Hew the coefficient varies with y' ~R 
 
 (Bazin) 
 
 In Bazin's [formula A and B are constant for any given 
 degree of roughness of perimeter.
 
 SULLIVAN'S NEW HYDRAULICS. 11 
 
 V=( _ 1000e _ \l ..... (D'Arcy and Bazin) 
 V-08534R + .35 ) 
 
 y _ |2gRS ............................ (Fanning) 
 
 In Panning's formula m = y a It is a direct coefficient 
 
 which decreases asV* increases or as the roughness decreases 
 and also varies with R. The mean values of m for channels in 
 earth of ordinary roughness vary from 0.05 for R= 0.25 to m 
 =0.002 for R=25.00. For very rough channels the value of m 
 would be greater because V* would decrease as the rough - 
 cess increased. To show the theory of this formula it should 
 
 be written VJL X V S and m=x'2 g R The 
 
 g 
 value of -yg depends upon the degree of roughness only and 
 
 varies with R instead of / R^ as it should. 
 
 V=140v/RS 11 f RS . .... ................. (Neville) 
 
 V=v/ 1067.02 RS +0-0556 0.236 (Prony) 
 
 V=v/10567.80RS + 2671.64 (Girard) 
 
 V=v/8976 50 RS + 0.0120.109 (D'Aubuisson) 
 
 V=-/ 8975.43 RS+0.011589 0.1089 ...... (Eytelwein) 
 
 V=1(KVRS ................ (Pole, Leslie, Beardmore) 
 
 ^225 R v 
 
 (Humphreys & Abbot) 
 
 In Humphreys & Abbot's formula R ^y et p_L. \yidth an( * m 
 1.69 
 
 ~!/R +1. 5 
 
 It will be noted that a majority of these formulas make
 
 12 SULLIVAN'S NEW HYDRAULICS. 
 
 no provision whatever for different degrees of roughness 
 or different classes of wet perimeter, and hence the computed 
 results will be the same for rough, stony channels of irreg- 
 ular cross section as for smooth channels in firm earth with 
 uniform cross sections. The experimental coefficients devel- 
 oped from actual guagings of different clasees of streams, and 
 tabulated in the following pages of this work show that the 
 value of C varies from 27 to 75 in channels of like dimensions 
 and slope, but of different degrees of roughness of wet peri- 
 meter. The different classes of perimeter must therefore be 
 classified and the unit value of C for each class must be es- 
 tablished experimentally by actual guagings. When the 
 proper unit value of the coefficient for each degree of rough- 
 ness is thus established, it must thereafter vary correctly 
 with all changes of conditions as to slope, hydraulic mean 
 depth, ete,,so that the one unit coefficient will accurately apply 
 to all channels in the same class of roughness, regardless of 
 dimensions and slope or velocity of flow. 
 
 Ganguillet & Kutter recognized the necessity of classify- 
 ing the degrees of roughness of wet perimeter andof.establish- 
 ing the unit value of th^ coefficient for each class. They 
 adopted the unit value of their coefficient of roughness, n, 
 for each degree of roughness, and this value of n was to ap- 
 ply to all perimeters of like roughness, regardless of the di- 
 mensions of the channel, but they failed to discover the law 
 which governs the true variation of n and hence the value of 
 their C will not vary correctly with changing conditions. 
 
 Mr. J. T. Panning also recognized the necessity of classi- 
 fying coefficients in accordance with the degree of roughness 
 of the perimeter, but he adopted a system of direct coeffi- 
 cients for each velocity and for each hydraulic mean depth, 
 instead of determining the unit value for each class of peri- 
 meter. The difficulty with such direct coefficients is that 
 they will apply only to cases exactly similar to the conditions 
 under which they were determined. The result is that we 
 must have a separate coefficient for each velocity in the same 
 channel, and for each change in hydraulic mean depth, and
 
 SULLIVAN'S NEW HYDRAULICS. 13 
 
 for each degree of roughness. It is a fixed, inflexible quan- 
 tity whose value must be ascertained by experiment for ev- 
 ery change in any of the conditions. When the student of 
 hydraulics investigates and compares the conflicting theories 
 of flow and of the variation of the coefficient as set forth in 
 the old formulas, he is simply bewildered and discouraged, 
 for he can discover no satisfactory reason for adopting any 
 one of them in preference to another. The writer therefore 
 hopes to be pardoned for offering what he conceives to be the 
 rational solution of these difficulties. 
 
 MARVIN E. SULLIVAN.
 
 CONTENTS. 
 
 Introductory.--Evolution of the Formula. 
 Discussion of Present Data of Flow. 
 Reverse Variation of Coefficients Explained. 
 
 CHAPTER I. 
 
 SECTION 1. The law of falling bodies. 
 " 2. The laws of fluid friction. 
 
 CHAPTER II. 
 
 SECTION 3. Properties of the circle and of open channels. 
 " 4. Coefficients of resistance. 
 " 5. Coefficients of velocity. 
 ' 6. The law of variation of coefficients. 
 " 7. Deduction of general formulas for flow. 
 " 8. Variation in the coefficient illustrated. 
 ' 9. Practical determination of coefficients of resist- 
 
 ance. 
 
 " 10, Conversion of coefficients. 
 ' 11. Determination of coefficients of velocity. 
 " 12. Value of coefficient affected by density of peri- 
 
 meter. 
 " 13. To determine the value of the coefficient in cases 
 
 where the flow is in contact with different 
 
 classes of perimeter. 
 14. Tables of cofficients deduced from data of flow 
 
 in all classes of pipes, conduits, flumes, canals 
 
 and rivers, with remarks and discussions of 
 
 each group. 
 " 15. Roughness of wet perimeter defined. 
 
 CHAPTER III. 
 SECTION 16. General formulas in terms ot diameter in feet.
 
 SULLIVAN'S NEW HYDRAULICS. 15 
 
 SECTION 17. General formulas in terms of pressure, quantity 
 
 and diameter. 
 " 18. General formulas in terms of hydraulic mean 
 
 radius. 
 
 " 19. Application and limitation of formulas. 
 " 20, General formulas using C instead of m. 
 " 21. General formulas in terms of hydraulic radius 
 
 using C. 
 " 22. Special formula for vertical pipee. 
 
 CHAPTER IV. 
 
 SECTION 23. Table for ascertaining discharge or velocity in 
 cast iron pipes. Table No. 2 for discharge of 
 asphaltum coated pipes. . 
 
 " 24. Table for velocity and discharge of brick lined 
 circular sewers and conduits flowing full. 
 
 " 25. Egg shaped brick sewers, elementary dimensions 
 of. Table for velocity and discharge of egg 
 shaped sewers. 
 
 " 26. Short formulas for use with foregoing tables. 
 27. Table No. 5. Value of d, and r with roots and 
 powers. 
 
 " 28. Trapezoidal canale. To find mean radius and 
 area. Tables for velocity and discharge of trap- 
 ezoidal canals. 
 
 " 89. Rectangular canals, flumes and conduits. Tables 
 for velocity and discharge. 
 
 " 30. Table showing fall per mile, distance in which 
 there is a fall of one foot, together with values 
 of S and v/ST 
 
 " 31. Table and rules for finding required slope of 
 cast iron pipe to generate any required velocity. 
 
 " 32. Head in feet lost by friction in cast iron pipe. 
 Table No. 17 for finding friction loss for any ve- 
 locity. 
 
 " 33. Formulas and table for finding loss by friction in 
 any class of pipe for a given discharge.
 
 16 SULLIVAN'S NEW HYDRAULICS. 
 
 SECTION 34. Formulae and table for friction loss in asphaltum 
 coated pipe for any velocity. 
 
 " 35. Flow and resistance in tire hose, with formulas. 
 
 " 36. Pressure at hydrant or steamer required to force 
 the discharge of a given number of gallons per 
 minute. 
 
 " 37. Friction loss in fire nozzles. Formulas and dis- 
 cussion. Table No. 20, showing friction loss in 
 fire nozzles. 
 
 " 38. Friction loss in ring fire nozzles. 
 
 " 39. Friction loss in hydraulic power nozzles, re- 
 ducers, &c. 
 
 " 40. Multipliers for finding friction loss in cast iron 
 giants. 
 
 " 42. Total head or slope of cast iron pipe to cause 
 given discharge. 
 
 " . 43. To find diameter of pipe required. 
 
 " 44. Loss by friction in cast imn pipe for given dis- 
 charge. 
 
 ' 45. Table of multipliers for finding friction loss in 
 cast iron pipe for any given discharge. 
 
 " 46. Friction loss for given discharge of asphaltum 
 coated pipe. Table No. 23 for friction loss per 
 100 feet length. 
 
 " 47. To find the discharge from the amount of fric- 
 tion lose. 
 
 " 48. To find the discharge from slope and diameter. 
 
 11 49. Power at pump required to force a given dis- 
 charge. 
 
 " 50. To find the discharge from the pressure. 
 
 " 51. Lbs. pressure lost by friction for a given dis- 
 charge. 
 
 " 52. Slope required to cause a given discharge. Ta- 
 ble No. 24 for finding any required slope. 
 
 CHAPTER IV. 
 SECTION 53. Wooden stave pipe.
 
 SULLIVAN'S NEW HYDRAULICS. 17 
 
 SECTION 54. Wooden pipes compared with other classes of 
 pipe. 
 
 " 55. Earthware or vitrified pipe. 
 
 " 56. Table No. 56, elementary dimensions of pipes. 
 
 " 57. Length in feet of small pipes to hold one U. S 
 gallon. 
 
 " 58. Decimal equivalents to fractional parts of a 
 lineal inch. Fractional inches in equivalent 
 decimals of a foot. Tenths of a foot in equiva- 
 lent inches. 
 
 " 59. Conversion tables of weights and measures for 
 converting U. S. to metrical and metrical to U. 
 S. measures. 
 
 CHAPTER V. 
 
 SECTION 60. Work, power and horse-power defined. Form- 
 ulas for finding the horse-power of a stream. 
 
 " 61. To find cubic feet of water required to gener- 
 ate a given power. 
 
 " 62. To find the net head required to generate a 
 given power. Efficiency of water wheels de- 
 fined. 
 63. Head of water defined. 
 
 " 64. To find the diameter of a pipe which will carry 
 a given quantity of water with a given loss of 
 head by friction. 
 
 " 65. To find the required area and diameter of noz- 
 zle to discharge a given quantity. 
 
 " 66, Pipe lines of irregular diameter. 
 
 " 67. A power main with nozzle and water wheel to 
 run at a given speed and develop a given power. 
 
 " 68. Table No. 36. Eleventh roots and powers. 
 Converse Lock Joint pipe. Remark 3. 
 
 " 69. Friction loss at bends in pipes; formulae. 
 
 " 70. Weisbach and Rankine's formulas for friction at 
 bends. 
 
 " 71. Results of different formulas compared.
 
 18 SULLIVAN'S NEW HYDRAULICS. 
 
 SECTION 72. Resistance at bends. Ronnie's experiments. 
 
 " 73. Thickness of pipe shell proportional to diame- 
 ter and pressure. 
 
 " 74. Value of S in water pipe formulas. 
 
 " 75. Riveting and riveted pipe. 
 
 76. Proportions of single and double riveted lap 
 joints. 
 
 " 77. Table of decimal equivalents to fractional 
 parts of an inch. 
 
 " 78. Weight and thickness of sheet iron and sheet 
 steel. 
 
 " 79. Rules for finding weight of riveted pipe. 
 
 " 80. Tests for strength of lap riveted joints. 
 
 " 81. Testing iron and steel plates for defects. 
 
 " 82. Pipe joints how made. 
 
 " 83. Formula for proportions of reducers for joining 
 large to small pipes. 
 
 CHAPTER VI. 
 
 SECTION 84. Flow in open channels permanent and uniform 
 flow. 
 
 " 85. Resistances and net mean head in open chan- 
 nels. 
 
 " 86. Ratio of surface, mean and bottom velocities. 
 
 " 87. The eroding velocity. 
 
 " 88. Eroding velocity in straight canals of uniform 
 section. 
 
 " 89. Slope required to generate given bottom veloc- 
 ity. 
 
 " 90. Stability of channel bed. 
 
 " 91. Adjustment of grade, bottom velocity and side 
 slopes. 
 
 " 92. Dimensions of canals to discharge given 
 quantities. 
 
 " 93. Allowance in cross-eection of canal for leakage 
 and evaporation. 
 
 " 94. Flume forming part of canal. 
 
 " 95. Float measurement of mean velocity in canals.
 
 SULLIVAN'S NEW HYDRAULICS. 19 
 
 APPENDIX I. 
 
 SECTION 96. Weirs and weir coefficients. Discussion. 
 
 APPENDIX II. 
 SECTION 97. Water works rules and data. 
 
 " 98. Quantity of water required per person. 
 
 " 99. Consumption and cost per 1,000 gallons in var- 
 ious cities. 
 
 " 100. Formulas and tables for diameter of pipe re- 
 quired. 
 
 " 101. Formulas for conduits, pipes, etc. 
 
 ' 102. Formulas for diameter to maintain a given 
 pressure while discharging. 
 
 " 103. Friction heads,velocities and discharge for given 
 diameters and slopes. 
 
 ' 104. Formulas for thickness and weight of cast iron 
 pipe. 
 
 " 105. Weight and dimensions of cast iron pipe made 
 by the Colorado Fuel and Iron Company. 
 
 " 106. Weight per foot length of cast iron pipe for 
 150 and 200 pounds pressure. 
 
 " 107. "Standard" cast iron pipe. 
 
 108. Cost per 100 feet of pipe and laying in Denver, 
 Colorado. 
 
 " 109. Cost per foot of pipe and laying in Boston, 
 Massachusetts. 
 
 " 110. Cost of trenching, laying, calking, etc., in Om- 
 aha, Nebraska. 
 
 " 111. Weston's table for estimating cost of pipe lay- 
 ing. 
 
 112. Table showing cubic yards of excavation in 
 trench per foot. 
 
 113. Bell-holes in pipe trench. 
 
 " 114. Proper depth of trench for pipe laying. 
 
 " 115. Amount of trenching and laying per man per 
 
 day. 
 " 116. Amount of lead required per joint for cast iron 
 
 pipes.
 
 "There is in this world but one work worthy of a man, 
 the production of a truth, to which we devote ourselves, and 
 in which we believe." Taine.
 
 INTRODUCTORY. 
 
 The evolution of the formula and discussion of the present 
 available data of flow, with an explanation of the reverse 
 variation of coefficients, 
 
 The general formula for flow as herein finally presented 
 may justly be called the result of the combined labors of 
 Galileo and all subsequent writers and experimentalists, in- 
 cluding the present writer. The present writer has accepted 
 and adopted from all former writers on hydraulics such prin- 
 ciples and theories as have been thoroughly proven true and 
 general, and has rejected all theories of doubtful or uncertain 
 value and supplied the deficiencies thus arising by original 
 investigations and experiments. The foundation of the form- 
 ula was the discovery, early in the seventeenth century, of 
 the law of falling bodies by Galileo. In his investigations of 
 flow in rivers Galileo failed to recognize the nature of the 
 resistance of the solid wet perimeter and the difference be- 
 tween the resistance of a solid in contact with a liquid, and 
 that of two solid bodies in contact. His investigations there- 
 fore resulted in failure. Later it was discovered by Torri- 
 celli, a pupil of Galileo, that resistances aside, the square of 
 the velocity is directly proportional to the head or inclination, 
 or in other words, that the velocity would be as the square 
 root of the head or elope. 
 
 Brahms discovered that the acceleration which 
 would occur according to the law of gravity did not actually 
 occur, but that the velocity of flow became constant. His 
 investigations established the fact that the solid wet peri-
 
 22 SULLIVAN'S NEW HYDRAULICS. 
 
 meter offered a resistance to the flow which opposed the ac- 
 celeration that would otherwise occur, and he assumed tht 
 this resistance was directly proportional to the hydraulic 
 mean radius, or to the area of cross-section of the column of 
 water divided by the wet girth. In the latter part of the 
 eighteenth century, Du Buat instituted a series of experi- 
 ments from the results of which he discovered that the 
 velocity of flow depended upon the slope of the water surface 
 or head, and that in channels of uniform area and grade, 
 when equilibrium was attained, the flow became uniform and 
 the resistance equalled the acceleration of gravity. Thus 
 each investigator has contributed some valuable discovery or 
 fact which has been able to stand, while many of their as- 
 sumptions have been proven wholly erroneous. 
 
 Du Buat also discovered that the resistance of a solid in 
 contact with a liquid, was in no manner increased or de- 
 creased by a change of pressure between the liquid surface 
 and the solid surface. In other words he discovered that 
 the pressure with which a liquid is pressed upon a solid does 
 not affect the friction between them. Du Buat and Prony 
 each discovered, as a consequence of the law of gravity, that 
 the head or slope had no influence whatever upon the value 
 or variation of the coefficient, but they erroneously assumed 
 also that the character of the wet perimeter had no influence 
 upon the coefficient. It was the opinion of Du Buat (and 
 adopted by Prony) that the nature of the walls and bottom of 
 a channel could not affect the coefficient because, as Du Buat 
 observed, "A layer of water adheres to the walls, and is there 
 fore to be considered as the wall proper which surrounds the 
 flowing mass." With this view, he supposed all perimeters 
 to be practically "water perimeters",|and consequently equally 
 smooth. It remained for D'Arcy and Bazin to demonstrate 
 by many practical experiments that this latter assumption of 
 Du Buat and Prony was entirely without foundation. 
 
 As a result of the experiments of D'Arcy and Bazin the 
 fact was established that the coefficient of flow would vary 
 directly as the degree of roughness or smoothness of wet
 
 SULLIVAN'S NEW HYDRAULICS. 23 
 
 perimeter. Bazin stated also that the coefficient varied with 
 the value of the hydraulic mean radius, thus confirming the 
 observations of Brahms. D'Arcy and Bazin recognized that 
 the slope or head had no influence upon the value or variation 
 of the coefficient, and hence omitted that feature in their 
 formula, and assumed with Brahms that the total resistance 
 for any given degree of roughness would be directly propor- 
 tional to R. the hydraulic mean radiue. They were correct 
 in their assumptions thus far, but they failed to go one step 
 farther and provide for the acceleration as well as the re- 
 sistance, or in other words to ascertain the mean resistance of 
 all the particles of the entire cross-section by taking the 
 product of total retardation by total acceleration. They 
 adopted and embodied in their formula simply the feature 
 of total retardation without modification by the acceleration. 
 Hence they failed to ascertain the mean resistance of the 
 entire cross-section, and as a necessary result of adopting 
 total resistance instead, their formula gives results too low 
 in large pipes or channels and the larger the pipe or channel, 
 the greater the error will become. 
 
 Ganguillet and Kutter proposed a formula based partly 
 on Bazin's formula and partly upon the results of some ill 
 assorted guagings. While this latter formula has become 
 popular and is considered as standard by many engineers, it 
 is really based upon theories which are directly contradic- 
 tory of both the laws of friction and of gravity,and a short in- 
 vestigation will expose the fact that it can be applied with 
 accuracy only to open channels of very slight inclination, and 
 whose mean radii approach closely to unity. The discussion 
 of coefficients will point out the reasons why this is true. 
 
 The writer would also remark that the published tables 
 of data in relation to flow in pipes and open channels are, in 
 a large majority of cases, wholly unreliable, as many contract- 
 ing engineers have recently discovered to their great cost. 
 
 Coefficients should never be based upon data of uncer- 
 tain value, as the results must depend upon the correctness 
 of the coefficient used.
 
 24 SULLIVAN'S NEW HYDRAULICS. 
 
 The data of guagings of rivers at different stages and for 
 various depths of flow are nearly all worthless for scientific 
 purposes for one or more of the following reasons: 
 
 1 . The data fail to show whether the stream was rising 
 or falling or stationary when the mean velocity and 
 corresponding alope of water surface were ascer- 
 tained. 
 
 Where a stream is either rising or falling with 
 considerable rapidity, there is little or no relation be- 
 tween the slope of the water surface and the actual 
 mean velocity then prevailing. The same depth of 
 flow or guage height at the same point does not 
 necessarily always produce the same slope of water 
 surface. The slopes are usually thus recorded as 
 corresponding to a certain guage height without 
 actual measurement. The same slope and guage 
 height on a rising river will cause a much greater ve- 
 locity and give a higher coefficient of flow than upon 
 a falling river. The difference in value of the veloc- 
 ity of flow and of the coefficient will depend upon the 
 magnitude of the freshet the distance it extends up 
 stream the suddenness and rapidity of the rise or 
 fall. In a rising or falling stream equilibrium is lost 
 and the actual effective slope which is generating the 
 velocity at such times is very different from the ap- 
 parent slope, and can be ascertained only from the 
 mean velocity actually existing at the time, and from 
 a previous knowledge of the degree of roughness of 
 the stream in that locality. The effective slope may 
 then be found by formula for S. 
 
 2. Guaging stations are always located at narrow, deep 
 sections of the stream, and the hydraulic radius thus 
 roughly measured is given as the mean hydraulic 
 radius of the stream. This is never the true nor 
 even scarcely approximate, mean hydraulic radius, 
 except at the particular point where measured.
 
 SULLIVAN'S NEW HYDRAULICS. 25 
 
 3. In many cases the mean velocities tabled are deduced 
 from the surface velocities by some absurd formula 
 which is basad upon the theory that there is a con- 
 stant ratio between the maximum surface velocity 
 and the mean velocity, and that this ratio is the same 
 in all classes and dimensions and degrees of rough- 
 ness of channels. 
 
 4. The general slope is usually taken and is assigned as 
 the local slope. They are usually very different ex- 
 cept at extreme high water, when the general and 
 local slope are nearly equal. 
 
 5. In turbulent streams, or in very large streams it is 
 impossible, for many reasons to ascertain the slope of 
 water surface, especially the high water slope. The 
 slopes assigned in such cases are simply the record 
 of a guess, and have no value for scientific purposes. 
 
 6. The method of ascertaining the mean velocity as 
 finally tabled, is frequently by mid-depth floats. 
 These floats vary in the time of passing over the same 
 course by as much as 25 per cent, depending upon 
 the number of whirls, boils and cross-currents en- 
 countered. The mean is taken as the actual mean 
 velocity, or as bearing a given fixed ratio thereto, re- 
 gardless of formation of the channel bed. The in- 
 equalities of the bottom of the stream make it impos- 
 sible to adjust a float to mid depth. If the mid depth 
 velocity were absolutely known, it is not known 
 what relation it bears to the actual mean velocity. 
 The mean velocity may be either above or below mid- 
 depth. That will depend upon the magnitude and 
 roughness of the channel at the given place. 
 
 7. Many rivers are affected by gulf tides, as the Missis- 
 sippi river as far up as Donaldsonville, and the river 
 Seine at Poissy, Triel and Meulon, where the water 
 surface fluctuated as much as two feet during the 
 time of the guagings there. This is so marked on
 
 36 SULLIVAN'S NEW HYDRAULICS, 
 
 the Mississippi river at Carrollton, La., as to actually 
 produce reverse slopes, as noted by the river engi- 
 
 8. Data are frequently published of the gaugings of a 
 channel at different stages where the value of the 
 hydraulic mean radius increases four or five hundred 
 per cent., and the discharge increases by a thousand 
 per cent, or more, and yet the same slope is assigned 
 for all stages! As an example of this kind, see the 
 ten gaugings of the Saone under the direction of M. 
 Leveille, 1858-9. Here the hydraulic radius varies 
 from R=3.88 to R=15.83, and yet the slope of water 
 surface is given as S=.00004 for each of the ten 
 gaugings. The gaugings of the Weser by Funk are 
 of no value. Bazin remarks; '-It is to be noted 
 that Funk has almost always adopted the same 
 slope for an entire group of experiments." Bazin also 
 states that in the experiments of Brunning on the 
 Rhine, "the slopes were not measured at all, but 
 subsequently computed so as to make the results 
 accord with the formula." 
 
 It is well known that the gaugings of the Mississippi 
 River under the direction of Humphreys and Abbot 
 during the year 1858 are of very doubtful value. The 
 areas had been measured at the gauging stations 
 seven years before, and were assumed to have remain- 
 ed constant ever afterward, when in fact the area at 
 a given point in that river is frequently altered by as 
 much as 14,000 square feet within twenty-four hours 
 by scour. In 1858 the velocities were taken at a 
 depth of only five feet below surface, and the mean 
 velocities were calculated by an empirical formula of 
 no value. Du Buat's mean velocities as tabled for 
 the Canal du Jard, were deduced from surface float 
 velocity by Du Buat's formula. Du Buat's formula 
 for ascertaining the mean from the surface velocity 
 was based on his experiments on a very small wooden
 
 SULLIVAN'S NEW HYDRATLICS. 27 
 
 trough of smooth perimeter, and has long since been 
 discarded as being of no value. 
 
 If the present available tables of data were assorted 
 carefully and the worthless were rejected, there 
 would little remain. These remarks are made here 
 in order to call attention to the need of obtaining 
 new and accurate data, and to prevent too great 
 reliance upon the value of such data as are now 
 available. The data relating to flow in pipes and 
 conduits are equally bad and untrustworthy. The 
 data relating to asphaltum coated pipes except those 
 of Hamilton Smith Jr., and to wrought iron pipes 
 are especially of uncertain value, and no expensive 
 enterprise should be based upon them without ad- 
 ditional experiment. Some of the more recent data 
 relating to flow at different depths in large masonry 
 conduits of comparatively short length, show by the 
 value of the slope of water surface as compared with 
 the slope of the bottom of the conduit, that there 
 would have been no water in the upper end of the 
 conduit at all. It is probable that equilibrium had 
 not bem attained at the time of gauging. Any 
 other explanation renders the data absurd, and this 
 explanation renders them worthless. In a channel 
 of uniform grade, croes-section and roughness of 
 perimeter, the slope of the water surface will be the 
 same as the slope of the channel bed as soon as uni- 
 form flow is established. If this were not the case, 
 uniform flow could never occur, because the water 
 would be of greater depth at one point than at 
 another, and the velocities would be inversely as the 
 depths or wetted areas. An investigation of the data 
 of flow which is now available is discouraging to a 
 degree. It is a misfortune common to us all. In 
 large rivers where the roughness of perimeter and 
 the area of cross-section vary at almost every foot in 
 length, and where scour or fill is constantly in pro-
 
 SULLIVAN'S NEW HYDRAULICS, 
 
 gross, it is impossible that equilibrium in its true 
 sense, should ever be established. The flow is alter- 
 nately checked by rough perimeter and increased 
 area due to scour, and accelerated by reaches of 
 straight, smooth perimeter where the area is con 
 tracted. The flow is similar to that in a compound 
 pipe made up of lengths alternately large and small, 
 and alternately smooth and rough. The velocity is 
 necessarily inversely as the areas, in case the supply 
 of water is constant. 
 
 For these reasons the local slope over a very short 
 length of channel, at normal stages of the stream, is 
 the slope that must be used in the application of a 
 slope formula. Otherwise the result by formula will 
 be of no value. 
 
 The value of the coefficient will usually decrease with 
 increase in depth of flow at any given point along a 
 natural channel, after the depth exceeds the usual 
 dpth of flow. This is due to the simple fact that 
 the bed is silted and worn smoother up to the depth 
 of ordinary flow than the sides above the usual flow. 
 Hence as depth of flow increases the proportion of 
 the rougher side wall perimeter increases also, and 
 thereby decreases the value of the coefficient as depth 
 of flow and ratio of rough perimeter increase. It 
 frequently occurs, however, that the reverse of this 
 is true, as for example in channels having very 
 rough, stony bottoms and comparatively regular 
 side walls, In this latter case the coefficient will 
 increase as depth of flow increases because with 
 each gain in depth there is a gain of the smooth 
 over the rough perimeter, and the mean of the 
 roughness of the perimeter considered as a whole 
 becomes less and less at each successive increase of 
 depth. In either class of channels the value of the 
 coefficient must vary directly with the mean of the 
 roughness of the entire wet perimeter taken as a
 
 SULLIVAN'S NEW HYDRAULICS. 29 
 
 whole. It therefore follows that if the whole 
 perimeter be of equal and uniform roughness or 
 smoothness throughout, the coefficient will remain 
 absolutely constant for all depths of flow. 
 
 Large masonry conduits, not being adapted to 
 withstand pressure from within, are built on small 
 grades or inclinations and given free discharge. It is 
 nearly always found that the coefficient in such con- 
 duits is greater for very small depths of flow than for 
 greater depths. This is explained by the fact that 
 much cement or mortar is dropped upon the invert or 
 bottom during construction and is ground into the 
 pores and joints of the brick by the tramping of the 
 masons. The floor is worn smooth by reason of this, 
 and the slight inclination of the conduit and low ve- 
 locity permit of the deposit of a very fine, dense silt 
 upon the bottom which settles in and fills up all the 
 irregularities and depressions along the bottom thus 
 presenting a smooth, uniform, contiguous bottom peri- 
 meter to the flow. The side walls, although of the 
 same material, are much rougher than the invert or 
 bottom, because the rough projections of sand along 
 the sides of the brick are not rubbed off, and the 
 pores and small cavities are not filled and plugged by 
 mortar tramped in under pressure, and by the deposit 
 and settlement of fine silt, as occurs on the bottom. 
 This is, however, not true of open canals with paved 
 bottoms and masonry side walls where the slope is 
 sufficiently great to generate a velocity at the bottom 
 sufficient to prevent the deposit of silt or to scour out 
 the joints of the masonry floor. In this latter case 
 the bottom has no advantage of the sides so far as re- 
 lates to roughness, unless it is better constructed, or 
 is composed of smoother material, or is in better re- 
 pair than the side walls. In any given case the value 
 of the coefficient will be directly as the mean rough- 
 ness of the entire wetted portion of the perimeter, or
 
 30 SULLIVAN'S NEW HYDRAULICS, 
 
 as the ratio of smooth to rough perimeter as the 
 
 depth of the flow varies. 
 
 With these general introductory remarks upon the evolu- 
 tion of the formula for flow, the uncertain value of the present 
 available data of flow, and the causes of contrary variation in 
 the value of the coefficient, the reader will be better prepared 
 to understand what follows.
 
 CHAPTER I. 
 
 Of the Laws of Gravity and the Laws of Friction Between a 
 Liquid and a Solid. 
 
 /. The Law of Falling Bodies Ae the law of falling bod- 
 ies, or of gravity, and the law of friction between a liquid and 
 a solid include all the elements of the flow of water, it is of 
 prime importance that these laws should never be lost sight 
 of in any investigation or application of hydraulic formulas. 
 The moment that a theory or a formula deviates from the re- 
 quirements of any one of these natural laws, that moment it 
 must fail. These laws must be observed in their entirety. 
 No provision must be either excluded or violated. The pen- 
 alty is certain failure to the extent of the evasion or violation. 
 
 Let g=feet per second by which gravity will accelerate 
 the descent of a falling body. g=32.2 at sea level. 
 
 2g=64.4. 
 
 v =velocity in feet per second. 
 
 H=height in feet, total fall in feet, or total head in feet. 
 
 t=time in seconds. 
 
 A body falling freely from rest will descend 16.1 feet in 
 the first second of time,(t) and will have acquired a velocity, at 
 the end of the first second, of 32.2 feet per second, and will 
 be accelerated in each succeeding second 32.2 feet, so that for 
 each additional second of time consumed in falling, there will 
 be a gain in the rate of descent equal to 32.2 feet. At the end 
 of the first second the rate of velocity will be 32.2 feet per 
 second, at the end of the second second of time, the rate of 
 velocity will be 64.4 feet per second, and BO on for any num- 
 ber of seconds, adding 32.2 feet to the rate of velocity for each 
 second of time. 
 
 Velocity is the rate of motion. Acceleration is the gain
 
 32 SULLIVAN'S NEW HYDRAULICS. 
 
 in this rate. The acceleration or gain in rate of motion in 
 the case of a body falling freely, is 32.2 feet per second, and 
 consequently the velocity, (v) at any time (t) is equal to gXt, 
 or to the acceleration per second (g) multiplied by the num- 
 ber of seconds of time (t). The distance in feet (H) fallen 
 through by a body in the first second is 16.1 feet, or one half 
 g, and the distance fallen in any given time(t)is as the square 
 of that time (t 8 ). Consequently the velocities are as the 
 square roots of the distances or vertical heights fallen 
 through, or as -j/ H. As gravity produces the velocity of 2 
 in falling through the height 1, the height in feet fallen mul- 
 tiplied by 2g will equal the square of the velocity in feet per 
 second or 
 
 v*=2gH (1) 
 
 From this fundamental law of gravity we have 
 
 v=-/2 gH=/ 64.4H =8.025 V / H .......... (2) 
 
 v=gt ...................................... (4) 
 
 g=I =JZl=32.2 at sea level ................ (5) 
 
 t 2H 
 
 ......... (6) 1 
 
 The velocity head, or that portion of the head which is 
 producing the velocity of flow in any case is therefore 
 
 -=r ....... ..... ; ....................... (7 > 
 
 And the velocity generated by any velocity head is equal 
 v= /2g hv=8.025 y "hv .................... (8) 
 
 2. The Laws of Friction as Applied to a Liquid in con- 
 tact with a Solid Surface The results of many very careful 
 experiments establish the correctness of the following rules: 
 I. The friction on auy given unit of surface will be directly
 
 SULLIVAN'S NEW HYDRAULICS. 33 
 
 as the roughness or smoothness of that surface. 
 
 II. The total resistance will be as the total number of unite 
 
 of friction surface. 
 
 III. The friction on any given unit of surface will be aug- 
 mented as the square of the velocity with which the 
 liquid is impelled along that surface. 
 
 IV. The friction between the molecules or particles of the 
 liquid themselves, is infinitely small, and may be en- 
 tirely neglected. 
 
 V. The friction between a liquid and a solid is not affected 
 by the pressure with which the liquid is pressed per- 
 pendicularly upon the solid. The friction is entirely 
 independent of the amount of radial pressure. 
 
 VI. The mean resistance of all the particles of the entire 
 cross section of the liquid vein considered as a whole, 
 will be as the total retardation or loss of velocity by re- 
 sistance, as modified by the total acceleration or free 
 and unretarded flow, or as the product of total retard- 
 ation by total acceleration. Total acceleration will be 
 as the square root of the net free head. Total retarda- 
 ation will be as the square root of the head consumed 
 or loet by resistance. 
 
 The mean resistance, or mean loss of head, of all the 
 particles of the entire cross section taken as a whole 
 will be as the product of total retardation by total ac- 
 celeration. 
 
 The mean velocity of all the particles in a cross-section 
 will be as the square root of the mean head of all the 
 particles.
 
 CHAPTER II. 
 
 Of Coefficients and their Variation- 
 
 3. Properties of the Circle IK order to exhibit the 
 properties of the circle, and the relations of area to friction 
 surface in both open and closed channels, and the relations 
 common to both open channels of any form and to circular 
 closed channels or pipes, and to also show the relation of 
 theee common properties to the value and variation of the 
 coefficients, the following tables of circles and of open chan- 
 nels of various forms will he referred to. The notation here 
 given will be followed throughout: 
 
 H = total head in feet. 
 
 h"=friction head, or head required to balance the total 
 resistence. 
 
 h v =velocity head in feet in the total length /. 
 
 Z=1ength in feet of pipe or channel. 
 
 v=mean velocity in feet per second. 
 
 d=diameter in feet. 
 
 a=area in square feet. 
 
 p=wet perimeter in lineal feet, or friction surface. 
 
 r= ^hydraulic mean radius in feet. 
 n=coefficient of friction or of resistance. 
 m=ccefficient of flow or of velocity. 
 
 total head in feet H 
 
 S= total length in feet= r =8ine of lo P e = to * al head P* 
 foot. 
 
 h" 
 S'= =friction head per foot length of channel or pipe 
 
 Sy = Velocity head per foot length of pipe or channel.
 
 SULLIVAN'S NEW HYDRAULICS, 
 
 35 
 
 In full pipes or circular closed channels r= = d X -25, 
 and d =4r. a=d s X.7854, or a=(4r)X-7854=r 8 Xl2.5664. 
 TABLE OF CIRCLES. 
 
 d 
 
 FEET 
 
 v/d 
 
 FEET 
 
 r 
 
 FEET 
 
 a 
 
 SQ FEET 
 
 P 
 
 FEET 
 
 BELATI'N 
 OF p to a 
 
 0.50 
 1.00 
 2.00 
 4.00 
 8.00 
 16.00 
 32.00 
 
 0.707 
 1.000 
 1.4142 
 2.000 
 2.828 
 4.0CO 
 5.657 
 
 0.125 
 0.25 
 0.50 
 1.00 
 2.00 
 4 00 
 8.00 
 
 0.1C635 
 0.78o4 
 3.1416 
 12.5664 
 50.2656 
 201.0624 
 804.2196 
 
 1.5708 
 3.1416 
 6.2832 
 12.5664 
 25.1328 
 50.2656 
 100.5312 
 
 p=8a 
 p=4a 
 p=2a 
 p= a 
 p=y,a 
 p=&a 
 P=Ha 
 
 It will be observed that the diameter d, is doubled here 
 each time, and that the result of doubling d is to also double 
 r and p. It follows therefore that in circular closed channels 
 and pipes d, r and p vary in the same ratio. As d, r and p 
 all vary exactly in the rame ratio, and as the area varies as d a 
 or r*, and as d or r must therefore vary as the square root of 
 the area, it follows that the friction surface p, must also vary 
 as the square root of the area. It will be observed that when 
 d, r or p is doubled, the area is increased four times. Hence if 
 the friction surface p is doubled the area is increased four 
 times. The right hand column of the table shows how rap- 
 idly the friction surface p gains on the area as the diameter 
 is reduced from four feet, and also the reverse gain of area 
 over friction surface as the diameter is increased above four 
 feet. In pipes or circular closed channels flowing full, the 
 the same value of d or r always represents the same length 
 of wet perimeter, because the parimeter or circumference of 
 a circular closed channel or pipe is always equal to dX3.1416, 
 or to rX12.5P64. As the area is always as d 2 or r 8 and as the 
 friction surface varies as d, r, p or ^/ a , it follows that the 
 same value of d, r or p in circular closed channels and pipes 
 flowing full, will always represent the same value of the area 
 and of the wet perimeter or circumference. Such circular 
 full channels may therefore be compared one with another, 
 by simple proportion, because in such channels,
 
 36 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 a : a : : d 1 : d*, or a : a : : r* : r* 
 
 r:r::d:d, orr:r::p:p 
 
 p :p::d : d, or j/a : >/ a::p:p 
 
 In open channels, however, r is not necessarily an index 
 of either the extent of the area or of the perimeter, and there- 
 fore open channels of different forms cannot be thus compared 
 one with another, but in all cases r expresses the ratio of a to 
 p in the given case. 
 
 TABLE OF OPEN CHANNELS. 
 
 Channel Area, a 
 
 Peri- 
 meter, p 
 
 a 
 r= 
 P 
 
 r* 
 
 Flume 10- x20' 
 Mississippi River... 
 Lamer Canal 
 River Seine 
 Chaz illy Canal 
 
 200.00 
 15911.00 
 50.40 
 
 i-o22 00 
 11.30 
 
 40.00 
 1612.00 
 31.00 
 518.00 
 10.80 
 
 5.00 
 9.87 
 1.81985 
 
 i- :^~2 
 1.0462 
 
 25. (C 
 97.427 
 3.31 
 
 m n 
 
 1.09453 
 
 While we cannot compare these open channels one with 
 another as in the case of pipes, yet if we take the data for any 
 one pipe or for any one open channel it will be found in any 
 case that 
 
 p : r : : a : r* 
 
 In other words the friction e irface p varies as r, and the area 
 varies as r* in any possible shape or form of open or closed 
 channel. As p : r : : a : r* in any form of channel it follows that 
 r bears the same relation to a and also to p in any given chan- 
 nel or pipe, as it does in any other channel or pipe, for r= a 
 
 p 
 
 in any given case. The properties which are common to all 
 shapes and classes of channels and pipes are that, in any 
 given case, the area varies as r" and the friction surface var- 
 ies as r or as y a, regardless of the shape of the pipe or chan- 
 nel. These properties which are common to all classes acd 
 forms of channels and pipes are the only two which affect the 
 coefficients. Hence the form or shape or size of the pipe or 
 channel does not affect the application of the coefficients 
 which vary with these properties which are common to all
 
 SULLIVAN'S NEW HYDRAULICS. 37 
 
 possible forms of waterways. The tables were given not only 
 to illustrate the above facts, but for other reasons which will 
 be referred to when the application of certain formulas to open 
 channels is discussed. 
 
 Brahms discovered and announced these common re- 
 lations as early as the middle of the eighteenth century, 
 but like his successors, he mistook the total resistance for the 
 mean resistance or in other words he did not modify the 
 effects of total resistance by that of total acceleration. Since 
 that time, coefficients have been made to vary either as r or 
 asi/~F~~, and also as some other factor such as slope or velocity. 
 
 4. Coefficients of Friction or of Resistance In general 
 terms a coefficient may be defined as the constant amount or 
 per cent by which the head per foot length of pipe or channel 
 must be reduced on account of loss by frictional resistances. 
 
 In any constant diameter, or in any open channel of con- 
 stant hydraulic radius, the friction will be directly as the 
 total friction surface and directly as the roughness of that 
 surface, and will increase directly as the square of the 
 velocity. As the amount of resistance per foot length of pipe 
 or channel is always directly proportional to v s in any given 
 case, it follows that the amount of friction head per foot 
 length (S") required to balance it must also always be direct- 
 ly proportional to v s otherwise one could not balance the 
 other, and uniform flow could never occur. In any given 
 pipe or channel, if the head or slope increases, the square of 
 the velocity, and consequently the friction, will increase in 
 the same ratio, for v 8 is always directly proportional to the 
 header slope. Hence the ratio of friction head per foot 
 length S", to the square of the velocity, v 8 , is necessarily a 
 constant for all heads, slopes and velocities. The coefficient 
 of resistance n, in any given diameter or hydraulic radius is 
 simply the expression of this ratio of S" to v 8 . It follows 
 therefore, as this ratio is necessarily a constant, that a 
 change of slope or velocity can have no possible effect upon 
 the value of the coefficient. As long as the diameter or 
 mean hydraulic radius remains constant, the coefficient of 
 
 210991
 
 38 SULLIVAN'S NEW HYDRAULICS, 
 
 Q It 
 
 resistance is n= 5- for all slopes and velocities, and will be 
 
 constantjfor all elopes and velocities because S" and v 2 must 
 always vary exactly at the same rate. It is evident that any 
 formula which causes the coefficient to vary in any manner, 
 or to any extent whatever, with a change of head, slope or 
 velocity, violates the law of gravity which shows that H or S 
 must be directly proportional to v 2 in all cases. It also 
 violates the law of friction which declares the friction to be 
 always proportional to v 8 . The results computed by such a 
 formula for any given diameter with different slopes, or for 
 any given open channel with different elopes must necessarily 
 be erroneous at least to the extent that the value of the 
 coefficient was made to vary with changing slopes. The 
 value of the coefficient for any given diameter or for any 
 given hydraulic radius will depend upon the degree of rough- 
 ness of the wet perimeter. A rough perimeter will offer 
 great resistance to the flow and will require a considerable 
 head or inclination to generate a small velocity. In such 
 
 S" 
 case the ratio (n) of rfwill be large, because S" will be large 
 
 and v* will be small. This ratio will, however, be constant 
 for any given degree of roughness in a pipe or channel where 
 r is constant. 
 
 5. Coefficient of Velocity Where the discharge is free 
 in a pipe or channel, and the value of r remains constant, 
 the totalhead will be consumed in balancing the resistance 
 and in generating the velocity of flow. The resistance must 
 be balanced before flow can ensue. The resistance being as 
 v a in all cases, the coefficients of velocity represents the ratio 
 of total head H, to v 8 , or rather Sto v a if the discharge is free 
 If the discharge is throttled so that a portion of the head is 
 converted into radial pressure, then this pressure head is 
 neither converted into velocity nor lost by resistance. In this 
 
 latter case the coefficient of velocity is the ratio oflttpl, in
 
 SULLIVAN'S NEW HYDRAULICS. 39 
 
 which S v is the velocity head per foot length, and S" is the 
 friction head per foot length. Where the discharge is free, 
 
 S= total head per foot length, and the coefficient of velocity, 
 
 g 
 m -. As H or S is always directly proportional to v 8 
 
 (v 8 2gH) it follows that if S be increased in any given di- 
 ameter or hydraulic radius, v 8 will also increase at the same 
 
 o 
 rate, and hence m= -will necessarily be a constant in any 
 
 given hydraulic radius regardless of the value of the slope or 
 velocity. If it be admitted that the fundamental laws of 
 gravity, V 8 =2 g H, and V=-j/ 2g H are correct, and that 
 the frictional resistances on any given surface will increase 
 as v a , it must also be admitted that the ratio (m) of S tn v 8 is 
 always constant after equilibrium is attained, and that as a 
 necessary result, the head, slope or velocity can have no pos- 
 sible effect upon the value of the coefficient of velocity. 
 
 6. The Law of Variation of CoefficientsThe coefficient 
 of resistance n, and the coefficient of velocity m, have so far 
 been considered only as applied to a constant hydraulic rad- 
 ius or constant diameter, and it has been shown that in no 
 possible case can the slope or velocity affect the value of the 
 coefficients in any diameter or hydraulic radius. The effect of 
 variation of hydraulic radius or of diameter, upon the value 
 of the coefficient will next be investigated. 
 
 As the area in any given open channel varies with r 8 and 
 in any given circular closed channel or pipe as r s or d 8 , and 
 as the wet perimeter or friction surface in any shape of pipe 
 or open channel varies as r, d or p, it follows that the friction 
 surface p (which is as r or d) must vary in any given case as 
 I/!L Area is as d 8 or r 8 . Consequently / a is as d or r. 
 The total resistance will be directly as the total friction sur- 
 face which is as d, r or ^^7 The total area or free flow in any 
 given case varies with d 8 orr 8 . As area gains over wet peri- 
 meter a greater number of particles of water are set free from 
 the resistance of the perimeter, or acquire a head equal to th e
 
 40 SULLIVAN'S NEW HYDRAULICS. 
 
 elope of the channel or water surface. This does not increase 
 the head of the particles already free of resistance, but simply 
 adds to their number. The number of these unresisted parti" 
 cles will increase directly as the area, or as d 8 or r s . Total 
 acceleration will increase as the square root of the net free 
 head or free flow, which is therefore as d or r. Total retard- 
 ation will be as the square root of the total head lost by re- 
 sistance. The head lost by resistance will be directly as the 
 amount of friction surface, which is as d or r, but the total 
 retardation or loss of acceleration due to this loss of head, 
 will be as the square root of the head lost, or as ^"d" r i/~rT 
 Then total acceleration ie directly proportional to the 
 square root of the area or net free head, or to d or r, or y&. 
 Total retardation or loss of velocity is directly proportional 
 to the square root of the loss of head, or to ^ d or ^/ r 4 y a. 
 It follows therefore that the mean loss of head, or mean re- 
 sistance, of all'the particles of the cross-section taken as a 
 whole, will be as the total acceleration modified by the total 
 retardation, or the mean loss of head wi'l be inversely as 
 d /~d~ or V T~= /"r 5 ^ or i/~&*. 
 
 The mean loss of head will be inversely as \/~r* or 
 because the acceleration increases as i/ a or d or r while re- 
 tardation is only as -j/ d or i/ r, or 4 j/ a. If the value of 
 the coefficient of resistance n be found for any degree of 
 roughness when d or r=l, then it will vary from this unit 
 point inversely as -/ r 8 or -/ d 3 , and the general formula for 
 the value of the coefficient becomes, n=___Xi/ d 3 , or n = 
 
 These expressions are equivalent to n= r ^ r ' or 
 
 n _h"d 1 /~d" 
 
 Z v* 
 It is apparent that the coefficient of resistance or friction
 
 SULLIVAN'S NEW HYDRAULICS, 41 
 
 n, will vary for any given degree of roughness, only with the 
 variation in the value of -^ cl^or/ ~r". For the same de- 
 gree of roughness, no other factor will affect its value in any 
 manner. 
 
 Now as the mean loss of head is inversely as ^/ d 8 or 
 I/ r 8 the mean gain in head of the entire cross section taken 
 as a whole, will be directly as ^/ d 8 " or -/ T 8 ^ The mean veloc- 
 ity of the entire cross section, or the gain in the mean veloc- 
 ity, will be directly proportional to the square root of the net 
 mean head, or to the square root of the gain in the net mean 
 
 I y-^ 
 
 head,or-yf " 
 
 The friction head h"is therefore inversely as i/r~*~OT v/lT 8 " 
 
 The velocity head is directly as v/T 1 or ,/~d. 
 
 The velocity of flow is directly as f/'d 8 " or f/T 8 ". It 
 is understood that in these cases the elope remains constant. 
 
 The coefficient of velocity, m, if determined for any given 
 degree of roughness when d or r = 1, will therefore vary 
 from this unit point directly as v /~r^~ or i/~d*. 
 
 (9) 
 
 n=J 7^=^ X ' /dl U0) 
 
 ^^-^X^ <> 
 
 ci 
 
 (12) 
 
 _ 
 
 AB these coefficients for any given degree of roughness 
 vary only with ^"d 8 or v/T^.the value of d or r may be in 
 
 Q 
 
 inches or feet, while the constant g- may remain in feet 
 in either case, or all the values may be expressed in metres.
 
 42 SULLIVAN'S NEW HYDRAULICS, 
 
 The value of any given constant slope is made more effec- 
 tive directly as v/r~ increases, because the mean gain in 
 head increases directly as ,/ r 3 or the number of unre- 
 sisted particles increases as v/T^T The mean head and mean 
 
 velocity both gain without a change in slope. This does not 
 
 o 
 
 affect the constant ratio g because as S is made more effec- 
 tive by an increase in ^/ r 3 , v 2 increases in the same 
 ratio. 
 
 7. Formula for Mean Velocity Ry transposition in 
 equation (11) we have 
 
 V H x-V/= V m -c 18 ) 
 
 But for each given degree of roughness of friction sur- 
 face m is a constant equal to the ratio-^j, and varies only as 
 l/r 8 . Hence we may take the square root of the reciprocal 
 
 /J_ / v8 
 and write>-\/ m = \8./^i~ whence 
 
 73 (14) 
 
 In this case C is a constant which applies to all pipes or open 
 channels of the given degrees of roughness represented by C. 
 
 V 8 
 
 In other words C represents -^-g-which is constant for any 
 
 given roughness and only varies with 4 ;/r 3 . If we replace C 
 by K in equation (14) and reduce the formula to the Chezy 
 form, that is, if we write 
 
 v=C v /rsT (15) 
 
 then, C=K 4 i/r , which, when multiplied by y^rs equals 
 C Vr T ~ 1 /S7~In the Chezy form it is seen that C=K Vr~I 
 or in other words, that for any given degree of roughness of 
 friction surface represented by K, the coefficient C will vary 
 only as 4 ^/r .
 
 SULLIVAN'S NEW HYDRAULICS. 43 
 
 If we write simply. v=CVS, then C=K 4 1 /r. 
 
 The result is the same in either case. 
 
 The value of C in any formula in the Chezy form must 
 yary only as the roughness and as J/r or $/d. 
 
 If a series of pipes or open channels of equal roughness 
 be selected, it will be found that C: C: : /r~: e/r~regardless 
 of the slopes or dimensions of the channels. If C fails to vary 
 only as J/r in the Chezy form of formula for a series of chan- 
 nels of equal roughness, then it will be found that C y/rs will 
 not equal v. This will be illustrated by the following pairs 
 of open channels each pair being nearly equal in roughness, 
 but varying in the values of the slope and hydraulic radius. 
 
 8. Variation of C Illustrated In the following tables 
 we shall give the values of our C as found by the formula 
 
 C=-l => for each channel. We will also give the value 
 
 of the Chezy C for each channel which is required to make 
 C v/rs=v. It will be found in each case that barring the 
 slight difference in the degree of roughness in each pair of 
 channels the Chezy C which will cause C ^/rs to equal v, 
 will vary only as J/r , and their values in such class of chan- 
 nels may be found or compared by the simple proportion 
 C : C :: t/F~: J/rT The values of the Chezy C were deter- 
 mined by the formula, C= in all the following tables' 
 
 V rs 
 
 The values as given in the translation of Ganguillet and Kut- 
 ter are only approximate, being sometimes in error by as 
 much as 12 or 15. The values of Kutter's n, or constant co- 
 efficient of roughness, are also given for each channel. These 
 values of n are transcribed from Hering & Trautwines Trans- 
 lation, second edition. These values of n show that it is not 
 a constant, but is an auxiliary quantity which must be used 
 as r and s vary in order to balance the erroneous variation of 
 C with the slope.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 Pair No. 1. Slopes equal. Radii vary slightly. R> 1 
 meter. 
 
 NAME OF 
 CHANNEL 
 
 R 
 
 FEET 
 
 f/R~ 
 
 FEET 
 
 S 
 SLOPE 
 
 V 
 FEET 
 SEC. 
 
 SULLI- 
 VAN'S 
 
 c 
 
 KUT- 
 
 TER'S 
 n 
 
 CHEZY 
 C 
 
 Seine 
 (PariB) 
 Seine 
 (Paris) 
 
 9.50 
 10.90 
 
 1.7556 
 1.8170 
 
 .00014 
 
 .00014 
 
 3.37 
 3.741 
 
 52.85 
 52.71 
 
 .0240 
 .0238 
 
 92.40 
 95.77 
 
 The channel where R=10.9G is very slightly rougher, as 
 sbown by Sullivan's C, than the firet channel. *As the slopes 
 are equal, Kutter's n has to vary only with the slight differ- 
 ence in values of r,J order that c ^/rs" will equal v, and in 
 order that c: c: : /~r~: $/r~. 
 
 Pair No. 2. Slopes nearly equal. Small difference in R. 
 R > 1 meter. 
 
 NAME OF 
 CHANNEL 
 
 R 
 
 FEET 
 
 t/R 
 
 FEET 
 
 S 
 
 SLOPE 
 
 V 
 
 FEET 
 SEC. 
 
 SULLI 
 
 VAN'S 
 C 
 
 KUT- 
 TER'S 
 n 
 
 CHEZY 
 
 C 
 
 Seine 
 (Triel) 
 Seine 
 (Poissy) 
 
 12.40 
 15.90 
 
 1.876 
 2.000 
 
 .00060 
 .00062 
 
 2.359 
 2.911 
 
 46.12 
 46.43 
 
 .0295 
 .0285 
 
 86.43 
 92.70 
 
 The Chezy Ovaries only as /r in Pair 2. It is not af- 
 fected by the slight difference in elope. Where R=15.90 the 
 channel is very slightly smoother than where R=12.40. Yet 
 Kutter's n must be reduced because of the slight increase of 
 slope and hydraulic radius. As Kutter's C will increase with 
 decrease in elope where R is greater than 1 meter, or 3281 
 feet, n must be increased where R=12.40 because this slope is 
 least, and if n were taken as a constant for both channels, it 
 would make C too great for the first channel. 
 
 Pair No 3. 
 equal nearly. 
 
 R > 1 meter. Rand S vary. Roughness 
 
 NAME OF 
 CHANNEL 
 
 R 
 
 FEET 
 
 FEET 
 
 S 
 SLOPE 
 
 V 
 FEET 
 SEC. 
 
 SULLI- 
 VAN'S 
 C 
 
 KUT- 
 TER'S 
 
 n 
 
 CHEZY 
 C 
 
 La 
 Fourche 
 
 15.70 
 
 1988 
 
 .0000438 
 
 2.798 
 
 53.40 
 
 .0205 
 
 106.30 
 
 Mississip- 
 pi Rmr 
 
 72.00 
 
 2.913 
 
 .0000205 
 
 5.929 
 
 53.00 
 
 .0277 
 
 154.30
 
 SULLIVAN'S NEW HYDRAULICS. 45 
 
 Note the difference in value of Kutter'e n for these two 
 channels of equal roughness. 
 
 In Pair No. 3 R is greater than one meter, and in this 
 case Kutter's C will increase as slope decreases. As the 
 slope of the Mississippi river is much less than that of 
 Bayou La Fourche, if n were used as a constant for both, the 
 value of Kutter's C would- be greatly too large for the Mis- 
 sissippi. Therefore, in order to balance the error of increase 
 in Kutter's C with decrease in slope, the value of n must be 
 increased in proportion as slope decreases. Otherwise his 
 GI/ rs will not equal v. It is seen from Pair No. 3 that when 
 the required value of the Chezy or Kutter C is obtained 
 which will make C v /~re~=\, then C:C: : V~T : V~, re- 
 gardless of the difference in slope. Kutter admits, in his 
 work on Hydraulics (pages 99 and 132) that n is not a con- 
 stant for the same degree of roughness if there is much vari- 
 ation in the dimensions of the channels to which it is applied. 
 His n might be made a constant like our C for each degree 
 of roughness, and regardless of the dimensions of the chan- 
 nels, if it were made to vary only as J/TT, for all slopes and 
 all dimensions of channels, whether R were greater or less 
 than one meter. It is absurd that C, and consequently the 
 velocity, should be proportionately less for a steep slope in a 
 large channel than for a small slope. Of course the value of 
 I/ S remains in any case, but decrease in C as S increases in 
 large channels amounts to reducing the actual value of S by 
 the amount that C is there made to decrease. It cannot be 
 justified upon any sound theory, and the above tables show 
 that it is not sustained by fact. It is equally erroneous that 
 C will increase with an increase in slope in small chan- 
 nels where R is less than one meter, and in which the 
 ratio of friction surface to the quantity of water passed 
 is much greater than in large channels. The laws of grav- 
 ity and of friction do not reverse themselves at the point 
 where R=l meter, nor at any other value of R. As Kut- 
 ter's n is not a constant for the same degree of roughness 
 where the slopes vary or where R varies, it is very mislead-
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 ing when viewed as an index of roughness, which is sup- 
 posed to be its special function. 
 Pair No. 4. R< 1 Meter. Roughness Equal. R and S Vary 
 
 Name of 
 
 R 
 
 VK~ 
 
 S 
 
 v 
 
 Sulli 
 
 Kut- 
 
 Chezy 
 
 Channel 
 
 Feet 
 
 Feet 
 
 Slope 
 
 Ft Sec 
 
 van's C 
 
 ter's n 
 
 C 
 
 Rhine Forest 
 
 0.42 
 
 .8051 
 
 .0142 
 
 2.332 
 
 37.50 
 
 .0337 
 
 30.13 
 
 Simme 
 
 
 
 
 
 
 
 
 Canal 
 
 1.32 
 
 1.072 
 
 .0170 
 
 5.993 
 
 37.37 
 
 .0361 
 
 40.06 
 
 In Pair No. 4, R is lesa than one meter in either channel. 
 For this reason Kutter's C will increase with increase of 
 slope. Hence the steeper the slope becomes where R is less 
 than one meter, the greater we must increase the value of 
 his n in order to cut down this unnatural increase in C. We 
 find by simple proportion in Pair No. 4. as in all other cases 
 where the roughness is equal, that C:C: : *|/r:*- l /r, simply, 
 and regardless of difference in slope. Kutter's n must be 
 trimmed or increased in such manner as to cause C to vary 
 only as *y'r, otherwise his C^/rs will not equal v. It is there- 
 fore neither a constant nor an index of roughness, but is an 
 uncertain and misleading quantity. See Kutter'e discussion 
 of the variation of his n at pages 99, 110 and 132 of Hering 
 and Trautwine's edition of Kutter'e work. Also see Trans- 
 lators preface. 
 Pair No. 5. R and S vary. Roughness Equal. 
 
 Name of 
 Channel 
 
 R 
 
 Feet 
 
 t/r 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Ft Sec 
 
 Sulli- 
 van's C 
 
 Kut- 
 ter's r 
 
 Chezy 
 C 
 
 Grosbois Ca- 
 nal 
 Seine (Paris) 
 
 1.71 
 14.50 
 
 1.143 
 1.951 
 
 .000441 
 .00014 
 
 1.51 
 4.232 
 
 48.08 
 48.12 
 
 .0284 
 .0255 
 
 55.50 
 93.92 
 
 In Pair No. 5, the value of R is less than 1 meter in one 
 case, and greater in the other, and there is a difference in 
 slope also. Notwithstanding both these facts, C must vary 
 only as 4 |/r as shown in the table, or C^/rs will not equal v. 
 
 Sullivan's C in all the above tables is C=A/-; =^; and ap-
 
 SULLIVAN'S NEW HYDRAULICS. 47 
 
 plies in the formula, v=C$/r*~ ^ST" Its unit value is con- 
 stant for all slopes and all dimensions of pipes or open 
 channels of the same degree of roughness. It is 
 simply the square root of the reciprocal of m. It 
 has been shown that slope or velocity cannot affect the value 
 
 Q 
 
 of m, as it is the expression of the ratio-^j I tB numer- 
 ical value depends only upon the degree of roughness of peri- 
 meter. The formula for m or n or C as heretofore given, will 
 give the unit value of the coefficient directly, that is, its value 
 for r or d=l. It therefore does not matter whether the for- 
 mula for ascertaining the coefficient is applied to the data of 
 a very small or very large channel, the result will be the value 
 of the coefficient for r=l, or d=l, as the case may be. From 
 this unit point the coefficient varies with the inverse value 
 of i/ r 8 or y' d 8 if it is n that is sought. The coefficient m 
 of velocity, varies from the unit value as found by formula 
 
 form, directly as i/~d*or l /~r^. The variation of C will be 
 as the {/T~if the formula is written v=C 1 /~r6, or if it 
 written v=C X V~ i/~rs. If we write v=C ,/S" then C 
 must vary as f/r 3 . This latter form is equivalent to the 
 form v=C X V~** /~S. in which C is the constant for any 
 given degree of roughness of perimeter. This last form has 
 been adopted in all the foregoing and following tables. For 
 the reason that m or C, as found by formula from the data 
 of guagings will be the unit value, and will differ in value 
 only as the degree of roughness differs, the mere develop- 
 ment of the unit values of the coefficient for a series of pipes 
 or open channels will at once classify such pipes or chan- 
 nels, and exhibit their relative degrees of roughness. Those 
 which give like values of the coefficient are of similar degrees 
 of roughness, because the unit value of the coefficient is not 
 affected by any element or factor except the degree of rough- 
 ness. 
 
 The coefficient C or m does not, and should not, vary, ex-
 
 48 SULLIVAN'S NEW HYDRAULICS. 
 
 cept as the roughness of perimeter varies. For this reason 
 our in or G is an absolute index of the roughness for it cannot 
 vary with any other factor. We have shown that the effect- 
 ive value of the slope S is increased as -^ r 3 increases, because 
 the net meau head, or net gain in area over friction surface 
 is as >/ r 3 . But whatever increases or makes the mean head, 
 or S, more effective, must alao increase the value of v* in the 
 same ratio. 
 
 The effective slope S, is as S i/T 5 " , and the mean veloc- 
 
 ity is as,. /S i/ r 3 . Now in the formula for m or C. m= - ^ 
 and C= | Y . In either formula an increase in the value 
 
 = | Y 
 
 ^S/r 3 
 
 r 3 will cause the value of v 8 to increase in the same 
 ratio. It is then apparent that where the values of Sv/T 3 " are 
 equal, the velocities must be equal unless the resistances 
 caused by roughness of perimeter are greater in the one case 
 than in the other. It is also apparent from an inspection of 
 the formula for m or G that as v s will increase in the same 
 ratio as Sv/~r*" increases, m or C will be constant for all val- 
 ues of r or d if the roughness of perimeters is the same. 
 
 In the velocity formula, v=CV~r T Xv/~ST we see that the 
 mean velocity increases not only as ,/ S but also as the 
 square root ot ^/ r 3 , which is $/ r 3 , not because m or C var- 
 ies, but because the value of S is made more effective as v/~r^ 
 increases. 
 
 9. Practical Determination of Coefficients of Resistance. 
 
 The resistance to flow, or loss of head by friction, is exactly 
 equal to the amount of head, pressure, or force required to 
 balance it. In a pipe of uniform diameter and roughness the 
 friction will be the same in one foot length of pipe as in any 
 other foot length, hence the total friction will be directly as 
 the length and roughness of the pipe. Friction in any given 
 diameter and roughness of pipe will increase with the square
 
 SULLIVAN'S NEW HYDRAULICS. 49 
 
 of the velocity. Hence the head lost by friction, or the head 
 which is consumed in balancing friction, must also increase 
 as the square of the velocity. The friction or loss of head for 
 any given velocity in different diameters will be inversely as 
 y' d 8 or v/r 8 , because total acceleration is proportional to 
 the square root of the area, or to d or r, while total retarda- 
 tion is proportional only to j/cf or i/F". Hence the mean loss 
 of head of all the particles of water will be inversely propor- 
 tional to the resultant of total acceleration and total retarda- 
 tion, or to dy/ d = i/d 8 , or r i/ r = i/r 8 - (See columns 
 headed d.y/d, and "Relation of P to A," in table of circles, 
 ante, 3). 
 
 The mean of many experiments shows that a cast iron 
 pipe of ordinary density or specific gravity, one foot in diam- 
 eter and clean, will require a total head of one foot in a length 
 of 2,500 feet, in order to cause it to generate a velocity of one 
 foot per second. The discharge being free, it is evident that 
 the total head of one foot has been lost by resistance except 
 that part of the one foot head which remained to generate 
 the mean velocity of one foot per second. As the velocity 
 head is not lost by resistance, and as we wish to determine 
 the numerical value of the coefficient of resistance n, the ve- 
 locity head must be deducted from the total head of one foot 
 in order to find the total head lost by friction. By the law of 
 gravity we find that the head which generates any given ve- 
 
 In the case we are now considering v ff =l, and conse- 
 
 100 
 quentlv the velocity head hv=-gj^=.01552795 feet. Deduct- 
 
 ing this velocity head, which was not lost, from the total 
 head of one foot, and we find that the total head lost by fric- 
 tion in the 2,500 feet of 12-inch pipe while v*=l was equal to 
 1.00 .01552795=.98447205 feet. Therefore the head lost per 
 
 .98447205 
 foot length of pipe while v j =l, and d=l, was 2500 
 
 753
 
 50 SULLIVAN'S NEW HYDRAULICS. 
 
 =.00039379 feet=n. As the friction will be as the number 
 of feet length of the constant diameter, and will increase as 
 V T , then, as long as d remains constant, the total head in feet 
 lost by friction, h"=n X I Xv 8 . But if the value of d 
 changes, or the formula is to be applied to a pipe of like 
 roughness, but of a different diameter, we have seen that 
 the friction will be inversely as ^/ d 3 . Henee the general 
 formula which will apply equally to all diameters of this 
 given degree of roughness will be 
 
 n * y8 
 
 v/d 3 )/ d 8 
 
 We might have found the value of n directly by applying 
 formula (10) ( 6). 
 
 Xv/^ F =mX-9845 (10) 
 
 v 2 
 
 Q // 
 
 As the ratio otj is always constant for any given de- 
 gree of roughness, regardless of slope or velocity, and as it 
 varies from the unit point, or d=l, and v*=l, only 
 as v/cl 1 varies, we may find the unit value of the co- 
 efficient from any diameter and velocity whatever. 
 
 S" 
 It is simply necessary to find the ratio-^ in any 
 
 case, and when the value of-|j is multiplied by l /~d f , the re- 
 sult will be the unit value of n. When this unit value of n 
 is inserted in formula (16) it is made to vary inversely as ^/ d* 
 as exhibited in formula (16). To make it appear more clearly 
 we write 
 
 n 
 
 It consequently does not matter what head, diameter or 
 velocity we may select for the purpose of finding the unit
 
 SULLIVAN'S NEW HYDRAULICS. 51 
 
 value of n. The formula for n will always give the unit 
 value, regardless of the size of the pipe to which the for- 
 mula is applied. As the unit value of n is not affected by 
 any factor except the degree of roughness, it is a faithful in- 
 dex of roughness, and when the value of n for a series of dif- 
 ferent classes of perimeter has been found, it exhibits the 
 direct difference in roughness per unit of perimeter, between 
 the different classes. 
 
 10. Conversion of the Coefficient. The coefficient 
 may be determined in terms of diameter in feet, or diameter 
 in inches, or in terms of r instead of d, or in terms of cubic 
 feet or gallons. If the value of n has been found for any 
 given degree of roughness, it may be converted to any de- 
 sired terms. Thus, if the value of n has been found in terms 
 of d in feet, as above, it may, be converted to terms of r in 
 feet by simply multiplying it by 0.125 or dividing by eight. 
 If n was originally found in terms of r, and it is desired to 
 convert it to terms of d in feet, multiply by eight. If n is in 
 terms of d in feet, it may be converted to terms of d in inches 
 by multiplying by v /(r2) ff =41.5692. ^s n, for any given de- 
 gree of roughness, varies only with ^/"d^ the value of d may 
 be in meters, inches or feet, as may be most convenient, h", 
 I and v* may remain in feet or meters. 
 
 m=-;and n = mX-9845, for any given degree of rough- 
 
 //. Determination of Coefficients of Velocity. We have 
 just seen that a coefficient of resistance (n) represents only 
 the head per foot length of pipe which is lost or consumed in 
 balancing the resistance to flow. A coefficient of velocity, 
 however, must represent not only the head per foot length 
 required to balance the resistance, but also the head per 
 foot length required to generate the velocity of flow, or it 
 must represent S"-|-Sv in any case. If the diameter or 
 hydraulic radius is constant, and the discharge is free and 
 full bore, the total head per foot length S, will be converted
 
 52 SULLIVAN'S NEW HYDRAULICS. 
 
 into velocity of flow except that part of S which is consumed 
 in balancing friction. In this case, S"+Sv=S, and S must 
 be used in the formula for determining the value of m the 
 coefficient of velocity. Where the discharge is partially 
 throttled, as by a reducer at discharge, or by a valve partly 
 closed, only a part of the total head per foot length will be 
 consumed by resistances and in generating velocity, and the 
 remainder of the head will remain as radial pressure within 
 the pipe. As the head due to this pressure is neither lost 
 by resistance nor engaged in generating velocity of flow, it 
 has no connection with the value of the coefficient of velocity 
 m. If the discharge is free, then 
 
 H v/r S S,/r n 
 
 m= ^s ^iXv/r= -^I-=;9845 < 17 > 
 If the discharge is throttled, then 
 
 For the ordinary cast iron pipe described in section 9, 
 the coefficient of velocity would be 
 
 -WM.m terms of d in feet. 
 
 The coefficient m may be converted to terms of d in 
 inches, or r in feet or to any other terms in the same manner, 
 and by the use of the same multipliers, as n may be con- 
 verted. (See 10) 
 
 The velocity coefficient m applies to open or closed chan- 
 nels alike and its unit value depends only on the degree of 
 roughness of perimeter. The value of m as found by the form- 
 ula is always the unit value, and is equally as accurate an 
 index of roughness as is the coefficient n. The remarks in 
 regard to n in this respect ( 9)apply to m with equal force. 
 
 The coefficient m is to be used in the formula, 
 
 4
 
 SULLIVAN'S NEW HYDRAULICS. 53 
 
 If m was determined in terms of r, it must not be used 
 in formula (20) which is in terms of d, until it has been con- 
 verted to like terms with those in the formula. If m is in 
 terms of d in inches, then d in the formula must also be in 
 inches. In other words m must be in the bame terms as the 
 formula in which it is used is expressed. 
 
 The value of m in terms of d in feet for average cast iron 
 pipe is m=.0004. If it is desired to use C instead of m then 
 
 = 50.00 and 
 
 The value of C may be found directly and without refer- 
 ence to m by the formula 
 
 0=4 
 
 or C = 
 
 '8,/r* 
 
 This will give the unit value of C directly, and C is a 
 constant like m or n, which depends on the roughness of 
 perimeter. 
 
 If we have m=.0004 for ordinary cast iron pipe, in terms 
 of diameter in feet, we may convert it to terms of r in feet by 
 
 0004 
 simply dividing by 8. We then have -^ = .00005 = m in 
 
 terms of r in feet. We may convert m to C in terms of r in 
 feet by taking the square root of its reciprocal in terms of r, 
 and we have 
 
 v/20000 = 141.42 = C in terms of r. 
 
 Then, v = C {/r^ ,/S. 
 
 The unit values of n, m and C may be found in all classes 
 of pipes and channels, and may be converted at pleasure as 
 shown. The law governing the flow of water and the value 
 and variation of the coefficients, is exactly the same in open
 
 54 SULLIVAN'S NEW HYDRAULICS, 
 
 channels as in pipes. The same formulas apply to all equally 
 well BO far as the coefficients and the formulas for flow are 
 concerned. Of course the unit value of the coefficient must 
 be found experimentally for each class or degree of Toughness 
 of friction surface. When the unit value of the coefficient is 
 determined for any given degree of roughness, it then applies 
 to all forms and dimensions of pipes and channels which fall 
 within that degree of roughness. These remarks apply to n, 
 m and C alike. The roughness or smoothness of perimeter 
 affects the flow in a large river in the same manner as in a 
 email canal. In a large, deep river the area of the cross- 
 section of the column of water is greater in proportion to the 
 wet perimeter than in a small stream, and hence the ratio of 
 free particles of water is greater than in small channels, but 
 the effect of roughness of perimeter is the same in both cases. 
 The unit value of m and C distinctly establish these facts. 
 It is the influence of the great values of r in large rivers that 
 has led some hydraulicians to conclude that the character of 
 the perimeter does not materially affect the flow in such 
 streams. 
 
 12. Coefficients Affected by Specific Gravity, or Den- 
 sity of Material. In a series of experiments with new, clean 
 cast iron pipes the writer was perplexed by the fact that one 
 12 inch new, clean pipe would not generate the same mean 
 velocity as another new, clean 12 inch pipe, when the con- 
 ditions were exactly the same in each case. The difference 
 was so great in the case of one pair of 12 inch new pipes, 
 that the experiment was repeated a number of times, but 
 always with the same result. As no other explanation could 
 be given the writer concluded to ascertain if it was caused by 
 the difference in density or specific gravity of the two pipes, 
 which were from different foundries. The shells were of 
 equal thickness, but on weighing a few lengths of the pipe 
 from each lot, it was found that the pipe which generated 
 the least velocity was much lighter than the other. The 
 investigation thus begun led to experiments with pipes of 
 different metals and different specific gravities. The results
 
 SULLIVAN'S NEW HYDRAULICS, 55 
 
 then obtained seem to confirm the correctness of the view 
 that the density of the friction surface has a marked influ- 
 ence upon the flow and upon the value of the coefficient. 
 There may be some difference also between the values of the 
 coefficient for a surface of granular metal and a surface cf 
 fibrous metal, although the specific gravities of the two 
 metals may be equal. It appears that the flow over earthen 
 perimeters of equal regularity of cross-section will be affected 
 by the nature and specific gravity of the particular kind of 
 earth. The flow in a cement lined pipe or channel which is 
 clean and free of fine silt, will be affected by the fineness of the 
 cement and also of the sand used, as well as by the propor- 
 tion of sand to cement in the mortar lining. Even in pure 
 cement linings, it is noticed that the flow will be affected by 
 the quality and fineness of the cement used. Classification of 
 perimeters is therefore difficult. 
 
 It is stated by Professor Merriman that "it is proved by 
 actual gaugings that a pipe 10,000 feet long and one foot in 
 diameter discharges about 4.25 cubic feet per second under 
 a head of 100 feet. The mean velocity then is 
 
 v= -=5.41 feet per second." ("Treatise on hy- 
 
 draulics." page 165, fifth edition.) It will be noted that the 
 character of the pipe, whether cast iron, wrought iron, riveted 
 or welded, coated or uncoated, is not mentioned. It was 
 certainly a remarkably smooth pipe. If the value of the co- 
 efficient m is developed for this pipe we shall have 
 
 m= -Xv/ d 3 =.00034165, in terms of d in feet. 
 
 m= ^-Xi/ r=.00004270625, in terms of r in feet. 
 
 The average value of m for clean cast iron pipe is 
 
 m=.01662768, in term of d in inches. 
 
 m=.000i in terms of d in feet. 
 
 m=.00005 in terms of r in feet. 
 The writer made a numberof experiments with 6", 12'
 
 56 SULLIVAN'S NEW HYDRAULICS. 
 
 and 24" cast iron pipes which were new and absolutely clean 
 and of the greatest density that the writer has ever dis- 
 covered before or since in cast iron pipes. The water was 
 pure mountain water from the melting snow on the granite 
 hills. The pipes were laid straight and perfectly jointed, 
 and the discharge was perfectly free, into a large measuring 
 tank. Under these perfect experimental conditions, the value 
 of m as developed by the three pipes was 
 m=. 000368 in terms of d in feet. 
 m=.000046 in terms of r in feet. 
 
 Such favorable conditions as these scarcely ever occur in 
 actual water works building, and do not continue if they 
 originally exist. 
 
 In later experiments with new clean cast iron pipes of in- 
 ferior quality and very low specific gravity, the values of the 
 coefficient of flow developed were 
 
 m=.01721 in terms of d in inches: C=7.622. 
 
 m=.000414 in terms of d in feet: C=49.14. 
 
 New, clean cast iron pipe of average weight per cubic 
 unit as long as it remains clean gives, 
 
 m=.01663 in terms of d in inches: C=7 .755. 
 
 m=.0004 in terms of d in feet: C=50.00. 
 
 m=.00005 in terms of r in feet: C=141.42. 
 
 It is therefore evident that where the pipes are made of 
 the same class of metal and are new and clean, the value of 
 the coefficient will bear a close relation to the specific grav- 
 ity, or density, of the pipe metal. The fact that clean leaden 
 or brass pipe will generate a much greater velocity of flow 
 under the same conditions than will a clean iron pipe of 
 equal diameter can be accounted for in no othei manner than 
 the difference in specific gravity of the different metals. 
 
 These facts demonstrate the important influence of even 
 very small degrees of roughness of perimeter upon the flow 
 and consequently upon the value of the coefficients. Low 
 specific gravity in metal indicates that it is porous and its 
 surface is affected by innumerable small cavities, rendering it
 
 SULLIVAN'S NEW HYDRAULICS. 57 
 
 irregular. The specific gravity of cast iron varies from 6.90 
 to 7.50; of steel, from 7.70 to 7.90; of wrought iron from 7.60 
 to 7.90. 
 
 While the specific gravity of a metal, or of stone or brick, 
 01- earth where the cross section is equally uniform, undoubt- 
 edly affects the flow, yet other substances of much less spec- 
 ific gravity, when applied as a lining or coating, will greatly 
 increase the flow. Thus the specific gravity of asphaltum 
 varies from 1 to 1.80 according to its purity, and an asphaltum 
 coated pipe will generate a much higher velocity of flow than 
 a clean iron pipe. The coefficients developed by asphaltum 
 coated pipes, however, vary like cement lined pipes, with the 
 quality of the material, or the proportion of pure asphaltum 
 to the other ingredients u^ed in the manufacture of the coat- 
 ing comtound. It would appear therefore that while the 
 specific gravity of one metal may be compared with that of 
 another metal, or the specific gravity of one class of as- 
 phaltum coating compound may be compared with another, 
 as to its probable resistance to flow, we cannot compare ma- 
 terials of wholly different natures with each other, and judge 
 of the relative resistance by the respective densities. The 
 values of m for asphaltum coated double riveted wrought iron 
 pipe when new varies with quality of the coating as follows: 
 m=.000036 in terms of r in feet, to m=.000044. 
 m=.000288 in terms of d in feet, to m=. 000352. 
 
 The average value of m for such coating while in prime 
 condition may be taken as m=.00033, in terms of d in feet. 
 The average value of the coefficient of resistance in pipe thus 
 coated is about n=.000325 in terms of d in feet. The average 
 value of n for common cast iron pipe while clean is n=.0003938 
 in terms of d in feet. 
 
 Ordinary lead pipe gives m=.000135 in terms of d in feet, 
 or 0=86.07. In terms of r in feet, ordinary lead pipe gives 
 m=.000016875, or C=243.20. Lead pipe varies in specific grav- 
 ity, and the coefficient varies with the specific gravity. Very 
 dense, smooth lead pipe gives values of C in terms of r as high 
 as C=297.00 before the pipe becomes incrusted or scaled.
 
 58 SULLIVAN'S NEW HYDRAULICS 
 
 13 Value of C Where the Flow is in Contact with Dif- 
 ferent Classes of Perimeter at the Same Time. 
 
 The sides of a channel may be rough and covered with 
 vegetation while the bottom is smooth and clean. In such 
 case the value of C will decrease as depth of flow increases, 
 because of the gain in ratio of rough to smooth perimeter as 
 depth increases. On the contrary the bottom may be rough, 
 stony and irregular, while the sides are smooth, clean and 
 regular. In the latter case the value of C will increase as 
 depth of flow increases, because of the gain in ratio of smooth 
 to rough perimeter as depth of flow increases. In all such 
 cases it is necessary to arrive at the mean or the average 
 roughness of the combined classes of perimeter. If the flow 
 is two feet deep in a canal six feet wide on the bottom and 
 the sides are smooth and vertical, while the bottom is rough 
 and stony, let us suppose that the sides correspond with C 
 =60, and the bottom with C=30. Then we have the two 
 smooth sides equal 4 feet and the rough bottom equal 6 feet 
 and the whole perimeter equal 10 feet. 
 
 Then, l_=Smooth perimeter where C=60. 
 
 6 
 -TQ = rough uerimeter where C=30. 
 
 4X60 240 6X30 180 
 
 And ~io~ = lo = 24> ~io-=To~ =18 - And 24 
 
 +18= 42. 
 
 The value of C for this combination of perimeters would 
 be 42. 
 
 14. Tables of Coefficients. In the following tables 
 of coefficients as developed from the published data of exper- 
 iments, the groups are arranged with reference to smoothness 
 or roughness of wet perimeter. The remarks in regard to the 
 available data for this purpose, which were made in the in- 
 troductory to this volume, should not be forgotten. Only a 
 part of the available data have been used, and that was sim- 
 ply a choice between evils in many cases. The writer is in-
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 debted to Mr. Charles D. Smith, C. E., of Visalia, California, 
 for the data of the guagings by him of sixteen canals in the 
 vicinity of Visalia, California. It is believed that these data, 
 all of which are given the common name of "Visalia Canal," 
 are good and reliable. The writer is also indebted to Mr. J. 
 T. Fanning for a diagram of the results of experiments by 
 him on cast iron pipes of diameters ranging from 4 inches 
 to 96 inches, and exhibiting the average value of the coeffi- 
 cient in such pipes; and for guagings of the New Croton 
 aqueduct recently, made by Mr. Pteley, and for numerous 
 valuable suggestions. The writer is indebted to Mr. Otto 
 Von Geldern,C. E., of San Francisco, for the guagings of the 
 Sacramento river by C. E. Grunsky, C. E. 
 
 GROUP No. 1, STRAIGHT LEAD PIPE. (Rennie.) 
 
 L'GTH 
 
 DIAM. 
 
 S 
 
 V 
 
 COEFFICIENT 
 
 COEFFICIENT 
 
 yd' 
 
 FEET 
 
 FEET 
 
 SLOPE 
 
 FEET 
 
 m ^Xi/d 3 
 
 'c r* 
 
 FEET 
 
 
 
 
 
 
 ~V Sl/d3 
 
 
 "15:00 
 
 0.0417 
 
 .26666 
 
 5.00 
 
 .0000908 
 
 105.00 
 
 .008515 
 
 Straight lead pipe. (W. A. Provis.) 
 
 100.00 
 
 0.125 
 
 .02917 
 
 3.09 
 
 .0001350 
 
 86.07 
 
 .04119 
 
 80 00 
 
 125 
 
 .03646 
 
 H.396 
 
 .' 001397 
 
 81.60 
 
 0*419 
 
 60.00 
 
 0.125 
 
 .04861 
 
 3.903 
 
 .0001410 
 
 84.21 
 
 .04419 
 
 The coefficients for pipes are in terms of diameter in feet. 
 Straight Lead Pipe. (W. A. Provis.) 
 
 L'GTH 
 
 DIAM. 
 
 S 
 
 V 
 
 COEFFICIENT 
 
 COEFFICIENT 
 
 /d 8 
 
 FEET 
 
 FEET 
 
 SLOPE 
 
 FEET 
 
 S 
 
 i 
 
 FEET 
 
 
 
 
 SEC. 
 
 m = V ,XV d3 
 
 ' = ^S/d3 
 
 
 40. 
 20. 
 
 0.125 
 0.125 
 
 .07292 
 .14583 
 
 4.759 
 6.150 
 
 .0001422 
 .0001703 
 
 83. b6 
 76.55 
 
 .04419 
 .04419 
 
 REMARK. The coefficient m or C , includes all resistances 
 to flow, including the resistance to entry into the pipe. In 
 such very short pipes, where the velocity is considerable, the 
 effect of resistance to entry will materially affect the coeffi- 
 cient. For this reason a general pipe formula for ordinary 
 lengths of pipe will not apply with accuracy to short tubes 
 or very short pipes. A special formula for short pipes or 
 tubes should be applied in such cases. It is not known
 
 60 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 whether all the above lead pipes of different lengths were of 
 the same quality and in the same condition or not. It is 
 probable that they were, and that the decrease in length 
 of pipe and increase in velocity greatly affected the resist- 
 ance to entry. The resistance to entry of a pipe cut off 
 square and flush with the inner walls of the reservoir is al 
 ways equal to .505 of the head generating the velocity of 
 flow through such pipe. Hence in order to obtain the true 
 coefficient of flow due only to the resistance of the inner cir 
 cumference of the pipe, the entry head should first be de- 
 
 v 8 
 ducted. The entry head=-^-X-505. 
 
 The data of experiments on very short pipes are not re- 
 liable, and should never be relied upon. They have no appli- 
 cation to long pipes. 
 
 Lead Pipe (Iben) Example of erroneous data. 
 
 L'GTH 
 
 FEET 
 
 TOTAL 
 HEAD 
 FEET 
 
 DIAM. 
 FEET 
 
 !/d 
 
 FEET 
 
 AL- 
 LEGED 
 VELOC 
 ITIES 
 
 COEFFICIENT 
 
 s 
 m =VirXi/d3 
 
 COEFFICIENT 
 
 =A/ ~ 
 
 ^S/ d 8 
 
 350.30 
 350.30 
 
 17.71 
 122.01 
 
 0.082 
 0.082 
 
 .02384 
 .02384 
 
 2.70 
 9.11 
 
 .000162^4 
 .0001000447 
 
 78.36 
 99.97 
 
 REMARK Here are the alleged results of two experiments 
 on the same pipe the only difference in conditions being a 
 change of head. As the length, diameter and roughness 
 were absolutely the same in both cases, the only possible ef- 
 fect of varying the head would be that the velocity would 
 vary directly as the square root of the head varied, and 
 nothing else. 
 
 Where all the other conditions are constant,the velocity will 
 vary directly as the square root of the head > and the resist- 
 ance, or loss of head by friction, will vary directly as the 
 square of the velocity. If this is not true, then the law of 
 gravity and the law of friction as accepted by the scientists 
 are necessarily erroneous, and all scientific calculations based 
 upon those laws must fail. 
 
 In the first experiment with this pipe of constant length, 
 diameter and roughness, the head was 17.71 feet, and velocity 
 was 2.70 feet per second. As all conditions remained constant 
 except an increase in head, then by the law of gravity and of
 
 SULLIVAN'S NEW HYDRAULICS. 61 
 
 friction we would have 
 
 V/H : ^/H :: v : v; or 4.148 : 11.08 :: 2.70 : 721 
 In the last experiment, Iben makes v==9.11 instead of 
 7.21. 
 
 If the velocity was correct in the first experiment, or 
 v=2.70, then the head lost by friction for this velocity was 
 equal to the total head minus the head which remained to 
 generate the 2 70 feet velocity. The head required to generate 
 
 2.70 feet per second velocity was hv= V * = (2 70)2 =0.1132 ft. 
 
 64.4 64.4 
 
 The head lost by friction at this velocity was therefore 17.71 
 .1132=17.59 feet, and v s =7.29. Now, if the law of friction 
 is correct, to wit, that friction will increase in a constant di- 
 ameter and length as the square of the velocity, then the loss 
 of head in feet by friction in this pipe when the velocity in- 
 creased to 9 11 feet per second, would be 
 v 8 : v 8 ::head lost : head lost, or 
 7.29 : 83.00:: 17.59 : 211.00. 
 
 In other words in Iben's second experiment where the 
 total head was only 122.00 feet, he was able to lose 211.00 feet 
 by friction, and still have remaining 1.29 feet head to generate 
 the 9.11 feet per second velocity, which is alleged to have oc- 
 curred. It is conclusive that the laws of friction and of grav- 
 ity are absurd, or such data are in error. 
 
 All correct experimental data of flow for the same length, 
 diameter and roughness of pipe will necessarily develop the 
 
 same value of either of the coefficients, n, m or C, regardless 
 
 o 
 
 of all changes in head or velocity, because the ratio -^ is nec- 
 essarily constant in any given pipe. The foregoing illustra- 
 tration is given as a suggestion of a correct method of testing 
 the value of such published data of flow as are now available. 
 Most of such data are furnished by experiments of a century 
 or more ago, and have been translated from one language to 
 another and reduced from one system to another, and printed 
 and reprinted until the accumulated errors, added to the 
 original crude methods in vogue a century ago, render them
 
 62 SULLIVAN'S NEW HYDRAULICS. 
 
 of very uncertain value. The writer is aware that Panning 
 and other very eminent hydraulicians have been of opinion 
 that m will decrease or C increase with the velocity in a 
 constant diameter, but this theory is not sustained by the re- 
 sults of Fanning's experiments on a constant diameter (See 
 Group No. 4) nor by the results of experiments by the writer 
 (Group No. 3). That theory cannot be accepted without first 
 rejecting the law of gravity and of resistance as now generally 
 accepted. If C increases with an increased velocity in a con- 
 stant diameter, it is obvious that resistance does not increase 
 
 S 
 as rapidly as v 8 , and hence the ratioy would not be constant 
 
 but would vary with the velocity. If that is true, then v* = 
 2gH the fundamental law of gravity is necessarily untrue, 
 and all our learned discussions of equilibrium and of uniform 
 flow are mere theoretical myths and rubbish. Either that 
 theory or the law of gravity and resistance must be rejected, 
 for both cannot stand. The experimental data now available 
 afford as much evidence to sustain an opposite theory as to 
 sustain the above theory, and hence these opposite results 
 destroy both theories, and prove only the erroneousness of the 
 data. The evidence to sustain one theory destroys that which 
 sustains the opposite theory, and the laws of gravity and of 
 resistance positively refute both theories, and establish the 
 theory that m or C is constant for all velocities in a constant 
 diameter, except as slightly affected by the resistance to 
 entry into the pipe. If the entry to the pipe is in the form of 
 the vena contraota, then the velocity cannot affect the value 
 of C or m at all.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 63 
 
 GROUP No. 2. 
 Asphaltum Coated Pipe. 
 
 COATED PIPES. 
 [Hamilton Smith Jr.] 
 
 Lgth. 
 Feet 
 
 Diam. 
 Feet 
 
 v/d 3 
 Feet 
 
 S 
 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient. 
 S/d* 
 
 m y8 
 
 Coefficient 
 
 C P~ 
 A/S^/d 8 
 
 1200.00 
 
 2.154 
 
 3J61 
 
 .01641 
 
 12.605 
 
 .0003265 
 
 55.34 
 
 700.00 
 
 1.056 
 
 1.085 
 
 .00668 
 
 4.595 
 
 .0003432 
 
 54.00 
 
 700.00 
 
 1.056 
 
 1.085 
 
 .01428 
 
 6.962 
 
 .0003200 
 
 55.90 
 
 700.00 
 
 1.0b6 
 
 1.085 
 
 .02219 
 
 8.646 
 
 .0003220 
 
 55.73 
 
 700.00 
 
 1.056 
 
 1.085 
 
 .03319 
 
 10.706 
 
 .0003142 
 
 56.40 
 
 4440.00 
 
 1.416 
 
 1.685 
 
 .06672 
 
 20.143 
 
 .0002771 
 
 60.07 
 
 700.00 
 
 0.911 
 
 0.8695 
 
 .0085 
 
 4.712 
 
 .0003330 
 
 54.80 
 
 700.00 
 
 0.911 
 
 0.8695 
 
 .01334 
 
 6.094 
 
 .0003123 
 
 56.58 
 
 700.00 
 
 0.911 
 
 8695 
 
 .01695 
 
 6.927 
 
 .0003072 
 
 57.05 
 
 700.00 
 
 0.911 
 
 0.8695 
 
 .02559 
 
 8.659 
 
 .0003000 
 
 57.73 
 
 700.00 
 
 .230 
 
 1.364 
 
 .01097 
 
 6.841 
 
 .00032000 
 
 55.90 
 
 700.00 
 
 .230 
 
 1.364 
 
 .01227 
 
 7.314 
 
 .00031264 
 
 56.56 
 
 700.00 
 
 .230 
 
 1.364 
 
 .01646 
 
 8.462 
 
 .000313.^6 
 
 56.48 
 
 700.00 
 
 .230 
 
 1.364 
 
 .02470 
 
 10.593 
 
 .00030025 
 
 57.71 
 
 700.00 
 
 .230 
 
 1.364 
 
 .03231 
 
 12.090 
 
 .00030150 
 
 57.58 
 
 REMARK. The slight variation of C or m in the same 
 diameter and length is due to errors in weir or orifice coeffi- 
 cients used in determining the velocities. The above pipes 
 were double riveted lap seam wrought iron pipes put together 
 like stove-pipe joints. Some of the velocities were determin- 
 ed by weir and others by orifice measurement. The differ- 
 ence in value of C for different diameters is due to difference 
 in quality of the coating. (See 12). In applying the above 
 coefficients it should be remembered that these pipes were 
 new and laid straight, and had free discharge and high veloci- 
 ties which would prevent any deposit in them. The propor- 
 tion of asphaltum in the coating is not stated. This is im- 
 portant and should be known. 
 
 Cast Iron Asphaltum Coated Pipe. [Lampe]. 
 
 Legth 
 Feet. 
 
 Diam. 
 Feet 
 
 V/d 3 
 Feet 
 
 S 
 
 Slope. 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 S/d 3 
 
 Coefficient 
 
 r~v*~ 
 P. ./ v 
 
 - v * 
 
 "Vs^/d* 
 
 26,000 
 26,000 
 26000 
 26.000 
 
 1.373 
 1.373 
 1.373 
 1.373 
 
 1.609 
 1.609 
 1.609 
 1.609 
 
 .000594 
 .001376 
 .00163 
 .00195 
 
 1.577 
 2.479 
 2.709 
 3.090 
 
 .0003840 
 
 .(1003601) 
 
 .0003574 
 
 .0003300 
 
 51.03 
 52.69 
 52.91 
 55.04 
 
 REMARK. This pipe had been in use five years. Velocity 
 was judged of by reservoir contents and pressure guage. 
 The last coefficient is probably the true one. As the veloci- 
 ties tabled in the constant length and diameter do not cor- 
 respond with the slopes tabled, it is impossible to ascertain 
 whether either of the coefficients are correct or not. Only
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 one of them can be correct. The last one IB about the aver- 
 age value of the coefficient for such coated pipes. 
 Cast Iron Asphal turn Coated Pipe. [D'Arcyl. 
 
 L'gth. 
 Feet 
 
 Diam. 
 Feet 
 
 1/d* 
 Feet 
 
 S 
 
 Slope 
 
 V 
 
 Feet 
 Sec 
 
 Coefficient 
 Sv/d" 
 
 Coefficient 
 
 C= IVv* 
 
 V* 
 
 ^Sy^d 8 
 
 365.00 
 365.00 
 365.00 
 365.00 
 365.00 
 
 0.6168 
 0.6168 
 0.6168 
 0.6168 
 0.6168 
 
 0.4844 
 0.4844 
 0.4844 
 0.4844 
 0.4844 
 
 .00027 
 .00368 
 .02250 
 .10980 
 .14591 
 
 0.673 
 
 2.487 
 6.342 
 14.183 
 16.168 
 
 .00028SO 
 .0002882 
 .0002710 
 .0002644 
 .0002704 
 
 58.82 
 58.90 
 60.74 
 61.50 
 60.95 
 
 REMARK. Velocities determined by orifice. Variation 
 in C is due to error in orifice coefficients used. This pipe was 
 quite short, and must have had a remarkably smooth coating. 
 The coefficients developed by this pipe are too high for safe 
 use in ordinary practice. Lap welded wrought iron pipe in 
 long lengths with few joints, when coated with asphaltum 
 and oil, give C=60.00. It will be noted that D'Arcy's data 
 generally give the value of C too high. As would be expect- 
 ed from a series of experiments especially planned with ref- 
 erence to the most favorable conditions. 
 
 The weir and orifice coefficients should be standardized 
 in the same manner as m or C, so that a given form of weir 
 or orifice would have a unit coefficient which would vary 
 with i/r s for any dimensions of weir notch or orifice. The 
 results would then be uniform and correct. 
 
 Such weir formula might take the form, q=A ~5~-\/ 
 
 " * m 
 
 The value of m would depend upon the form of the weir 
 only, and would, apply to all dimensions of weirs of that 
 given form. Before this kind of a weir formula could be 
 successfully adopted, however, it would be necessary to so 
 construct the weir as to suppress all contraction of the dis- 
 charge, for the contraction seems to follow no law. (See 
 Apendix.) 
 
 The Loch Katrine Cast Iron Pipe . Coated with Dr. Smith's 
 Coal Pitch. [Gale]. 
 
 Lgth 
 
 3M 
 Miles 
 
 Diam. 
 
 Feet 
 
 /d 
 Feet 
 
 S 
 Slope 
 
 V 
 Feet 
 Sec. 
 
 Coefficient 
 ST/d 8 
 
 H):=: " 
 
 Coefficient 
 
 c \! v " 
 
 ^Sv/ds 
 
 33 m. 
 
 4.00 
 
 8.00 
 
 .000947 
 
 3.458 
 
 .0006344 
 
 39.70 
 
 This pipe probably had large deposits of gravel in it. It
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 was evidently very rough from some cause. We give its 
 coefficient here simply because this particular pipe has been 
 the subject of so much discussion. See Flynn'e "Flow of 
 Water," page 34, for remark of Rankine and Humber on this 
 pipe. 
 
 GROUP No. 3. 
 Clean cast iron pipes not coated. (See 12.) (Sullivan.) 
 
 L'gth 
 Feet 
 
 2,800 
 2,800 
 
 Diam. 
 Feet. 
 
 Feet 
 
 8 
 
 Slope 
 
 Feet 
 Sec. 
 
 1.648 
 2.771 
 
 3.296 
 5.540 
 
 Coefficient 
 
 Coefficient 
 
 52.08 
 52.11 
 52.10 
 52.11 
 52.11 
 
 REMARK. These experiments were the foundation of the 
 writer's formula. They were made with the greatest possible 
 care. The writer being aware that a weir or orifice coeffici- 
 ent determined by the use of one degree of convergence of the 
 edges of the plate would not apply to another degree of con- 
 vergence or divergence, and having discovered discrepancies 
 of several per cent, in velocities thus determined, 
 did not rely on such measurements in the above ex- 
 periments, but erected a large measuring tank into which 
 the pipe discharged. The velocities were then determined 
 
 by the formula v= cubic feet 8ecopd . The pipes were remark- 
 area in sq. feet 
 
 ably dense and smooth, and had never before been wet. 
 They were laid straight and perfectly jointed. In doubling 
 the diameters and increasing the head four times, as will be 
 observed in the above table, it was the purpose to test the 
 law of gravity as well as to test the effect upon the flow of 
 doubling the diameter while the head remained constant. 
 A study of the results thus obtained resulted in the form- 
 ula for flow herein presented. 
 
 It may be remarked here that the coefficients developed 
 by the experiments under these exceedingly favorable cir- 
 cumstances with absolutely clean, very dense, straight pipes, 
 are not to be relied on for average weight cast iron pipes laid 
 in the ordinary manner. For average weight new cast iron 
 pipe, as long as it remains clean, m=.0004, and C=50. 
 
 The nature of the water which flows in a pipe which is 
 not coated may materially roughen the walls and reduce the
 
 GO 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 value of the coefficient in a very short time. Allowance should 
 always be made for this deterioration by adopting diameters 
 amply large. 
 
 GROUP No. 4. 
 Cement mortar lined wrought iron pipes, (Fanning.) 
 
 L'gth 
 
 Diam- 
 
 yd 8 
 
 S 
 
 V 
 
 Coefficient 
 
 Coefficient 
 
 Feet 
 
 eter 
 Feet 
 
 Feet 
 
 Slope 
 
 Sec. 
 
 o~i/ d" 
 
 C / 
 
 v a 
 
 
 8171 00 
 
 1.667 
 
 2.153 
 
 .00044 
 
 1.488 
 
 .0004300 
 
 48.22 
 
 8171.00 
 
 1.667 
 
 2.153 
 
 .00073 
 
 1.925 
 
 .0004241 
 
 48.56 
 
 8171.00 
 
 1.667 
 
 2.153 
 
 .00104 
 
 2.329 
 
 .0004130 
 
 49 20 
 
 8171.00 
 
 1.667 
 
 2.153 
 
 .00134 
 
 2.598 
 
 .0004274 
 
 48.38 
 
 8171.00 
 
 1.667 
 
 2.153 
 
 .00158 
 
 2.867 
 
 .0004139 
 
 49.15 
 
 8171.00 
 
 1.667 
 
 2.153 
 
 .00199 
 
 3.271 
 
 .0004004 
 
 49 97 
 
 8171.00 
 
 1.667 
 
 2.153 
 
 .00228 
 
 3.439 
 
 .0004151 
 
 49.08 
 
 8171.00 
 
 1.667 
 
 2.153 
 
 .00272 
 
 3.741 
 
 .0004183 
 
 48.92 
 
 8171.00 
 
 1.667 
 
 2.153 
 
 .00300 
 
 3.920 
 
 .0004203 
 
 48.78 
 
 8171.00 
 
 1.667 
 
 2.153 
 
 .00313 
 
 4.000 
 
 .0004212 
 
 48.72 
 
 8171.00 
 
 1 667 
 
 2.153 
 
 .00320 
 
 4.040 
 
 .0004221 
 
 48.67 
 
 REMARK. This was a force main, and velocities were 
 measured at the pump. Considering slight errors in calcula- 
 tions of slip, it is seen how nearly constant the coefficients 
 are. If there were no errors of slip, &c., there would result 
 but one constant value of m and C throughout, The above 
 guagings were remarkably accurate if the conditions under 
 which they were made be considered. They show great care 
 and excellent judgment on the part of the experimentalist. 
 Under more favorable conditions, still closer results would 
 have been had. From the values of the coefficient it is prob- 
 able that the lining of this pipe was one third sand and two- 
 thirds cement. Neat cement linings develop higher values of 
 C than the above, while the above coefficients agree closely 
 with those for linings of one-third sand and two-thirds ce- 
 ment. 
 
 The value of C does not increase with an increased veloc- 
 ity in a constant diameter, as has been claimed by some au- 
 thors. If so, the last value of C in the above table should be 
 the greatest.
 
 SULLIVAN'S NEW HYDRAULICS. 
 GROUP No. 5. 
 
 67 
 
 Wooden conduits, planed poplar, closely jointed. (D'Arcy 
 & Bazin.) 
 
 L'gth 
 Feet 
 
 Feet 
 
 J/R3 
 
 Feet 
 
 S 
 Slope Feet Sec, 
 
 230.58 
 230.58 
 280.58 
 230.58 
 
 230.58 
 
 0.505 
 0.5C5 
 0.505 
 0.505 
 
 o.r,or, 
 0. :,(>:, 
 o.-,o:, 
 0.505 
 
 .000475 
 .001076 
 
 < ).:<>! i 
 
 .002911 
 .00(072 
 
 .00576 
 .006614 
 
 1.666 
 2.519 
 3.372 
 4.225 
 5.068 
 5.527 
 5.914 
 6.373 
 
 .00006143 
 
 .00005S53 
 
 .(KKHWITO 
 .00005948 
 
 .(MHKMilK.KI 
 
 .oooo:>.vi:> 
 
 129.10 
 130.60 
 
 129.75 
 129.10 
 130.70 
 
 REMARK. This conduit had a bottom width of 2.624 feet 
 and was 1.64 feet in depth. The velocities were determined 
 by weir measurement. The values of C developed illus- 
 trate the uncertain application of weir coefficients even in 
 the same small channel and for small differences in head, and 
 when applied by persons of great experience and sound judg- 
 ment. The value of the true coefficient in this conduit was 
 probably C=129.00 in each case. The value of the coefficient 
 for planed wood surfaces will doubtless vary with the density 
 of the wood. The coefficient will be greater in conduits in 
 which the boards are laid parallel to the flow than where the 
 flow is across the grain of the wood and the joints. Assum- 
 ing that m=.00006 is the true coefficient in terms of r in feert 
 for planed hard wood surfaces, we may reduce to terms of d 
 in feet (See 10) by multiplying by 8, and we have m=.00048 
 or. C=45.64 in terms of d in feet. This permits of a direct 
 comparison of the relative degrees of resistance to flow in 
 wooden pipes of planed staves closely jointed, and in iron 
 pipes, Thus 
 
 Lead pipes C=85.00 } 
 
 Asphaltum coated pipes, C=56.00 
 
 Clean cast iron pipes, C=50.00 ^All in terms of diam- 
 
 Clean planed hard wood, C=45.64 ] eter in feet. 
 
 Cement (one third sand) C=48.50 I
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 Wooden conduits, Planed boards. (D'Arcy & Bazin) 
 
 Surface 
 Width 
 Feet 
 
 R 
 
 Feet 
 
 v/R 3 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 m _Sv/71T 
 
 Coefficient 
 
 n_ / v" 
 
 v * 
 
 ^S,/^ 
 
 3.16 
 3.62 
 3.89 
 4.08 
 4.53 
 4.59 
 
 0.390 
 .537 
 .632 
 .717 
 1.015 
 1.148 
 
 0.24355 
 .39350 
 .50240 
 .60710 
 1.0225 
 1.2300 
 
 .0015 
 .0015 
 .0015 
 .0015 
 .0015 
 .0015 
 
 2.61 
 3.23 
 3.71 
 4.04 
 5.00 
 5.54 
 
 .00005363 
 .00005660 
 .00005475 
 .C0005580 
 .00006131 
 .00006011 
 
 136.55 
 132.95 
 135.35 
 134.80 
 127.70 
 128.90 
 
 REMARK. The velocities in this table were determined by 
 surface floats and Pitot-D'Arcy tube measurements. The ve- 
 locities thus determined are undoubtedly too high. The weir 
 measurements given in the preceding table are more nearly 
 correct. A large majority of the guagings by D'Arcy and 
 Bazin were made by surface float and Pitot tube measure- 
 ments of velocity. They are not reliable when so made. This 
 table is introduced here to show that velocities thus deter- 
 mined are too high, and the fluctuating values of C show that 
 this method of guaging is not at all reliable. Data of flow de- 
 termined by such methods should be avoided. It is not in- 
 tended to convey the idea that all of D'Arcy and Bazin's 
 guagings are unreliable, but to show that such guagings as 
 are made by surface floats or by Pitot tube are worthless, 
 whether made by them or any one else. Some of D'Arcy's data 
 are good. Actual tank measurement of the discharge is the 
 only really accurate method of determining the velocity which 
 has so far been adopted. Weir measurement can be made 
 accurate by adopting unit coefficients for weirs similar to mor 
 C as suggested in a remark under Group No, 2, and the Ap- 
 pendix I. 
 
 Uiiplaned boards, well jointed and without battens. 
 
 The average value of m = . 000070 in terms of r in feet. 
 C=119.60 in terms of r in feet. 
 
 Ordinary Flume 6X5 feet Straight. 
 
 Clarke 
 
 Length. 
 Feet. 
 
 R 
 
 Feet 
 
 jiA 8 
 
 jFeet 
 
 S 
 Slope 
 .000435 
 
 \Feet 
 jSec 
 
 Coefficient 
 
 i Coefficient 
 
 ! c p 1 " 
 
 
 V s 
 
 ' V Sl /r 3 
 
 2500. 
 
 1.45 
 
 jl.746 
 
 .000088 ; 106.30 
 
 sewage. The grease and slime may affect the flow consider- 
 ably, ae well as the solid matter mixed with the sewage.
 
 SULLIVAN'S NEW HYDRAULICS. 69 
 
 Bough Irrigation Flume. Highline Flume, Colorado. (Wilson) 
 
 Length 
 Feet 
 
 R [v' r8 
 Feet jFeet 
 
 S V 
 
 Feet 
 Slope iSec. 
 
 Coefficient 
 v*~~ 
 
 ICoefficient 
 
 
 
 3000 
 
 4.50 J9.546 
 
 00099432:6.7657 
 
 .00020733 
 
 j 69.50 
 
 REMARK This is a rough bench flume with many abrupt 
 bends. For a cut and description of this flume see "Irriga- 
 tion Engineering" by Herbert M. Wilson, C. E., pages 173 
 and 174. The bends reduce the value of C considerably be- 
 low its value for a straight flume. 
 
 GROUP No. 6, 
 
 Stone and brick lined Channels. Chazilly Canal. D'Arcy 
 and Bazin. 
 
 
 Depth 
 
 R 
 
 g 
 
 
 Coefficient 
 
 Coefficient 
 
 V'iath 
 
 
 
 
 Feet 
 
 m- 8 ^' 3 
 
 r / v ' 
 
 Feet 
 
 Feet 
 
 Feet 
 
 Slope 
 
 Sec. 
 
 V s 
 
 -Vs v /7T- 
 
 4.04 
 4.10 
 4.14 
 
 4.18 
 
 0.50 
 0.70 
 1.00 
 
 1.20 
 
 0.41 
 0.57 
 0.68 
 0.77 
 
 .0081 
 .0081 
 .0081 
 .0081 
 
 5.73 
 
 7.52 
 8.19 
 8.75 
 
 .000064765 
 .OOOOtJ]i!34 
 .OU0067713 
 .0 0071483 
 
 124.29 
 127.37 
 121.52 
 118.30 
 
 REMARK This canal is lined with smooth ashlar or cut 
 stone. The gaugings wera probably by surf ace floats or Pitot 
 tube which accounts for the fluctuating values of C developed. 
 If this is not the true cause, then the bottom and the sides 
 to a depth of .70 feet must be very much smoother than the 
 walls are above that depth. The last value of C is probably 
 nearest the correct value. See 13. 
 
 Roquefavour Aqueduct. 
 sides. {D'Arcy & Bazin.) 
 
 Neat cement bottom. Brick 
 
 Surface 
 Width 
 Feet 
 
 Depth 
 Feet 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 Sy'r* 
 
 Coefficient 
 C- / v * 
 
 m Y 
 v a 
 
 A/Sv/ r* 
 
 7.40 
 
 2.50 1 1.504 
 
 .00372 
 
 10.26 
 
 .(WOJ652 
 
 123.85 
 
 REMARK. This aqueduct is nearly rectangular and at this 
 depth of flow the smooth cement bottom forms more than 
 half the wet perimeter. It should therefore develop a greater 
 value of C than the stone lined Chazilly canal of the preced- 
 ing table. In a smooth bottomed canal similar to this aque- 
 duct where the bottom is much smoother than the sides, the
 
 70 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 value of C should be greatest for the least depths of flow, be- 
 cause as depth increases the proportion of the rougher side 
 perimeter becomes greater. 
 
 Aqueduct de Crau. Hammer dressed stone. (D'Arcy & 
 Bazin. 
 
 Surface 
 Width 
 Feet 
 
 Depth 
 Feet 
 
 R 
 ?eet 
 
 S 
 
 Slope 
 
 V 
 
 Feet. 
 Sec. 
 
 Coefficient 
 tn S ' /TF 
 
 Coefficient 
 
 C-J V * 
 
 V* 
 
 ^Sv/ r" 
 
 8.50 
 
 3.00 
 
 1.774 
 
 .00084 
 
 5.55 
 
 .0000668 
 
 122.57 
 
 Sudbury Conduit. Hard brick, well jointed. (Fteley & 
 Stearns, 1880.) 
 
 L'gth 
 Feet 
 
 Greatest 
 Depth 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 Feet. 
 Sec. 
 
 Coefficient 
 m- S ^ 
 
 Coefficient 
 
 C- / v * 
 
 V* 
 
 W3 
 
 4,200 
 
 1.518 
 2.037 
 2.519 
 3.561 
 
 1.078 
 1.385 
 1.628 
 2.049 
 
 .0001928 
 
 .noiniej 
 
 . 00019 M 
 .1001929 
 
 1.827 
 2.139 
 2.372 
 2.72J 
 
 .00006460 
 .00006851 
 .00007115 
 .00; 07648 
 
 124.33 
 120.82 
 118.60 
 114.35 
 
 REMARK. Velocities measured by weir. Only four of 
 these guagings are given because the slopes of water surface 
 in the others are so different from the slope of the conduit 
 and from each other as to show that equilibrium and uniform 
 flow had not ensued when the guagings were made. The co- 
 efficients are remarkably high for a plain brick perimeter. 
 The silt deposit on the bottom also affects the flow. 
 
 New Croton 
 (Fteley, 1895.) 
 
 Aqueduct. Hard brick, well jointed 
 
 Depth 
 
 Area 
 
 R 
 
 S 
 
 V 
 
 Coefficient 
 
 Coefficient 
 
 above 
 
 So 
 
 
 
 Feet 
 
 O / 3 
 
 / V 2 
 
 center of 
 Invert. 
 
 oq. 
 
 Feet 
 
 Feet 
 
 Slope 
 
 Sec. 
 
 
 
 V-2 
 
 \Sv/r 3 
 
 1.10 
 
 9.24 
 
 0.7434 
 
 00013257 
 
 1.0969 
 
 .0000706267 
 
 118.97 
 
 1.50 
 
 14.12 
 
 1.0656 
 
 .00013257 
 
 1.4338 
 
 .0000709351 
 
 118.71 
 
 . 2.10 
 
 21.57 
 
 1.4886 
 
 .00013257 
 
 1.7731 
 
 .0000766000 
 
 114.26 
 
 3.00 
 
 33.04 
 
 2.0236 
 
 .00013257 
 
 2.1281 
 
 .0000842174 
 
 108.97 
 
 4.00 
 
 46.14 
 
 2.5137 
 
 00013257 
 
 2.4102 
 
 .0000906000 
 
 105.08 
 
 5.20 
 
 62.20 
 
 2.9947 
 
 00013257 
 
 2.6560 
 
 .0000974027 
 
 101.35 
 
 6.80 
 
 83.89 
 
 3.4998 
 
 .00013257 
 
 2.8894 
 
 .000103930 
 
 98.09 
 
 9.20 
 
 115.78 
 
 4.0062 
 
 00013257 
 
 3.0989 
 
 .000110689 
 
 95.05 
 
 11.00 
 
 136.93 
 
 4.1417 
 
 .00013257 
 
 3.1519 
 
 .000112500 
 
 94.28 
 
 12.50 
 
 150.55 
 
 4.0031 
 
 00013257 
 
 3.0977 
 
 .000110600 
 
 95.09 
 
 12.842 
 
 152.81 
 
 3.9161 
 
 '00013357 
 
 3.0625 
 
 .000109530 
 
 95.55
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 71 
 
 REMARK. Mr. Fteley states in his report that the veloc- 
 ities for depths below 1.90 feet are not as accurate as those 
 for greater depths, as the bottom or invert has slight silt de- 
 posits. It is evident that the bottom is very much smoother 
 than the sides, or the guaging apparatus was greatly at 
 fault. With the assistance of a very smooth silted bottom 
 the side walls and arch are apparently so rough as to run the 
 value of C below its value for common brick masonry. This 
 is a conduit of the horse shoe form and the velocities were 
 measured by meter. The result does not commend meter 
 guagings. From the slope of water surface it appears that 
 uniform flow was attained in each case before the guagings 
 were made. See 13. 
 
 First Class Brick Conduits Washed Inside With Cement.* 
 (Fteley.) 
 
 Name of 
 Conduit 
 
 R 
 
 Feet 
 
 S 
 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 Coefficient 
 
 ^ 
 
 C =V^ 
 
 Sudbury 
 Cochituate 
 
 2.4588 
 1.4170 
 
 .00020 
 .0000496 
 
 3.029 
 1.000 
 
 .000084000 
 .000083637 
 
 109.11 
 109.34 
 
 *See "Water Supply Engineering" by J. T. Fanning, p. 445, 
 Ninth Edition. 
 
 Washington, D. C., Aqueduct, Brick Conduit. Completed 
 1859. See Fanning, P 445.) 
 
 
 
 R 
 
 Feet 
 
 S 
 
 Slope 
 
 v 
 Feet Sec. 
 
 Coefficient 
 m Sl/7F 
 
 Coefficient 
 
 c r^~ 
 
 
 -^S/T' 
 
 
 
 1.8735 
 
 .00015 
 
 1.893 
 
 .000107218 
 
 96.60 
 
 REMARK. This is about the correct value of C for ordi- 
 nary brick perimeters after several year's use. Where spe- 
 cially smooth or scraped brick are used or a cement wash is 
 applied the value of C will be greater. Pure cement linings 
 in channels of uniform cross section and good alignment de- 
 velop an average value of C=150.00 in terms of r in feet. The 
 value of C will vary somewhat with different qualities acd 
 fineness of pure cement linings, and uniformity of the walls.
 
 72 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 Sudbury Conduit. Hard Brick With Surfaces Scraped. 
 (Fteley & Stearns 1880.) 
 
 Greatest 
 
 R 
 
 S 
 
 V 
 
 Coefficient 
 
 Coefficient 
 
 Depth 
 
 Feet 
 
 Slope 
 
 Ft. Sec. 
 
 Sv/r 3 
 
 
 
 
 
 
 V* 
 
 
 0.719 
 1.055 
 1.076 
 1.187 
 1.224 
 1.328 
 1.415 
 
 0.493 
 0.762 
 0.778 
 0.858 
 0.885 
 0.957 
 1.016 
 
 .0001640 
 .0001742 
 .0000983 
 .0000246 
 .0001715 
 .0000746 
 .0000140 
 
 1.079 
 1.423 
 1.098 
 0.550 
 1.577 
 1.064 
 0.443 
 
 .000048763 
 .000057200 
 .000005950 
 .000064450 
 .000057600 
 .000061700 
 .000073000 
 
 143.21 
 132.28 
 133.65 
 124.85 
 131.79 
 127.75 
 117.10 
 
 REMARK. This conduit is of the horse shoe form and 600 
 feet in length. Velocities were determined by weir. The 
 conduit has a grade S=.00016. Compare the slopes in the 
 above table with that of the couduit. Also compare the 
 depths of flow with the corresponding velocities tabled. It 
 is quite remarkable to note the great changes in S for such 
 very small changes in R in a uniform channel with a grade 
 S=.00016. As the slope of water surface is so different from 
 that of the bottom of the conduit, it necessarily follows that 
 the depth of flow must have been different at each successive 
 point along the conduit, and the value of r was different at 
 each different point. The velocities were inversely as the 
 depths or wetted cross sections and hence were greatest 
 where the depths were least. Uniform flow had not occurred 
 and hence the effective value of S could not be known. 
 
 A comparison of the values of C for this conduit with 
 those for carefully dressed poplar conduits (Group No. 5) and 
 for average weight clean cast iron pipes would show this 
 brick surface to be smoother than either of the others. This 
 is, of course, not the fact. Because of the great number of 
 joints and resulting small irregularities of a brick wall, it is 
 scarcely possible that such wall should be more uniform and 
 smooth than a carefully constructed conduit of unplained 
 boards of hard wood, unless the wall were coated. In the 
 latter case the wetted perimeter would consist of the coating 
 and not of brick. Such data, although from eminent author- 
 ity, cannot be accepted. The last value is nearest correct.
 
 SULLIVAN'S NEW HYDRAULICS. 73 
 
 Brick lined channel. (D'Arcy and Bazin) 
 
 Area 
 
 R 
 
 g 
 
 
 Coefficient 
 
 Coefficient 
 
 
 
 
 
 m- 8 ^ 13 
 
 r / V " 
 
 Sq. Feet 
 
 Feet 
 
 Slope 
 
 Feet Sec. 
 
 v 
 
 ^vi2E 
 
 6.22 
 
 0.7554 
 
 .0049 
 
 6.69 
 
 
 118.67 
 
 REMARK. Velocity determined by surface float and Pitot 
 tube which almost invariably gives the mean velocity much 
 too high. This error results in giving too great a value to C 
 for ordinary plain brick perimeters. 
 
 Croton Aqueduct. Brick. Completed 1842. 
 Page 445). 
 
 (See Fanning, 
 
 2.3415 .00021 
 
 .0001677 
 
 77.50 
 
 REMARK. This conduit is of the horse shoe form. It 
 probably contains deposits of gritty material which reduce C 
 to so low a value. 
 
 Brooklyn Conduit. Brick. Completed 1859. 
 Page 445) 
 
 (See Fanning 
 
 2.5241 .00010 
 
 REMARK. As masonry conduits are permanent invest- 
 ments it is best to adopt a coefficient value low enough to 
 allow for deposits and future deterioration of perimeter. 
 
 Concrete Conduits. Old. Different stages of ruin. (See 
 Fanning, page 445). 
 
 Name of 
 Conduit 
 
 R 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet Sec. 
 
 Coefficient 
 m= S J Al 
 
 V 2 
 
 Coefficient 
 r 1 v * 
 
 -Vsv/73- 
 
 94.87 
 
 84.52 
 104.77 
 
 117.00 
 
 Metz 
 Pont du 
 Gard 
 Pont Pyla 
 Mont- 
 pellier 
 
 0.915 
 
 1.250 
 0.6109 
 
 0.25 
 
 .00100 
 
 .00040 
 .00166 
 
 .00030 
 
 2.783 
 
 2.000 
 2.950 
 
 0.716 
 
 .00011175 
 
 .00014000 
 .00009110 
 
 .00007310 
 
 REMARK. In response to a recent inquiry of the writer 
 Mr. Fanning states that he visited these conduits a few years 
 ago and that some of them appeared to be in excellent re- 
 pair. They are constructed of hydraulic concrete, and are 
 rectangular in form.
 
 74 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 Spillway of Grosbois Reservoir. Ashlar laid in Cement. 
 (D'Arcy and Bazin) 
 
 Surface 
 
 Depth 
 
 R, 
 
 s 
 
 v 
 
 Coefficient 
 
 Coefficient 
 
 Width 
 Feet 
 
 Feet 
 
 Feet 
 
 Slope 
 
 Feet 
 Sec. 
 
 S,/r 
 m= 
 
 C =A!ST^ 
 
 5.98 
 6.01 
 6.05 
 6.07 
 
 0.36 
 .55 
 .71 
 
 .84 
 
 0.324 
 .467 
 .580 
 .662 
 
 .101 
 .101 
 .101 
 .101 
 
 12.29 
 16.18 
 18.68 
 21.09 
 
 .00012331 
 .00012313 
 .00012786 
 .00012230 
 
 90.05 
 90.12 
 
 88.45 
 90.42 
 
 Covered with a slimy deposit. 
 
 Tail race Grosbois reservoir. 
 (D'Arcy & Bazin.) 
 
 Ashlar laid in cement. 
 
 Surface 
 Width 
 Feet 
 
 Dep'h 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 ST/~T 
 
 Coefficient 
 
 r i~~** 
 
 m - v * 
 
 -V Sv /rT 
 
 6.00 
 6.10 
 6.10 
 6.10 
 
 0.49 
 .77 
 .97 
 1.16 
 
 0.424 
 .620 
 .745 
 .852 
 
 .037 
 .037 
 .037 
 .037 
 
 9.04 
 11.46 
 13.55 
 15.08 
 
 .00012499 
 .00013750 
 .00012958 
 .00012800 
 
 89.45 
 85.28 
 87.85 
 88.30 
 
 Covered with a light slimy deposit. Joints partly damaged. 
 Surface float. 
 
 Grosbois Conduit. Horseshoe form, 
 set in mortar. (D'Arcy & Bazin.) 
 
 Stone masonry 
 
 6.46 
 6.50 
 
 2.21 
 2.75 
 3.12 
 
 0.98 
 1.29 
 1.49 
 1.60 
 
 1.32 
 1.90 
 2.12 
 2.47 
 
 .000115118 
 
 86.50 
 93.27 
 
 REMARK. Bottom is rougher than sides. No deposit. 
 Joints not damaged. As D'Arcy & Bazin nearly always give 
 the slope of the bottom of the conduit, it is probable that 
 these guagings were made at different places along the con- 
 duit, as the slopes are different. The values of C may be at- 
 tributed to the rough bottom and smooth sides and also to er- 
 rors in guaging with Pitot tube and floats. For ascertaining 
 the correct value of C for any given depth in such channels 
 see 13.
 
 Groisbois Canal. 
 (D'Arcy &Bazin.) 
 
 SULLIVAN'S NEW HYDRAULICS, 75 
 
 Roughly hammered stone masonry. 
 
 Sur- 
 face 
 Wdth 
 Feet 
 
 D'pth 
 
 Feet 
 
 R 
 
 Feet 
 
 s 
 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 Coefficient 
 
 m v 2 
 
 A/S,/r 
 
 3.50 
 3.50 
 3.60 
 3.90 
 
 0.90 
 1.20 
 1.30 
 1.60 
 
 0.62 
 .71 
 
 .0600 
 .0290 
 .0141 
 .0121 
 
 13.93 
 11.23 
 8.36 
 7.58 
 
 .00015610 
 .00013757 
 .00015420 
 .00017400 
 
 80.04 
 85.26 
 80.53 
 75.82 
 
 REMARK. From the difference in slope it is probable 
 that these guagings were at different places where the rough- 
 ness was different. Otherwise the guagings are at fault. C 
 should be constant, unless the roughness of perimeter was 
 different at different depths of flow. 
 
 Qrosbois Canal. Stone Masonry. Broken Stones on 
 the Bottom. (D'Arcy & Bazin.) 
 
 Sur- 
 face 
 Wdth 
 Feet 
 
 D'pth 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 *- 
 
 Coefficient 
 
 =Vs^ 
 
 6.80 
 6.90 
 6.90 
 7.00 
 
 1.50 
 2.00 
 2.40 
 2.70 
 
 0.88 
 1.23 
 1.40 
 1.50 
 
 .000648 
 .000671 
 .000683 
 .000683 
 
 1.47 
 
 2.02 
 2.34 
 
 2.78 
 
 .00024755 
 .00022434 
 !<KX)206G 
 .0001624 
 
 63.55 
 66.76 
 69.57 
 78.45 
 
 REMARK. The effect of the loose, broken stones and mud 
 deposits on the bottom, is to reduce the value of the coeffi- 
 cient C in the ratio that the mean of the different degrees of 
 roughness increases. If the depth of flow were reduced to .50 
 foot, the value of C would not exceed 45, because the rough 
 bottom perimeter would controJ. It is probable that if the 
 sides alone were considered apart from the rough bottom 
 the value of C would be 90.00. The value of C for different 
 depths of tlow in such channels will be different for each 
 depth, and may be determined by the rule given in 13. 
 Compare with New Croton Aqueduct.
 
 76 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 Grosbois Canal. Stone Masonry in Bad Order. (D'Arcy and 
 Bazin) 
 
 Surface 
 Width 
 Feet 
 
 6.80 
 6.90 
 7.00 
 7.00 
 
 Depth 
 Feet 
 
 1.60 
 2.40 
 2.90 
 3.30 
 
 R 
 Feet Slope 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 .00017610 
 .00014115 
 
 Coefficient 
 
 C=Jo-V 
 
 61.58 
 70.95 
 75.36 
 
 84.18 
 
 REMARK. Broken stones and mud on the bottom. 
 Sides fairly smooth. Rule given in 13 applies. 
 
 Solani Embankment. Sides of Stone Masonry. Stepped. 
 (Cunningham). 
 
 Surface 
 Width 
 
 Depth | R 
 
 1 S ! V 
 
 iFeet 
 
 Coefficient 
 Sv/r 3 
 
 Coefficient 
 
 Feet 
 
 Feet iFee 
 
 iSlope i Sec, 
 
 ra v s 
 
 ~\Sv/r 3 
 
 150.00 
 150.00 
 160.00 
 164.00 
 170.10 
 
 1.50 ;i.69 
 2.30 :2.26 
 4.10 14.07 
 9.10 17.84 
 11.00 19.31 
 
 i. 000090 ! 0.44 
 i. 000148 i 0.87 
 i. 000215 i 1.79 
 J.UC0215 i 3.43 
 -.000227 i 4.02 
 
 .00102128 
 .00066400 
 .00055090 
 .000401162 
 .000400944 
 
 31.28 
 38.81 
 42.61 
 49.92 
 49.94 
 
 REMARK This channel has a bottom width of 150 feet 
 The side slopes are of stone masonry, built in steps. The 
 steps are broken and sunken in many places. The bottom is 
 of clay and boulders, very irregular, with bars of brick and 
 boulders built across at frequent intervals to prevent scour. 
 As depth of flow increases the ratio of smoother side peri- 
 meter increases, and the mean of the different degrees of 
 roughness becomes of a lesser degree of roughness. Hence 
 the value of C will increase with each increase in depth. 
 
 GROUP No. 7, RUBBLE AND RIP RAP. 
 
 Chazilly canal. Bottom of earth. One side wall of 
 mortar rubble and the other side wall of dry laid rubble. 
 (D'Arcy & Bazin.) 
 
 Surf. 
 Wdth 
 
 Feet 
 
 D'pth 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet Sec. 
 
 Coefficient 
 m4? 
 
 Coefficient 
 
 r / v * 
 
 V 8 
 
 A/Sv/r* 
 
 8-50 
 9.50 
 9.80 
 10.20 
 
 1.30 
 2.00 
 2.40 
 2.70 
 
 1.00 
 1.36 
 1.54 
 1.67 
 
 .000525 
 .000450 
 .000462 
 .000487 
 
 1.01 
 1.38 
 1.58 
 1.74 
 
 .00051465 
 .00037470 
 .00035347 
 .00034730 
 
 44.08 
 51.66 
 53.20 
 53.66
 
 SULLIVAN'S NEW HYDRAULICS, 
 
 77 
 
 REMARK If these guagings were all made at the same 
 point, the values of C show that the earth bottoms and rub- 
 ble footings were much rougher than the masonry side walls 
 higher up. See 13. 
 
 Turlock canal rock cut. Partly excavated in slate rock, 
 other parts of dry laid rubble and rip rap. ("IrrigationEogi- 
 neering" by H. M. Wilson, p. 82-83.) 
 
 Surf. 
 Wdth 
 Feet 
 
 Dpth 
 Feet 
 
 R 
 
 Feet 
 
 s 
 
 Slope 
 
 V 
 
 Feet Sec. 
 
 Coefficient 
 
 SV/TS" 
 
 *=-?r- 
 
 Coefficient 
 
 -^ 
 
 50.00 
 
 10.00 
 
 5.90 
 
 .0015 
 
 7.50 
 
 .000382 
 
 51.18 
 
 This rock cut is 6,200 feet in length and forms part of the 
 Turlock canal, California. 
 
 River Waal. Gravel bottom, 
 laid rubble. (Krayenhoff.) 
 
 Sides revetted with dry 
 
 17.25 11.10 .0001044 3.165 I 
 
 Description of this rubble,etc. from Beaumont's Geology, 
 Paris, 1845. 
 
 Head Race, Kapnikbanya, Hungary. (Rittinger) 
 Bottom is paved. Sides are of dry laid rubble not smooth as 
 bottom. 
 
 
 Depth 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 Coefficient 
 
 C I 
 
 
 
 
 0.26 
 0.45 
 
 0.213 
 0.344 
 
 .0038 
 .0038 
 
 1.37 
 1.83 
 
 .000200 
 .000229 
 
 70.71 
 66.08 
 
 REMARK. The value of C for rubble will depend on the 
 size and shape of the stones. If the stones are small and 
 laid closely the coefficient will be much greater than if large, 
 irregular stones are laid with large spaces and projections. 
 
 Tail Race. Staukau. Hungary, Bottom paved. Sides of 
 dry laid rubble. (Rittinger) 
 
 
 Depth 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 Feet 
 Sec. 
 
 1.257 
 1.491 
 1.643 
 
 Coefficient 
 Sv/r 3 
 
 Coefficient 
 
 P / V " 
 
 m - v * 
 
 '-A/Sv/.o 
 
 
 0.42 
 0.56 
 0.69 
 
 0.289 
 iMr.ii 
 0.419 
 
 .0025 
 .0025 
 .0025 
 
 .0002457 
 .0002390 
 .0002500 
 
 63.80 
 64.73 
 63.25
 
 78 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 Mill Race. Pricbram, Hungary. Very rough, irregular 
 bottom of earth. 
 
 Side walls of dry laid rubble. Bottom 2.07 feet width. (Rit- 
 tinger). 
 
 Bottom 
 Width 
 Feet 
 
 Depth 
 Feet 
 
 R 
 
 Feet 
 
 S 
 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 Sv/r 8 
 
 Coefficient 
 r- / y8 
 
 -VSv/r" 
 
 2.07 
 2.07 
 2.07 
 2.07 
 2.07 
 2.07 
 
 0.41 
 0.44 
 0.70 
 0.80 
 0.86 
 0.90 
 
 0.316 
 0.336 
 0.472 
 0.548 
 0.560 
 0.566 
 
 .0022 
 .0022 
 .0022 
 .0022 
 .0022 
 .0022 
 
 A 9 
 
 0.588 
 1.953 
 1.135 
 1.190 
 I 269 
 
 .00258236 
 .001239473 
 .0007855758 
 .000692858 
 .000651000 
 .000581962 
 
 19.675 
 28.400 
 35.670 
 37.987 
 39.200 
 41.450 
 
 REMARK. This is a good illustration of the effect of a 
 combination of perimeters of different degrees of roughness, 
 which is referred to in 13, The rough bottom and large 
 rough rubble footings at the bottom of the side walls almost 
 prevented any bottom velocity of flow. 
 
 Grosbois Canal. Rough, trapezoidal canal. The bottom 
 of earth; one Bide slope rip-rapped, the other of earth with 
 some little vegetation. 
 
 The bottom is covered with stones and loose boulders. 
 (D'Arcy and Bazin) 
 
 Surface 
 Width 
 Feet 
 
 Depth 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 S,/r 3 
 
 Coefficient 
 
 c / v2 
 
 m V 2 
 
 ViVr" 
 
 9.10 
 11.20 
 12.40 
 13.40 
 
 1.70 
 2.30 
 2.60 
 2.90 
 
 1.05 
 1.37 
 1.52 
 1.64 
 
 .000936 
 .000936 
 .000957 
 .000964 
 
 1.08 
 1.37 
 1.56 
 1.71 
 
 .00087200 
 .00080000 
 .00073100 
 .00069231 
 
 33.86 
 35.36 
 36.98 
 38.00 
 
 GROUP No. 8. IRRIGATION CANALS. 
 
 A series of Calif ornia Irrigation Canals carefully guaged. 
 By Charles D. Smith, C. E., of Visalia, California. (1895). 
 No. 1. A new canal in common loam just completed. Weir 
 measurement. 
 
 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 Feet 
 Sec. 
 
 Coefficient 
 S,/r 8 
 
 Coefficient 
 
 c- / v8 
 
 m - v * 
 
 C ' -VSv/r 8 
 
 
 
 0.99 
 
 .0006 
 
 1.33 
 
 .000334 
 
 54.72 
 
 See Group No. 11.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 79 
 
 No. 2. An old canal in common loam. In only fair conditi on. 
 By meter. 
 
 R 
 Feet 
 
 S 
 Slope 
 
 v 
 Feet 
 Sec. 
 
 Coefficient 
 Sv/r" 
 
 *=-^r- 
 
 Coefficient 
 
 / v 
 
 c =VsTvr 
 
 0.85 
 
 .001 
 
 1.52 
 
 .0003392 
 
 54.30 
 
 No. 3, An old canal in common loam recently cleaned but 
 not punned. By weir. 
 
 No. 4. A canal in sandy gravel, good repair. Firm gravel. 
 By meter. 
 
 1.40 
 
 4.02 
 
 56.87 
 
 No 5. A new canal. In river sand. 
 
 By meter. 
 
 1.16 
 
 .00175 
 
 49.83 
 
 Nos. 6 and 7. Canals in clay with loose gravel on the bottom, 
 otherwise clean. By meter. 
 
 .00177 
 .00194 
 
 3.46 
 3.51 
 
 66.04 
 64.73 
 
 Nos. 8, 9 and 10. Canal in firm earth with clay bottoms. 
 Good condition. By meter. 
 
 2.00 
 
 .0004 
 
 2.255 
 
 .00022249 
 
 67.08 
 
 3.35 
 
 .00001 
 
 0.531 
 
 .00021740 
 
 67.22 
 
 3.34 
 
 .0000375 
 
 1.032 
 
 .00021486 
 
 68.22 
 
 Nos. 11, 12 and 13. Canals in very heavy, smooth earth, 
 recently cleaned, trimmed and punned and put in excellent 
 order. Guaged by weir. 
 
 .000184553 
 .000195000 
 
 Nos. 14 and 15. Old canals grown up with weeds reaching 
 nearly to the surface. Weir and meter, 
 
 1.13 
 1.77 
 
 .00060 
 
 0.868 
 0.845 
 
 .001154 
 
 No. 16 Very crooked old slough in firm earth. By meter. 
 
 0.91 I .0030 | 3.086 | .00027354 | 60.47
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 GROUP. No. 9. SMOOTH CANALS IN EARTH. 
 
 Mill race, Kagiswyl, Switzerland. Side slopes of firm 
 earth, smooth. Bottom covered with fine gravel. Guaged 
 by meter. (Epper.) 
 
 R 
 
 Feet 
 
 S 
 
 Slope 
 
 Feet Sec. 
 
 Coefficient 
 m-SiA 8 
 
 V 2 
 
 Coefficient 
 
 c- / y8 
 
 A/S^r" 
 
 1.040 
 1.387 
 1.410 
 
 .001754 
 .001255 
 .001200 
 
 2.817 
 3.139 
 3.221 
 
 .00023447 
 .00020774 
 .000193711 
 
 65.30 
 69.40 
 71. 85 
 
 REMARK. Gravelly bottom reduces C as depth decreases. . 
 See 13. 
 
 Clean caual in firm earth and in beet order. Straight. (Watt.) 
 
 Surf. 
 Wdth 
 Feet 
 
 Dpth 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet Sec. 
 
 Coefficient 
 m- S ^ r3 
 
 Coefficient 
 0= / v8 
 
 V* 
 
 VST/r* 
 
 18.00 
 
 4.00 
 
 2.40 
 
 .0000631 
 
 1.134 
 
 .00018216 
 
 74.10 
 
 Mill race. Flachau, Hungary. Clean ditch in firm earth. 
 (Rittinger.) 
 
 
 0.55 
 0.86 
 
 0.467 
 0.703 
 
 .0020 
 .0020 
 
 1.953 
 2.199 
 
 .00016742 
 .00024350 
 
 77.46 
 64.58 
 
 REMARK. This is an example of remarkably bad guaging. 
 The writer has never known the smoothest and firmest peri- 
 meters of earth with best alignment to develop a higher value 
 of C than 75.00. In a clean canal with earth perimeter there 
 should be very little variation in C, especially for BO small a 
 change in depth. Rittinger's experimental data of flow are 
 usually much better than the average of such data, but the 
 above is evidently untrustworthy. 
 
 Linth canal. Grynau. Clean canal in common loam. 
 Side slopes a little irregular. Rod floats. (Legler.) 
 
 Surf. 
 Wdtb 
 Feet 
 
 Dpth 
 Feet 
 
 R 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet Sec. 
 
 Coefficient 
 
 --* 
 
 Coefficient 
 
 ^jg 
 
 123.00 
 
 
 5.14 
 7.12 
 
 8.87 
 9.18 
 
 .00029 
 .00032 
 .00036 
 .00037 
 
 3.414 
 4.418 
 5.40 
 5.53 
 
 .0002900 
 .0003115 
 .0003278 
 .00033648 
 
 58.74 
 56.70 
 55.30 
 54.52 
 
 REMARK. The slight irregularities of the side slopes 
 cause the value of C to decrease as the depth increases and
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 81 
 
 includes a greater proportion of side elope perimeter which is 
 rougher than the bottom. The results of guagings in such 
 channels as this are probably what led Kutter to suppose 
 that the value of C would decrease with an increase in slope 
 where RT>1 meter: The perimeter above the usual depth of 
 flow in a channel of any size whatever is exposed to freezing 
 and thawing, the burrowing of insects and the growth of veg- 
 etation. The change of slope or of hydraulic radius has no 
 effect upon the roughness. The value of C depends upon the 
 mean of the different degrees of roughness. See NOB. 8, 9, 10, 
 Group No. 8, and Solani Embankment, Group No. 6, where 
 the hydraulic radii are both less and greater than one meter 
 or 3.281 feet, and where the slopes increase with R. It will 
 be seen that it is the roughness of perimeter alone that af- 
 fects the unit value of C and that C varies with f/ r 8 only, 
 from its unit value as tabled for the same degree of rough- 
 ness. Kutter's C should vary only as {/r for any given de- 
 gree of roughness, and for different degrees, it should vary 
 as the mean of the roughness and as J/r, but should not be 
 
 o 
 
 affected by the slope at all, because-^- is necessarily con- 
 stant for all slopes. The recent gaugings of the Mississippi 
 entirely explode Kutter's theory. 
 
 GROUP No. 10. RIVERS. 
 
 Mississippi River, Carrolton, La. Bottom is fine sand 
 and the sides of alluvium, fairly stable. (Miss. River Com. 
 Report, 1882.) 
 
 Surface 
 Width 
 Feet 
 
 Depth 
 Feet 
 
 R 
 Feet 
 
 S 
 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 m _Sy/r* 
 y 
 
 Coefficient 
 
 0=J v* 
 
 V Sv/r3 
 
 2647.00 
 2565.00 
 2582.00 
 2359.00 
 2423.00 
 
 93.00 
 90.00 
 92.00 
 86.00 
 89.00 
 
 63.10 
 63.40 
 57.20 
 57.60 
 57.70 
 
 .0000165 
 .0000127 
 ! 0000139 
 .0000097 
 
 .0000112 
 
 5.90 
 5.08 
 4.46 
 2.95 
 3.73 
 
 .00024000 
 .00025000 
 .00032220 
 .00048745 
 .00035300 
 
 64.54 
 63.25 
 58.31 
 44.78 
 59.72 
 
 REMARK. The values of R were taken as nearly equal as 
 could be selected from the Report so that slope alone would 
 show its effect in connection with the various degrees of rough- 
 ness at different depths. The writer acknowledges that he 
 has little confidence in the correctness of these guagings, but 
 the various slopes and velocities tabled probably bear some re- 
 lation to the actual slopes and velocities. It does not appear 
 that fhe value of either Kutter's C or that of the writer de- 
 creases as slope increases. The values of Kutter's C for the
 
 82 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 above guagings are given below, as transcribed from hie 
 work. 
 
 Surface 
 Width 
 Feet 
 
 Depth 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Kutter'e 
 C 
 
 Kutter's 
 n 
 
 2359.00 
 2423.00 
 2582.00 
 2565.00 
 2647.00 
 
 86.00 
 89.00 
 92.00 
 90.00 
 93.00 
 
 57.60 
 57.70 
 57.20 
 63.40 
 63.10 
 
 .0000097 
 .(1000112 
 .0000139 
 .0000127 
 .0000165 
 
 2.95 
 3.73 
 4.46 
 5.08 
 5. 
 
 124.8 
 146.7 
 158.2 
 179.0 
 182.9 
 
 .0452 
 .0354 
 .0290 
 .0261 
 .0218 
 
 REMARK. The value of the writer's C for a depth of 86 
 feet, in the first table above, corresponds with the average 
 value of C for rough, sandy perimeters in rivers, and is prob- 
 ably about the true value for this place. These are double 
 float, or mid-depth guagings. Kutter's n is not as constant or 
 as good an index of roughness as is chaimed for it. 
 
 Sacramento River, Freeport, California. Bottom of shift- 
 ing sand. Sides of earth. Straight reach. Guaged by me- 
 ter. (C. E. Grunsky.) 
 
 Date of 
 Guag- 
 ings 
 
 Area 
 Sq. 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 n- 8 ^ 8 
 
 Coefficient 
 
 c =Vs^ 
 
 V* 
 
 March llrh 
 14th 
 
 17th 
 18th 
 19th 
 28th 
 May 26th 
 
 14,540 
 14,920 
 14.880 
 14.750 
 14.690 
 14,570 
 12,160 
 
 23.45 
 23.99 
 23.92 
 23.79 
 23.69 
 23.54 
 19.93 
 
 .0000744 
 .0000786 
 .0000675 
 .0000750 
 .0000713 
 .0000778 
 .0000580 
 
 3.994 
 4.157 
 3.974 
 3.897 
 3.741 
 3.383 
 2.879 
 
 .00053000 
 .00052867 
 .00050000 
 .00057290 
 .00058720 
 .00077637 
 .00062246 
 
 43.45 
 43.49 
 44.72 
 41.78 
 41.27 
 35.89 
 40.08 
 
 REMARK. The low water area at this place is 4,590 square 
 feet. From the dates and areas given it will be seen that the 
 guagings were made during high water, and that the river 
 was not stationary, or that continual scour or fill was going 
 on. Mr. Grunsky says in his report: "The river bottom is 
 sand. The river is there (at Freeport) surcharged with sand 
 brought in by its tributaries in quantities greater than the 
 water can assort, according to volume and yelocitiy of flow. 
 At the high stages of the river the changes in the contours of 
 the bottom are rapid and sometimes sudden. Boils are of fre- 
 quent occurrence. The river is full of whirls " (Report, p. 
 86.) At pages 96, 97 of his report Mr. Grunsky says: To pre- 
 pare a scale of discharge representing the volume of the 
 river's flow at various elevations of the water surface, for a
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 locality such as Freeport, was, in view of the shifting position 
 of the river bottom, an uncertain undertaking. * * * 
 Neither could any reasonably correct relation between water 
 surface elevation and velocity be established." Report Com. 
 Public Works to Governor of California, 1894. 
 
 River Rhine in Rhine Forest. Bed of coarse gravel. 
 (La Nicca.) 
 
 R 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 ro-Sv/r" 
 
 Coefficient 
 
 n- / V 
 
 V 2 
 
 VSv/r 
 
 0.42 
 0.76 
 1.21 
 
 .0142 
 .0142 
 .0142 
 
 2.332 
 4.526 
 6.032 
 
 .000710 
 .000483 
 .000520 
 
 37.5"> 
 45.50 
 44.47 
 
 Simme Canal. Canton Berme. Very coarse gravel. 
 (Wampfler.) 
 
 1.32 
 1.36 
 
 1.82 
 1.87 
 
 .0170 
 .0116 
 .0065 
 .0070 
 
 5.993 
 4.491 
 4.92 
 5.373 
 
 
 37.37 
 
 40.38 
 38.94 
 40.16 
 
 Mississippi River. Columbus, Ky. Rocky bluffs and 
 gravel. (Humphreys & Abbott.) 
 
 65.90 | 0000658 I 6.957 .OX)7516 36.48 
 
 Mississippi River, Vicksburg, Miss. Rocky bluffs and 
 Gravel. (Humphreys & Abbot. 
 
 .000678 
 
 River Izar. Coarse gravel bed. (G. ebenau.) 
 
 River Rhine. Boulders and gravel. Large stones on the 
 bottom. 
 
 21.65 .001 I 8.858 .001284 27.92
 
 84 SULLIVAN'S NEW HYDRAULICS. 
 
 River Seine at Paris. Fairly regular reach, 
 while rising. (Poiree.) 
 
 Guaged 
 
 Area 
 
 R 
 
 S 
 
 V 
 
 Coefficient 
 
 Coefficient 
 
 Sq. Feet 
 
 Feet 
 
 Slope 
 
 Feet Sec. 
 
 Sv/r 8 
 
 p _ / V* 
 
 
 
 
 
 V 8 
 
 V SvA 8 
 
 1978 
 
 5.70 
 
 .000127 
 
 2.094 
 
 .0003940 
 
 50.38 
 
 2570 
 
 7.10 
 
 .000133 
 
 2.264 
 
 .0004909 
 
 45.13 
 
 3176 
 
 8.40 
 
 .000135 
 
 2.418 
 
 .0005620 
 
 42.18 
 
 3692 
 
 9.50 
 
 .000140 
 
 3.370 
 
 
 52.85 
 
 4421 
 
 10 90 
 
 .000140 
 
 3.741 
 
 ! 0003600 
 
 52.71 
 
 5108 
 
 12.20 
 
 .000140 
 
 3.816 
 
 .0004090 
 
 49.44 
 
 6372 
 
 14.50 
 
 .000140 
 
 4.232 
 
 .0004316 
 
 48.12 
 
 6929 
 
 15.00 
 
 .000140 
 
 4.512 
 
 .0004000 
 
 50.00 
 
 8034 
 
 15.90 
 
 .000172 
 
 4.682 
 
 .0004974 
 
 44.84 
 
 8668 
 
 16.80 
 
 .000131 
 
 4.800 
 
 .0003915 
 
 50.54 
 
 9522 
 
 18.40 
 
 .000103 
 
 4.689 
 
 .0003700 
 
 51.98 
 
 REMARK. The guagings were made by floats, bazin says 
 they are good. It is seen from the areas recorded that the 
 river was rising. Considering tb.3 different degrees of rough- 
 ness of the sides as the water rose above its usual depth of 
 flow, and the great difficulty of ascertaining the true slope 
 on a rapidly rising river the results are quite satisfactory 
 The slope for r=15.90 is probably an error. See the discus- 
 sion of these and other data by Gen. H. L. Abbot in the 
 Journal of the Franklin Institute for May, June, July, 1873. 
 The guagings of the Seine at Triel, Menlon and Poissy have 
 been condemned because the water surface was affected by 
 tidal oscillations as great as two feet while the guagings and 
 slopes were taken. It was also rising at that time as shown 
 by the areas. The slope of the water surface under such con- 
 ditions could not be determined with any accuracy. 
 
 Ohio River, Point Pleasant, W. Va., Mid-depth floats. (Ellet). 
 
 Area 
 Sq. Feet. 
 
 R 
 Feet 
 
 S 
 
 Slope 
 
 v 
 Ft Sec 
 
 Coefficient 
 Sr/r 3 
 m=-V- 
 
 Coefficient 
 
 r / v * 
 
 ^-AMVr" 
 
 7218.00 
 
 6.72 
 
 .0000933 
 
 2.515 
 
 .000257 
 
 62.38 
 
 Great Nevka River, Surface floats. 8-10 rule applied. 
 (Destrem). 
 
 15554.00 
 
 17.40 | 
 
 .0000149 
 
 2.049 
 
 .00025748 | 
 
 62.32 
 
 Mississippi River. Quincy, 
 Clarke). 
 
 111. Sandy alluvium. (T. C. 
 
 15911.00 
 51610.00 
 
 9.87 
 16.27 
 
 .00007434 
 .00007434 
 
 2.941 
 
 3.898 
 
 .00026526 
 .00032135 
 
 61.40 
 55.78
 
 SULLIVAN'S NEW HYDRAULS. 
 
 85 
 
 REMARK. The first gauging at Quincy was at low water 
 when the flow was entirely in contact with its usual peri 
 meter which is somewhat smoother and less irregular than 
 the banks above the usual lo?7 water depth. The second 
 gauging was at high water after permanent high water con- 
 ditions had obtained. The slope of water surface was the 
 same for both stages of the river, showing that stationary 
 conditions had occurred. 
 
 Speyerbach Creek. Firm earth bed. (Grebenau) 
 
 Area 
 Sq. Feet 
 
 R 
 Feet 
 
 S 
 Slope 
 
 V 
 Feet Sec. 
 
 Coefficient 
 
 Coefficient 
 
 m =^l. 
 
 V s 
 
 ' v a 
 
 r< / 
 
 -Vs^Ti- 
 
 30.20 
 
 1.54 
 
 .0004666 
 
 1.814 
 
 .00026931 
 
 60.93 
 
 River Neva. Surface floats. 8 10 rule applied- 
 43461.00 35.40 .000139? I 3.23 I 
 
 (Destrem). 
 59/70 
 
 River Elbe. Steep banks. Coarse gravel and small 
 boulders. (Harlacher.) 
 
 Surface 
 Width 
 Feet 
 
 Depth 
 Feet 
 
 R 
 Feet 
 
 S 
 Slope 
 
 V 
 Feet 
 Sec. 
 
 Coefficient 
 
 S^r" 
 m= ^ 
 
 V 8 
 
 Coefficient 
 
 C =A/sr 
 
 343 00 
 
 452.00 
 
 6.20 
 11.80 
 
 3.51 
 
 7.77 
 
 .00038 
 .00041 
 
 2.49 
 4.95 
 
 0004030 
 .0003708 
 
 49.80 
 52.00 
 
 REMARK. In a channel like this with gravel and small 
 bouldeis on the bottom the value of Cfor a depth of 1.50 feet 
 would not exceed 40 if the channel were narrow. In a wide 
 bottomed rough channel with steep banks smoother than the 
 bottom, it will require a considerable depth of flow to include 
 sufficient side wall to balance the rougher bottom perimeter. 
 The above guagings were by meter. 
 
 River Salzach, Bavaria. At different places and stages. 
 Meter. (Reich.) 
 
 R 
 Feet 
 
 S 
 
 Slope 
 
 V 
 Feet 
 Sec. 
 
 Coefficient 
 m=^ r * 
 
 V 2 
 
 Coefficient 
 
 C= A/S7FT 
 
 3.45 
 3.52 
 4.96 
 5.00 
 5.20 
 7.00 
 
 .000280 
 .000348 
 .000290 
 .000607 
 .000410 
 .00036 
 
 2.686 
 3.618 
 3.510 
 5.543 
 5.094 
 4.118 
 
 .0002487 
 .0001760 
 .0002600 
 .0002190 
 .0001800 
 .000393 
 
 63.40 
 75.40 
 62.00 
 67.60 
 74.53 
 50.44
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 REMARK. These guagings were made in 1885 with the 
 meters then in use. The nature of the perimeter is not stated, 
 but it is safe to state that no natural channel will develop a 
 value of C as high as 75. The mill race at Pricbratu with its 
 masonry side walls and smooth clay bottom, and the smooth- 
 est, best aligned canals in firm earth and in perfect order, only 
 give C=T5. See next group. 
 
 GROUP No. 11 CANALS. 
 
 Mill race at Pricbram, Hungary. Side walls of masonry. 
 Smooth clay bottom 1.88 feet width. Trapezoidal. (Rittin- 
 ger.) 
 
 Depth 
 Feet 
 
 R 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet Sec. 
 
 Coefficient 
 m =Ji^ 
 
 V s 
 
 Coefficient 
 
 n_ / V 
 
 A/S;/r 
 
 0.54 
 0.66 
 
 0.373 
 0.425 
 
 .0010 
 .0010 
 
 1.127 
 1.254 
 
 .00017937 
 .00017621 
 
 74.67 
 75.33 
 
 See Nos. 11, 12 and 13 in group No. 8, also see 
 group No. 9. 
 
 Realtore canal. Common loam bed in only fair condi- 
 tion. (D'Arcy & Bazin.) 
 
 Surface 
 Wdth 
 Feet. 
 
 Dpth 
 Feet 
 
 R 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 1 Coefficient 
 
 m _S;/r | c / v* 
 
 v V Sv/r* 
 
 19.70 
 
 4.50 
 
 287 
 
 .00043 
 
 2.54 ! .000324667 ! 55.51 
 
 Marseilles canal. Common loam bed in only fair condi 
 tion. (D'Arcy & Bazin.) 
 
 2.90 I .00043 2.536 
 
 Henares canal, Spain. Common loam bed in fair condi- 
 tion. (See Fanning.) 
 
 4.92 | 2.95 |. 000326 | 2.2% | .000313328 
 
 Lauter canal. Gravelly soil. Bed in fair condition. 
 (Strauss.) 
 
 29.50 
 
 
 1.82 
 
 .000664 
 
 2 106 
 
 .00036758 
 
 52.16 
 
 See Group No. 8, California canals. 
 
 Rivers, creeks and canals grouped according to roughness
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 87 
 
 of perimeter at the given depths. Areas are given in all cases 
 where known. Perimeters are described as fully as available 
 information will permit. The guagings are good, bad and 
 worthless. It is difficult to separate them without more pre- 
 cise knowledge of the exact conditions under which they were 
 made. The slopes of some rivers were measured while the 
 stream was rising and the velocities were taken when the 
 stream was falling. A fair average value of C may be arrived 
 at for each class of perimeters from what has already been 
 shown together with the following groups. 
 
 GROUP No. 12. 
 
 Shallow canals grown up in weeds reaching nearly to the 
 water surface. 
 
 Name of 
 Channel 
 
 Area I R 
 J^etJFeet 
 
 S 
 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 Sv'r* 
 
 m = .-*- 
 V s 
 
 Coefficient 
 
 =V^ 
 
 Visalia 
 Canal 
 Viealia 
 Canal 
 
 ! 1.77 
 j 1.13 
 
 .00035 
 .00060 
 
 0.845 
 0.868 
 
 .001154 
 .00095658 
 
 30.00 
 32.33 
 
 GROUP No. 13. 
 
 Large canals with quantities of weeds and bushes on the 
 margins and shallow places. 
 
 Cavour 
 Canal 
 C. &0. C. 
 Feeder 
 C.&O. C. 
 Feeder 
 
 799.10 
 119.00 
 121.00 
 
 5.58 
 3.70 
 3.70 
 
 .000357 
 .0006985 
 .0006985 
 
 2.60 
 2.723 
 3.032 
 
 .0006964 
 .0006700 
 .0005410 
 
 37.85 
 38.64 
 43.00 
 
 GROUP No. 14. 
 
 Large streams with very rough banks and with large 
 stones and gravel on the bottom . 
 
 River 
 Rhine 
 River 
 Rnine 
 River Izar 
 
 13725.50 
 
 4650.10 
 1063.40 
 
 21.65 
 
 7.67 
 6.04 
 
 .00100 
 
 .00125 
 .00250 
 
 8.858 
 
 4.921 
 7.212 
 
 .001284 
 
 .001096 
 .000710 
 
 27.92 
 
 30.20 
 37.54
 
 88 SULLIVAN'S NEW HYDRAULICS. 
 
 GROUP No. 15. 
 
 Shallow channels with very coarse gravel and email 
 boulders on the bottom. 
 
 Name of 
 Channel 
 
 Dpth 
 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 V s 
 
 Coefficient 
 
 c ' v 
 
 \ fcn/rs 
 
 Schwarza 
 River 
 
 0.95 
 
 0.80 
 
 .0090 
 
 2.528 
 
 .001007 
 
 31.47 
 
 Schwarza 
 
 
 
 
 
 
 
 River 
 
 1.20 
 
 0.99 
 
 .0052 
 
 2.544 
 
 .0007914 
 
 35.55 
 
 Solani Em- 
 
 
 
 
 
 
 
 bankment 
 
 1.50 
 
 1.69 
 
 .000090 
 
 0.440 
 
 .00102128 
 
 31.28 
 
 Bimme 
 
 
 
 
 
 
 
 Canal 
 
 
 1.32 
 
 .0170 
 
 5.993 
 
 .00072 
 
 37.37 
 
 River 
 Rhine 
 
 
 0.42 
 
 .0142 
 
 2.332 
 
 .00071 
 
 37.50 
 
 GROUP No. 16. 
 
 Channels with one rough, stony bank and with gravel 
 bottoms. One bank of earth. 
 
 Name of 
 Channel 
 
 Dpth 
 
 Feet 
 
 R 
 
 Feet 
 
 S 
 
 Slope 
 
 V 
 
 Feet 
 
 Coefficient 
 
 V 2 
 
 Coefficient 
 
 M'ssissippi 
 
 
 
 
 
 
 
 River* 
 
 88.00 
 
 65.90 
 
 .0000680 
 
 6.957 
 
 .0007516 
 
 36.48 
 
 M ssissippi 
 
 
 
 
 
 
 
 Riverf 
 
 100.00 
 
 64.10 
 
 .0000638 
 
 6.949 
 
 .0006780 
 
 38.40 
 
 Grosbois 
 
 
 
 
 
 
 
 CanalJ 
 
 1.70 
 
 1.05 
 
 .0039360 
 
 1.080 
 
 .0008720 
 
 33.86 
 
 Grosbois 
 
 
 
 
 
 
 
 Canal 
 
 2.30 
 
 1.37 
 
 .0009360 
 
 1.370 
 
 .0007997 
 
 35.36 
 
 Grosbois 
 
 
 
 
 
 
 
 Canal 
 
 2.60 
 
 1.52 
 
 .000957 
 
 1.560 
 
 .0007310 
 
 36.98 
 
 Grosbois 
 
 
 
 
 
 
 
 Canal 
 
 2.90 
 
 1.64 
 
 .000964 
 
 1.710 
 
 .0006923 
 
 38.00 
 
 *At Columbus, Kentucky. Blutf on left bank composed 
 of strata of coarse sand, coarse brown clay, blue clay, fine 
 sand, coarse gravel, limestone, pudding stone, iron ore. 
 
 f At Vicksburg, Miss. Bluff forms left bank and is com- 
 posed of strata of blue clay, logs, carbonized wood, marine 
 shells, sand full of shells, sandstone. See "Levees of the Mis- 
 sissippi River," by Humphreys & Abbot, pages 28,29. (1867.) 
 
 JGravel and pebbles on the bottom. One side slope rip- 
 rapped with rough stone the other side slope of earth.
 
 SULLIVAN'S NEW HYDRAULICS. 89 
 
 GROUP No. 17. 
 
 Channels in firm earth with low stumps and roots on the 
 bottom. 
 
 Name of 
 Channel 
 
 Area 
 
 X, 
 
 R 
 
 Feet 
 
 s 
 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 -* 
 
 Coefficient 
 . 
 
 A/fcVr" 
 
 Bayou Pla- 
 quemine 
 Bayou Pla- 
 quemine 
 
 3560.00 
 4259.00 
 
 18.30 
 15.30 
 
 .0002064 
 .0001437 
 
 5.198 
 3.959 
 
 .000598 
 .00054875 
 
 40.88 
 42.69 
 
 REMARK. This bayou was guaged by Humphreys & Ab- 
 bot with mid-depth floats. It is simply an overflowed coule, 
 which was formerly covered by a thick forest of cypress 
 trees. These trees were cut down and the water brought 
 into the Plaquemine in 1770 by means of a small canal con- 
 necting with the Mississippi river. As the dirt washed from 
 around the stumps the Navigation company had them recut. 
 See "Levees of the Mississippi River," page 204, note. This 
 bayou varies in width from 200 to 300 feet, and in depth from 
 20 to 35 feet. There is luxuriant plant growth along the mar- 
 gins. 
 
 GROUP No. 18. 
 
 Grosbois canal. Earth bed in bad repair, with many 
 patches of vegetation. 
 
 Surface 
 Width 
 Feet 
 
 Dpth 
 Feet 
 
 R 
 
 Feet 
 
 S 
 
 Slope 
 
 Feet 
 Sec. 
 
 Coefficient 
 m - S^r 
 
 V s 
 
 Coefficient 
 
 -J& 
 
 10.10 
 12.30 
 13.50 
 14.70 
 
 1.70 
 2 40 
 2.80 
 3 10 
 
 1.06 
 1.41 
 1.60 
 1.76 
 
 .00042 
 .00047 
 .00047 
 .00045 
 
 0.89 
 1.18 
 1.31 
 1.39 
 
 .0005785 
 .000u6505 
 .000554326 
 .000o44 
 
 40 95 
 42.06 
 42 47 
 
 42.86
 
 90 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 GROUP No, 19. 
 Channels with gravelly bottoms and rough, irregular banks 
 
 Name of 
 Channel 
 
 Area 
 Sq. 
 Feet 
 
 R 
 Feet 
 
 S 
 Slope 
 
 Feet 
 Sec. 
 
 Coefficient 
 Sv/r" 
 
 Coefficient 
 
 m V 8 
 
 Mississippi 
 River 
 Feeder 
 Chazilly 
 Feeder 
 Chazilly 
 River Rhine 
 Seine (Poissy) 
 
 150365.00 
 11.30 
 
 18.80 
 19135.00 
 10400.00 
 
 57.40 
 1.04 
 
 1.41 
 
 16 50 
 17.80 
 
 .0000481 
 .0004450 
 .0009930 
 
 .(HXHIWT 
 .0000750 
 
 6.310 
 0.962 
 
 1.789 
 3.575 
 3.330 
 
 .00052400 
 .00053100 
 
 .00051450 
 .00051235 
 .00050800 
 
 43.69 
 43.40 
 
 44.10 
 44.17 
 44.37 
 
 GROUP No. 20. 
 
 Rivers and Canals with beds of sand and with irregular side 
 Slopes of earth. 
 
 Name of 
 Channel 
 
 Area 
 Sq. 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec 
 
 Coefficient 
 
 Coefficient 
 
 V 2 
 
 Seine 
 
 
 
 
 
 
 
 
 8034.00 
 
 15.90 
 
 000172 
 
 4.682 
 
 .0004974 
 
 44.83 
 
 ^Pari.) 
 
 2570. 00 
 
 7.10 
 
 000133 
 
 2.264 
 
 .0004909 
 
 45.13 
 
 Chazilly 
 
 22.20 
 
 1.54 
 
 000986 
 
 1.959 
 
 .00049 
 
 45.16 
 
 Feeder 
 
 
 
 
 
 
 
 Chazilly 
 
 9.50 
 
 0.96 
 
 000792 
 
 1.234 
 
 .0004878 
 
 45.28 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 23.00 
 
 1.63 
 
 000479 
 
 1.434 
 
 .00048456 
 
 45.40 
 
 Mississip- 
 
 
 
 
 
 
 
 pi River 
 Seine 
 
 179502.00 
 
 64.50 
 
 .0000436 
 
 6.825 
 
 .0004845 
 
 45.42 
 
 (Poissy) 
 
 9733.00 
 
 16.80 
 
 .0000670 
 
 3.101 
 
 .00048 
 
 45.65 
 
 Seine 
 
 
 
 
 
 
 
 (Triel) 
 Seine 
 
 6375.00 
 
 12.40 
 
 .0000600 
 
 2.359 
 
 .0 047 
 
 46.12 
 
 (Poissy) 
 
 8996.00 
 
 15.90 
 
 .0000620 
 
 2.911 
 
 .0004638 
 
 46.43 
 
 Feeder 
 
 
 
 
 
 
 
 Chazilly 
 
 22.90 
 
 1.57 
 
 .0004350 
 
 1.401 
 
 .000456 
 
 46.83 
 
 M?s^ 6 River 
 
 5010.10 
 
 10.85 
 
 .0000289 
 
 1.509 
 
 .0004536 
 
 46.95 
 
 Saalach 
 
 96.76 
 
 1.34 
 
 .001164011.970 
 
 .00045238 
 
 47.02 
 
 Seine 
 
 
 
 
 
 
 (Poisay) 
 
 7475.00 
 
 13.60 
 
 .00005002.372 
 
 .0004457 
 
 47.34 
 
 See Sacramento River, Group No, 10.
 
 SULLIVAN'S NEW HYDRAULICS, 91 
 
 GROUP No. 21. 
 
 Natural Channels with sandy gravel bottoms and fairly 
 regular sides of earth. Canals in common loam in bad repcir 
 
 Name of 
 
 Area 
 
 R 
 
 S 
 
 V 
 
 Coefficient 
 
 Coefficient 
 
 
 q ' 
 
 
 
 Feet 
 
 Sv/r 3 
 
 c / v * 
 
 Channel 
 
 Feet 
 
 Feet 
 
 Slope 
 
 Sec 
 
 v a 
 
 \ a 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 19.40 
 
 1.41 
 
 .000858 
 
 1.815 
 
 .00043515 
 
 47.90 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 18.10 
 
 1.38 
 
 .00045 
 
 1.296 
 
 .00043280 
 
 48.07 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 27.20 
 
 1.71 
 
 .000441 
 
 1.510 
 
 .00043230 
 
 48.08 
 
 Seine 
 
 
 
 
 
 
 
 (Paris) 
 
 6372.00 
 
 14.50 
 
 .00014 
 
 4.232 
 
 .0 04316 
 
 48.12 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 25.40 
 
 1.69 
 
 .00033 
 
 1.296 
 
 t . 00043155 
 
 48.14 
 
 Seine 
 
 
 
 
 
 
 
 (Poissy. 
 
 7952.00 
 
 14.20 
 
 .000054 
 
 2.595 
 
 .00042900 
 
 48.28 
 
 Izar 
 
 300.10 
 
 1.85 
 
 .0025 
 
 3.997 
 
 .00042430 
 
 48.54 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 17.20 
 
 1.38 
 
 .00045 
 
 1.326 
 
 .000414 
 
 49.18 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 20.90 
 
 1.56 
 
 .000525 
 
 1.575 
 
 .0004138 
 
 49.23 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 32.00 
 
 1.85 
 
 .00 '33 
 
 1.411 
 
 .0004168 
 
 49.00 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 22.90 
 
 1.56 
 
 .000842 
 
 1.998 
 
 .00041 
 
 49.39 
 
 Feeder 
 
 
 
 
 
 
 
 Chazilly 
 
 14.10 
 
 1.18 
 
 .000929 
 
 1.703 
 
 .00041068 
 
 49.34 
 
 Seine 
 
 
 
 
 
 
 
 (Paris) 
 
 5108. CO 
 
 12.20 
 
 .00014 
 
 3.816 
 
 .0004 9 
 
 49.44 
 
 Visalia 
 
 
 
 
 
 
 
 Canal 
 
 
 1.16 
 
 .00175 
 
 2.33 
 
 .0004026 
 
 49.83 
 
 Rhine 
 
 14149.80 
 
 9.72 
 
 .OOJ112 
 
 2.91 
 
 .0004008 
 
 49.95 
 
 Seine 
 
 
 
 
 
 
 
 (Paris 
 
 6929.00 
 
 15.00 
 
 .00014 
 
 4.512 
 
 .0004 
 
 50.00 
 
 Seine 
 
 
 
 
 
 
 
 (Paris) 
 
 1978.00 
 
 5.70 
 
 .000127 
 
 2.094 
 
 .000394 
 
 50.38 
 
 Salzacb 
 
 40 5.60 
 
 7.00 
 
 .00036 
 
 4.118 
 
 . 00393 
 
 50.44 
 
 Seine 
 (Paris) 
 
 8668.00 
 
 W.80 
 
 .000131 
 
 4.80 
 
 .0003915 
 
 50.54 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 26.80 
 
 1.71 
 
 .000493 
 
 1.683 
 
 .00039 
 
 50.64 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 14.90 
 
 1.21 
 
 .000808 
 
 1.667 
 
 .000387 
 
 50.83 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 25.90 
 
 1.71 
 
 .000515 
 
 1.746 
 
 .0003775 
 
 51.46 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 15.40 
 
 1.30 
 
 .000555 
 
 1.480 
 
 .00037557 
 
 51.60 
 
 Seine 
 
 
 
 
 
 
 
 (Paris) 
 
 9522.00 
 
 18.40 
 
 .(XWlCtt 
 
 4.689 
 
 .00037 
 
 51.98 
 
 Lauter 
 
 
 
 
 
 
 
 Canal 
 
 56.40 
 
 1.82 
 
 .000664 
 
 2.106 
 
 .00036756 
 
 52 16 
 
 Saalach 
 
 86.90 
 
 1.38 
 
 .0010357 
 
 2.155 
 
 .000362 
 
 52.56 
 
 Seine 
 (Paris) 
 Seine 
 
 3692.00 
 
 9.50 
 
 .00014 
 
 3.37 
 
 .0003578 
 
 52.85 
 
 (Paris) 
 
 4421.00 
 
 10.90 j. 00014 
 
 3.741 
 
 .00036 
 
 52.71
 
 92 SULLIVAN'S NEW HYDRAULICS. 
 
 GROUP No. 22. 
 
 Channels revetted with rough angular rubble, dry laid; 
 channels in firm earth with rough, uneven bottoms and irreg- 
 ular side slopes. 
 
 Name of 
 Channel 
 
 Area 
 Square 
 Feet 
 
 R 
 
 Feet 
 
 s 
 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 m-Syr 
 
 Coefficient 
 
 C= / V 
 
 V 8 
 
 VSv/r* 
 
 River 
 
 
 
 
 
 
 
 Waal* 
 
 14782.00 
 
 11.10 
 
 .0001044 
 
 3.165 
 
 .00038607 
 
 50.88 
 
 Turlock 
 
 
 
 
 
 
 
 Rock Cut 
 
 
 5.90 
 
 .0015 
 
 7.50 
 
 .000382 
 
 51.18 
 
 Mississippi 
 
 
 
 
 
 
 
 River 
 
 134942.00 
 
 52.10 
 
 .0000303 
 
 5.558 
 
 .0003693 
 
 52.03 
 
 Mississippi 
 River 
 
 193968.00 
 
 72.00 
 
 .0000205 
 
 5.929 
 
 .000356 
 
 53.00 
 
 Bayou La 
 
 
 
 
 
 
 
 Fourche 
 
 286'. 00 
 
 15.70 
 
 .0000438 
 
 2.789 
 
 .000352 
 
 53.30 
 
 Bear River 
 
 
 
 
 
 
 
 Canal 
 
 
 5.63 
 
 .00018939 
 
 2.67 
 
 .00035487 
 
 53.00 
 
 River 
 
 
 
 
 
 
 
 Rhine 
 
 6304.00 
 
 11.20 
 
 .0000999 
 
 3.277 
 
 .0003486 
 
 53.57 
 
 Seine 
 
 
 
 
 
 
 
 LMeulan] 
 
 6488.00 
 
 7.70 
 
 .000087 
 
 2.313 
 
 .00034734 
 
 53.66 
 
 *See Group No. 7. 
 
 GROUP No. 23. 
 
 New canals in loam, or light soil, just completed; old can- 
 als in similar soil with weeds along the margin; canals in 
 fairly go 3d condition but with pebbles on the bottom. 
 
 Name of 
 Channel 
 
 Area 
 Square 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 Coefficient 
 n_ pH 
 
 m v 
 
 VsT/r"~ 
 
 Visalia 
 Canal 
 
 Visalia 
 
 Idaho !? 81 
 &I Canal 
 Feeder' 
 Grosbois 
 
 11.80 
 
 0.85 
 0.99 
 7.232 
 1.050 
 
 .0010 
 .'006 
 .00037878 
 .00031 
 
 1.52 
 1.33 
 4.70 
 0.817 
 
 .0003392 
 .000334 
 .00033347 
 .000343 
 
 54.30 
 54.72 
 54.77 
 54.03 
 
 REMARK The flow in a new canal is never as great at 
 first as it will become after the bed is saturated with water 
 and the loose material is dissolved and deposited in the pores 
 of the earth and in the little depressions and irregularities 
 along the perimeter.
 
 SULLIVAN'S NEW HYDRAULICS, 
 
 93 
 
 GROUP No. 24. 
 
 Clean channels with bottoms of fine gravel and sand 
 well settled, and with banks of sandy loam; channels in 
 sandy alluvium; canals in ordinary loam in fair condition but 
 not recently cleaned. (Average for canals in ordinary con 
 dition). 
 
 Name of 
 Channel 
 
 Area 
 Sq. 
 Feet 
 
 R 
 
 Feet 
 
 S 
 Slope 
 
 Feet 
 Sec. 
 
 Coefficient. 
 Sj/r 3 
 
 Coefficient 
 
 m v s 
 
 Marseilles 
 Canal 
 
 66.00 
 
 2.90 
 
 .00043 
 
 2.536 
 
 .00033 
 
 55.04 
 
 Eealtore 
 
 
 
 
 
 
 
 Canal 
 
 
 2.87 
 
 .00043 
 
 2.540 
 
 .000324667 
 
 55.51 
 
 Eiver 
 
 
 
 
 
 
 
 Tiber 
 
 2355.00 
 
 9.40 
 
 .001306 
 
 3.413 
 
 .00032335 
 
 55.62 
 
 Seine 
 
 
 
 
 
 
 
 (Meulan) 
 
 5982.00 
 
 7.10 
 
 .00009 
 
 2.31 
 
 .000318876 
 
 55.75 
 
 Eiver 
 Ha me 
 
 306.40 
 
 5.70 
 
 .0001559 
 
 2.558 
 
 .0003213 
 
 55.71 
 
 Miss. River 
 
 51610.00 
 
 16.27 
 
 .00007434 
 
 3.898 
 
 .00032135 
 
 55.78 
 
 Henares 
 
 
 
 
 
 
 
 Canal 
 
 
 2.95 
 
 .000326 
 
 2.296 
 
 .000313328 
 
 56.40 
 
 Mississip- 
 
 
 
 
 
 
 
 pi Eiver 
 
 78828.00 
 
 31.20 
 
 .0000223 
 
 3.523 
 
 .0003132 
 
 56.49 
 
 Visalia 
 
 
 
 
 
 
 
 Canal 
 
 
 1.40 
 
 .00302 
 
 4.02 
 
 .00030951 
 
 56.87 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 18.00 
 
 1.42 
 
 .00029 
 
 1.26 
 
 .000309 
 
 56.89 
 
 * At Quincy, Illinois, gauged by Thomas C. Clarke, C. E. 
 GROUP No. 25. 
 
 Rivers and canals in good condition, having beds of fine 
 sand and small pebbles, with fairly regular banks of firm 
 loam. 
 
 Name of 
 
 Area 
 
 R 
 
 S 
 
 V 
 
 Coefficient 
 
 Coefficient 
 
 
 Sq. 
 
 
 
 Feet 
 
 S;/ r 8 
 
 C/ 
 
 Channel 
 
 Feet 
 
 Feet 
 
 Slope 
 
 Sec. 
 
 V 2 
 
 
 Hooken- 
 
 
 
 
 
 
 
 bach Creek 
 Hocken- 
 
 10.30 
 
 0.88 
 
 .0007966 
 
 1.463 
 
 .000307287 
 
 57.00 
 
 bach Creek 
 
 10.50 
 
 0.87 
 
 .0007783 
 
 1.440 
 
 .00030463 
 
 57.28 
 
 Misssissip- 
 pi Eiver 
 
 195349.00 
 
 72.40 
 
 .0000171 
 
 5.887 
 
 .000304 
 
 57.35 
 
 Upper* 
 
 
 
 
 
 
 
 Miss. Eiver 
 
 3441.00 
 
 4.42 
 
 .0002227 
 
 2.611 
 
 .00030355 
 
 57.40 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 30.80 
 
 1.78 
 
 .000275 
 
 1.467 
 
 .0003034 
 
 57.48 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 10.90 
 
 0.96 
 
 .00025 
 
 0.886 
 
 .0003 
 
 57.74
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 * At Fort Snelling, Minnesota. It is apparent from the 
 areas and hydraulic mean radii in Group 25, that the effect 
 of rough or smooth perimeter is the same in a very large 
 channel as in a very small one. These perimeters are almost 
 exactly alike, and develop like coefficients, regardless of size 
 or slope. 
 
 GROUP No. 26. 
 
 Rivers and canals in alluvial soil, or firm earth mixed with 
 tine eand, in good condition, and free of stones and weeds. 
 
 Name of 
 
 Area 
 
 R 
 
 S 
 
 V 
 
 Coefficient 
 
 Coefficient 
 
 Channel 
 
 Square 
 Feet 
 
 Feet 
 
 Slope 
 
 Feet 
 Sec. 
 
 m= *v;' 
 
 c =Vs^ 
 
 Bayou La 
 
 
 
 
 
 
 
 Fourche 
 
 3738.00 
 
 15.70 
 
 .0000447 
 
 3.076 
 
 .0002948 
 
 58.24 
 
 Visalia 
 
 
 
 
 
 
 
 Canal 
 
 
 0.93 
 
 .(004 
 
 1.110 
 
 .000291 
 
 58.62 
 
 Eiver 
 
 
 
 
 
 
 
 Rhine 
 
 5341.00 
 
 7.60 
 
 .0001174 
 
 2.917 
 
 .00028905 
 
 58.83 
 
 Huben- 
 
 
 
 
 
 
 
 graben 
 
 3.80 
 
 0.59 
 
 .0013 
 
 1.424 
 
 .00029 
 
 58.74 
 
 River 
 
 
 
 
 
 
 
 Neva 
 
 43461.00 
 
 35.40 
 
 .0000139 
 
 3.230 
 
 .00028065 
 
 59.70 
 
 Marseilles 
 
 
 
 
 
 
 
 Canal 
 
 
 3.386 
 
 .000333 
 
 2.720 
 
 .00028065 
 
 59.70 
 
 GROUP No. 27. 
 
 Canals in heavy loam in excellent repair; natural chan 
 nels with very fine sand on firm and regular bottoms with 
 sandy loam banks in excellent condition, free of weeds and 
 stones. 
 
 Name o f 
 Channel 
 
 Area 
 Square 
 Feet 
 
 R 
 
 Feet 
 
 S 
 
 Slope 
 
 V j 
 Feet! 
 Sec.j 
 
 Coefficient 
 B _Sv/r 
 
 Coefficient 
 
 v 8 
 
 V s 
 
 \Si/r 3 
 
 Speyer- 
 bach Creek 
 
 30.20 
 
 1.54 
 
 .0004666 
 
 1.814! 
 
 .00026931 
 
 60.93 
 
 
 15911.00 
 
 9.87 
 
 .00007434 
 
 2.941; 
 
 .00026526 
 
 61.40 
 
 Feeder 
 
 
 
 
 
 
 
 Grosbois 
 
 24.20 
 
 1.57 
 
 .000246 
 
 1.362! 
 
 .00026080 
 
 61.88 
 
 Great 
 
 
 
 
 
 
 
 Nevka 
 
 15554.00 
 
 17 40 
 
 .0000149 
 
 2.049! 
 
 .00025748 
 
 62.32 
 
 Ohio 
 
 
 
 
 
 
 
 River 
 
 7218.00 
 
 672 
 
 .0000933 
 
 2.515! 
 
 .00025700 
 
 62.38
 
 SULLIVAN'S NEW HYDRAULICS. 95 
 
 GROUP No. 28. 
 Canals in smooth clay with loose pebbles on the bottom. 
 
 Name of 
 
 Area 
 Square 
 
 R 
 
 VPont 
 
 s 
 
 CJIona 
 
 V 
 
 Feet 
 
 Coefficient 
 m- 8 ^" 
 
 Coefficient 
 
 c / v " 
 
 
 Feet 
 
 
 
 Sec. 
 
 V* 
 
 AWr 8 
 
 Visalia* 
 Canal 
 Feeder 
 Grosbois 
 Viealia 
 Canal 
 
 17.10 
 
 1.32 
 1.32 
 1.34 
 
 .00194 
 
 .000275 
 .00177 
 
 3.510 
 1.336 
 
 3.460 
 
 .00023862 
 .00023366 
 000229-254 
 
 64.73 
 65.37 
 66.04 
 
 *A few weeds along the margin in patches. 
 
 GROUP No. 29. 
 
 Canals in very firm, heavy soil, with clay bottoms worn 
 smooth, but not recently trimmed and punned; natural 
 streams of good alignment with clay bottoms, and fine grain- 
 ed, firm and uniform alluvial banks, free of stones and vege- 
 tation . 
 
 Name of 
 
 Area 
 
 R 
 
 S 
 
 V 
 
 Coefficient 
 
 Coefficient 
 
 
 Sq- 
 
 
 
 Feet 
 
 m Sv/r 8 
 
 IV V * 
 
 Channel 
 
 Feet 
 
 Feet 
 
 Slope 
 
 Sec. 
 
 V B 
 
 ~^Sv/r 8 
 
 Visalia 
 
 
 
 
 
 
 
 Canal 
 Visalia 
 
 
 2.00 
 
 .000400 
 
 2.255 
 
 .00022249 
 
 67.08 
 
 Canal 
 Yssel 
 
 
 3.35 
 
 .000010 
 
 0.531 
 
 .0002174 
 
 67.82 
 
 T,o,h EiVer 
 
 1930.00 
 
 15.90 
 
 .0001166 
 
 2.773 
 
 .00021728 
 
 67.84 
 
 Katrine 
 
 
 2.525 
 
 .0001578 
 
 1.7126 
 
 .0002158 
 
 68 05 
 
 Visalia 
 Canal 
 Bayou La 
 
 
 3.34 
 
 .0000375 
 
 1.032 
 
 .00021486 
 
 68.22 
 
 Fourche 
 Bayou La 
 
 3025.00 
 
 13.00 
 
 .0000373 
 
 2.843 
 
 .0002145 
 
 68.27 
 
 Fourche 
 
 2957.00 
 
 12.80 
 
 .0000366 
 
 2.807 
 
 .0002126 
 
 68.53 
 
 REMARK The bottom of this portion of Bayou La Four- 
 che is clay, and the banks are leveed. The banks are of 
 heavy, alluvial soil. Its bends are few and gentle. There 
 are no boils, whirls, nor eddies. It resembles an artificial 
 channel very much. For a general description see "Levees of 
 the Mississippi River", page 198.
 
 96 SULLIVAN'S NEW HYDRAULICS. 
 
 GROUP No. 30. 
 
 Canals in very firm, smooth, dense earth, recently cleaned, 
 trimmed and punned, and put in the best condition. 
 
 Name of 
 Channel 
 
 Area 
 Sq. 
 Feet 
 
 R 
 
 Feet 
 
 s 
 
 Slope 
 
 V 
 
 Feet 
 Sec. 
 
 Coefficient 
 
 Coefficient 
 
 V s 
 
 ^"""VSv/r 8 
 
 Visalia 
 Canal 
 Visalia 
 Canal 
 Visalia 
 Canal 
 English 
 Canal 
 
 50.00 
 
 1.13 
 1.09 
 0.92 
 2.40 
 
 .00060 
 .00060 
 .001165 
 .0000631 
 
 1.88 
 1.87 
 2.36 
 1.134 
 
 .00020396 
 .000195 
 .000184553 
 .00018216 
 
 70.02 
 71.61 
 73.73 
 74.10 
 
 IS Roughness of Perimeter Defined. The foregoing 
 tables of coefficients might be greatly enlarged by the ad- 
 dition thereto of the data of many other pipes and channels, 
 but such matter would be simply cumulative. It is believed 
 that the tables given cover all cases as accurately as the pub- 
 lished data will permit, and it was not deemed neccessary to 
 give but a few examples of each class in order to assist in 
 selecting the value of the coefficient in any ordinary case. 
 The inaccuracies which abound in the data of flow in all 
 classes of pipes and channels are due in great part to the 
 failure of weir and orifice coefficients. The writer is aware 
 that a general belief in the accuracy of weir measurement has 
 become very great, but the fact remains that such measure- 
 ments are very frequently erroneous to a very considerable 
 extent. Meter measurements of velocity are still less reliable 
 When better methods are discovered and adopted, we shall 
 have more reliable data than we now have. In the consid- 
 eration of the degree of roughness of any given channel, the 
 alignment, uniformity of cross-section, freedom from grit 
 gravel, stones and vegetation, are not, by any means, all that 
 are to be considered. The nature of the material in contact 
 with the flow, as to density and compactness, is as important 
 as any or all other features. The coefficients show that for 
 clean canals in earth, the value varies from about 56 to 75 as 
 the nature of the earth forming the perimeter varies. The
 
 SULLIVAN'S NEW HYDRAULICS. 97 
 
 amount of sand, and whether coarse or fine, which enters in- 
 to the majority of different classes of earth, hae a great effect 
 upon the flow and upon the value of the coefficient. Every 
 table of data of open channels abundantly proves the incor- 
 rectness of the idea that the character of the perimeter has 
 no influence upon flow in very large channels. The Missis- 
 sippi river at Columbus and Vicksburg with depths of 88 and 
 100 feet respectively, develop the same value of the coeffi- 
 cient as very small ditches having the same kind of perime- 
 ter. (See Group No. 16). There is no reason why this should 
 not be the case, and it would be strange if it were not the 
 the case. The flow in large rivers is nearly always overesti- 
 mated, especially where meters or surface floats are used for 
 determining the velocity. Insufficient attention has been 
 given the character of the perimeter and its effect upon the 
 flow of the water in contact therewith and affected by the re- 
 actions therefrom. The velocity of the film of water in con- 
 tact with and affected by the sides and bottom has never 
 been considered of great importance in determining the mean 
 velocity of the whole cross section in large streams, and yet 
 if this outer layer of water thus affected were deducted from 
 the whole, at least one fourth the total area would be sub- 
 tracted.
 
 CHAPTER III, 
 
 Of the Deduction of the General Formulas. 
 
 16 Formulas in Terms of Diameter in Feet. For large 
 pipes and circular channels flowing full, a set of formulas in 
 terms of diameter in feet will be most convenient. For 
 small pipes the coefficients may be in terms of diameter in 
 inches. 
 
 FORMULA FOB Loss OP HEAD BY FRICTION. 
 
 By formula (10) 6, the coefficient of friction n, is 
 
 S" 
 
 (10) 
 
 Hy transposition in (10) we have the formula for loss of 
 head in feet by friction 
 
 _ n 
 
 h == ~ lv 
 
 In which, h"= total head in feet lost in the length in feet, I 
 d=diameter of pipe in feet. 
 n=coefficient in terms of diameter in feet. 
 Z=length of pipe in feet. 
 v=velocity in feet per second. 
 
 FORMULA FOR HEAD IN FEET LOST PER FOOT LENGTH OF 
 
 PIPE. 
 S" 
 As n =^jf-X i/d 8 , we have by transposition, 
 
 S "=VcT*Xv*....^ ............................ (22) 
 
 In which, 
 
 S"=head in feet lost by friction per foot length of pipe. 
 n=unit value of the coefficient of resistance which in- 
 creases as v s , and is inversely as i/d s . 
 
 FORMULA FOR MEAN VELOCITY OF FLOW. 
 By equation (12) the coefficient of velocity m, is
 
 SULLIVAN'S NEW HYDRAULICS. 
 Hd^d S ff _ S^/d 8 
 
 And by transposition in (12) we have, 
 
 In which, 
 
 v mean velocity in feet per second. 
 
 H=total head in feet, where discharge is free. 
 
 fl=h"+bv where discharge is throttled ( 5). 
 
 1= length of pipe in feet. 
 
 d=diameter in feet. 
 
 m coefficient of velocity determined in terms of d in 
 feet. 
 
 Where the altitude is sufficient to affect the value of g, 
 the formula may be written, 
 
 , when m- / y8 ; H:= 
 
 In this case the value of m must be found according to 
 the value of 2gH at the given altitude. 
 
 FORMULA FOR TOTAL HEAD REQUIRED TO GENERATE A 
 
 GIVEN VELOCITY. 
 miv* mlv* 
 
 The slope (S) required to generate a given mean velocity 
 is 
 
 S = m -^n ^-^rrXd* (25) 
 
 To find the length in feet I, in which there must be the 
 given head in feet H, or fall in feet equal H, in order to 
 generate the given mean velocity v: 
 
 Hdy/d_H y yd* (26) 
 
 m v s v s m
 
 100 SULLIVAN'S NEW HYDRAULICS. 
 
 FORMULAS IN TERMS OP CUBIC FEET PER SECOND AND DI- 
 
 AMETER IN FEET. 
 
 Letq=cubic feet per second discharged,=AreaXvelocityi 
 a= area of pipe in square feet. 
 
 Then a=d s X-7584, and v=/ X~ whence 
 
 q v/T~m=d 2 .785VH ^d 8 or q 1 /m=d ir .7854 v /S 1 /d 
 
 whence 
 
 8 
 
 (28) 
 
 I .61685 IS i/d*i_ / .6165 y /a /HII . . .(29) 
 9 \ m * m 
 
 Hence the diameter in feet required to cause the dis- 
 charge of a given number of cubic feet per second is 
 
 (28) 
 If total loss of head is predetermined then 
 
 And the slope required to cause a given diameter to dis- 
 charge a given quantity in cubic feet per second will be 
 m q* m q* 
 
 And, 
 
 qm? ._JE_xx__il 
 [= 61685^/c
 
 SULLIVAN'S NEW HYDRAULICS. 101 
 
 _ , q* v i . . /am 
 
 .616853/d" - .61( 
 hVd" .61685 
 
 H .GieSSy'd 1 ! 
 m = ; s : 
 
 _H_JP1685j/dij_ 
 m q* 
 
 /Hyd".61685_ /S|/d"X. 61685 (36) 
 
 I/ " m { K " m 
 
 As v=-^- it appears from an inspection of (29) and (36) 
 
 that the relative discharges will be ao f/d 11 . 
 
 The slopes, or heads and lengths being equal, then 
 
 q : q : : ^/d 11 : fc/d 11 , provided the roughnesses are 
 equal. 
 
 (See Table No. 18, 33.) 
 
 17 Formulas in Terms of Pressure, Diameter and 
 Quantity. Head in feet and pressure in pounds per square 
 inch are convertible terms. Pressure increases directly 
 as head increases, and the velocity will be proportional to 
 either ,/H or /P. When H=2.3041 feet, P=l Ib. per square 
 inch. Hence the coefficients determined in terms of H will 
 not apply in a formula in terms of P. The coefficients may, 
 however, be converted from terms of H or S to terms of P as 
 pointed out in 10 and as follows:-- 
 p 
 
 P=HX-434, and H=-jg|-=PX23041. Hence if we have 
 
 the value of n or m in terms of H and d in feet, and wish to con- 
 vert to terms of pressure in pounds per square inch P, and 
 diameter in feet d, we divide the value of n or m in terms of 
 H and d, by 2.3041, and the result is the value of n or m in 
 terms of Pand d.
 
 102 SULLIVAN'S NEW HYDRAULICS. 
 
 Tt ,_ n Zv* nlv* 
 
 .(38) 
 
 V/d 8 '" dj/d 
 In which, 
 
 P'=total Ibo. per squan inch pressure lost by friction. 
 n=coefficient of resistance in terms of P' and d. 
 Let P=total pressure in Ibs. per square inch. 
 P'=total pressure lost by friction. 
 Pv=velocity pressure. 
 When the discharge is free, P =P Pv, 
 To find the pressure in pounds per square inch required 
 to balance the friction and generate a mean velocity v, in 
 feet per second: 
 
 *> 
 
 q=av=$/d 11 \/ p X -7854 -H ^ 
 
 q^nTT^Kd'VPX .7854,whence 
 
 To find the diameter in feet to discharge the quantity q, 
 in cubic feet per second, through the length I, when the 
 total pressure is P: 
 
 > 8 q* 11 / m 8 ll/Z 8 q* 
 
 d*= K -3S66- X I/pi"' " (43) 
 
 To find the total pressure required to balance the re- 
 sistance and force the discharge of q cubic feet per second 
 through a pipe of given length and diameter in feet (Lifting 
 weight of water not included). 
 
 I m q 8 m q 8 
 
 ~".616853i/d TT = .616853 X ^d 11 ^ * ) 
 
 To find the pressure lost by friction while discharging a 
 given quantity in cubic feet per second:
 
 SULLIVAN'S NEW HYDRAULICS. 103 
 
 n/ 
 
 P '=.6mWdii (45) 
 
 The length of pipe in feet through which a given pres- 
 sure in pounds per square inch will force a given quantity 
 of discharge is, 
 
 P/d" X .61685 
 
 mq 2 
 
 To find the coefficient of resistance n, in terms of q, d 
 and P: 
 
 . 61685 
 
 To find the coefficient of velocity in terms of q, d and 
 ^~ (48) 
 
 **1 
 
 18. Formulas In Terms of Hydraulic Radius (r) and 
 Slope (S). 
 
 m I v 8 m I v 8 
 
 Hy/r 3 Hry/r 
 
 mv* mv* 
 
 mv mv* ' ( 5 ) 
 
 Hrv/r Sv/r 8 S 
 
 m =-T7"~ = -^~ = -v^Xv^ 3 (51) 
 
 h"rvT 8 
 
 I v 8 = ~ v s ~~ v 
 
 = ^1-Xl/r" I 
 
 The length in which there must be a fall of one foot in 
 order to generate any given mean velocity v, is 
 
 ^=^-=-m7 2 - <) 
 
 / TT / m ^ \ /H T/r 3 /Sr/r 
 
 v =i/ H ^ ("vr^ i/ x ^-= v-^~- 
 
 V** X \/-^r (54)
 
 104 SULLIVAN'S NEW HYDRAULICS. 
 
 Area in square feet =12.5664Xr 2 . q=av. 
 
 q=12.5664rXe/' 8 Xl/ / - a 7 (55) 
 
 qT/m^f/riiXi/S X 12.5664, whence, 
 i X 157.91 44 
 
 q 2 
 
 m= 
 
 n JLi^=. ...(57) 
 
 S " = "l57.9U4Vr rf " = 1573144" X 7^ (58) 
 
 S= 157.914Vri'i (59) 
 
 H =i57:9WFn- > 
 
 157.9144^11 
 
 m 
 
 * 8 
 
 ....(61) 
 ...(62) 
 
 -v' - ' T 7 ' 91i4 <) 
 
 '-V SBSOSg-xB* ' (64> 
 
 117 q*m 2 
 
 V 249\36:958"XS 2 " '"^ 
 ^157^/rii ^ 
 
 19. Application and Limitations of the Foregoing 
 Formulas. As heretofore noted under the table of circles 
 and of open channels (3) r is not necessarily an index of ca- 
 pacity in open channels as it is in pipes and circular channels 
 flowing full. Hence in open channels the formulas (63) and 
 (55) for q will not necessarily give accurate results, unless the 
 value of r was originally determined in terms of q when the
 
 SULLIVAN'S NEW HYDRAULICS. 105 
 
 channel was designed. In channels having side slopes of 2 to 
 1 the formula for q will usually apply quite accurately. For 
 the same reason the formula for r does not apply to open 
 channels in general, but only to those in which the value of r 
 was determined, or is to be determined in terms of q. All the 
 formulas apply with exactness to pipes and circular closed 
 channels flowing full. All the formulas in terms of r, except 
 those just noted, apply to all forms of open or closed chan- 
 cels. These exceptions in the case of open channels, do not, 
 however, affect the general application of the coefficients, be- 
 cause the coefficient depends upon the relations of a to p 
 which is always expressed in any given case by r which is 
 
 equal in all cases, and the friction surface p, always bears 
 
 P 
 
 the same relation to r that r* bears to the area in any given 
 case whether r is an index of capacity or of length of peri- 
 meter or not. 
 
 20 Formulas in Which C is Used Instead of m. 
 
 In the tables of coefficients heretofore developed the 
 values of both m and C were given in order that either form 
 of the formula might be applied in any case at pleasure. All 
 the formulas using the coefficient C instead of m may be de- 
 duced from the following: 
 
 v=C t/r !/r /S (67) 
 
 v=C f/r t/rS (68) 
 
 v=C e/i 8 i/S=C 1 /S7' :I " ( 69 ) 
 
 v=C t/d !/d v/S (70) 
 
 v=C e/d !/dS". (71) 
 
 v=C t/d 8 1 /S=C 1 /S7d r , (72) 
 
 v=C S/d 8 !/?-!// : (73) 
 
 v=C /r 3 /H -r- i/l (74) 
 
 Area in square feet, A = d 8 X -354 
 
 Area in square feet, A = r 8 X 12.5664 
 
 q=Av. The same limitations mentioned in the preced-
 
 106 SULLIVAN'S NEW HYDRAULICS 
 
 ing section will also be observed in the formulas in this form 
 relating to q and r in open channels. 
 
 FORMULAS IN TERMS OF DIAMETER IN FEET USING C. 
 By transposition in formula (72) we have, 
 
 v*-c t/d 8 " 
 
 
 
 "(YD) 
 
 J -CVd 8 
 
 r /"HZ v 
 
 (?()) 
 
 ~V S!/d 8 ~ ^3X^8 
 M 
 
 (70 
 
 2 Xi/d 8 
 C 2 H v/d 8 
 
 (78) 
 
 q = d s X -7854 XCX t/d 8 X i/S = t/d 11 
 X-7854 (80) 
 
 (79) 
 v/S X 
 
 t/a q di' q4 
 
 
 C^S-X.7854' S 2 C*.3805 
 
 
 , 11 / q 4 
 
 
 21. Formulas in Terms of Hydraulic Radius in Feet 
 Using C. 
 
 By transposition in formulas (69) and (74) we have 
 
 (82) 
 
 C =l/S7F 
 
 8= 
 
 H= 
 
 C H 
 
 q=Av=12.5664Xr 8 XCX*/r 8 X 
 
 t/r^xcysxia.sees
 
 SULLIVAN'S NEW HYDRAULICS, 107 
 
 11 / q 4 
 
 I/ 24936.958XC 4 
 
 " 157.9144 
 I q 8 
 
 7.9144 " " <(90) 
 
 C* 1 /r^ 157.9144 " 
 |= 157.9144 y"0'H ........................ (92) 
 
 C== 125664 ,/SX t/r 11 
 
 A set of formulas in terms of pressure in pounds per 
 square inch and diameter in feet or inches may be deduced 
 in like manner from equation (73). It is not deemed neces- 
 sary to deduce the formula in all its possible forms and 
 terms, as that is a simple matter which may be performed 
 at the pleasure of the person using it, and would require un- 
 necessary space here. 
 
 22. Special Formula for Vertical Pipes. Because 
 of the relation of H to I in all formulas the ordinary 
 formulas for flow will not apply to a pipe in a vertical 
 or nearly vertical position. In such case H and I in- 
 
 TT 
 
 crease at tne same rate, and hence -y=l, regardless 
 
 of the head or length. On account of this fact all the 
 formulas of the different writers on hydraulics will give 
 the same velocity for a head of a hundred feet as for a head 
 of 1,000 feet. It is therefore necessary to use a special form- 
 ula in such case. In a vertical pipe the water is supported 
 at no point whatever by any portion of the pipe walls. The 
 effect of gravity is not impeded except by the roughness of 
 the pipe walla. In such vertical pipe there is a gain of one 
 foot head for each foot of length. The resistance to entry 
 and the pipe wall friction will be the only loss of head. Hence
 
 108 SULLIVAN'S NEW HYDRAULICS. 
 
 if the sum of their effects be deducted from the total head, 
 the velocity should equal that due to the remainder of the 
 head. On this theory the following formula is proposed: 
 
 TH- (-=- 
 
 -) 
 
 The head, slope, velocity, or quantity may be found by 
 the principles given in 52, and table No. 24. 
 
 CHAPTER IV. 
 
 Of Tables for Rapid Calculation of Velocity and Discharge 
 in Open and Closed Channels, Friction Loss, &c. 
 
 23. Table for Velocity and Discharge. Clean, Average 
 Weight Cast Iron Pipes, Not Coated. In tables No. 1 and 
 No. 2 the diameters are given in inches, the areas in square 
 feet, and the discharge in cubic feet per second. 
 How to use Tables No. 1 and No. 2. 
 
 To find the mean velocity in feet per second: Multiply 
 the quantity in column No. 5 opposite the given diameter in 
 inches by ,/sT For v/S^ see table No. 15, 30. For S, see 
 Table No. 16, 31. 
 
 To find the discharge in cubic feet per second: Multiply 
 the quantity in column No. 6 opposite the given diameter by 
 ,/S. 
 
 v=C X V& v/~ST q = AV= AC X t/d s " l /sT Take 
 d in inches. 
 
 For average weight clean cast iron pipe, C = 7.756 when 
 d = inches.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE. No. 1. 
 Clean cast iron pipe, not coated. 
 
 109 
 
 Col. 1 
 Diam. 
 Inch's 
 
 Col. 2 
 Inches 
 
 Col. 3 
 
 t/d 8 
 
 Inches 
 
 Col. 4 
 Area 
 Sq. Feet 
 
 Col. 5 
 For 
 Velocity 
 
 Col. 6 
 For 
 Discharge 
 ACXK d8 
 
 Vt 
 & 
 
 0.35355 
 0.65227 
 
 0.5946 
 0.8059 
 
 .001366 
 .003068 
 
 4.6117 
 6.2505 
 
 .006300 
 .019176 
 
 1.00 
 
 1. 
 
 1. 
 
 .005454 
 
 7.7560 
 
 .042301 
 
 1.34 
 
 1.3975 
 
 1.1820 
 
 .008522 
 
 9.1675 
 
 .078125 
 
 
 1.8360 
 
 1.3550 
 
 .01227 
 
 10.5093 
 
 .128949 
 
 i'. 
 
 2.3152 
 
 1.5210 
 
 .01670 
 
 11.7968 
 
 .197006 
 
 2 
 
 2.8284 
 
 1.6810 
 
 .02232 
 
 13.0378 
 
 .291003 
 
 3 
 
 5.1961 
 
 2.2790 
 
 .04909 
 
 17.6759 
 
 .867709 
 
 I 
 
 8. 
 
 2.8284 
 
 .08726 
 
 21.9370 
 
 1.91422 
 
 5 
 
 11.1803 
 
 3.3439 
 
 .13630 
 
 25.9352 
 
 3.53496 
 
 6 
 
 14.6969 
 
 3.8340 
 
 .19635 
 
 29.7365 
 
 5.83876 
 
 7 
 
 18.5202 
 
 4.3040 
 
 .26730 
 
 
 8.92295 
 
 8 
 
 22.6274 
 
 4.7570 
 
 .34910 
 
 36 '.8952 
 
 12.88014 
 
 9 
 
 27. 
 
 5.1960 
 
 .44180 
 
 40.3001 
 
 17.80458 
 
 10 
 
 31.6227 
 
 5.6231 
 
 .54540 
 
 43.6127 
 
 23.78636 
 
 11 
 
 36.4828 
 
 6.0400 
 
 .66000 
 
 46.8462 
 
 30.91849 
 
 12 
 
 41.5692 
 
 6.4470 
 
 .7854 
 
 50.0029 
 
 39.27000 
 
 13 
 
 46.8721 
 
 6.8460 
 
 .9218 
 
 53.0975 
 
 48.94527 
 
 14 
 
 52.3832 
 
 7.237 
 
 1.069 
 
 56.1301 
 
 60.00307 
 
 15 
 
 58.0747 
 
 7.622 
 
 1.227 
 
 59.1162 
 
 72.53557 
 
 16 
 
 64. 
 
 8. 
 
 1.396 
 
 62.0480 
 
 86.61900 
 
 17 
 
 70.0927 
 
 8.372 
 
 1.576 
 
 64.9332 
 
 102.3347 
 
 18 
 
 76.3675 
 
 8.738 
 
 1.767 
 
 67.7719 
 
 119.7529 
 
 19 
 
 82.8190 
 
 9.100 
 
 1.969 
 
 70.5796 
 
 138.8300 
 
 20 
 
 89.4427 
 
 9.457 
 
 2.182 
 
 73.3484 
 
 160.0462 
 
 21 
 
 96.2340 
 
 9.810 
 
 2.405 
 
 76.0863 
 
 182.9876 
 
 22 
 
 103.189 
 
 10.158 
 
 2.640 
 
 78.7854 
 
 208.0000 
 
 23 
 
 110.304 
 
 10.504 
 
 2.885 
 
 81.4690 
 
 235.0380 
 
 24 
 
 117.575 
 
 10.844 
 
 3.1416 
 
 84.1060 
 
 264.2274 
 
 25 
 
 125. 
 
 11.180 
 
 3.409 
 
 86.7120 
 
 295.6012 
 
 26 
 
 132.574 
 
 11.514 
 
 3.687 
 
 89.3025 
 
 329.2583 
 
 27 
 
 140.296 
 
 11.844 
 
 3.976 
 
 91.8620 
 
 365.2433 
 
 28 
 
 148.162 
 
 12.172 
 
 4.276 
 
 94.4060 
 
 403.6800 
 
 29 
 
 156.169 
 
 12.496 
 
 4.587 
 
 96.9189 
 
 444.5670 
 
 30 
 
 164.316 
 
 12.820 
 
 4.909 
 
 99.4319 
 
 488.1112 
 
 31 
 
 172.600 
 
 13.139 
 
 5.241 
 
 101.9061 
 
 534.0898 
 
 32 
 
 181.0193 
 
 13.456 
 
 5.585 
 
 104.3647 
 
 582.8768 
 
 33 
 
 189.5705 
 
 13.768 
 
 5.940 
 
 106.7846 
 
 634.3005 
 
 36 
 
 216.0000 
 
 14.698 
 
 7.069 
 
 113.9977 
 
 805.8497 
 
 40 
 
 252.8822 
 
 15.907 
 
 8.726 
 
 123.3747 
 
 1076.5676 
 
 44 
 
 291.8629 
 
 17.086 
 
 10.558 
 
 132.5190 
 
 1399.1356 
 
 48 
 
 332.5537 
 
 18.237 
 
 12.567 
 
 141.4461 
 
 1777.5531 
 
 54 
 
 396.8173 
 
 19.920 
 
 15.905 
 
 154.4995 
 
 2457.3145 
 
 60 
 
 464.7580 
 
 21.560 
 
 19.635 
 
 167.2193 
 
 3283.3509 
 
 72 
 
 606.9402 
 
 24.710 
 
 29.607 
 
 191.6507 
 
 5674.2022 
 
 84 
 
 769.8727 
 
 27.746 
 
 38.484 
 
 215.1979 
 
 8281.6759 
 
 96 
 
 940.6040 
 
 30.670 
 
 50.265 
 
 237.8765 
 
 11956.8622 
 
 120 
 
 1314.5341 
 
 36.250 
 
 78.540 
 
 281.1550 
 
 22081.9137 
 
 REMARK. In large cast iron pipes, or in thick small pipes 
 there is great liability to blow holes and rough places. The
 
 110 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 thicker the pipe shell is, the more liable it is to be rough. It 
 might be well to take C=7.65 in terms of diameter in inches 
 for cast iron pipes of 48 inches diameter or greater, and for 
 other and smaller diameters that are equally thick as 48 inch 
 pipe. Large pipes are never as perfect or as smooth as med- 
 ium diameters and thicknesses. 
 
 This fact has led some engineers to conclude that the law 
 of friction in pipes was slightly different in large pipes from 
 what it is in medium diameters. It is claimed that this 
 change occurs at about a diameter of 48 inches. It is due 
 simply to the rougher casting of large pipes which require 
 thickness. There is no change in the law of friction at any 
 diameter whatever. Very small cast iron pipes are also cast 
 thick to prevent breakage in handling and are usually as 
 rough as the very large diameters. Pipes less than six inches 
 diameter and over 36 inches diameter, are usually rougher to 
 some extent than the intermediate diameters. 
 
 q=A ~~ 
 
 TABLE No. 2. 
 
 Asphaltum coated pipes. C=8.b7, d=inches. 
 
 Col. 1 
 
 Col. 2 
 
 Col. 3 
 
 Col. 4 
 
 Col. 6 
 
 Col. 6 
 
 Diam 
 
 s~fta 
 
 $/~d* 
 
 Area 
 
 cxt/in^ 
 
 ACX/7F*- 
 
 Inch's 
 
 Inches 
 
 Inches 
 
 Sq. 
 
 For 
 
 For 
 
 
 
 
 Feet 
 
 Velocity. 
 
 Discharge 
 
 6 
 
 14.6969 
 
 3.834 
 
 .19635 
 
 33.2407 
 
 6.42681 
 
 7 
 
 18.5202 
 
 4.304 
 
 .2673 
 
 37.3156 
 
 9.97445 
 
 8 
 
 22.6274 
 
 4.757 
 
 .3491 
 
 41.2432 
 
 14.39800 
 
 9 
 
 27. 
 
 5.196 
 
 .4418 
 
 44.9493 
 
 19.85860 
 
 10 
 
 31.6227 
 
 5.623 
 
 .5454 
 
 48.7522 
 
 26.58945 
 
 11 
 
 36.4828 
 
 6.040 
 
 .6600 
 
 52.3668 
 
 34.56208 
 
 12 
 
 41. 5692 
 
 6.447 
 
 .7854 
 
 55.8955 
 
 43.90032 
 
 13 
 
 46.8721 
 
 6.846 
 
 .9213 
 
 59.3548 
 
 54.71325 
 
 14 
 
 52.3832 
 
 7.237 
 
 1.069 
 
 62.7448 
 
 67.07419 
 
 15 
 
 58.0747 
 
 7.622 
 
 1.227 
 
 66.0827 
 
 81.08347 
 
 16 
 
 64. 
 
 8. 
 
 1.396 
 
 69.3600 
 
 96.82656 
 
 17 
 
 70.0927 
 
 8.372 
 
 1.576 
 
 72.5852 
 
 lit. 39427 
 
 18 
 
 76.3675 
 
 8.738 
 
 1.767 
 
 75.7584 
 
 133 . 86509 
 
 19 
 
 82.8190 
 
 9.100 
 
 1.969 
 
 78.8970 
 
 155.34819 
 
 20 
 
 89.4427 
 
 9.457 
 
 2.182 
 
 81.9922 
 
 178.90698 
 
 21 
 
 96.2340 
 
 9.810 
 
 2.405 
 
 85. '527 
 
 204.55174 
 
 22 
 
 103.189 
 
 10.158 
 
 2.640 
 
 88.0698 
 
 232.50443 
 
 23 
 
 110.304 
 
 10.504 
 
 2.885 
 
 91.0697 
 
 262.73603 
 
 24 
 
 117.575 
 
 10.844 
 
 3.1416 
 
 94.0L74 
 
 295.36541 
 
 25 
 
 125. 
 
 11.180 
 
 3.409 
 
 96.9306 
 
 330.43641 
 
 26 
 
 132.574 
 
 11.514 
 
 3.687 
 
 99.8264 
 
 368.05986 
 
 27 
 
 140.296 
 
 11.844 
 
 3.976 
 
 102.6874 
 
 407.88542 
 
 28 
 
 148.162 
 
 12.172 
 
 4.276 
 
 105.4312 
 
 450.82398 
 
 29 
 
 156.169 
 
 12.496 
 
 4.587 
 
 108.3403 
 
 496.957C4 
 
 30 
 
 164.316 
 
 12.820 
 
 4.909 
 
 111.1494 
 
 545.63240
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 Ill 
 
 TABLE No. 2 Continued. 
 
 Col. 1 
 
 Diam. 
 Inch's 
 
 Col. 2 
 v/d 8 
 Inches 
 
 Col. 3 
 
 e/d s 
 
 Inches 
 
 Col. 4 
 Area Sq. 
 Feet. 
 
 Col. 5 
 CXt/d 8 
 Velocity 
 
 Col. 6 
 
 ACXf/d 8 
 For Disch'g. 
 
 31 
 
 172.600 
 
 13.139 
 
 5.241 
 
 113.9151 
 
 597.02919 
 
 32 
 
 181.0193 
 
 13.456 
 
 5.585 
 
 116.6635 
 
 651.56576 
 
 33 
 
 189.5705 
 
 13.768 
 
 5.940 
 
 119.4685 
 
 709.64324 
 
 34 
 
 198.2523 
 
 14.081 
 
 6.305 
 
 122.0822 
 
 769.72871 
 
 35 ' 
 
 207.U62S 
 
 14.390 
 
 6.681 
 
 124.7613 
 
 833.52624 
 
 86 
 
 216. 
 
 14.698 
 
 7.069 
 
 127.431B 
 
 900.80267 
 
 87 
 
 225.0622 
 
 15.002 
 
 7.467 
 
 130.0673 
 
 963.93283 
 
 38 
 
 234.2477 
 
 15.300 
 
 7.876 
 
 132.6510 
 
 1044.75927 
 
 40 
 
 252.8822 
 
 15.907 
 
 f-OC 
 
 8. /26 
 
 137.9137 
 
 1203.43495 
 
 44 
 
 291.8629 
 
 17.086 
 
 10.558 
 
 148.1356 
 
 1564.01587 
 
 48 
 
 332.5537 
 
 18.237 
 
 12.567 
 
 158.1148 
 
 1987.02869 
 
 54 
 
 3%. 8173 
 
 19.920 
 
 15.905 
 
 172.7064 
 
 2746.89529 
 
 M 
 
 464.7580 
 
 21.560 
 
 19.635 
 
 186.9252 
 
 3670.27630 
 
 72 
 
 6f!94<r> 
 
 24.710 
 
 29.607 
 
 214.2357 
 
 6342.87637 
 
 84 
 
 769.8727 
 
 27.746 
 
 38.484 
 
 240.5478 
 
 9257.24164 
 
 96 
 
 940.6040 
 
 80.670 
 
 50.265 
 
 265.9089 
 
 1S365. 41086 
 
 REMARK This table relates to asphaltum coated pipes 
 not to pipes coated with coal tar, nor to compound coatings 
 made of only one part asphaltum. What is meant by as- 
 phaltum coated pipes is that class of pipes which have been 
 properly coated with a compound composed of 18 to 20 per 
 cent of crude petroleum and the remainder of asphaltum. 
 The coating compound to be heated to 300 degrees, Fahr., 
 and the pipe to remain submerged in the hot bath until the 
 pipe metal attains the same temperature as that of the bath. 
 Coal tar coatings do not form quite as smooth a surface as 
 the above described coating, and hence do not develop as 
 high values of C. If d is taken in feet, then m =.00032, and 
 C=55.90 as the average value of the coefficients for asphal- 
 tum and oil coated pipes. The value of C or m will vary 
 slightly with the quality or purity of the asphaltum used. 
 (See group No. 2.) 
 
 24. Table for Velocity and Discharge of Brick Lined 
 Circular Conduits or Sewers Flowing Full. In the follow- 
 ing Table No. 3 the diameters are in feet, the areas in square 
 feet, and the discharge in cubic feet per second. The coeffi- 
 cient is in terms of diameter in feet and is based upon the 
 discharge of Washington, D. C., aqueduct,. (See Group 6.)
 
 112 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 ;or v= 
 
 m=.0008577; C= 
 
 34.00 in terms of diameter in feet. q=A CXt/d* >/! 
 
 TABLE No. 3 
 Circular brick conduits and sewers. C=34.00. 
 
 Col. 1 
 Diana. 
 Feet 
 
 Col. 2 
 v/d 3 
 Feet 
 
 Col. 3 
 
 t/d s 
 Feet 
 
 Col. 4 
 Area 
 Sq Feet 
 
 Col. 5 
 For Vel. 
 CXt/d" 
 
 Col. 6 
 For Disch'g 
 ACXt/d s 
 
 1.50 
 
 1.837 
 
 1.355 
 
 1.767 
 
 46.070 
 
 81.4057 
 
 2.00 
 
 2.8-28 
 
 1.681 
 
 3.142 
 
 57.154 
 
 179.5778 
 
 2.50 
 
 3.953 
 
 1.988 
 
 4.909 
 
 67.592 
 
 331.8091 
 
 3.00 
 
 5.196 
 
 2.279 
 
 7.068 
 
 77.486 
 
 537.6711 
 
 4.00 
 
 8. 
 
 2.828 
 
 12.566 
 
 96.166 
 
 1208.8016 
 
 5.00 
 
 11.180 
 
 3.344 
 
 19.635 
 
 113 6% 
 
 2232.4210 
 
 6.00 
 
 14.697 
 
 3>34 
 
 28.274 
 
 130.356 
 
 3685.6855 
 
 7.00 
 
 18.5^0 
 
 4.304 
 
 38.485 
 
 146.336 
 
 5631.7410 
 
 8.00 
 
 22.627 
 
 4.757 
 
 50 266 
 
 161.738 
 
 8129.9223 
 
 9.00 
 
 27. 
 
 5.1% 
 
 63.617 
 
 176.664 
 
 11238.8337 
 
 10.00 
 
 31.623 
 
 5.623 
 
 78.540 
 
 191.182 
 
 15015.4343 
 
 11.00 
 
 36.4b3 
 
 6.040 
 
 95.033 
 
 205.360 
 
 19515.9769 
 
 12.00 
 
 41.569 
 
 6.447 
 
 113.100 
 
 219.198 
 
 24791.2938 
 
 13.00 
 
 46.872 
 
 6.846 
 
 132.730 
 
 232 764 
 
 30894 . 7657 
 
 14.00 
 
 52.38< 
 
 7.237 
 
 153.940 
 
 246.058 
 
 37878.1685 
 
 NOTE. Compare the values of the coefficients of the new 
 Croton aqueduct for a depth of 9 feet with those of the Wash- 
 ington aqueduct both in group No. 6. The above value of 
 C in terms of diameter in feet is about correct for plain brick. 
 
 25. Egg Shaped Brick Sewers and Conduits. IK egg 
 
 shaped sewers the vertical diameter is one and one-half times 
 the horizontal or greatest transverse diameter. Radius of in- 
 vert, % vertical diameter. Radius of sides equal vertical diam- 
 eter. Let d=greatest transverse diameter in feet. 
 
 a=area in square feet. 
 
 p=wetted perimeter in lineal feet. 
 
 r=hydraulic mean depth=L 
 P 
 Then, in egg shaped sewers and conduits, 
 
 a=d*X-284 for \ full depth 
 
 a=d 8 X-755825 for f full depth. 
 
 a=d*Xl-148525 for full depth. 
 The wet perimeter in lineal feet will be, 
 
 p=dXl-3747 for \ full depth.
 
 SULLIVAN'S NEW HYDRAULS. 113 
 
 p=dX23941 for | full depth. 
 p=dX3.965 for full depth. 
 
 The mean hydraulic depths, ' r~=r, will be, 
 
 r=dX-2066 for full depth. 
 
 r=dX-3157 for | full depth. 
 
 r=dX-2897 for full depth. 
 
 See "Hydraulic Tables" by P. J. Plynn; Van Nostrand'e Sci- 
 ence Series No. 67, and also see "Treatise on Hydraulics" by 
 Prof. Merriman, p. 235. (5th. Edition.) 
 
 TABLE FOR VELOCITIES AND DISCHARGES OP EGG SHAPED 
 
 BRICK CONDUITS AND SEWERS PLOWING TWO-THIRDS 
 
 FULL DEPTH. 
 
 As this class of conduits are not circular in form, the 
 coefficient is in terms of hydraulic mean depth (r) in feet, 
 and the value of the coefficient used in the following table 
 is that developed by the Washington, D. C., aqueduct, (See 
 Group No. 6). This table is to be used in the same manner 
 as Tables Nos. 1,2 and 3. 
 
 v=CX t/r 8 ,/S, and q=ACXt/r 8 i/S. C=96.00 
 TABLE No. 4. 
 
 Areas, hydraulic depths, velocities and discharges for % 
 Full Depth. 0=96. 
 
 Col. 0. 
 
 Col. ICol. 1 
 
 Col. 2 
 
 Col. 4 
 
 Column 5. 
 
 Column C 
 
 Trans. 
 Diam. 
 
 r 
 Feet 
 
 j/r' 
 
 Feet 
 
 J 
 
 Area 
 Sq.Ft 
 
 For velocity 
 CXKr 8 
 
 For Dischg 
 AC X V** 
 
 1.50 
 
 0.474 
 
 0.3263 
 
 0.5713 
 
 1.701 
 
 54.8443 
 
 93.2910 
 
 2.00 
 
 0.631 
 
 0.5'U2 
 
 0.70.O 
 
 3.025 
 
 67.9680 
 
 205.6032 
 
 2.50 
 
 0.789 
 
 0.7008 
 
 0.8372 
 
 4.724 
 
 80.3712 
 
 379.3535 
 
 3.00 
 
 0.947 
 
 0.9216 
 
 0.0600 
 
 6.802 
 
 92.1600 
 
 626.8723 
 
 3.50 
 
 1.105 
 
 1.1615 
 
 1.0780 
 
 9.259 
 
 103.4880 
 
 958.1954 
 
 4.00 
 
 1.263 
 
 1.419 
 
 1.19LO 
 
 12.093 
 
 114.3360 
 
 1382.6653 
 
 4.50 
 
 1.421 
 
 1.694 
 
 1.302 
 
 15.305 
 
 124.9920 
 
 1913.0025 
 
 5.00 
 
 1.579 
 
 J.984 
 
 1.408 
 
 18.895 
 
 135.1680 
 
 2555 . 3994 
 
 6.00 
 
 1.894 
 
 2.606 
 
 1.614 
 
 27.210 
 
 154.9440 
 
 4216.0262 
 
 7.00 
 
 2.210 
 
 3.285 
 
 1.812 
 
 37.035 
 
 173.9520 
 
 6442.3123 
 
 8.00 
 
 2.526 
 
 4.015 
 
 2.004 
 
 48.373 
 
 192.3840 
 
 9306.1912 
 
 9.00 
 
 2.841 
 
 4.789 
 
 2.188 
 
 61.222 
 
 210.0480 
 
 12859.5586 
 
 10.00 
 
 3.157 
 
 5.610 
 
 2.368 
 
 75.583 
 
 227.3280 
 
 17182.1322 
 
 11.00 
 
 3.473 
 
 6.472 
 
 2.544 
 
 91.455 
 
 244.2240 
 
 22335.5059 
 
 Small sewers should be circular in form. See 55.
 
 114 SULLIVAN'S NEW HYDRAULICS. 
 
 26 Formulas for Use in Connection With the Fore- 
 going Tables. 
 
 In the tables for pipes and conduits are the tabular val- 
 ues of 
 
 CXKd 8 , CX^r 8 , A C XS/d* and A 
 Now 
 
 If the slope and mean velocity have been decided upon, 
 
 y 
 
 then the value of CX^ / d 8 = TQ- and opposite this value of 
 
 V* 
 
 is the required diameter to generate the given veloc- 
 ity. 
 
 If a given diameter is required to discharge a given 
 number of cubic feet per second, then the grade or slope may 
 be found thus: 
 
 / q 
 
 V b A CXf/d 
 
 The grade to generate a given velocity in feet per second 
 may be found thus: 
 
 If the quantity to be discharged and the grade are given, 
 then the required diameter will be found thus: 
 
 ACXv/d^yg. Look for the diameter which corresponds 
 
 to the value of A CXv/'d 8 in the table. 
 
 The general formulas already given are so simple that re- 
 sort to these formulas is not necessary.
 
 SULLIVAN'S NEW HYDRAULICS. 115 
 
 27 General Table of Values of r or d, With Roots- 
 
 TABLE No. 5 
 
 r or d 
 
 V^r or^/d 
 
 y'r 8 or v/d 
 
 ^'r or t/d 
 
 0.20 
 
 0.4472 
 
 0.089440 
 
 0.2990 
 
 .22 
 
 .4690 
 
 .103180 
 
 .3212 
 
 .24 
 
 .4899 
 
 .117576 
 
 .3429 
 
 .26 
 
 .5099 
 
 .132574 
 
 .3641 
 
 1 
 
 .5291 
 
 .5477 
 
 .148148 
 .164310 
 
 .3849 
 .4053 
 
 .32 
 
 .5656 
 
 .180992 
 
 .4244 
 
 .34 
 
 .5831 
 
 .19S254 
 
 .4452 
 
 .36 
 
 .6000 
 
 .216000 
 
 .4647 
 
 .38 
 
 .6164 
 
 .234232 
 
 .4840 
 
 .40 
 
 .6324 
 
 .252960 
 
 .5030 
 
 .42 
 
 .6481 
 
 .272202 
 
 .5217 
 
 .44 
 
 .6633 
 
 .291852 
 
 .5402 
 
 .46 
 
 .6782 
 
 .311972 
 
 .5585 
 
 .48 
 
 .6928 
 
 .332544 
 
 .5767 
 
 .50 
 
 .7071 
 
 354550 
 
 .5946 
 
 .52 
 
 .7211 
 
 .374972 
 
 .6124 
 
 .54 
 
 .7348 
 
 .396792 
 
 .6299 
 
 .56 
 
 .74<<3 
 
 .419048 
 
 .6473 
 
 .58 
 
 .7616 
 
 .441728 
 
 .6646 
 
 .60 
 
 .7746 
 
 .464760 
 
 .6817 
 
 .62 
 
 .7874 
 
 .488188 
 
 .6987 
 
 .64 
 
 .8 
 
 .512 
 
 .7155 
 
 .66 
 
 .8124 
 
 .536184 
 
 .7322 
 
 .68 
 
 .8246 
 
 : 560728 
 
 .7488 
 
 .70 
 
 .8366 
 
 ! 585620 
 
 .7653 
 
 .72 
 
 .8485 
 
 .610920 
 
 .7816 
 
 .74 
 
 .8602 
 
 .636548 
 
 .7978 
 
 .76 
 
 .8718 
 
 .662568 
 
 .8139 
 
 .78 
 
 8832 
 
 .688896 
 
 8300 
 
 .80 
 
 !8944 
 
 .715520 
 
 .8459 
 
 .82 
 
 .9055 
 
 .742510 
 
 .8617 
 
 .84 
 
 .9155 
 
 .769020 
 
 .8774 
 
 .86 
 
 .9273 
 
 .797478 
 
 .8930 
 
 .88 
 
 .9380 
 
 .825440 
 
 .9086 
 
 .90 
 
 .9487 
 
 .853830 
 
 .9240 
 
 .92 
 
 .9591 
 
 .882872 
 
 .9394 
 
 .94 
 
 .96 
 
 .9695 
 .9798 
 
 .911330 
 
 .940308 
 
 .9546 
 .9698 
 
 .98 
 1.00 
 
 .9899 
 1. 
 
 .970102 
 1. 
 
 .9849 
 1. 
 
 1.02 
 
 1.010 
 
 1.0302 
 
 1 015 
 
 1.04 
 
 1.020 
 
 1.0600 
 
 1.029 
 
 1.06 
 
 1.029 
 
 1.0907 
 
 1.045 
 
 1.08 
 
 1.039 
 
 1.1521 
 
 1 059 
 
 .10 
 
 1.049 
 
 1.1540 
 
 1.074 
 
 .12 
 
 1.058 
 
 1.1850 
 
 1.089 
 
 .14 
 
 1.068 
 
 1.2175 
 
 1.104 
 
 .16 
 
 1.077 
 
 1.2 94 
 
 1.118 
 
 .18 
 
 1.086 
 
 1.2815 
 
 1.132 
 
 .20 
 
 1.095 
 
 1.3140 
 
 1.146 
 
 .22 
 
 1.104 
 
 1.3469 
 
 1.160 
 
 .24 
 
 1.114 
 
 1.3800 
 
 1.175 
 
 .26 
 
 1.123 
 
 1.4150 
 
 1.189
 
 116 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE No. 5. Continued. 
 
 r or d 
 
 y/r or i/d 
 
 v/r 8 or !/d 
 
 e/r" or f/d 
 
 1.28 
 
 131 
 
 1.4480 
 
 .203 
 
 1.30 
 
 .144 
 
 1.4872 
 
 .217 
 
 1.32 
 
 .150 
 
 1.5180 
 
 .239 
 
 1.35 
 
 .161 
 
 1.5673 
 
 .252 
 
 1.40 
 
 .183 
 
 1.6562 
 
 .287 
 
 1.45 
 
 .214 
 
 1.7603 
 
 .326 
 
 1.50 
 
 .225 
 
 1.8375 
 
 .355 
 
 1.55 
 
 .245 
 
 1.9297 
 
 .399 
 
 1.60 
 
 .265 
 
 2.0240 
 
 .422 
 
 1.65 
 
 .284 
 
 2.1186 
 
 .455 
 
 1.70 
 
 .304 
 
 2.2168 
 
 .488 
 
 1.75 
 
 .323 
 
 2.2852 
 
 .511 
 
 1.80 
 
 .341 
 
 2.4138 
 
 .554 
 
 1.85 
 
 .360 
 
 2.5160 
 
 .568 
 
 1.90 
 
 .378 
 
 2.6182 
 
 .618 
 
 1.95 
 
 .396 
 
 2.7122 
 
 .647 
 
 2. 
 
 .414 
 
 2.8284 
 
 .663 
 
 2.05 
 
 .431 
 
 2.9335 
 
 .713 
 
 2.10 
 
 .459 
 
 3.0639 
 
 .750 
 
 2.15 
 
 .466 
 
 3.1519 
 
 .775 
 
 2.20 
 
 .483 
 
 3.2626 
 
 .806 
 
 2.25 
 
 .500 
 
 3.3750 
 
 .837 
 
 2.30 
 
 .526 
 
 3.5098 
 
 .873 
 
 2.35 
 
 .533 
 
 3.6025 
 
 .904 
 
 2.40 
 
 .549 
 
 3.7176 
 
 .928 
 
 2.45 
 
 .565 
 
 3.8342 
 
 1.958 
 
 2.50 
 
 .581 
 
 3.9525 
 
 1.988 
 
 2.55 
 
 .597 
 
 4.0723 
 
 2.018 
 
 2.60 
 
 .612 
 
 .1912 
 
 2.047 
 
 2.65 
 
 .638 
 
 .3407 
 
 2.083 
 
 2.70 
 
 .643 
 
 .4361 
 
 2 106 
 
 2.75 
 
 .658 
 
 .5595 
 
 2.135 
 
 2.80 
 
 .673 
 
 .6844 
 
 2.164 
 
 i:S 
 
 .688 
 .703 
 
 .8108 
 .9387 
 
 2.193 
 2.222 
 
 2.95 
 
 .717 
 
 5.0651 
 
 2.250 
 
 3. 
 
 .732 
 
 5.1960 
 
 2279 
 
 3.05 
 
 .746 
 
 5.3253 
 
 2.308 
 
 3.10 
 
 .761 
 
 5.4591 
 
 2.336 
 
 3.15 
 
 .775 
 
 5.5912 
 
 2 364 
 
 3.20 
 
 : .789 
 
 5.7248 
 
 2.392 
 
 3.25 
 
 
 5.8597 
 
 2.421 
 
 3.30 
 
 !816 
 
 5.9928 
 
 2.448 
 
 3.35 
 
 .830 
 
 6.1305 
 
 2.476 
 
 3.40 
 
 .844 
 
 6.2696 
 
 2.504 
 
 3.45 
 
 .857 
 
 6.4066 
 
 2.531 
 
 3.50 
 
 .871 
 
 6.5485 
 
 2.559 
 
 3.55 
 
 .884 
 
 6.6882 
 
 2.586 
 
 3.60 
 
 .897 
 
 6.8292 
 
 2.613 
 
 3.65 
 
 .910 
 
 6.9715 
 
 2.640 
 
 3.70 
 
 .923 
 
 7.1151 
 
 2.667 
 
 3.75 
 
 .936 
 
 7.26 
 
 2.694 
 
 3.80 
 
 .949 
 
 7.4062 
 
 2.721 
 
 3.85 
 
 .962 
 
 7 5537 
 
 2.746 
 
 3.90 
 
 .975 
 
 7.7025 
 
 2.775 
 
 3.95 
 
 1.987 
 
 7.8486 
 
 2.801
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE NO. 5. Continued. 
 
 117 
 
 r or d 
 
 y'r or y'd. 
 
 ,/f 8 or ,/d 8 
 
 t/r 8 or e/d 8 
 
 4. 
 
 2. 
 
 8. 
 
 2.828 
 
 4.05 
 
 2.012 
 
 8.1486 
 
 2.854 
 
 4.10 
 
 2.024 
 
 8.2984 
 
 2.881 
 
 4.15 
 
 2.037 
 
 8.4535 
 
 2.908 
 
 4.20 
 
 2.049 
 
 8.6058 
 
 2.933 
 
 4.25 
 
 2.061 
 
 8.7592 
 
 2.960 
 
 4.30 
 
 2.073 
 
 8.9139 
 
 2.986 
 
 4.35 
 
 2.085 
 
 9.0698 
 
 3.012 
 
 4.40 
 
 2.097 
 
 9.2268 
 
 3.037 
 
 4.45 
 
 2.109 
 
 9.3850 
 
 3.064 
 
 4.50 
 
 2.121 
 
 9.5445 
 
 3.089 
 
 4.55 
 
 2.133 
 
 9.7051 
 
 3.115 
 
 4.60 
 
 2.144 
 
 9.8624 
 
 3.140 
 
 4.65 
 
 2.156 
 
 10.0254 
 
 3.165 
 
 4.70 
 
 2.168 
 
 10.1896 
 
 3.192 
 
 4.75 
 
 2.179 
 
 10.3502 
 
 3.218 
 
 4.80 
 
 2.191 
 
 10.5168 
 
 3.243 
 
 4.16 
 
 2.202 
 
 10.6797 
 
 3 268 
 
 4.90 
 
 2.213 
 
 10.8437 
 
 3.293 
 
 4.95 
 
 2.225 
 
 11.0137 
 
 3.319 
 
 5. 
 
 2.236 
 
 11.1800 
 
 3.344 
 
 5.05 
 
 2.247 
 
 11.3473 
 
 3.369 
 
 5.10 
 
 2.258 
 
 11.5158 
 
 3.393 
 
 5.15 
 
 2.269 
 
 11.6853 
 
 3.419 
 
 5.20 
 
 2.280 
 
 11.8560 
 
 3.444 
 
 5.25 
 
 2.291 
 
 12.0277 
 
 3 468 
 
 5.30 
 
 2.302 
 
 12.2006 
 
 3 493 
 
 5.35 
 
 2.313 
 
 12.3745 
 
 3.518 
 
 5.40 
 
 2.823 
 
 12.5442 
 
 3.542 
 
 5.45 
 
 2.334 
 
 12.7203 
 
 3 567 
 
 5.50 
 
 2.845 
 
 12.8975 
 
 3.592 
 
 5.55 
 
 2 356 
 
 13 0758 
 
 3 616 
 
 5.60 
 
 2.366 
 
 13.2496 
 
 3^640 
 
 5.65 
 
 2.377 
 
 13.4300 
 
 3 665 
 
 5.70 
 
 2.388 
 
 13.6116 
 
 3.689 
 
 5.75 
 
 2.398 
 
 13.7885 
 
 3.713 
 
 5.80 
 
 
 13.9664 
 
 3 737 
 
 5.85 
 
 2 412 
 
 14.1453 
 
 3.761 
 
 5.90 
 
 2^429 
 
 14.3311 
 
 3.786 
 
 5.95 
 
 2.439 
 
 14.5120 
 
 3 810 
 
 6. 
 
 2.449 
 
 14.6940 
 
 3.834 
 
 6.05 
 
 2.460 
 
 14.8830 
 
 3 858 
 
 6.10 
 
 2.470 
 
 15.0670 
 
 3 881 
 
 6.15 
 6.20 
 
 2.480 
 2.490 
 
 15.2520 
 15.4380 
 
 31905 
 3 929 
 
 6.25 
 
 2.500 
 
 15.6250 
 
 3 953 
 
 6.30 
 6.35 
 
 2.510 
 2.520 
 
 15.8130 
 16.0020 
 
 3.977 
 4.000 
 
 6.40 
 
 2.530 
 
 16.1920 
 
 4 024 
 
 6.45 
 
 2.540 
 
 16.3830 
 
 4 047 
 
 6.50 
 
 2.550 
 
 16.5750 
 
 4.071 
 
 6.55 
 
 2.560 
 
 16.7680 
 
 4 094 
 
 6.60 
 
 2.569 
 
 16.9554 
 
 4l 118 
 
 6.65 
 
 2.579 
 
 17 . 1503 
 
 4 140 
 
 6.70 
 
 2.588 
 
 
 4 164 
 
 6.75 
 
 2.598 
 
 1715365 
 
 4.188
 
 118 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE No. 5 Continued. 
 
 r or d 
 
 l/r or \/d 
 
 j/r* or -j/d 8 
 
 V* or yd* 
 
 6.80 
 
 2.607 
 
 17.7276 
 
 4.211 
 
 6.85 
 
 2.617 
 
 17.9264 
 
 4.234 
 
 6.90 
 
 2.627 
 
 18.1263 
 
 4.257 
 
 6.95 
 
 2.636 
 
 18.3202 
 
 4.280 
 
 7. 
 
 2.645 
 
 18.5150 
 
 4.304 
 
 7.05 
 
 2.655 
 
 18.7177 
 
 4.327 
 
 7.10 
 
 2.665 
 
 18.9215 
 
 
 7.15 
 
 2.6H 
 
 19.1191 
 
 4^373 
 
 7.20 
 
 2.683 
 
 19.3176 
 
 4.395 
 
 7.25 
 
 2.692 
 
 19.5170 
 
 4.418 
 
 7.30 
 
 2.702 
 
 19.7246 
 
 4441 
 
 7.35 
 
 2.711 
 
 19.9258 
 
 4.464 
 
 7.40 
 
 2.720 
 
 20.1280 
 
 4.487 
 
 7.45 
 
 2.729 
 
 20.3310 
 
 4.510 
 
 7.50 
 
 2.739 
 
 20.5425 
 
 4.532 
 
 7.55 
 
 2.748 
 
 20.7474 
 
 4.555 
 
 7.60 
 
 2.756 
 
 20.9456 
 
 4.578 
 
 7.65 
 
 2.766 
 
 21.1600 
 
 4.600 
 
 7.70 
 
 2.775 
 
 21.3675 
 
 4.622 
 
 7.75 
 
 2.784 
 
 21.5760 
 
 4.642 
 
 7.80 
 
 2.793 
 
 21.7854 
 
 4.668 
 
 7.85 
 
 2.802 
 
 22.0000 
 
 4.690 
 
 7.90 
 
 2.811 
 
 22.2069 
 
 4.712 
 
 7.95 
 
 2.819 
 
 22.411Q 
 
 4.735 
 
 8. 
 
 2.828 
 
 22.6240 
 
 4.759 
 
 8.05 
 
 2.837 
 
 22.8378 
 
 4.779 
 
 8.10 
 
 2.846 
 
 23.0526 
 
 4.801 
 
 8.15 
 
 2.855 
 
 23.2682 
 
 4.823 
 
 8.20 
 
 2.864 
 
 23.4848 
 
 4.846 
 
 8.25 
 
 2.872 
 
 23.6940 
 
 4.868 
 
 8.30 
 
 2.881 
 
 23.9123 
 
 4.890 
 
 8.35 
 
 2.890 
 
 24.1315 
 
 4.912 
 
 8.40 
 
 2.898 
 
 24.3432 
 
 4.934 
 
 8.45 
 
 2.907 
 
 24.5641 
 
 4.950 
 
 8.50 
 
 2.915 
 
 24.7775 
 
 4.978 
 
 8.55 
 
 2.924 
 
 25. 
 
 5 
 
 8.60 
 
 2.932 
 
 25.2152 
 
 5.013 
 
 8.65 
 
 2.941 
 
 25.4396 
 
 5.044 
 
 8.70 
 
 2.949 
 
 25.6563 
 
 5 066 
 
 8.75 
 
 2.958 
 
 25.8825 
 
 .088 
 
 8.80 
 
 2.966 
 
 26.1008 
 
 .109 
 
 8.85 
 
 2.975 
 
 26.3300 
 
 .131 
 
 8.90 
 
 2.983 
 
 26.5487 
 
 .153 
 
 8.95 
 
 2.992 
 
 26.7784 
 
 .175 
 
 9. 
 
 3. 
 
 27. 
 
 196 
 
 9.05 
 
 3.008 
 
 27.2224 
 
 '217 
 
 9.10 
 
 3.016 
 
 27.4456 
 
 5 239 
 
 9.15 
 
 3.025 
 
 27.6787 
 
 5 261 
 
 9.20 
 
 3.033 
 
 27.9036 
 
 5^283 
 
 9.25 
 
 3.041 
 
 28.1293 
 
 5.304 
 
 9.30 
 
 3.049 
 
 28.3*57 
 
 
 9.35 
 
 3.058 
 
 28.5923 
 
 5i348 
 
 9.40 
 
 3.066 
 
 28.8204 
 
 5 369 
 
 9.45 
 
 3.074 
 
 29.0493 
 
 5.390 
 
 9.50 
 
 3.082 
 
 29.2790 
 
 5.411 
 
 9.55 
 
 3.091 
 
 29.5190 
 
 5.433
 
 SULLIVAN'S NEW HYDRAULICS. 
 TABLE No. 5 Continued. 
 
 119 
 
 r or d 
 
 y'r or y'd 
 
 y'r 8 or -j/d 8 
 
 f/r or f/d 8 
 
 9.60 
 9.65 
 9.70 
 9.75 
 9.80 
 9.85 
 9.90 
 9.95 
 10. 
 
 3.098 
 3 106 
 3.114 
 3.123 
 3.131 
 3.138 
 3.146 
 3.154 
 3.162 
 
 29.7408 
 29.9729 
 30.2058 
 30.4492 
 30.6838 
 30.9093 
 81.1454 
 
 31 ! 6200 
 
 5.454 
 5.475 
 5.496 
 5.518 
 
 5^560 
 5.581 
 5.602 
 5.623 
 
 28. Tables for Velocity and Discharge of Trapezoidal 
 Canals. In Pig. 1, let A, E, F, D, equal the width of the 
 water surface in feet. Let B C equal bottom width of canal 
 in feet, and E B or P C, equal greatest depth of water in 
 feet. 
 
 TO FIND THE AREA IN SQUARE FEET. 
 
 Multiply E D by E B, or F A by B 1 C. Or secondly: Add 
 together the width of water surface and the bottom width in 
 feet, and divide the sum by 2. Then multiply the quotient 
 by the depth F C or E B in feet. In either case the result 
 will equal the area in square feet. 
 
 TO FIND THE LENGTH A E OR F D IN FEET. 
 
 If the side elopes A B and D C are 1 to 1, then AE=E B
 
 120 SULLIVAN'S NEW HYDRAULICS. 
 
 and P D=F C. If the side slopes are \y z horizontal to 1 vert, 
 ical, then A E=E BXl-50. If the side slopes are 2 horizontal 
 to 1 vertical, then A E=E BX2.00. 
 
 TO FIND THE WETTED PERIMETER IN LINEAL FEET. 
 
 The length of B C, or of the bottom width in feet, is, of 
 course, always known. It is, therefore, only required to find 
 the length in feet of the side slopes A B and D C which when 
 added to B C, will equal the total wetted girth or perimeter- 
 If the side slopes are 1 to 1, then the length A B or D C is 
 equal to the diagonal of a square, or equal to the depth of 
 water E BX 1.41421. 
 
 The length of either side slope for any rate of slope what- 
 ever is the same as the hypotenuse of a right angled triangle, 
 
 and A B=V(AE) 8 +(E B) 8 or D C=v/(F D) 8 +(P C) 8 . 
 
 Adding together the lengths in A B, B C, and C D, we 
 have the wetted perimeter (p) in feet. The hydraulic mean 
 
 depth in feet is then r= area ip Bquare feet =4 
 wet perimeter in feet p 
 
 In the following tables of trapezoidal canals the value of 
 the area in square feet, and the hydraulic mean depth r, and 
 of $/r 3 for each additional half foot depth of water in each 
 canal is given, so that the velocity and discharge for each 
 depth of flow may be readily ascertained. The value of m or 
 C will depend upon the material forming the wetted perimeter, 
 and the condition of the canal a& to good or bad repair. The 
 value of m or G may be selected from the tables of values de- 
 veloped in the groups of rivers and canals heretofore given. 
 The following tables show the area for each depth of water. 
 The discharge for any given depth will equal the area for that 
 depth multiplied by the mean velocity. The slope required to 
 generate any desired mean velocity in feet per second for any 
 depth of flow will be
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 121 
 
 The distance or length in feet (I) of canal in which there 
 must be a fall of 1 foot in order to generate a given mean vel- 
 ocity in feet per second may be found by the formula, 
 
 HOW TO USE THE FOLLOWING TABLES. 
 
 To find the mean velocity for any given depth, multiply 
 
 t/r 8 for that depth by <V S, or multiply t/r 8 by J 
 
 Vm 
 
 To find the discharge in cubic feet per second for any 
 given depth of flow, multiply t/r 3 by areaXCVS, or multiply 
 
 t/r 8 by areaX-J-. For values of v/S, see 30, Table No. 15. 
 
 \ m 
 
 tol. 
 
 Trapezoidal canal. 
 
 TABLE No. 6. 
 Bottom width 2 feet. 
 
 Side slopes 1 
 
 Depth of 
 Water in ft. 
 
 Area 
 Square Feet 
 
 Feet 
 
 V/r 
 Feet 
 
 t/r 
 Feet 
 
 1.00 
 1.50 
 2.00 
 2.50 
 3.00 
 
 3.00 
 5.25 
 8.00 
 11.25 
 15.00 
 
 0.6213 
 0.8400 
 1.0450 
 1.240 
 1.430 
 
 0.4897 
 0.7699 
 1.068 
 1.380 
 1.710 
 
 0.6998 
 0.8774 
 1.034 
 1.177 
 1.308 
 
 REMARK. In climates where the earth freezes in winter, 
 side slopes of earth will not stand if they are steeper than 1% 
 to 1 even in very firm earth. In lighter soil in frosty climates 
 the side slopes should vary from 1% to 1 to 3 to 1, according to 
 the nature of the soil.
 
 122 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE No. 7. 
 Trapezoidal canal. Bottom width 4 feet. Side slopes 1 to 1. 
 
 Depth of 
 Water in ft. 
 
 Area 
 Square Feet 
 
 Feet 
 
 V* 3 
 Feet 
 
 t/r 
 Feet 
 
 l.0 
 
 5.00 
 
 0.732 
 
 0.6263 
 
 0.7914 
 
 1.50 
 
 8.25 
 
 .000 
 
 1.000 
 
 .000 
 
 2.00 
 
 12.00 
 
 .2426 
 
 1.385 
 
 .176 
 
 2.50 
 
 16.25 
 
 .4700 
 
 1.782 
 
 .335 
 
 3.00 
 
 21.00 
 
 .762 
 
 2.339 
 
 .530 
 
 .50 
 
 26.25 
 
 .888 
 
 2.594 
 
 .611 
 
 .00 
 
 32.00 
 
 2.089 
 
 3.019 
 
 .737 
 
 .50 
 
 38.25 
 
 2.280 
 
 3.443 
 
 1.855 
 
 .00 
 
 45.00 
 
 2.480 
 
 3.905 
 
 1.976 
 
 .50 
 
 52.25 
 
 2.670 
 
 4.383 
 
 2.089 
 
 6.00 
 
 60. 00 
 
 2.861 
 
 4.836 
 
 2.199 
 
 6.50 
 
 68.25 
 
 3.050 
 
 5.327 
 
 2.308 
 
 7.00 
 
 77.00 
 
 3.235 
 
 5.819 
 
 2.412 
 
 8.00 
 
 96.00 
 
 3.605 
 
 6.844 
 
 2.616 
 
 TABLE No. 8. 
 Trapezoidal canal. Bottom width 4 feet. Side slopes 1*^ to 1. 
 
 Depth of 
 Water in ft 
 
 Area Square 
 Feet 
 
 Feet 
 
 3/r 
 
 Feet. 
 
 f/r" 
 Feet. 
 
 1.00 
 
 5.500 
 
 0.7231 
 
 0.6149 
 
 0.7841 
 
 1.50 
 
 9.375 
 
 .0000 
 
 1.0000 
 
 .000 
 
 2.00 
 
 14.000 
 
 .2488 
 
 1.3960 
 
 .181 
 
 2.50 
 
 19.375 
 
 .4880 
 
 1.815 
 
 .347 
 
 3.00 
 
 25.500 
 
 .7200 
 
 2.256 
 
 .502 
 
 3.50 
 
 32.375 
 
 .8370 
 
 2.490 
 
 .578 
 
 4.00 
 
 40.000 
 
 2.1710 
 
 3.099 
 
 .788 
 
 4.50 
 
 48.375 
 
 2.4000 
 
 3.718 
 
 .928 
 
 5.00 
 
 57.500 
 
 2.6100 
 
 4.216 
 
 2.053 
 
 6.00 
 
 78.000 
 
 3.0420 
 
 5.306 
 
 2.303 
 
 7.00 
 
 101.500 
 
 3.4730 
 
 6.472 
 
 2.544 
 
 8.00 
 
 128.000 
 
 3.9000 
 
 7.702 
 
 2.775 
 
 Trapezoidal canal. 
 
 TABLE No. 9. 
 Bottom width 6 feet. 
 
 Side slopes 1 to 1. 
 
 Depth of 
 Water in ft. 
 
 Area Square 
 Feet 
 
 Feet 
 
 Felt. 
 
 Feet. 
 
 1.00 
 
 7.00 
 
 0.7929 
 
 0.7060 
 
 0.8403 
 
 1.50 
 
 11.25 
 
 1.0980 
 
 1.1510 
 
 .0725 
 
 2.00 
 
 16.00 
 
 1.3726 
 
 1.6090 
 
 .2680 
 
 2.50 
 
 21.25 
 
 1.6280 
 
 2.077 
 
 .4420 
 
 3.00 
 
 27.00 
 
 1.8639 
 
 2.545 
 
 .595 
 
 3.50 
 
 33.25 
 
 2.0900 
 
 3.022 
 
 .738 
 
 4.00 
 
 40.00 
 
 2.3100 
 
 3.511 
 
 .874 
 
 4.50 
 
 47.25 
 
 2.5200 
 
 4.000 
 
 2.000 
 
 5.00 
 
 52.00 
 
 2.5800 
 
 4.144 
 
 2.036 
 
 5.50 
 
 63.25 
 
 2.9340 
 
 5.025 
 
 2.242 
 
 6.00 
 
 72.00 
 
 3.1345 
 
 5.548 
 
 2.355 
 
 7.00 
 
 91.00 
 
 3.5270 
 
 6.624 
 
 2.574 
 
 8.00 
 
 112.00 
 
 3.9100 
 
 7.731 
 
 2.780
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 123 
 
 Trapezoidal canal. 
 
 TABLE No. 10. 
 Bottom width 8 feet. 
 
 Side elopes 2 to 1. 
 
 Depth of 
 Water Feet 
 
 Area 
 Square Feet 
 
 Feet 
 
 V/r' 
 Feet 
 
 Feet 
 
 1.00 
 
 10.00 
 
 0.8018 
 
 0.7179 
 
 0.8473 
 
 1 50 
 
 16.50 
 
 1.1210 
 
 1.187 
 
 1.089 
 
 2.00 
 
 24.00 
 
 1.4164 
 
 1.685 
 
 1.298 
 
 2.50 
 
 32.50 
 
 1.7000 
 
 2.216 
 
 1 489 
 
 3 00 
 
 42.00 
 
 1.9600 
 
 2.744 
 
 1.656 
 
 3 50 
 
 52.50 
 
 2.2200 
 
 
 1.819 
 
 4.00 
 
 64.00 
 
 2.470 
 
 3 882 
 
 1.970 
 
 4.50 
 
 76.50 
 
 2.720 
 
 4^486 
 
 2.118 
 
 5.00 
 
 90.00 
 
 2.964 
 
 5.103 
 
 2.259 
 
 6.00 
 
 120.00 
 
 3.445 
 
 6.394 
 
 2.528 
 
 7.00 
 
 154.00 
 
 3.910 
 
 7.732 
 
 2.781 
 
 Trapezoidal canal. 
 
 TABLE No. 11. 
 Bottom width 8 feet. 
 
 Side slopes 1 to 1. 
 
 Depth of 
 Water Feet 
 
 Area 
 Square Feet 
 
 r 
 Feet 
 
 
 
 fr/r 
 Feet 
 
 1.00 
 
 9.00 
 
 0.831 
 
 0.7576 
 
 0.8704 
 
 1.50 
 
 14.25 
 
 1.164 
 
 1.256 
 
 1.121 
 
 2.00 
 
 20.00 
 
 1.464 
 
 1.771 
 
 1.331 
 
 2.50 
 
 26.25 
 
 1.741 
 
 2.297 
 
 1.516 
 
 3.00 
 
 33.00 
 
 2.000 
 
 2.828 
 
 1.682 
 
 3.50 
 
 40.25 
 
 2.248 
 
 3.370 
 
 
 4.00 
 
 48.00 
 
 2.485 
 
 3.917 
 
 1.979 
 
 4.50 
 
 56.25 
 
 2.710 
 
 4.461 
 
 2 112 
 
 5.00 
 
 65.00 
 
 2.935 
 
 5.029 
 
 2^242 
 
 5.50 
 
 74.25 
 
 3.153 
 
 5.598 
 
 2.366 
 
 6.00 
 
 84.00 
 
 3.364 
 
 6.170 
 
 2.484 
 
 7.00 
 
 105.00 
 
 3.777 
 
 7.341 
 
 2.709 
 
 Trapezoidal canal. 
 
 TABLE No. 12. 
 Bottom Width 10 feet. 
 
 Side elopes 1 to 1 
 
 Depth of 
 Water Feet 
 
 Area 
 Square Feet 
 
 Fe'et 
 
 Feet 
 
 Feet 
 
 1.00 
 
 11.00 
 
 O.a574 
 
 0.7939 
 
 0.891 
 
 2.00 
 
 24.00 
 
 1.5320 
 
 1.896 
 
 1.377 
 
 2.50 
 
 31.25 
 
 1.8300 
 
 2.475 
 
 1.574 
 
 3.00 
 
 39.00 
 
 2.1100 
 
 3.065 
 
 1.750 
 
 3.50 
 
 47.25 
 
 2.3743 
 
 3.658 
 
 1.912 
 
 4.00 
 
 56.00 
 
 2.6270 
 
 4.258 
 
 2.063 
 
 4.50 
 
 65.25 
 
 2.8700 
 
 4.862 
 
 2.205 
 
 5.00 
 5.50 
 
 75.00 
 85.25 
 
 3.1060 
 3.3350 
 
 5.474 
 6.090 
 
 2^468 
 
 6.00 
 
 96.00 
 
 3.5600 
 
 6.717 
 
 2.591 
 
 7.00 
 
 119.00 
 
 3.9930 
 
 7.979 
 
 2.825 
 
 8.00 
 
 144.00 
 
 4.4130 
 
 9.271 
 
 3.045
 
 124 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 Trapezoidal canal. 
 2tol. 
 
 TABLE No. 13. 
 Bottom width 10 feet. 
 
 Side elopes 
 
 Depth of 
 Water Feet 
 
 Area 
 Square Feet 
 
 Fe^t 
 
 Feet 
 
 t/r" 
 Feet 
 
 1.00 
 
 12.00 
 
 0.8222 
 
 0.7455 
 
 0.8634 
 
 2.00 
 
 28.00 
 
 1.478 
 
 1.797 
 
 1.340 
 
 2.50 
 
 37.50 
 
 1.774 
 
 2.363 
 
 1.537 
 
 3.00 
 
 48.00 
 
 2.049 
 
 2.933 
 
 1.713 
 
 3.50 
 
 59.50 
 
 2.320 
 
 3.534 
 
 1.880 
 
 4.00 
 
 72.00 
 
 2.581 
 
 4.146 
 
 2.036 
 
 4.50 
 
 &5.50 
 
 2.840 
 
 4.786 
 
 2.187 
 
 5.00 
 
 100.00 
 
 -3.093 
 
 5.440 
 
 2.332 
 
 5.50 
 
 115.50 
 
 3.340 
 
 6.104 
 
 2.471 
 
 6-00 
 
 132.00 
 
 3.584 
 
 6.785 
 
 2.605 
 
 7.00 
 
 168.00 
 
 4.068 
 
 8.493 
 
 2.914 
 
 8.00 
 
 208.00 
 
 4.543 
 
 9.683 
 
 3.111 
 
 29. Table for Velocity and Discharge of Rectangular 
 Channels, Flumes, Masonry Conduits etc. The value of the 
 coefficient to be used with the following table will depend 
 upon the nature and condition of the lining of the flume or 
 channel. According to the experiments of D'Arcy and Bazin, 
 the average value of C for unplaned board flumes, well joint- 
 ed, and without strips or battens on the inside is C=U9.00, or 
 m=.00007. For nicely dressed lumber flumes, well jointed 
 and without battens on the inside, their experiments give C 
 =128.00 as an average. If we refer to the last two flumes in 
 Group No. 5, one at Boston gives C=106.30, and the High- 
 line in Colorado gives C=70.00. The data of flow in wooden 
 conduits are very unsatisfactory. The density of the wood, 
 the closeness of joints, the alignment of the flume, gritty de- 
 posits etc.. all affect the value of C in any case. Where the 
 flume is constructed of rough, very knotty, lumber and has 
 battens on the inside to cover the joints, it is proable that
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 125 
 
 the value of the coefficient will be about C=80.00, if the 
 alignment of the flume is fairly direct. For channels lined 
 with brick, ashlar, rubble etc., see the groups of such chan- 
 nels for value of C. See table No. 15 for value of /S. 
 
 TABKE No. 14 
 Flumes and other rectangular channels. 
 
 Width 
 Feet 
 
 Depth of 
 Water feet. 
 
 Area 
 
 Sq. Feet. 
 
 r 
 
 Feet. 
 
 Feet. 
 
 t/r3 
 Feet. 
 
 1.5 
 
 0.50 
 
 0.75 
 
 0.300 
 
 0.1643 
 
 0.4054 
 
 1.5 
 
 1.00 
 
 1.50 
 
 .429 
 
 0.2810 
 
 0.5301 
 
 2.0 
 
 0.75 
 
 1.50 
 
 .429 
 
 0.2810 
 
 0.5301 
 
 2.0 
 
 1.50 
 
 3.00 
 
 .600 
 
 0.4647 
 
 0.6817 
 
 3.0 
 
 1.00 
 
 3.00 
 
 .600 
 
 0.4647 
 
 0.6817 
 
 3.0 
 
 1.50 
 
 4.50 
 
 .750 
 
 0.6495 
 
 0.8059 
 
 3.0 
 
 2.00 
 
 6.00 
 
 .860 
 
 0.7975 
 
 0.8930 
 
 4.0 
 
 1.50 
 
 6.00 
 
 .860 
 
 0.7975 
 
 0.8930 
 
 4.0 
 
 2.00 
 
 8.00 
 
 1.000 
 
 1.0000 
 
 1.0000 
 
 5.0 
 
 1.50 
 
 7.50 
 
 .937 
 
 0.9070 
 
 0.9524 
 
 5.0 
 
 2.00 
 
 10.00 
 
 .111 
 
 .171 
 
 1.082 
 
 5.0 
 
 3.00 
 
 15.00 
 
 .363 
 
 591 
 
 .261 
 
 6.0 
 
 2.00 
 
 12.00 
 
 .200 
 
 .314 
 
 .147 
 
 6.0 
 
 2.50 
 
 15.00 
 
 .363 
 
 .591 
 
 .261 
 
 6.0 
 
 3 00 
 
 18.00 
 
 .500 
 
 .837 
 
 .355 
 
 6.0 
 
 4.00 
 
 24.00 
 
 .714 
 
 2.244 
 
 .498 
 
 8.0 
 
 3.00 
 
 24.00 
 
 .714 
 
 2.244 
 
 .498 
 
 8.0 
 
 4.00 
 
 32.00 
 
 2.000 
 
 2.828 
 
 .682 
 
 8.0 
 
 5.00 
 
 40.00 
 
 2.222 
 
 3.312 
 
 .820 
 
 8.0 
 
 6.00 
 
 48.00 
 
 2.400 
 
 3.718 
 
 1.928 
 
 10.0 
 
 4.00 
 
 40.00 
 
 2.222 
 
 3.312 
 
 1.820 
 
 10.0 
 
 5.00 
 
 50.00 
 
 2.500 
 
 3.953 
 
 1.988 
 
 10.0 
 
 6.00 
 
 60.00 
 
 2.727 
 
 4.503 
 
 2.122 
 
 10.0 
 
 7.00 
 
 70.00 
 
 2.916 
 
 4.979 
 
 2.231 
 
 12.0 
 
 4.00 
 
 48.00 
 
 2.400 
 
 3.718 
 
 1.928 
 
 12.0 
 
 5.00 
 
 60.00 
 
 2.727 
 
 4.503 
 
 2.122 
 
 12.0 
 
 6.00 
 
 72.00 
 
 3.000 
 
 5.196 
 
 2.279 
 
 12.0 
 
 7.00 
 
 84.00 
 
 3.230 
 
 5.805 
 
 2.410 
 
 14.0 
 
 5.00 
 
 70.00 
 
 2.916 
 
 4.979 
 
 2.231 
 
 14.0 
 
 6.00 
 
 84.00 
 
 3.230 
 
 5.805 
 
 2.410 
 
 30. Table of Values of Slopes S and ^S. 
 
 The distance in feet I, in which there is a fall of one foot is
 
 126 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE No. 15. 
 Value of S and i/S. 
 
 Fall per 
 Mile in Feet 
 
 Fall 
 One In 
 
 Slope 
 S 
 
 s 
 
 0.50 
 
 10560.00 
 
 .0000947 
 
 .009731 
 
 0.75 
 
 7042.25 
 
 .0001420 
 
 .011915 
 
 1.00 
 
 5280.00 
 
 .0001894 
 
 .013762 
 
 1.76 
 
 3000.00 
 
 .0003333 
 
 .018255 
 
 2.00 
 
 2640.00 
 
 .0003788 
 
 .019463 
 
 2.64 
 
 2000.00 
 
 .0005000 
 
 .022361 
 
 3.00 
 
 1760.00 
 
 .0005682 
 
 .023836 
 
 3.18 
 
 1660.00 
 
 .0006024 
 
 .024544 
 
 3.30 
 
 1600.00 
 
 .0006250 
 
 .025000 
 
 3.38 
 
 1560.00 
 
 .0006410 
 
 .025318 
 
 3.52 
 
 1500.00 
 
 .0006667 
 
 .025820 
 
 3.62 
 
 1460.00 
 
 .0006849 
 
 .026171 
 
 3.70 
 
 1427.00 
 
 .0007007 
 
 .026472 
 
 3.75 
 
 1408.00 
 
 .0007102 
 
 .026650 
 
 3.80 
 
 1389.00 
 
 .0007199 
 
 .026832 
 
 8.85 
 
 1371.00 
 
 .0007294 
 
 .027007 
 
 3.90 
 
 1354.00 
 
 .0007385 
 
 .027176 
 
 4.00 
 
 1320.00 
 
 .0007576 
 
 .027524 
 
 .20 
 
 1257.00 
 
 .0007955 
 
 .028205 
 
 .40 
 
 1200.00 
 
 .0008333 
 
 .028868 
 
 .50 
 
 1173.00 
 
 .0008525 
 
 .029198 
 
 .60 
 
 1148.00 
 
 .0008710 
 
 .029514 
 
 .70 
 
 1123.00 
 
 .0008905 
 
 .029841 
 
 .75 
 
 1111.00 
 
 .0009000 
 
 .030001 
 
 .80 
 
 1100. 00 
 
 .0009090 
 
 .030151 
 
 4.90 
 
 1078.00 
 
 .0009276 
 
 .030457 
 
 5.00 
 
 1056.00 
 
 .0009469 
 
 .030773 
 
 5.10 
 
 1035.00 
 
 .0009662 
 
 .031083 
 
 5.20 
 
 1015.00 
 
 .0009852 
 
 .031388 
 
 5.28 
 
 1000.00 
 
 .0010000 
 
 .031623 
 
 6.00 
 
 880.00 
 
 .0011364 
 
 .033710 
 
 7.00 
 
 754.30 
 
 .0013258 
 
 .036411 
 
 8.00 
 
 660.00 
 
 .0015151 
 
 .038925 
 
 9.00 
 
 586.60 
 
 .0017044 
 
 041286 
 
 10 00 
 
 528.00 
 
 .0018940 
 
 .043519 
 
 11.00 
 
 480.00 
 
 .0020833 
 
 .045643 
 
 12.00 
 
 440.00 
 
 .0022730 
 
 .047673 
 
 13 00 
 
 406.10 
 
 .0024621 
 
 .049620 
 
 14.00 
 
 377.10 
 
 .0026515 
 
 .051493 
 
 15.00 
 
 352.00 
 
 .0028409 
 
 .053300 
 
 16 00 
 
 330.00 
 
 .0030303 
 
 .055048 
 
 17.00 
 
 310.60 
 
 .0032197 
 
 .056742 
 
 18.00 
 
 293.30 
 
 .0034090 
 
 058388 
 
 19.00 
 
 277 TO 
 
 .0035985 
 
 .059988 
 
 20 00 
 
 264.00 
 
 .0037878 
 
 .061546 
 
 21.00 
 
 251.40 
 
 .0039773 
 
 .063066 
 
 22.00 
 
 240.00 
 
 .0041666 
 
 .064549 
 
 23.00 
 
 229.60 
 
 .0043560 
 
 .066000 
 
 24.00 
 
 220.00 
 
 .0045454 
 
 .067419 
 
 25.00 
 
 211.20 
 
 .0047348 
 
 .068810 
 
 26. 
 
 203.10 
 
 .0049242 
 
 .070173 
 
 27. 
 
 195.20 
 
 .0051136 
 
 .071510
 
 SULLIVAN'S NEW HYDRAULICS. 
 TABLE No. 15. Continued. 
 
 127 
 
 Fall Per 
 Mile in Feet 
 
 Fall, 
 One In 
 
 Slc g pe 
 
 51. 
 
 52. 
 52.80 
 55.80 
 60.00 
 70.00 
 80.00 
 90.00 
 100.00 
 120.00 
 140.00 
 160.00 
 180.00 
 200.00 
 240.00 
 280.00 
 320.00 
 360.00 
 400.00 
 450.00 
 500.00 
 
 700.00 
 800.00 
 
 188.60 
 182.10 
 176.00 
 170.30 
 165.00 
 
 155.30 
 150.90 
 146.60 
 142 70 
 
 135.40 
 
 132.00 
 
 128.80 
 
 125.70 
 
 122.80 
 
 120.00 
 
 117.30 
 
 114.80 
 
 112.30 
 
 110.00 
 
 107.70 
 
 105.60 
 
 103.50 
 
 101.50 
 
 100.00 
 
 96.00 
 
 88.00 
 
 75.43 
 
 6600 
 
 58.66 
 
 52.80 
 
 44.00 
 
 37.71 
 
 33.00 
 
 ?933 
 
 26.40 
 
 22.00 
 
 18.86 
 
 16.50 
 
 14.66 
 
 13.20 
 
 11.73 
 
 10.56 
 
 880 
 
 7.54 
 
 .0053030 
 
 .U ).->-! '.KM 
 .0056818 
 .0058712 
 
 .0062500 
 .0064394 
 
 .0068182 
 
 .0070075 
 
 .0075757 
 .0077651 
 .0079545 
 
 .0085227 
 .0087121 
 
 .0098485 
 
 .01 
 
 .0104167 
 
 .0132576 
 .0151515 
 .0170455 
 
 .022727 
 .0265151 
 .0303030 
 
 .0378787 
 .0416667 
 
 .0681818 
 .0757575 
 .0852273 
 
 .1136364 
 .1325757 
 .1515151 
 
 .072822 
 .074111 
 .075378 
 
 .081417 
 .082572 
 .083711 
 
 .085944 
 .087039 
 .088120 
 .089188 
 .090244 
 
 .097312 
 
 .098281 
 
 .099241 
 
 .10 
 
 .102060 
 
 .106600 
 
 .115141 
 
 .137620 
 .150756 
 
 .174077 
 .184637 
 .194625 
 
 .261116 
 
 .275241 
 
 .307729 
 .337100 
 .364109 
 
 31 Table of Slopes tor Average Weight Clean Cast 
 Iron Pipes, Showing the Inclination Required in Each Di- 
 ameter to Generate a Mean Velocity of One Foot per Sec-
 
 128 SULLIVAN'S NEW HYDRAULICS. 
 
 and, from which the Slope Required to Generate any 
 other Mean Velocity may be Found. 
 
 fHdt/d j f m tl3 j s genera i formula we assign H 1 foot 
 mv* 
 
 and v*=l foot, we have, 2=1^1 as the formula for finding 
 
 m 
 
 the length in which there must be a total head, fall or slope of 
 one foot to generate a velocity of one foot per second. For 
 this class of pipe m is a constant, and in terms of diameter in 
 feet m=.0004, or in terms of diameter in inches m=.0004X 
 V/(l?) 3 =.01662768. Hence the length in feet I, in which there 
 must be a head or fall of one foot in order to generate a mean 
 velocity of one foot per second will be 
 
 I = 1/dS if d is taken in feet, and s= 
 .0004 
 
 The length in feet in which there must be a head or fall 
 of one foot in order to generate any given or desired mean 
 velocity in feet per second is, 
 
 d-^/d i/d 8 m v* /m v* 
 
 In which v s is the square of the given or desired velocity 
 in feet per second. The coefficient m may be in feet or in 
 inches as above but the mean velocity will be in feet per 
 second in either case. 
 
 The required slope S, to generate a mean velocity of one 
 foot is, 
 
 m m 
 
 S= , j 3 , and to generate any velocity is S= , ~ 3 X v*. 
 
 Hence if the slope for any diameter, which causes v=l 
 be taken from the following table, the required slope to 
 cause any other velocity may be found at once by multiply- 
 ing this slope from the table by the square of the desired 
 velocity, v*.
 
 SULLIVAN'S NEW HYDRAULS. 12 
 
 EXAMPLE. 
 
 From Table No. 16 it is seen that a slope of S=.0004 for 
 a pipe 12 inches diameter, will generate a mean velocity of 
 one foot per second. Required, the slope of a 12 inch pipe to 
 generate 5 feet per second velocity: 
 
 SOLUTION; From Table 16, take the slope for 1 foot 
 velocity, S .0004. Multiply this slope by the square of the 
 required velocity, and we have, 
 
 S=.0004X(o) 8 =.01,and l=-^-= ~= 100 feet. In other 
 
 words there must be a fall of one foot in a length of 100 
 feet. 
 
 TABLE No. 16. 
 
 Table giving the required slope to generate a mean 
 velocity of one foot per second in average weight clean cast 
 iron pipes. 
 
 .016628 1 T/d 
 
 For v=l, S= 
 
 Diameter 
 Inches 
 
 /d 8 
 Inches 
 
 S 
 
 Diameter 
 Inches. 
 
 T/d* 
 Inches 
 
 S 
 
 3 
 
 5.1961 
 
 .003200000 
 
 26 
 
 132.5740 
 
 .0001254242 
 
 4 
 
 8. 
 
 .002078500 
 
 27 
 
 140.2960 
 
 .0001185208 
 
 5 
 
 11.1803 
 
 .001487250 
 
 28 
 
 148.1620 
 
 .oooir^x, 
 
 6 
 
 14.6969 
 
 .001131156 
 
 29 
 
 156.1690 
 
 .0001064743 
 
 7 
 
 18.5202 
 
 .0008975830 
 
 30 
 
 164.3160 
 
 . 000101 -i.XX) 
 
 8 
 
 22.6274 
 
 .000734861 
 
 31 
 
 172.6000 
 
 .OCO(i<v-: j ,:>:;:> 
 
 9 
 
 27. 
 
 .0006158&2 
 
 32 
 
 181.0193 
 
 
 10 
 
 31.6227 
 
 .000525825 
 
 33 
 
 189.5705 
 
 !OOOU8771. > I} 
 
 11 
 
 36.4828 
 
 .0004=57764 
 
 34 
 
 198.2523 
 
 .000083S0790 
 
 12 
 
 41.5692 
 
 .000400000 
 
 35 
 
 207.0628 
 
 .OOUO!S<-:'4]4 
 
 13 
 
 46.8721 
 
 .000354752 
 
 36 
 
 216. 
 
 .00007f.'.ixl(K) 
 
 14 
 
 52.3832 
 
 
 37 
 
 225.0822 
 
 .000073SXI70 
 
 15 
 
 58.0747 
 
 ^ 000286320 
 
 
 234.2477 
 
 .00007098(80 
 
 16 
 
 64. 
 
 .000260000 
 
 40 
 
 252.8222 
 
 .00006.-75390 
 
 17 
 
 70.0927 
 
 .000237228 
 
 44 
 
 291.8629 
 
 
 18 
 
 76.3675 
 
 .0002177366 
 
 48 
 
 332.5537 
 
 JQBKOOOOM 
 
 19 
 
 82.8190 
 
 .0002007753 
 
 54 
 
 396.8173 
 
 . 00004 1'.':!41 
 
 20 
 
 89.4427 
 
 .0001859069 
 
 60 
 
 464.7580 
 
 .0000357777*5 
 
 21 
 
 96.2340 
 
 .0001727870 
 
 72 
 
 606.9402 
 
 .0000274. IO 
 
 22 
 
 103.1890 
 
 .0001611411 
 
 84 
 
 769.8727 
 
 .00002160000 
 
 23 
 
 110.3040 
 
 .0001516536 
 
 96 
 
 940.6040 
 
 :000017r,7,xm 
 
 24 
 
 117.5750 
 
 .0001414254 
 
 120 
 
 1314.5341 
 
 .00001264935 
 
 to 
 
 125. 
 
 .0001330240 
 
 

 
 130 SULLIVAN'S NEW HYDRAULICS. 
 
 32. Head in Feet Lost by Friction in Average Weight 
 Clean Cast Iron Pipes for Different Velocities of Flow. 
 
 By equation (10) the coefficient of resistance or friction is 
 b" di/d S" 
 
 (10) 
 
 From which the formula for head lost by friction h", is 
 n I v 8 n I v* n 
 
 h "=-d7o- = -7d^=v^x' v ' ................. < lb) 
 
 For a constant diameter and velocity the friction loss 
 will be directly as the length in feet ( I )of pipe, and will vary 
 as v* for different velocities. For constant degrees of 
 roughness of pipe n is a constant 
 
 As the friction loss is inversely as |/d 8 and directly as the 
 length and as v*, the loss in one foot length of any diameter 
 
 when v 2 =l, will be S" = / ^ 8 and for any other velocity it 
 
 u 
 will be S"= / j g X v>aQ d for any length in feet of pipe it 
 
 ii 
 will be /j 8 X*Xv*. Hence if we form a table which shows the 
 
 loss of head in feet for one foot length of pipe and for a velocity 
 of one foot per second, the loss for any other length in feet 
 will be found by multiplying the tabular quantity by the 
 given length in feet /, and the loss for any velocity will be 
 found by multiplying by the square of that velocity, v*. (See 
 9 and 10.) 
 
 TABLE No. 17. 
 
 Table showing the loss of head in feet by friction in one 
 foot length of clean cast iron pipe when v*=l.
 
 SULLIVAN'S NEW HYDRAULICS. 131 
 
 .01637 
 
 -, when 
 
 When v z =l, the loss per foot length =- i = 
 d=incheg. 
 
 Diam. 
 
 Inchet 
 
 T/d 3 
 Inches. 
 
 Bead lost in 
 ! eet per foot 
 length 
 
 Diam. 
 Inches 
 
 ;/d 8 
 Inches. 
 
 Hd lost in ft 
 per ft length 
 
 3 
 
 5.1961 
 
 .003150440 
 
 25 
 
 125. 
 
 .00013U96000 
 
 4 
 
 8. 
 
 .002046250 
 
 26 
 
 132.5740 
 
 .00 '12347820 
 
 5 
 
 11.1803 
 
 .0014641820 
 
 27 
 
 140.2960 
 
 .000116681710 
 
 6 
 
 14.6969 
 
 .0011138327 
 
 28 
 
 148.1620 
 
 .000110487170 
 
 7 
 
 18.5202 
 
 .0008839000 
 
 29 
 
 156.1690 
 
 .000104822340 
 
 8 
 
 22.6274 
 
 .0007234590 
 
 30 
 
 164.3160 
 
 .OOU0996251126 
 
 9 
 
 27. 
 
 .0006062963 
 
 31 
 
 172.6000 
 
 .(XX '094843569 
 
 10 
 
 31.6227 
 
 .0005176661 
 
 32 
 
 181.0193 
 
 .1 00(190435330 
 
 11 
 
 36.4828 
 
 .000448704CO 
 
 33 
 
 189.5705 
 
 .000' 186353094 
 
 12 
 
 41.5692 
 
 .0003937900 
 
 34 
 
 198.2523 
 
 .000082571551 
 
 13 
 
 46.8721 
 
 .00034924806 
 
 35 
 
 207.0628 
 
 .000079058190 
 
 14 
 
 52.3832 
 
 .000312:.(!177L' 
 
 36 
 
 216. 
 
 .000075787037 
 
 15 
 
 58.0747 
 
 .000281878341) 
 
 37 
 
 225.0622 
 
 .000072735444 
 
 16 
 
 64. 
 
 . 000255 7M -':>( i 
 
 38 
 
 234.2477 
 
 .000069883290 
 
 17 
 
 70.0927 
 
 . 0002335 47.V.M 
 
 40 
 
 252.8822 
 
 .0-10064 730000 
 
 18 
 
 76.3675 
 
 .000214358200 
 
 44 
 
 291.8629 
 
 .00005608800 
 
 19 
 
 82.8190 
 
 .00019766 OCO 
 
 48 
 
 332.5537 
 
 .0000492 '3100 
 
 20 
 
 89.4427 
 
 .000183022203 
 
 54 
 
 396.8173 
 
 .000041253239 
 
 21 
 
 96.2340 
 
 .00017016620(1 
 
 60 
 
 464.7580 
 
 .000035222632 
 
 22 
 
 103.1890 
 
 .00015Si;iU!'4(l 
 
 72 
 
 606.9402 
 
 .0000270000 
 
 23 
 
 110.3(MO 
 
 .00014810NW 
 
 84 
 
 769.8727 
 
 .000 212632556 
 
 
 117.5750 
 
 .000139230278 
 
 96 
 
 940.6D40 
 
 . (10001 74037000 
 
 REMARK. As the loss here tabulated is for one foot 
 length only and for a velocity of only one foot per second, none 
 of the decimals should be cut off especially in case the pipe is 
 of considerable length and the velocity is high, because the 
 losa increases directly as the number of feet in length and 
 also asv 8 . 
 
 How TO USE TABLE No. 17. 
 
 The table shows the loss of head in feet by friction for 
 oue foot length of pipe of each diameter, and for a velocity of 
 one foot per second. If the pipe is several hundred feet in 
 length, then move the decimal point two places to the right- 
 This will be equivalent to multiplying by 100, and will show 
 the loss of head in feet per 100 feet length for v"=l. Mul- 
 tiply this result by the square of the actual or proposed ve- 
 locity in feet per second and the result is the actual loss per 
 100 feet length for that velocity. If the pipe is several thousand
 
 132 SULLIVAN'S NEW HYDRAULICS. 
 
 feet in length then take out from the table the loss for one 
 foot length and v 2 =1, and move the decimal point three 
 places to the right. Multiply by the square of the actual or 
 proposed velocity in feet per second. The result will be the 
 actual loss of head in feet per 1,000 feet length of pipe. The 
 loss of head in feet per mile (5280 feet) of pipe equals the loss 
 for 1,000 feet multiplied by 5.28. 
 
 EXAMPLE. 
 
 What is the loss of head in feet in an 8 inch cast iron 
 pipe 750 feet in length when the velocity is six feet per sec- 
 ond ? 
 
 SOLUTION. 
 
 In table 17, opposite a diameter of 8 inches and in the 
 third column the tabular loss for one foot length of 8 inch 
 pipe when v s =l is .000723459. Multiplying this by 100 feet 
 length by moving the decimal point two places to the right, 
 and the loss for 100 feet =.0723459 when v s =l. As the act- 
 ual velocity is to be six feet per second, and as the loss varies 
 as v 2 in any given diameter the last result must be multiplied 
 by (Q) s =36, and we have the actual loss per 100 feet length= 
 .0723459X36=2.60445 feet, and for 750 feet the loss will be 
 2 60445X? 5=19 5334 feet. 
 
 33. Formula and Table for Ascertaining the Loss of 
 Head in Feet In any Class of Pipe While Discharging a 
 Given Quantity In Cubic Feet Per Second. 
 
 Let h"= total head in feet lost by friction in the length 
 I 
 
 d=diameter of pipe in feet. 
 
 q= cubic feet per second discharged. 
 
 Then the coefficient of resistance is 
 
 hyd" X .616853 _ Syd"X.616853 
 
 Zq* q* 
 
 And the head in feet lost by friction is 
 
 T- < See e< l uation 32 ->
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 133 
 
 If I be taken =1 foot length of pipe, then n is constant 
 for any given class of pipe, and we may take the quotient of 
 
 n Q ' 
 
 gifigK as a constant, which, when multiplied by yfp will 
 
 equal the loss of head in feet per foot of pipe for the given 
 discharge q. As q s ond V s are convertible terms we use the 
 same coefficient value in terms of either q or v. 
 
 The value of n in terms of diameter in feet for ordinary 
 cast iron pipes is n=.00039380. 
 
 The loss of head in one foot length is h"= fi1ft QgQ X 
 
 Then- 
 
 .00039380 
 
 !/d" ' '" .616853 
 h" = .OC063840 X: 
 
 .616853 
 
 =;.00063840. Whence 
 
 The following table gives 
 
 value of^/d 11 . 
 
 The slope required to cause a given diameter to discharge 
 
 q cubic feet, S= ^353 X^p 
 
 From tables Nos. 1 and 2, q=a cXt/d'Xv/S, and S= 
 
 TABLE No. 18. 
 " when d is taken in feet. (See 44. 45.) 
 
 Values of 
 
 Diameter 
 Inches 
 
 Diameter 
 Feet 
 
 i/d" 
 
 Feet 
 
 Diameter 
 Inches 
 
 Diameter 
 Feet 
 
 v/d" 
 Feet 
 
 3 
 
 0.2500 
 
 .0004883 
 
 24 
 
 2.00 
 
 45.25 
 
 4 
 
 0.3333 
 
 .002375 
 
 25 
 
 2.083 
 
 56.60 
 
 5 
 
 0.4167 
 
 .00811 
 
 26 
 
 2.166 
 
 70.17 
 
 6 
 
 0.5 
 
 .0221 
 
 27 
 
 2.25 
 
 86.50 
 
 7 
 
 0.5833 
 
 .05157 
 
 28 
 
 2.333 
 
 105.55 
 
 8 
 
 0.6667 
 
 .1075 
 
 29 
 
 2.416 
 
 128.00 
 
 9 
 
 0.75 
 
 .2055 
 
 30 
 
 2.50 
 
 154.40 
 
 10 
 
 0.8333 
 
 .3668 
 
 31 
 
 2.584 
 
 185.20 
 
 11 
 
 0.9167 
 
 .6198 
 
 32 
 
 2.666 
 
 219.90 
 
 12 
 
 1.0000 
 
 1.000 
 
 33 
 
 2.75 
 
 260.80 
 
 13 
 
 1.083 
 
 1.55 
 
 34 
 
 2.834 
 
 307.80 
 
 14 
 
 1.167 
 
 2.338 
 
 35 
 
 2.916 
 
 360.00 
 
 15 
 
 1.25 
 
 3.412 
 
 36 
 
 3.00 
 
 420.90 
 
 16 
 
 1.383 
 
 4.859 
 
 38 
 
 3.166 
 
 566.00 
 
 17 
 
 1.417 
 
 6.800 
 
 40 
 
 3.333 
 
 750.90 
 
 18 
 
 1.5 
 
 9.301 
 
 42 
 
 3.50 
 
 982.60 
 
 19 
 
 1.583 
 
 12.51 
 
 44 
 
 3.666 
 
 1268.00 
 
 20 
 
 1.667 
 
 16.62 
 
 48 
 
 4.00 
 
 2048.00 
 
 21 
 
 1.75 
 
 21.71 
 
 54 
 
 4.50 
 
 3914.00 
 
 22 
 
 1.833 
 
 28.01 
 
 60 
 
 5.00 
 
 6979.00 
 
 23 
 
 1.917 
 
 35.84 
 
 72 
 
 6.00 
 
 19050.00
 
 134 SULLIVAN'S NEW HYDRAULICS. 
 
 For asphaltum coated pipes take n=. 000325 in terms of 
 diameter in feet. Then for such coated pipes, 
 
 h "=-6^5lT X 7Sl-X l =--00051864 X ^TX / = 
 .00051861 
 
 q=cubic feet discharged per second. 
 Z=length of pipe in feet. 
 d=diameter of pipe in feet. See 44. 
 
 34. Asphaltum Coated Pipes. Table for Ascertaining 
 the Loss of Head in Feet for any Velocity. 
 
 By formula (16) 
 
 n I v* n Z n 
 
 h = -avdr=7d-*= x < V * = 7H* XV 
 
 The average value of n for this class of pipe is n = . 00032 
 in terms of diameter in feet, or n=.013302 in terms of diame- 
 ter in inches. In order to find the loss of head in feet by 
 friction per 100 feet length of pipe for any velocity, make Z= 
 100, and insert the value of n, and we have 
 
 1 00 X. 01 3302 
 Head lost per 100 feet length 
 
 Xv^-V rF~Xv s , if d is in inches, or'- :: 7^Xv F , if d is in feet. 
 yd 3 yd 3 
 
 TABLE No. 19. 
 
 Table showing loss of head in feet per 100 feet length of 
 asphaltum coated pipe when v s =l. To find the loss for any
 
 SULLIVAN'S NEW HYDRAULICS, 
 
 135 
 
 other velocity multiply the tabular loss by the square of that 
 velocity in feet per second. 
 
 Diam- 
 eter 
 In. 
 
 T/d 
 
 Inches 
 
 Head in Ft. 
 Lost per 100 
 Feet 
 
 Diam- 
 eter 
 In. 
 
 !/d 8 
 Inches 
 
 Head in Feet 
 Lost per 100 
 Feet 
 
 3 
 
 5.1961 
 
 .2560000 
 
 23 
 
 110.3040 
 
 .0120594 
 
 4 
 
 8. 
 
 .1662800 
 
 24 
 
 117.5750 
 
 .01131363 
 
 5 
 
 11.1803 
 
 .1190000 
 
 25 
 
 125. 
 
 .01064160 
 
 6 
 
 14.6969 
 
 .0905080 
 
 26 
 
 132.5740 
 
 .01003364 
 
 7 
 
 18.5202 
 
 .0718242 
 
 27 
 
 140.2960 
 
 .009481382 
 
 8 
 
 22.6274 
 
 .0588000 
 
 28 
 
 148.1620 
 
 .009000000 
 
 9 
 
 27. 
 
 .0492667 
 
 29 
 
 156.1690 
 
 .008517700 
 
 10 
 
 31.6227 
 
 .0420600 
 
 30 
 
 164.3160 
 
 .008095377 
 
 11 
 
 36.4828 
 
 .0364610 
 
 31 
 
 172.6000 
 
 .0077068366 
 
 12 
 
 41.5692 
 
 .0320000 
 
 32 
 
 181.0193 
 
 .0073483880 
 
 13 
 
 46.8721 
 
 .0283800 
 
 33 
 
 189.5705 
 
 .0070700000 
 
 14 
 
 52.3832 
 
 .0254000 
 
 34 
 
 198.2523 
 
 .0067096300 
 
 15 
 
 58.0747 
 
 .0229050 
 
 35 
 
 207.0628 
 
 .0064241400 
 
 16 
 
 64.0000 
 
 .02078436 
 
 36 
 
 216. 
 
 .006160000 
 
 17 
 
 70.0927 
 
 .01897770 
 
 38 
 
 234.2477 
 
 .005680000 
 
 18 
 
 76.3675 
 
 .01741840 
 
 40 
 
 252.8822 
 
 .005460000 
 
 19 
 
 82.8190 
 
 .01606140 
 
 42 
 
 272.2500 
 
 .004885950 
 
 20 
 
 89.4427 
 
 .01487200 
 
 44 
 
 291.8629 
 
 .004557600 
 
 21 
 
 96.2340 
 
 .01382250 
 
 48 
 
 332.5537 
 
 .004000000 
 
 22 
 
 103.1890 
 
 .01289000 
 
 54 
 
 396.8173 
 
 .003352000 
 
 What is the loss of head in feet by friction in a 22 inch 
 coated pipe 2500 feet in length, when the velocity is six feet 
 per second? 
 
 SOLUTION. 
 
 From table 19 we see that the loss in one hundred feet 
 length of 22 inch pipe is .01289 feet head when v=l. If v=6, 
 then v*=36,and .01289X36=.46404 feet lost per 100 feet length 
 of pipe. As there are 2,500 feet of pipe the total loss in the 
 whole length will equal the loss for 100 feet length multiplied 
 by the number of 100 feet, or 25, and we have .46404X25= 
 11.601 feet head lost in 2500 feet length when the velocity is 
 6 feet per second. 
 
 If this asphaltum coated pipe were replaced by an aver- 
 age weight clean cast iron pipe 22 inches in diameter, what 
 would be the loss of head in the cast iron pipe for 6 feet ve- 
 locity, and what slope would be required to cause the latter 
 pipe to generate 6 feet per second velocity? 
 SOLUTION. 
 
 From table No. 17 the loss of head per one foot length of
 
 136 SULLIVAN'S NEW HYDRAULICS. 
 
 22 inch cast iron pipe when v a =l is .00015864094. The loss 
 per 100 feet =.015864094, and when v=6 the loss per 100 feet 
 will be.015864094X(6) 2 =.571107384, and for 2500 feet, 
 .571107384X25=14.2777. The slope or fall in the 2500 feet must 
 therefore be 14.277711.601=2.6767 feet greater for the cast 
 iron pipe than for the aephaltum coated pipe. 
 
 The slope in either pipe which is required to generate the 
 given velocity is 
 
 m=.0004 for cast iron 
 m=.00033 for asphaltum coating 
 
 These values of m are in terms of diameter in feet. The 
 value of m may be converted to terms of diameter in inches 
 by multiplying by /(1 2) 8 =41.5692. (See 10, 12 and Group 
 No. 2, 14.) 
 
 The slopes to generate any given velocity may be found 
 from Tables No. 1 and No. 2 by the formula 
 
 s =( - - s = 
 
 Table No. 18 gives the different values of v/d 11 . TaDles 
 No. 1 and 2 give the values of f/d 3 and also of ACX W 'or 
 each diameter and class of pipe. When d=feet, the slope re- 
 quired to cause a cast iron pipe to discharge a given number 
 of cubic feet per second q, is 
 
 S= .000648456X-^ r - (See 42, 43). 
 
 From which the diameter in feet required to discharge a 
 given quantity when the slope is given, is 
 
 d= |/ / .0000004205X^/ / ^1, for clean cast iron, or 
 
 d=-i / 1 when d=inches. 
 
 See Tables Nos. 1 and 2 for value of AC, and see formulas
 
 SULLIVAN'S NEW HYDRAULICS. 137 
 
 35. Plow and Friction In Fire Hose. Fire hose is made 
 of different material, such as woven hose, lined with rubber, 
 or hose made entirely of leather. The resistance to flow will 
 depend upon the nature of the material which forms the lin- 
 ing. The resistance to flow in rubber lined hose is much 
 smaller than in leather hose, or in iron pipes of equal diam- 
 eter. Fire hose of all classes are made 2^ inches in diame- 
 ter, and therefore the area and friction surface are constan-t. 
 Head in feet and pressure in Ibs per square inch increase or 
 vary at the same rate. The quantity discharged per second 
 by a hose of constant diameter increases directly as the ve- 
 locity. In a constant diameter the velocity or quantity in- 
 creases as the square root of the head in feet, or as the 
 square root of the pressure in Ibs per square inch. The 
 friction increases as v a or q 8 in a constant diameter. The 
 pressure or the head is as v a or q s . The coefficient may there- 
 fore be determined in terms of head in feet or in terms of 
 pressure in Ibs per square inch and in terms of v* or q a . The 
 friction loss will then vary as the head or pressure or as v fl or 
 q 1 in the constant diameter. As fire hose are all 2% inches 
 diameter,we may use the direct value of the coefficients m and 
 n instead of the unit values. It is more convenient to have 
 the discharge of fire hose in gallons per minute than in cubic 
 feet per second, hence the formulas will be given in terms of 
 pressure in Ibs per square inch and discharge in gallons per 
 minute. 
 
 Let P=total guage pressure at hydrant or steamer. 
 
 P'^=total pressure lost by friction in the length I, in feet 
 of hose. 
 
 q=gallons per minute discharged by the hose. 
 
 n=coefficient of friction. 
 
 As the diameter is constant, the direct value of n will be 
 P' d n 
 
 n= rq^~' and p ' =-d~Xq 5 X i. 
 
 If 200 feet of rubber lined woven hose 2^ inches diame- 
 ter be laid out straight on a level with one end attached to a 
 hydrant or steamer, and with a smooth nozzle one inch chain-
 
 138 SULLIVAN'S NEW HYDRAULICS. 
 
 eter and 18 inches in length at the other end, and a 
 pressure guage at the hydrant end registers 50 pounds, 
 pressure per square inch, another guage attached at the butt 
 of the nozzle on the other end will register only 35 Ibs per 
 square inch, and the discharge will be 145 gallons per minute. 
 The pressure lost in the 200 feet of hose, (not including the 
 nozzle), was therefore P' =50 35=15 Ibs. Then, 
 
 And P'^' X q 2 X I =.000003567Xq 2 X I 
 
 q= gallons per minute. 
 
 Z=length in feet of hose. 
 
 The loes of pressure in Ibs per square inch in 2^ inch 
 rubber lined woven hose of any length and for any discharge 
 in gallons per minute will therefore be 
 
 P'=.000003567Xq 8 XZ- 
 
 In experiments with this class of hose the writer has ob- 
 served that the friction increases very slightly for low pres- 
 sures and decreases slightly for high pressures, be- 
 cause as the pressure within the hose becomes in- 
 tense, the rubber lining is compressed, enlarging the diame- 
 ter slightly and also causing the hose to straighten. An ex- 
 periment on 300 feet length of rubber lined hose with a 
 guage pressure of 156 Ibs per square inch at the hydrant end, 
 showed a pressure of 95 pounds at the butt of the nozzle, or a 
 loss by friction of 61 Ibs in 300 feet of hose while the dis- 
 charge was 239 gallons per minute. This gives the formula 
 
 P'=.00000356Xq*XZ 
 
 The difference in the value of the coefficient for very low 
 and very high pressures is so slight as to be of no practical im- 
 portance. It will be understood that the above formula does 
 not apply to leather hose, nor to any other than 2% inch rubber 
 lined hose. The coefficient is in its direct form, and conse- 
 quently applies only to the diameter for which it was deter- 
 mined.
 
 SULLIVAN'S NEW HYDRAULICS. 139 
 
 36 Pressure Required at Hydrant or Steamer to Force 
 the Discharge of a Given Quantity in Gallons per Min- 
 ute. As the hoee we are considering was partially throttled 
 by the one inch smooth nozzle at discharge, the total pressure 
 was not all neutralized by resistance nor converted into ve- 
 locity, but a large portion of it remained to balance the fric 
 tion in the nozzle and to generate the velocity through the 
 nozzle. Therefore, in order to ascertain the value of the co- 
 efficient of velocity m, we must taks P=P'+Pv only, for the 
 hose, (not the nozzle). 
 
 To do this, we must first find the value of Pv, or the amount 
 of pressure which generates the given velocity in the 2^ 
 inch hose. The quantity passing through the hose was 239 
 gallons per minute. 
 
 This is equal .5311 cubic feet per second. The area of 
 the hose is =.0341 square feet. The velocity in feet per sec- 
 ond through the hose was therefore 
 
 cubic feet .5311 
 v= ra -- :034T =15 ' 57 feet ' 
 
 The pressure causing this velocity was 
 Pv= o - =1.6337 Ibs per square inch. 
 Hence, P=rP'+Pv=61+1.6337=62.&34 Ibs. 
 
 p = -y- xq*X I ^'Xq'X l =Q00003656Xq 1 X l. 
 
 Therefore the total pressure at hydrant or steamer that 
 is required to force the discharge of a given number of gal- 
 lons per minute, (q) through any length in feet of 2J^ inch 
 rubber lined hose, will be 
 
 P=.000003G56Xq 8 X 1. 
 
 This does not include the pressure required to balance 
 the friction in the nozzle, nor to lift the weight of the water
 
 140 SULLIVAN'S NEW HYDRAULICS. 
 
 when the nozzle end of the hoze is elevated. This value of 
 P is that which is required to balance the friction in the 
 hose (not the nozzle) and to generate the velocity of flow in 
 the hose. If the discharge end of the hose is elevated, then 
 sufficient additional pressure must be added to the above 
 value of P to raise the weight of the given quantity to the 
 given height. 
 
 The pressure lost by friction in 2^ inch leather hose is 
 
 P'=.0000067464Xq 2 XZ 
 
 q=gallons discharged per minute. 
 
 Z=length in feet of hose. 
 
 From this value of the coefficient as compared with the 
 value of the coefficient for rubber lined hose, it is seen that 
 the friction loss in leather hose is nearly double that in rub 
 ber hose. For this reason leather hose has fallen into disuse 
 and will therefore not be discussed further. 
 
 37. Loss By Friction In Brass Fire Nozzles. 
 
 In conical pipes or nozzles which converge from a larger 
 to a smaller diameter, the velocity is inversely as the con- 
 stantly changing area and the resistance is inversely as ^/d 3 . 
 The velocity and resistance are therefore different at each 
 successive point along the length of such convergent pipe or 
 nozzle. The velocity is greatest in the portion having the 
 least diameter and least in the greatest diameter. If we take 
 the mean of all the varying velocities in such convergent noz- 
 zle, it will be found that this mean is very much greater 
 than the mean velocity through a pipe of uniform diameter 
 which uniform diameter is equal to the mean or averag-e 
 diameter of the convergent nozzle. It is therefore evident 
 that the friction in the nozzle will greatly exceed that in the 
 uniform diameter. 
 
 From the results of many experiments with very small 
 nozzles and large nozzles of cast iron from 8 to 12 feet in 
 length, the writer has discovered that the friction in a nozzle 
 or convergent pipe is nine times as great as in a pipe of uni- 
 form diameter which uniform diameter equals the mean di- 
 ameter of the convergent pipe, both being of the same mate-
 
 SULLIVAN'S NEW HYDRAULICS. 141 
 
 rial and same length, and discharging equal quantities of 
 water in equal times. 
 
 The coefficient of resistance n, for smooth brass in terms 
 of head and diameter in feet is n=.0003268, or nearly the 
 same as for asphaltum coated pipes. A smooth brass tire 
 nozzle 18 inches in length and converging from 2^ inches 
 inside diameter at the butt to a diameter of one inch at dis- 
 charge, discharged .17134566 cubic feet per second when the 
 guage pressure at the buit of the nozzle was 10 pounds per 
 square inch. As the velocity pressure is parallel to the walls 
 of the pipe, it is not shown by a pressure guage. In order to 
 find the friction loss in the nozzle we must find the total 
 pressure at the butt of the nozzle and then find the pressure 
 which causes the velocity of final discharge from the nozzle. 
 The difference between the total pressure at the butt of the 
 nozzle and the pressure due to the velocity of discharge from 
 the nozzle, is evidently equivalent to the pressure lost by 
 friction in the nozzle. 
 
 The pressure causing the velocity in the hose at the butt 
 of the nozzle is to be found and added to the guage pressure 
 at the butt of the nozzle. The velocity in the hose while 
 
 q _ .17135 
 discharging .17135 cubic feet per second was v= 
 
 5.0248. The pressure causing this velocity is Pv= 
 
 =.17 Ib. Add this to guage pressure at butt of nozzle and the 
 total pressure at the butt is P=10.17 Ibs. The area in square 
 feet of the one inch discharge of the nozzle is .0055. Conse- 
 quently the final velocity of discharge from this one inch 
 
 nozzle was v = =~~0055 =31.20 feet per second. The 
 
 pressure causing this final velocity of discharge from the noz- 
 
 v a ~y 4.34. 
 zlewasPv= 2 ' ' =6.55 Ibe. The pressure lost in the 
 
 nozzle b^ friction was therefore 10.17 6.55=362 Ibs, or 8.34 
 feet head while the discharge was .17135 cubic feet per sec-
 
 142 SULLIVAN'S NEW HYDRAULICS. 
 
 ond. The average or mean diameter of this nozzle was .1458 
 foot, and the area of this mean diameter was .0167 square 
 foot. Hence the velocity through the mean diameter while 
 
 discharging ,17i35 cubic feet per second was v^ = nig7~ 
 
 =10.26 feet. The coefficient of resistance of a smooth brass 
 pipe of uniform diameter is n=.0003268. Hence the loss of 
 head in feet in a smooth brass pipe of uniform diameter 
 equal to the mean diameter of this nozzle, and of equal length 
 
 .0003268 .0003268X1.50X105.2676 
 
 wouldbeh'=- 73f -XlXV= .0557 
 
 .9267 feet. This is equal to only one ninth part of the actual 
 loss in the convergent nozzle. Hence in a formula for friction 
 loss in a conical or convergent pipe or nozzle we must take 
 the square of three times the velocity through the mean di- 
 ameter (3Xv) a or (3Xq) 2 =9v 8 or 9q 8 , or we must find the co- 
 efficient of friction n in terms of quantity or velocity and 
 multiply by 9 for a convergent nozzle or pipe, or we must 
 consider the nozzle as a pipe of uniform diameter and as be- 
 ing 9 times as long as the nozzle. If we consider it as a uni- 
 form diameter then that diameter must be equal to the aver- 
 age diameter of the nozzle or conical pipe and nine times as 
 long. 
 
 Hence the general formula for loss of head in feet by 
 friction in conical pipes, reducers and nozzles will be 
 
 9v 
 
 In which 
 
 d=mean or average diameter of the convergent pipe. 
 v=velocity in feet per second in the mean diameter. 
 n=coefficient of friction in same terms as d. 
 The above value of n is iu terms of head and diameter in 
 feet.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 143 
 
 In a nozzle of given length and form the loss by friction 
 will vary directly as the head or pressure at the butt of the 
 nozzle, or directly as V s or q 8 . Hence a constant multiplier 
 may be determined for each form and length of nozzle, by 
 which the loss for any discharge, head or pressure may at 
 once be found. For example, if the formula is in terms of di- 
 ameter in feet, pressure in Ibs. per square inch at butt of noz- 
 zle (guage pressure +Pv.) and v 8 , then 
 .0001418X I X9 v s 
 
 P ': 
 
 -, for brass smooth (not ring) nozzles 
 
 From which the following table of constants was calcu- 
 lated: 
 
 TABLE No. 20. 
 
 Table of multipliers for finding pressure lost by friction 
 in brass smooth (not ring) fire nozzles. For any head or total 
 pressure. 
 
 Length of 
 Nozzle 
 Inches 
 
 Diameter 
 at Butt 
 Inches 
 
 Diameter 
 at Discharge 
 Inches 
 
 Lbs. pressure lost 
 equal total pres- 
 sure at butt mul- 
 tiplied by the dec- 
 imal below: 
 
 18.000 
 12.000 
 3.500 
 18.000 
 12.000 
 3.204 
 18.000 
 12.000 
 2.9125 
 
 2 1-2 
 2 1-2 
 2 1-2 
 2 1-2 
 2 1-2 
 2 1-2 
 2 1-2 
 21-2 
 2 1-2 
 
 !l-8 
 .1-8 
 1-8 
 .1-4 
 .1-4 
 .14 
 
 .356 
 .2373 
 .06922 
 .49 
 .325 
 .087 
 .474 
 .316 
 .0767 
 
 These multipliers exhibit the relative efficiency of fire 
 nozzles of different lengths and forms, and show the import- 
 ance of making nozzles and reducers of short length. For 
 the least loss and greatest efficiency the rate of convergence in 
 a reducer or nozzle should be one inch in a length of 2.33 in- 
 ches,which will conform to the shape of the contracted vein or 
 vena contracta. (See 80.) 
 
 If we wish to determine the direct coefficient for a given 
 length and form of nozzle in terms of gallons discharged per 
 minute and pressure in Ibs. per square inch, take the experi-
 
 144 SULLIVAN'S NEW HYDRAULICS. 
 
 mental data already given, for example, and we have 
 1=1.5 feet=18 inches 
 d=.1458 feet=mean diameter^ 2 ' 5 + 1 =1.75 inches 
 
 P' =10.17 6.55=3.62 Ibs. 
 
 Discharge=:.17185 cubic feet per second=77 gallons per 
 minute 
 
 P'd_ 3.62X1.75 _ 
 
 Z=feet, and demean diameter in inches 
 q=gallons per minute. 
 
 CAUTION. This last formula is in the direct form, and 
 will apply only to the given nozzle for which 
 it was determined. If the direct coefficient, 
 .000407, be multiplied by the constant length 
 in feet I of the given nozzle, then .000407X1.5 
 =0006105, and the loss of pressure by friction 
 in this given form and length of nozzle for 
 any discharge in gallons per minute is 
 
 P'=.0006105Xq 2 . 
 
 A direct constant may be found in the same manner for 
 each length and form of nozzle. 
 
 It is interesting to compare the values of n for different 
 materials when the unit values of n are all in the same terms. 
 Thus u=0001418 for smooth brass. n.=0000754 for rubber. 
 These are the unit values of n in terms of P' and diameter in 
 feet, showing that rubber offers less resistance to flow than 
 smooth brass or asphaltum coatings. 
 
 In a constant diameter of pipe, or in a constant length 
 and form of nozzle, the friction will increase or decrease di- 
 rectly as the pressure or head. Hence if a total pressure at 
 the butt of the nozzleiof 10.17 Ibs will cause a loss by friction 
 of 3.62 Ibs in the given nozzle, then a total pressure of one Ib. 
 
 at the butt would cause a friction loss= 3 ' 62 =.356 Ib., and 
 
 10.17
 
 SULLIVAN'S NEW HYDRAULICS, 145 
 
 any other total presssure at the butt would cause a loss of 
 P'=PX-356, for the given nozzle. 
 
 If a slope S .0004 in a cast iron pipe one foot diameter 
 will cause a loss of .0003938 foot head per foot length of pipe, 
 then the loss of head for any other slope of a one foot pipe 
 
 would be=^. 3 ? 3 ?_=.9845XS. And so of any other con- 
 
 .0004: 
 
 stant diameter or form of pipe or nozzle. 
 
 As friction increases as the square of the quantity dis- 
 charged, if the loss by friction in the nozzle is 3.62 Ibs. while 
 it is discharging 17 gallons per minute, the loss for a dis- 
 
 o Q q o 
 
 charge of one gallon per minute would be - 
 
 (77) 2 5929 
 
 .0006105 Ibs., and for any other discharge in gallons per min- 
 ute it would be = .0006105X(gallons) 2 . 
 
 If the loss of head in feet by friction in each foot length 
 of a 12 inch diameter cast iron pipe is .0003938 foot while the 
 pipe is discharging .7854 cubic foot per second, thon the loss 
 fora discharge of one cubic foot per second in such diameter 
 
 will be = 00 g^ 8 8 =.0006384 foot head per foot length and 
 
 for any greater or less discharge in cubic feet per second the 
 loss of head per foot length will be 
 
 h" = .0006384X (cubic feet per second) 8 . 
 Hence it is a simple matter to find the proper constant in 
 terms of head, pressure, velocity, slope or quantity for any 
 given form of nozzle or for any given diameter. 
 
 38 Friction In Ring Fire Nozzles. On account of the 
 abrupt shoulder or offset caused by the sudden contraction 
 of the diameter by the ring in what is termed a ring fire noz- 
 zle, very serious reactions and eddy effects occur in such noz- 
 zles, and the loss of head or pressure thus caused is very 
 great. In an experiment with a ring nozzle of brass, 18 inches 
 in total length, with a butt diameter of 2} inches and a ring 
 one inch diameter, and a total pressure at the butt equal to 
 23.237 feet head, the nozzle discharged . 13333 cubic feet per 
 second. The velocity through the one inch ring was there-
 
 146 SULLIVAN'S NEW HYDRAULICS. 
 
 fore v= q - 13333 =24.243 feet per second. The head 
 due to this final velocity of discharge from the nozzle was 
 
 Hv=-^-= 587>72 =9.126 feet head. 
 
 2g 64.4 
 
 Deducting this from the total head at the butt of the 
 nozzle, and the friction loss in the nozzle was 23,2379.126= 
 14.111 feet head or more than half the total pressure at the 
 butt of the nozzle. 
 
 39 Hydraulic Giants, Cast Iron Nozzles for Power 
 Mains, Reducers, and Conical Pipes In General. The 
 
 writer has made many experiments on cast iron giants or con- 
 vergent pipes of various dimensions and under heads of 20 
 to 600 feet at the base of the giant. The results of these ex- 
 periments confirm the correctness of the general formula 
 heretofore given for finding the loss by friction in nozzles, 
 reducers and convergent pipes that is to say, the friution 
 in a cast iron giant or convergent pipe, will be nine times as 
 great for the same discharge as it would be in a uniform di- 
 ameter equal to the mean diameter of the giant, reducer or 
 convergent pipe. Hence the general formula for head in 
 feet lost by friction in such giant or convergent pipe is 
 
 *xz .............. (95) 
 
 In this formula 
 
 d=the mean or average diameter of the giant. 
 
 v=velocity in the mean diameter in feet per second. 
 
 n=the usual coefficient of resistance for the class of cast 
 iron or other material. 
 
 I ^length in feet of giant. 
 
 If d is taken in inches then n must also be in the same 
 terms. 
 
 Cast iron giants for discharging water upon impulse 
 water wheels are required to be of the best metal and without 
 flaws. They are usually under high pressure and the veloci- 
 ties through them are terrific. Hence they are scoured and
 
 SULLIVAN'S NEW HYDRAULICS. U7 
 
 kept clean BO the coefficiennt will not increase after long use, 
 unless the water contains sand or gritty matter which cuts 
 the pipe walls and roughens them. 
 
 For this very dense, smooth cast iron, as usually found 
 in such nozzles, n= .0003623 in terms of diameter in feet. 
 Using the value of the mean diameter in feet of the cast iron 
 nozzle and the velocity v, through the mean diameter, and 
 the general formula for friction in such cost iron giants is 
 
 The coefficient n may be determined in terms of quantity 
 discharged per second or per minute so that the discharge 
 will correspond with a given loss of head. In an experiment 
 with a cast iron giant 8 feet in length and converging from 
 a diameter of fifteen inches at the base to a diameter of 3 
 inches at discharge, the loss of head in feet by friction while 
 the discharge was 8.845 cubic feet per second was 16.10 feet 
 head. 
 
 The mean diameter = == 9 inches =.75 foot. 
 
 Area of mean diameter=(.75) a X-7854=.4418 square foot. 
 
 Velocity through mean diameter ^ = ^ g =20022 ft. 
 
 per second. 
 
 Velocity in 15-inch diameter =7.209 feet per second. 
 
 Velocity of discharge in 3-inch diameter =180.16 feet per 
 second. 
 
 The mean of the velocities in all diameters =93.68 feet 
 per second. 
 
 Using the value of n applicable to this class of dense 
 cast iron and n=.0003623 in terms of head and diameter in 
 feet. Then, 
 
 .0003623X9 .0032607 
 
 b" = ^3 Xv 8 1= b X(20.022) 2X8 =16,10
 
 148 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 feet head lost by friction. This corresponds exactly with 
 the actual result. 
 
 In this given nozzle therefore, as the loss of head in feet 
 by friction was 16.10 feet while the discharge was 8.845 cubic 
 feet per second, the loss by friction for a discharge of one cu- 
 bic foot per second would be h' = 16 - 1 =.2058 foot, and for 
 
 (O.OiO) 8 
 
 any other discharge in cubic feet per second it would be h"= 
 .2058Xq*. Here q s =cubic feet per second discharged. A con- 
 stant for any other length and mean diameter of nozzle or 
 conical pipe may be readily found in the same manner in any 
 terms desired. (See Table No. 25, 56,) 
 
 40. Table of Multipliers for Determining the Loss of 
 Head in Feet by Friction in Clean Cast Iron Nozzles of 
 Given Dimensions. 
 
 TABLE No. 21, (See Table No. 26.) 
 
 
 
 
 Head in feet lost 
 
 Length 
 in Feet of 
 Nozzle 
 
 Greatest 
 Diameter 
 Inches 
 
 Least 
 Diameter 
 Inches 
 
 n nozzle equals ef- 
 'ective head at 
 aase of nozzle mul- 
 tiplied by the dec- 
 
 
 
 
 imal below 
 
 8 
 
 20 
 
 5 
 
 .0415 
 
 8 
 
 20 
 
 4 
 
 .02113 
 
 8 
 
 20 
 
 3 
 
 .00823 
 
 8 
 
 18 
 
 4 
 
 .0324 
 
 8 
 
 18 
 
 3 
 
 .012033 
 
 8 
 
 18 
 
 2 
 
 .003815 
 
 8 
 
 15 
 
 3 
 
 .031 
 
 8 
 
 15 
 
 2K 
 
 .01768 
 
 8 
 
 15 
 
 2 
 
 .0086 
 
 8 
 
 14 
 
 2 
 
 :<>iix5 
 
 8 
 
 12 
 
 1*6 
 
 .0098 
 
 8 
 
 12 
 
 2 
 
 .0244 
 
 8 
 
 12 
 
 1 
 
 .002394 
 
 8 
 
 10 
 
 1 
 
 .0058654 
 
 42: -The Total Head fn Feet H, or the Slope Required 
 to Cause the Discharge of a Given Quantity in Cubic Feet 
 Per Second in Ordinary Cast Iron Pipes. 
 
 By formula (30) the slope required to cause the discharge
 
 SULLIVAN'S NEW HYDRAULICS. 149 
 
 of a given number of cubic feet per second, is 
 
 m q 8 m q 2 q* 
 
 .616853-j/d 1 1 .616853 -j/o 11 ~ "''^y'd 11 
 
 The total head in feet in the length in feet I, required to 
 cause a given diameter of common cast iron pipe to discharge 
 a given quantity q, in cubic feet per second, is 
 
 H= ^g^ X-^nX I =.000648452X-^ n X I 
 
 In these formulas d is expressed in feet. In table No. 
 18 the values of y'd 11 are given. 
 
 43 The Slope or Total Head in Feet Being Given, to 
 Find the Diameter in Feet of Common Cast Iron Pipe 
 Required to Discharge a Given Quantity in Cubic Feet per 
 Second. 
 
 From the above formula, S=.000648452X-^ T - 
 Whence, 
 
 ,000648452Xq s 
 
 d "= -- s ~ 
 
 , qil _(.000648452)2Xq 4 
 
 - 
 
 i2632 
 
 = n/;jF 
 
 Or in terms of total head in feet, for the given value of 
 m. 
 
 44. Head in Feet Lost by Friction In Different Diame- 
 ters of Clean, Ordinary Cast Iron Pipe While Discharging 
 Given Quantities in Cubic Feet Per Second. 
 
 By formula (32) the head in feet lost by friction for a 
 given discharge is 
 
 h " == .616863 v /d" ............................... (32)
 
 150 SULLIVAN'S NEW HYDRAULICS. 
 
 The value of n in terms of diameter in feet for ordinary 
 clean cast iron pipe is n = . 0003938. Hence. . . . 
 
 .0006384 
 h"= I/dTrXq^XJ- It is convenient to have the loss of 
 
 head per 100 feet length of pipe, and therefore we may make 
 1=100 feet as a constant. The loss of head in feet by friction 
 in each 100 feet length of pipe for any given discharge in 
 cubic feet per second will then be 
 
 h"= ' /Jn Xq* Now if we take the quotent of-' /^n" 
 
 for each diameter of pipe in feet, the result will be a constant 
 for that diameter in feet, and when such constant is multi- 
 plied by the square of the discharge in cubic feet per second, 
 the product will equal the loss of head in feet per 100 feet 
 length of that diameter for the given discharge. 
 
 To facilitate such calculations the following table of 
 such constants is given. 
 
 45 Table of Multipliers for Determining the Loss of 
 Head in Feet by Friction Per 100 Feet Length of Ordi- 
 nary Clean Cast Iron Pipe for a Given Discharge In Cubic 
 Feet Per Second. 
 
 TABLE No. 22. 
 
 Multiply the constant which corresponds with the given 
 diameter on same line in the table by the square of the dis- 
 charge in cubic feet per second (q 8 ). The result will be the
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 151 
 
 loss of head in feet per 100 feet length of pipe for that dis- 
 charge. 
 
 Diam- 
 
 Inch's 
 
 Diam. 
 Feet 
 
 .06384 
 
 Diam 
 Inch's 
 
 Diam. 
 Feet. v 
 
 .06384 
 
 7"^*^- 
 
 "~ Constant 
 
 V/d 11 
 Constant 
 
 2 
 
 .1667 
 
 1214.611000 
 
 23 
 
 1.917 
 
 0.00178125 
 
 3 
 
 .25 
 
 130.737000 
 
 24 
 
 2.000 
 
 0.00141083 
 
 4 
 
 .3333 
 
 26.880000 
 
 25 
 
 2.0-3 
 
 0.00112791 
 
 5 
 
 .4167 
 
 7.871700 
 
 26 
 
 2.166 
 
 O.Q0090979 
 
 6 
 
 .5 
 
 2.900000 
 
 27 
 
 2.250 
 
 0.00073800 
 
 7 
 
 .5833 
 
 1.236000 
 
 28 
 
 2.333 
 
 0.00060483 
 
 8 
 
 .6667 
 
 0.594000 
 
 29 
 
 2.416 
 
 0.00050000 
 
 9 
 
 .75 
 
 0.310657 
 
 30 
 
 2.500 
 
 0.00041347 
 
 10 
 
 .8333 
 
 0.174045 
 
 31 
 
 2.584 
 
 0.000344708 
 
 11 
 
 .9167 
 
 0.10:3000 
 
 32 
 
 2.666 
 
 0.000290000 
 
 12 
 
 1.000 
 
 0.0o384 
 
 33 
 
 2.750 
 
 0.000244785 
 
 13 
 
 1.083 
 
 0.041187 
 
 34 
 
 2.834 
 
 0.000207407 
 
 14 
 
 1.167 
 
 0.027305 
 
 35 
 
 2.916 
 
 0.000177333 
 
 15 
 
 1.250 
 
 0.0187104 
 
 36 
 
 3.000 
 
 0.000151675 
 
 16 
 
 1.333 
 
 0.0131385 
 
 38 
 
 3.166 
 
 0.000112800 
 
 17 
 
 1.417 
 
 0.0093>>23 
 
 40 
 
 3.333 
 
 0.000085018 
 
 18 
 
 1.500 
 
 0.0(W8(i3-0 
 
 42 
 
 3.500 
 
 0.000064970 
 
 19 
 
 1.583 
 
 0.00510310 
 
 44 
 
 3.666 
 
 0.000050347 
 
 20 
 
 1.667 
 
 0. 003*41 l.V> 
 
 48 
 
 4.000 
 
 0.000*311714 
 
 21 
 
 1.750 
 
 0.00294000 
 
 54 
 
 4.500 
 
 0.0000163100 
 
 22 
 
 1.833 
 
 0.00227919 
 
 60 
 
 5.000 
 
 0.00000900415 
 
 For convenience in referring to the table No. 22, the di- 
 ameters are given first in inches and then in feet. The total 
 head per 100 feet length ia equal the loss of head per 100 
 feet divided by .9815, provided the diameter is constant and 
 
 the discharge is free, or H=h"Xl-01573= 9g45 . 
 
 46. Head in Feet Lost by Friction In Asphaltum 
 Coated Pipes While Discharging a Given Quantity in Cubic 
 Feet Per Second. it we refer to the table of values of m as 
 developed in Group No. 2 from the experiments of Hamilton 
 Smith Jr., and of D'Arey and Bazin, on this class of pipe, it 
 will be seon'that the value of m, the coefficient of velocity, 
 varies from m=.00028 to m=.0003432 in the experiments of 
 Smiti., and from m= 000271 to m=.000289 in the experiments 
 of D'Arcy. Smith's experiments were on lap seamed riveted
 
 152 SULLIVAN'S NEW HYDRAULICS. 
 
 pipes with Blip joints like stove pipe joints. D'Arcy's experi- 
 ments were on cast iron coated pipes which were free of rivet 
 heads and seams, but which were in shorter lengths and re- 
 quired more joints. The coefficient of friction n, for any given 
 class of perimeter, is always equal .9845 per cent of the value 
 of m for the given class of perimeter. Hence where the value 
 of m is known for any class of perimeter, the value of n for 
 
 n 
 that class is n=mX-9845, and m= . As it is prudent 
 
 to allow for errors in the experimental data from which the 
 above values of m were deduced and also for inferior quality 
 of the coating, and future deterioration of the coating and 
 slight deposits, we will adopt the value of n=. 00032 in 
 terms of diameter and head in feet. This should be a safe 
 and reliable value of n for either riveted pipe, welded pipe, or 
 cast iron pipe, which has been coated with asphaltum. The 
 coating material usually covers the rivet heads and fills the 
 longitudinal offset made by the lap of the plate. Hence there 
 should not be a great difference in the value of n or m for 
 either class of pipe after it has been coated. D'Arcy's coeffi- 
 cients are usually too small (that is, m or n, which makes C 
 too high) and the length of pipe used in his experiments was 
 rather short. The experiments of Smith are considered more 
 reliable. They are safer to use in practice at any rats. 
 
 TABLE No. 23. 
 
 Table No. 23 is based on the same principle as table No. 
 22, and its use is fully explained in 44, 45. 
 
 To USE TABLE No. 23. 
 
 To find the loss of head in feet per 100 feet length of as- 
 phaltum coated pipe for any given discharge in cubic feet per 
 second, multiply the constant in 3d column opposite the giv- 
 en diameter by the square of the discharge in cubic feet per 
 second, q s .
 
 SULLIVAN'S NEW HYDRAULICS. 153 
 
 .051884 
 
 Head in feet lost per 100 feet length, h' 
 d is in feet. 
 
 dll 
 
 Diam- 
 
 Diam- 
 
 .051864 
 
 Diam 
 
 Diam 
 
 .051864 
 
 eter 
 In. 
 
 eter 
 Feet. 
 
 Constant 
 
 eter 
 In. 
 
 eter 
 Feet. 
 
 Constant 
 
 2 
 
 .1667 
 
 986.758 
 
 23 
 
 1.917 
 
 0.00144710 
 
 3 
 
 .25 
 
 106.213 
 
 24 
 
 2.000 
 
 0.001146165 
 
 4 
 
 .3333; 
 
 21 . 417 
 
 25 
 
 2.0^3 
 
 0.000916325 
 
 5 
 
 .4167 
 
 6.400 
 
 26 
 
 2.166 
 
 0.000739120 
 
 6 
 
 .5 
 
 2.347 
 
 27 
 
 2.25 
 
 0.000599600 
 
 7 
 
 .5833 
 
 1.006 
 
 28 
 
 2.333 
 
 0.000491370 
 
 8 
 
 .6667 
 
 0.482460 
 
 29 
 
 2.416 
 
 0.000405200 
 
 9 
 
 .75 
 
 0.252380 
 
 30 
 
 2.5 
 
 0.000386000 
 
 10 
 
 .8333 
 
 0.141400 
 
 31 
 
 2.584 
 
 0.000280000 
 
 11 
 
 .9167 
 
 0.083680 
 
 32 
 
 2.666 
 
 0.000236852 
 
 12 
 
 1.000 
 
 0.051864 
 
 33 
 
 2.75 
 
 0.000199000 
 
 13 
 
 1.083 
 
 0.033460 
 
 34 
 
 2.834 
 
 0.000170000 
 
 14 
 
 .167 
 
 0.022183 
 
 35 
 
 2.916 
 
 0.000144070 
 
 15 
 
 .25 
 
 0.015200 
 
 36 
 
 3.000 
 
 0.000123222 
 
 16 
 
 .333 
 
 0.0106738 
 
 38 
 
 3.166 
 
 0.0000916325 
 
 17 
 
 .417 
 
 0.0076270 
 
 40 
 
 3.333 
 
 0.0000690690 
 
 18 
 
 .5 
 
 0.00557617 
 
 42 
 
 3.500 
 
 O.OOOOV27820 
 
 19 
 
 .583 
 
 0.004145M) 
 
 44 
 
 3.666 
 
 0.0003409000 
 
 20 
 
 .667 
 
 0.00312060 
 
 48 
 
 4.000 
 
 0.0000253241 
 
 21 
 
 .75 
 
 0.00240000 
 
 54 
 
 4.500 
 
 0.0000132509 
 
 22 
 
 .833 
 
 0.00185160 
 
 60 
 
 5.000 
 
 0.0000074314 
 
 REMARK The value of n used in above taole will allow 
 for the reduction of area and diameter by the thickness of 
 the coating, BO that the actual diameter before it is coated 
 may be used without any allowance for thickness of the coat. 
 
 47. To Find the Quantity Discharged when the Loss 
 of Head and Diameter are Given. The quantity in cubic 
 feet per second which is being discharged by any diameter 
 may be found from the loss of head as indicated by pressure 
 guages. We have just seen that the loss of head per 100 feet 
 length of coated pipe for a given discharge in cubic feet per 
 
 second is h" = 
 
 051864 
 
 Xq 2 . By transposing in this equation 
 
 we have the formula for finding the quantity discharged in 
 cubic feet per second from the amount of head in feet lost by 
 friction h", thus, 
 
 '' whence ' q= AJS&r
 
 154 SULLIVAN'S NEW HYDRAULICS. 
 
 d=feet, and h"=head in feet lost per 100 feet length of the 
 pipe. 
 
 A similar formula for cast iron pipe may be deduced 
 from the coefficient values given in 44. The values of ^/d 11 
 will be found in table No. 18. For ordinary cast iron pipe, 
 
 not coated, we have h"=' 06384 Xq*=loss per 100 feet length 
 j/d 1 1 
 
 of pipe. Hence the discharge in cubic feet per second cor- 
 responding with this loss of head in feet per 100 feet length 
 of pipe is 
 
 48- To Find the Quantity that a Given Slope will Cause 
 a Given Diameter to Discharge. 
 
 The slope required to cause the discharge of a given quan- 
 tity in cubic feet per second is S=- 
 .00064845^ 
 
 By transposition we have 
 
 / Si/d 11 / 
 
 q= I/ .0006^845 = 39.27 j/Syd" =39.27 Vd 11 X v/S, 
 
 H__ total head in feet 
 
 ~ I total length of pipe in feet 
 d=diameter in feet. 
 q=cubic feet per second discharged. 
 Table No 18 gives the values of yd", and Table No. 15 
 gives yS. 
 
 49 To Find the Total Pressure in Pounds Per Square 
 Inch that must be Exerted by a Pump Piston, or by Other 
 Means, in Order to Cause a Given Diameter of Asphaltum 
 Coated Pipe to Discharge a Given Quantity in Cubic Feet 
 Per Second. 
 
 By formula (44)
 
 SULLIVAN'S NEW HYDRAULICS. 155 
 
 As we have adopted n=. 00032 as the safe coefficient of 
 friction in terms of head and diameter in feet for asphaltum 
 coated pipes, the corresponding value of the coefficient of flow 
 
 would be m Q ^ =.00032503, in terms of head and diame- 
 ter in feet. 
 
 To reduce this value of m to terms of pressure in pounds 
 per square inch and diameter in feet, it is simply necessary to 
 divide by the number of feet head required to cause a pres- 
 sure of one pound per square inch. II=PX2.304, and P= 
 
 H 
 2.304 ' 
 
 Therefore if P=l pound per square inch, then H 1X2.- 
 304=2.304 feet. 
 
 00032503 
 
 Hence, m =~2~304 = 0001il07) * n terms of ^ an( * d in 
 feet. 
 
 .00014107 q" 
 Then, from formula (44), P= t6168 5^X ^/d l ^^ l= 
 
 .0002287 
 
 1/cin-Xq'xJ. 
 
 The total pressure to be exerted by the pump is there- 
 fore, 
 
 .0002287 
 
 P =Vd^ Xq Xl 
 
 d = diameter of coated pipe in feet. 
 
 J=length of pipe in feet. 
 
 q=cubic feet per second discharged. 
 
 See Table No. 18 for values of ^d* 1 . 
 
 CAUTION: It is assumed in the above formula that the 
 pipe is laid level, or that there is no differ- 
 ence in level between its two ends. If the 
 pipeia laid on a declivity, then this declivity 
 would supply a portion of the head or pressure.
 
 156 SULLIVAN'S NEW HYDRAULICS. 
 
 If the discharge end of the pipe is above the 
 pump, then additional pressure will be re 
 quired at the pump sufficient to raise the 
 weight of the given number of cubic feet per 
 second to a height in feet equal to the differ- 
 ence in level between the pump and th dis- 
 charge end of the pipe. 
 
 50. To Find the Quantity Discharged From the Pres- 
 sure. 
 
 By transposition in the above formulafor P, we have 
 
 coated pi? 6 - 
 
 P=toial pressure in pounds per square inch. 
 
 d-diameter in feet of pipe. 
 
 Z=length of pipe in feet. 
 
 See "Caution" above. For value of ^/d 11 see Table No 
 18. 
 
 For cast iron pipe, not coated, m=.0004 in terms of head 
 and diameter in feet. Hence in terms of P and d, it will be 
 
 m=^3Q|=.0001736Jl. Therefore P ' 616853 X 
 
 59.6 
 
 51. ~ Pounds Pressure Per Square Inch Lost by Friction 
 fora Given Discharge In Cubic Feet Per Second. 
 
 By formula (45) the pressure lost by friction for a given 
 discharge is 
 
 As we have just found the values of m in terms of diam- 
 eter in feet and pressure in Ibs per square inch, for coated
 
 SULLIVAN'S NEW HYDRAULICS. 157 
 
 pipes and for uncoated cast iron pipes, the corresponding val- 
 ues of n will be n=mX-9845. 
 
 Hence for asphaltum coated pipe n=.00014107X.9845== 
 .000138883415. 
 
 For cast iron pipe not coated, n=. 00017361 lX-9845= 
 .00017092. 
 
 The pressure in Ibs per square inch lost by friction for a 
 given discharge in cubic feet per second will be, for coated 
 pipe, 
 
 .00017092 q* .000225 
 
 ~ .616853 X 7d^~ >< /dH Xq X ' 
 
 And for cast iron pipe not coated, 
 
 .000138883415 xx q .000277 
 
 P '= .616853 X 7gn-X*= ^TdTlXq'X* 
 
 The quantity discharged may be found from the loss of 
 pressure thus 
 
 / P' -/d 11 
 q = V .000225X I ' f r C ated pipe * 
 
 / PVd 11 
 q "\ OOQ977N/ / ' ' or ca8 * i ron PiP e no * coated. 
 
 See table No. 18 for value of -/d' 1 . 
 
 52. Table lor finding the Slope of a Cast Iron Pipe 
 or the Total Head, in Feet Required to Cause a Given 
 Discharge in Cubic Feet per Second. 
 
 The quantity discharged by a constant diameter will be 
 directly as the velocity of flow. The velocity of flow will be 
 as i/H or -j/S. Hence S or H must vary as v s or q*. If the 
 slope or total head required in any given diameter of pipe, 
 one foot in length, to cause a discharge of one cubic foot per 
 second, be found, then, as S or H must vary as q 2 for that 
 given diameter, it follows that the slope or total head re- 
 quired for any other discharge will be equal to the slope or 
 head which causes a discharge of one cubic foot per second
 
 158 SULLIVAN'S NEW HYDRAULICS. 
 
 multiplied by the square of the desired discharge in cubic 
 feet per second, q*. 
 
 If the required slope S is found, then the total head in 
 
 TT 
 
 feet for any given length in feet will be H=SX M r S= = 
 
 rr 
 
 total head required per foot length. ' =~g~; H=SX I- 
 By formula (30), 
 
 tn Q ^ Q * 
 
 TT = - 00064845 X n"' 0004. 
 
 Hence the slope, or the total head in feet pei foot length 
 of any given diameter of ordinary cast iron pipe, not coated, 
 required to cause the discharge of one cubic foot per second 
 will be 
 
 /jii And the slope required to cause the dis- 
 charge of any greater or less quantity in cubic feet will be 
 . ,00061845 
 
 In which, 
 
 d=diameter of pipe in feet. 
 'q=cubicfeet per second. 
 
 And the total head in feet required in any given length 
 in feet of pipe will be H=SXf- 
 
 TABLE No. 24. 
 
 To find the slope required to cause any given diameter in 
 feet of uncoated cast iron pipe to discharge a given quantity 
 in cubic feet per second: Rule. Multiply the slope in the 
 following table (No. 24) which is opposite the .given diameter, 
 by the square of the desired discharge in cubic feet per sec- 
 ond, 
 
 H=S X l.
 
 SULLIVAN'S NEW HYDRAULICS, 
 
 159 
 
 Diam 
 eter 
 
 r/dll 
 froat 
 
 Slope 
 .00064845 
 
 Diam- 
 eter 
 
 v/d* 1 
 
 Pftftt 
 
 Slope 
 .00064845 
 
 Feet. 
 
 r eel 
 
 v/d 11 
 
 Feet 
 
 c 661 
 
 ^d" 
 
 .1(567 
 
 .00005256 
 
 12.33734 
 
 1.917 
 
 35.84 
 
 .0000180929 
 
 .25 
 
 .0004883 
 
 1.32800 
 
 2.000 
 
 45.25 
 
 .0000143300 
 
 .3333 
 
 .002375 
 
 .27303 
 
 2.083 
 
 56.60 
 
 .0000114567 
 
 .4167 
 
 .00811 
 
 .07996 
 
 2.166 
 
 70.17 
 
 .0000092410 
 
 .5 
 
 .Oi21 
 
 .0293416 
 
 2.25 
 
 86.50 
 
 .0000074:3653 
 
 .5833 
 
 .05157 
 
 .0125740 
 
 2.333 
 
 105.55 
 
 .00000614353 
 
 .6667 
 
 .1075 
 
 .0060800 
 
 2.416 
 
 128.00 
 
 .00000506600 
 
 .75 
 
 2055 
 
 .0031555 
 
 2.5 
 
 154.40 
 
 .0000042000 
 
 .8333 
 
 13668 
 
 .0017680 
 
 2.584 
 
 185.20 
 
 .0000035000 
 
 .9167 
 
 .6198 
 
 .00104622 
 
 2.666 
 
 219.90 
 
 .0000029500 
 
 .000 
 
 1.000 
 
 .000o4845 
 
 2.75 
 
 260.80 
 
 .00000248638 
 
 .083 
 
 1.55 
 
 .0004184 
 
 2.834 
 
 307.80 
 
 .00000210672 
 
 .167 
 
 2.338 
 
 .00027735 
 
 2.916 
 
 360.00 
 
 .00000180120 
 
 .25 
 
 3.412 
 
 .00019000 
 
 3.000 
 
 420.90 
 
 .00000154060 
 
 .343 
 
 4.859 
 
 .0001334533 
 
 3.166 
 
 566.00 
 
 .00000114570 
 
 .417 
 
 6.800 
 
 .OOOoa-,:;--m 
 
 3.333 
 
 750.90 
 
 .000000863563 
 
 .5 
 
 9.301 
 
 .0000097180 
 
 3.5 
 
 982.60 
 
 .000000660000 
 
 .583 
 
 12.51 
 
 .0000518345 
 
 3.666 
 
 1268.00 
 
 .000000511400 
 
 1.667 
 
 16.62 
 
 .0000390000 
 
 4.000 
 
 2048.00 
 
 .000000316621 
 
 1.75 
 
 21.71 
 
 .00002'.iNV"7 
 
 4.5 
 
 3914.00 
 
 .00000 '165674 
 
 1.833 
 
 28.01 
 
 .0000231500 
 
 5.000 
 
 6979.00 
 
 .000000092916 
 
 See Table No. 16. These tables apply to pipes flowing 
 full bore and with free discharge. q:q ::i/S:v/S, for a given 
 diameter. 
 
 S3. Wooden Stave Pipes. In the western states,where 
 irrigation is practiced on an extensive scale, and in localities 
 without railway facilities, wooden stave pipe, invented by Mr. 
 J. T. Fanning, and described in his "Treatise on Water Sup- 
 ply and Hydraulic Engineering" page 439. has been adopted 
 in many instances in recent years. 
 
 In the very dry atmosphere of the arid west these pipes 
 have not proven satisfactory in many cases where they were 
 laid on the surface or without sufficient covering. In such 
 cases it shrinks and warps and leaks badly. Where properly 
 covered and kept constantly full of water it has been quite 
 satisfactory. It has not been in general use for a sufficient 
 length of time to test its durability. That would, of course, 
 depend upon the kind of wood used in manufacturing the 
 staves, and upon whether it was perfectly seasoned and 
 sound. If perfectly seasoned and treated with tar oil or sul- 
 phate of copper, it should be very durable. The quantity of 
 this class of pipe which is being used of late years in the
 
 160 SULLIVAN'S NEW HYDRAULICS. 
 
 West for irrigation purposes in caseB where there is only 
 Email pressure to be sustained, and the general belief that 
 this wooden pipe is smoother and will give a higher dis- 
 charge under like conditions than uncoated iron pipes, de- 
 mands that it be given some notice here. 
 
 54. Coefficients of Flow in Wooden Stave Pipes 
 Compared with the Coefficients of Pipes of other Material. 
 
 By referring to the coefficient values developed from the 
 data of D'Arcy and Bazin, (See group No 5), it will be seen 
 that the average value of m for wooden conduits made of 
 closely jointed, planed poplar lumber is m = . 000060 in terms of 
 hydraulic mean radius in feet and head in feet. The rectan- 
 gular wooden conduits used in these experiments did not 
 contain the great number of joints which are necessary in 
 forming a circular conduit of wooden staves. It is fair to as- 
 sume then that the circular wooden conduit built up of narrow 
 staves with its many joints would not present a more uniform 
 surface to the flow than the rectangular conduit or flume of 
 planed, well jointed hard wood. 
 
 The nature of the wood of which the staves are made as 
 to density and freedom from knots, will undoubtedly affect 
 the value of the coefficient. It appears from the great num- 
 ber of experiments by D'Arcy and Bazin on such conduits 
 (only a few of which were quoted in Group No. 5) that m= 
 .00006 is about the average value of the coefficient in terms of 
 r in feet. 
 
 If this value of m be reduced to terms of diameter in feet, 
 we have for well jointed, planed hard wood conduits, m= 
 
 .00006X8=.00048, or C=^~- =45.64, in terms of head and 
 
 diameter in feet. For average cast iron pipe, not coated, m 
 .00040 and 0=50.00. For asphaltum coated riveted pipes, 0= 
 56.CO. For pipes lined with mortar composed of two-thirds 
 cement to one-third sand, 0=48.50. It is therefore apparent 
 that the wooden pipe offers much greater resistance to flow 
 than either of the others, and will therefore require a greater 
 diameter for an equal discharge.
 
 SULLIVAN'S NEW HYDRAULICS. 161 
 
 The slope required in a wooden pipe in order to cause it 
 to discharge a given quantity in cubic feet per second would 
 be 
 
 " v q' .MOM q* _ - 0007781 v ... 
 
 ~ .616853 X v/d 1 * T .616853 x v/d 11 "~ i/d 11 xq ' 
 and qiqii/Si^S. 
 
 And the diameter in feet required to discharge a given 
 quantity for a given slope will be 
 
 55. Earthenware Or Vitrified Pipe This class of 
 pipe is made in very short lengths and consequently requires 
 many joints. It is subject to unequal settlement and leaks 
 unless very great care is taken to secure a firm bearing or 
 foundation upon which to lay the pipe. It also requires care 
 and experience to make and properly cement the joints. If 
 the pipe is made of clay containing a high percentage of 
 aluminum and is thoroughly glazed and p roperly laid and 
 very carefully jointed, it develops a coefficient m=.00036 or C 
 52.70, in terms of diameter in feet and slope or head in feet. 
 It therefore offers less resistance to flow than very smooth, 
 dense, clean cast iron pipe, provided all the above conditions 
 as to laying and jointing are complied with. As these con- 
 ditions are scarcely ever fulfilled, it is not prudent to depend 
 upon a greater discharge from such pipe than from ordinary 
 clean cast iron pipe. Hence all the tables heretofore given 
 for cast iron pipe may be adopted as applying also to earth- 
 enware glazed pipe. This class of pipe is very extensively used 
 for house drains, small sewers, land drains and irrigation pur- 
 purposes, and in other rough work where great care and 
 thorough workmanship are not usually exercised. Hence it 
 is not safe to take the value of C greater than C=50, or m = 
 .0001 in terms of head or elope and diameter in feet. For 
 small sewers, not exceeding about 18 inches diameter, this 
 class of pipe serves well. The flow of sewage is probably not 
 eo great as that of clear water because of the suspended, solid
 
 162 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 matter that it carries. The value of C for a sewer would 
 therefore rot be quite BO great as for pure water flowing in 
 the samo class of pipe or conduit. C=50, should be a safe 
 value for fairly well laid and jointed earthenware glazed 
 pipe. In order to prevent deposits the mean velocity of flow 
 in a sewer should never be less than two and half feet per 
 second for small depths of flow. In order to ascertain the 
 mean velocity of flow in such sewer pipe when flowing only 
 part full, the coefficient maybe reduced to terms of hydraul 
 icmean depth r, in feet by multiplying m in terms of d in 
 feet by 0.125, or by dividing by 8. Then in terms of r in feet 
 
 0004 
 m = ! -g .0000."), and C 141.42. The mean velocity of flow 
 
 in a circular conduit, or in a pipe, will be the same for just 
 half full as for full, because-p- is the same for half full as 
 
 for full. 
 
 56 Table of Elementary Dimensions of Pipes. 
 
 TABLE No. 25. 
 
 Diam. 
 In. 
 
 Diam. 
 Feet 
 
 Area 
 Sq. 
 Feet 
 
 U.S. Gal. 
 In one 
 Ft.Lgth 
 
 Diam. 
 In. 
 
 Diam. 
 Feet 
 
 Area 
 Sq. 
 Feet 
 
 U.S. Gal 
 In one 
 Ft. Lsth 
 
 K 
 
 .0208 
 
 .0003 
 
 .0025 
 
 4.V4 
 
 3750 
 
 .1104 
 
 .8263 
 
 % 
 
 .0313 
 
 .0008 
 
 .0057 
 
 4.% 
 
 .3958 
 
 .1231 
 
 .9206 
 
 y* 
 
 .0417 
 
 .0014 
 
 .0102 
 
 5 
 
 .4167 
 
 .1364 
 
 1.020 
 
 % 
 
 .0521 
 
 .0021 
 
 .0159 
 
 6 
 
 .5 
 
 .1963 
 
 1.469 
 
 X 
 
 .0625 
 
 .0031 
 
 .0230 
 
 8 
 
 .6667 
 
 .3491 
 
 2.611 
 
 % 
 
 .0129 
 
 .0042 
 
 .0312 
 
 10 
 
 .8333 
 
 .5454 
 
 4.080 
 
 i. 
 
 .0833 
 
 .0055 
 
 .0408 
 
 12 
 
 
 .7854 
 
 5.875 
 
 i-k 
 
 .1042 
 
 .0085 
 
 .0638 
 
 14 
 
 !l67 
 
 1.069 
 
 7.997 
 
 l.V> 
 
 .125 
 
 .0123 
 
 .0918 
 
 16 
 
 .333 
 
 1.396 
 
 10.440 
 
 1.3 
 
 .1458 
 
 .0167 
 
 .1249 
 
 18 
 
 .5 
 
 1.767 
 
 13.220 
 
 2. 
 
 .1667 
 
 .0218 
 
 .1632 
 
 20 
 
 .667 
 
 2.182 
 
 16.320 
 
 2.M 
 
 '1875 
 
 .0276 
 
 .2066 
 
 22 
 
 .833 
 
 2.640 
 
 19.75 
 
 2-H 
 
 .2083 
 
 .0341 
 
 .2550 
 
 24 
 
 2. 
 
 3.142 
 
 23.50 
 
 2.X 
 
 .2292 
 
 .0412 
 
 .3085 
 
 26 
 
 2.167 
 
 3.6b7 
 
 27.58 
 
 3. 
 
 .25 
 
 .0*91 
 
 .3672 
 
 27 
 
 2.25 
 
 3.976 
 
 29.74 
 
 3.!4 
 
 .2708 
 
 .0576 
 
 .43C9 
 
 28 
 
 2.333 
 
 4.276 
 
 31.99 
 
 3 K 
 
 .2917 
 
 .0668 
 
 .4998 
 
 30 
 
 2.5 
 
 4.909 
 
 36.72 
 
 3.% 
 
 .3125 
 
 .0767 
 
 .5738 
 
 32 
 
 2.667 
 
 5.585 
 
 41.78 
 
 4. 
 
 .3333 
 
 .0873 
 
 .6528 
 
 34 
 
 2.833 
 
 6.305 
 
 47.15 
 
 4.M 
 
 .3542 
 
 498B 
 
 .7369 
 
 36 
 
 3. 
 
 7.069 
 
 52.88 
 
 231 cubic inchee=d U. S. gallon. 7.48052 U. S. gallons= 
 1 cubic foot.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 163 
 
 The area in square feet of a pipe is the same as the contents 
 Df one foot in length of the pipe in cubic feet. Hence by an 
 inspection of table No. 25, the diameter and also the velocity 
 required to carry a given number of cubic feet or of U. S. gal- 
 lons may be determined at once. If the velocity is one foot 
 per second in any diameter, the discharge in cubic feet per 
 second will equal the area in square feet of that diameter, or 
 the discharge in gallons per second will equal the number of 
 gallons in one foot length of pipe. For a discharge of 2, 3, 4. 
 etc times that quantity, the velocity must be 2, 3, 4, etc feet 
 per second. Tables No. 16 and 17 and 19 will show the slope 
 or head required to generate the required velocity, and also 
 the amount of head that will be neutralized by friction for 
 that velocity. The dimensions of the very small pipes given 
 in table No. 25 will be "found convenient in designing hy- 
 draulic giants and nozzles, and in selecting small service pipes, 
 and discharge pipes for small pumpd. See also Tables 22 and 
 23, and 26 and 27. Square inches multiplied by .00695= 
 square feet. 
 
 57. Length in Feet of Small Pipes Required to Hold 
 one U.S. Gallon of 231 Cubic Inches, and Areas Given in 
 Square Inches. 
 
 TABLE No. 26. 
 
 (1 square inch=.0069444 square feet). 
 
 Diam. 
 In. 
 
 Area 
 Sq. 
 Inches. 
 
 Length In 
 Feet to hold 
 1 Gallon. 
 
 Diam. 
 In. 
 
 Area 
 Sq. 
 Inches. 
 
 Length In 
 Feet to hold 
 1 Gallon. 
 
 U 
 
 .0490875 
 
 407. 43567 ;~0 
 
 2.% 
 
 5.412 
 
 3.5570 
 
 l / 
 
 .1963500 
 
 98.0S92083 
 
 2.% 
 
 5.940 
 
 3.2540 
 
 2 
 
 .4417875 
 
 43.5729833 
 
 2.X 
 
 6.492 
 
 2.9651 
 
 1. 
 
 .7854 
 
 24.5098000 
 
 3. 
 
 7.069 
 
 2.7225 
 
 1 ii 
 
 1.2271875 
 
 15.6862001) 
 
 3.^ 
 
 7.670 
 
 2.5097 
 
 1 H 
 
 1.7671500 
 
 10.893iOOO 
 
 3.ii 
 
 8.296 
 
 2.3200 
 
 1 K 
 
 2.4050 
 
 8.0)41650 
 
 3.% 
 
 8.946 
 
 2.1517 
 
 l.X 
 
 2.7610 
 
 6.9721000 
 
 3.V* 
 
 9.fi21 
 
 2. 
 
 2. 
 
 3.1416 
 
 6.1274100 
 
 3.X 
 
 10.320 
 
 1.8652 
 
 2.H 
 
 3.5470 
 
 5.4270000 
 
 8.V 
 
 11.040 
 
 1.7360 
 
 2.?4 
 
 3.9760 
 
 4.8415000 
 
 3.% 
 
 11.790 
 
 1.6166 
 
 2 K 
 
 4.9090 
 
 3.9214000 
 
 4. 
 
 12.570 
 
 1.5310 
 
 Length in feet to hold one gallon equals velocity in feet 
 per second required to discharge one gallon per second. The
 
 164 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 velocity must be 7.5 times as great to discharge one cubic 
 foot per second. 
 
 A 4 inch cast iron pipe cannot supply one fire hydrant 
 with the ordinary supply of 255 gallons per minute without a 
 loss of head in such pipe of nearly one foot in each 10 feet 
 length of 4 inch pipe. Add to this the friction loss in the 
 hydrant, the hose and the nozzle, and the resistance of the 
 atmosphere and wind, and it is apparent that a hydrant will 
 be of little service when attached to a four inch pipe of any 
 considerable length. 
 
 58. Decimal Equivalents to Fractional Parts of one 
 Lineal Inch. 
 
 TABLE No. 27. 
 
 1-32=. 0312 1 
 1-16=. 06250 
 3-32=. 09375 
 1-8 =.125 
 1-8 -I- 1-32=. 15625 
 1-8+1-16=. 1875 
 
 18 +3-32=. 21875 
 1-4= .25 
 1-4+1-32=. 28125 
 1-4 + 1-16=. 3125 
 1-4 +3-32=. 34375 
 38= .375 
 
 |3 8+1-32=. 40625 
 3 8+1-16=. 4375 
 1 3-8 +3-32=. 46875 
 1-2= .5 
 12+1-32=. 53125 
 1-2 + 1-16=. 5625 
 
 5-8 =.625 
 5-8+1-16=. 6875 
 3-4=. 75 
 3-4 + 1-16=. 8125 
 7-8= .875 
 7-8+3-32=. 96875 
 
 Fractional inches in equivalent decimals of a foot. 
 
 Frac. 
 
 Deci. 
 
 Equiv 
 
 Frac. 
 
 Deci. 
 
 Equiv 
 
 Frac. 
 
 Deci, 
 
 Equiv 
 
 Inch 
 
 Inch 
 
 dec ft. 
 
 Inch 
 
 Inch 
 
 dec ft. 
 
 Inch 
 
 Inch 
 
 dec ft. 
 
 1-32 
 
 .03125 
 
 .00?04 
 
 3-8 
 
 .375 
 
 .03125 
 
 23-32 
 
 .71875 
 
 .059895 
 
 1-16 
 
 .0625 
 
 .005208 
 
 1332 
 
 .40675 
 
 .033854 
 
 3-4 
 
 .75 
 
 0625 
 
 3-32 
 
 .09375 
 
 .007X12 
 
 7-16 
 
 .4375 
 
 .036458 
 
 25-32 
 
 .78125 
 
 .065104 
 
 1-8 
 
 .125 
 
 .010416 
 
 15-32 
 
 .46875 
 
 .039062 
 
 1316 
 
 .8125 
 
 .067708 
 
 5-32 
 
 .15625 
 
 .010420 
 
 1-2 
 
 .5 
 
 .041666 
 
 27-32 
 
 .84375 
 
 .070312 
 
 3-16 
 
 .1875 
 
 .015625 
 
 17-32 
 
 .53125 
 
 .044i7 
 
 7-8 
 
 .875 
 
 .072916 
 
 732 
 
 .21875 
 
 .018229 
 
 916 
 
 .5625 
 
 .046875 
 
 2932 
 
 .90625 
 
 .07552 
 
 14 
 
 .25 
 
 020833 
 
 19-32 
 
 .59375 
 
 .049479 
 
 15-16 
 
 .9375 
 
 .078125 
 
 932 
 
 .28125 
 
 .023437 
 
 5-8 
 
 .62> 
 
 .0-2083 
 
 31-32 
 
 .96875 
 
 .080729 
 
 5-16 
 
 .3125 
 
 .026041 
 
 21-32 
 
 .65625 
 
 .054607 
 
 1.00 
 
 1.00 
 
 .083333 
 
 11-32 
 
 .34375 
 
 .028645 
 
 11-16 
 
 .6875 
 
 .057291 
 
 
 
 
 Tenths of one foot in equivalent inches. 
 
 Foot 
 
 Inches 
 
 Foot 
 
 Inches 1 
 
 Foot 
 
 Inches 
 
 0.10 
 0.20 
 0.30 
 0.40 
 
 1 3 16 
 2.3-8 
 3.1932 
 4.25-32 i 
 
 0.50 
 0.60 
 0.70 
 0.80 
 
 6.00 
 7.3-16 i 
 8.3-8 ! 
 9.19-32 ! 
 
 0.90 
 
 u 
 
 10.25-32 
 12.00
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 165 
 
 59 Tables for Converting Measures, 
 
 TABLE No. 28. Lineal Measure. 
 
 Inch's 
 
 Feet 
 
 Yards 
 
 Fath. 
 
 Rods 
 
 Miles 
 
 Metres 
 
 l 
 
 12 
 36 
 72 
 
 198 
 7920 
 63360 
 
 .083333 
 1 
 3 
 6 
 16 l / s 
 660. 
 52SO. 
 
 .02778 
 .33333 
 1. 
 2. 
 
 220." 
 1760. 
 
 .013889 
 .16666 
 .5 
 1. 
 
 no! 4 
 
 880. 
 
 .005051 
 .060606 
 .181818 
 .363636 
 1. 
 40. 
 320. 
 
 .000016 
 .000189 
 .000563 
 .001136 
 .003125 
 .125 
 1.0 
 
 .0254 
 .304797 
 .914392 
 1.82878 
 5.02915 
 201.166 
 1609.33 
 
 TABLE No. 29. Land Measure (Lineal). 
 
 Inch's 
 
 Links 
 
 Feet 
 
 Yards 
 
 Chains 
 
 Miles 
 
 Metres 
 
 7 23-25 
 12 
 36 
 792 
 63360 
 
 .1261261 
 1. 
 1 17-33 
 4 6-11 
 
 100. 
 8000. 
 
 .083333 
 .066666 
 1. 
 3. 
 66. 
 5280. 
 
 .0277778 
 .222222 
 .333333 
 1 
 22. 
 1760. 
 
 .0012626 
 .01 
 .0151515 
 .0454545 
 1. 
 80. 
 
 .0000158 
 .00015 
 .00"1894 
 i 01X15682 
 .0125 
 1. 
 
 .0254 
 .201166 
 .304797 
 .914392 
 20.1166 
 1609.33 
 
 TABLE No. 30.* Metrical Equivalents. Lineal Measure. 
 
 
 Inches 
 
 Feet 
 
 Yards 
 
 Rods 
 
 Chains 
 
 Miles 
 
 1 Millimeter= 
 1 Centimeter= 
 1 Meter 
 1 Kilometer= 
 
 .03937 
 .393704 
 39.370432 
 
 .003281 
 .0328(19 
 3.2*0869 
 3280.8693 
 
 .001094 
 .Olf'936 
 1.093623 
 1093.6231 
 
 .001988 
 .198841 
 198.84057 
 
 .04971 
 49.710141 
 
 .000621 
 .621377 
 
 
 Milli- 
 meters 
 
 Centi- 
 meters 
 
 Meters 
 
 Kilo- 
 meters 
 
 Inch = 
 Foot = 
 Yard = 
 Rod = 
 Chain = 
 Mile = 
 
 25.399772 
 304.79727 
 914.391795 
 5029.15487 
 
 2.539977 
 30.47973 
 91.43918 
 502.9ln49 
 2011.66195 
 
 .253998 
 .304797 
 .914392 
 5.029155 
 20.11R62 
 1609.32956 
 
 .0003048 
 .0009144 
 .00"02915 
 .02011662 
 1.60933 
 
 ine. 
 
 *See "Rules and Tables" page 92, by Prof. W. J. M. Rank-
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 167 
 
 TABLE No. 33. Cubic Measure. 
 
 Cubic Inches 
 
 1.0 
 
 1728.0 
 46656.0 
 
 Cubic Feet I Cubic Yards ICubic Meters 
 
 .0005788 
 1.0 
 27. 
 
 .00000214 
 .037037 
 1.0 
 
 .000016387 
 
 .0283161 
 
 .764534 
 
 231 cubic inches=l U.S. gallon. 7.48052 U. S. gallons^ 
 1 cubic foot. 
 
 The actual weight of 1 U. S. gallon of water at its maxi- 
 mum density is 8.345008 pounds. The weight is, however, 
 adopted by law as 8.33888 pounds avoirdupois. 
 
 1 U. S. gallon=.13368 cubic foot. 1 cubic foot per second 
 =448.8312 gallons per minute, or 26929.872 gallons per hour, 
 or 646316.928 gallons per 24 hours. 1 cubic foot per second= 
 60 cubic feet per minute, or 3600 cubic feet per hour, or 86400 
 cubic feet per 24 hours. This will cover one acre of ground 
 to a depth of 1 98347 feet, or 1.98347 acres to a depth of one 
 foot iu 2i Lours, or supply 200 gallons per person per 24 hours 
 for 3,231 58 persons. An 8 inch pipe will carry it at a velocity 
 of 2.864 feet per second. 
 
 TABLE No. 34. Metrical Equivalents. Cubic Measure. 
 
 Cubic In. ;U. S. Gal-|CubicFt,'Cubic yd|Perches : 
 
 leu. centimtr. 
 1 cu. rlecin.etr. 
 1 cubic meter 
 
 .061025386 ! .000264179 .000035316 
 61.025386 , .264179 .035316 
 6 '025. 386 [ 264.179 [ 35.316 
 
 .001307986 | .001426893 
 1.307986 | 1.426893 
 
 
 
 
 Cubic Cent. 
 
 Cubic Deem. 
 
 Cubic Meters 
 
 1 cubic inch 
 1 U. 8. gallon 
 1 cubic foot 
 1 rubic yard 
 1 Perch 
 
 16.386623 . 
 3785.31 
 28316.0844 
 
 .016386623 
 3.78531 
 28.3160844 
 764.5343 
 700.82309 
 
 .00378531 
 .0283160844 
 .7J5343 
 .70082309 
 
 1 Perch=24.75 cubic feet. 
 
 TABLE No. 35. Pressure. (Thurston). 
 
 Pounds per sq. 
 Inch. 
 
 Kilograms per [Kilograms per 
 Sq. CentimeterjSq. Centimeter 
 
 Pounds per. 
 sq. Inch. 
 
 1.0 
 
 .07030S27 1 1.0 
 
 14.22308 
 
 REMARK. The foregoing conversion tables are given in 
 order that the formulas may be used and coefficients deter- 
 mined either in English or metrical terms.
 
 SULLIVAN'S NEW HYDRAULICS. 
 TABLE No. 31. Square Measure. 
 
 Sq. 
 Inches 
 
 Square 
 Feet 
 
 Square 
 Yards 
 
 Square 
 Rods 
 
 Square 
 Roods 
 
 Square 
 Acres 
 
 Square 
 Metres 
 
 i. 
 
 144. 
 
 1296. 
 39204. 
 1568160. 
 C272640. 
 
 .00(59444 
 1. 
 9. 
 272. k 
 lftS90. 
 435(10 
 
 .0007716 
 .1111111 
 1. 
 
 30. y t 
 
 1210. 
 4840. 
 
 .0000255 
 .0036731 
 .0330579 
 1. 
 40. 
 160. 
 
 .00000064 
 . .OIX;0918 
 .0008264 
 .025 
 1. 
 4. 
 
 .00000016 
 .00002:$ 
 .0002050 
 .00620 
 .25 
 1. 
 
 .0006452 
 .0929013 
 .836112 
 25.292 
 1011.6P6 
 4046.782 
 
 AcresX-C015625 = square miles. 1 square mile=27,878,400 
 square feet, or 3C97600 square yardb, or 640 acres, or one sec- 
 tion. One acre=10 square chains. Tho length of one chain 
 is 66 feet, or four rods. This Gunters chain has fallen into 
 disuse, and a steel tape 100 feet length is used instead. Areas 
 are taken in square feet, and when divided by 43,560, are re- 
 duced to acres. 
 
 TABLE No. 32* Metrical Equivalents. Square Measure. 
 
 
 Square 
 Inches 
 
 Square 
 Feet 
 
 Square 
 Yards 
 
 Acres 
 
 Square 
 Miles 
 
 1 sq. Centime- 
 
 
 
 
 
 
 ter= 
 
 .165003 
 
 .00107641 
 
 .00012 
 
 
 
 1 eq. Decime- 
 
 
 
 
 
 
 ter= 
 
 15.500309 
 
 .107541 
 
 .011960115 
 
 
 
 1 sq. Meter= 
 
 1550.030916 
 
 10.7641 
 
 1.1960115 
 
 .00024711 
 
 
 1 eq. Dekame- 
 
 
 
 
 
 
 ter=l Are= 
 
 15r-003.0916 
 
 1076.41 
 
 119. C011 5 
 
 .02411 
 
 .00003861 
 
 1 sq. Hectome- 
 
 
 
 
 
 
 ter=l Hectare 
 
 
 
 
 
 
 1 Kilometer= 
 
 
 1076.41 
 
 11960.115 2.4711 
 1196011.5 247.11 
 
 .003861 
 .3861 
 
 
 Sq. Centi- 
 meters 
 
 Sq. Deci- 
 meters 
 
 Sq. Meters. 
 
 Sq. Dekame- 
 ters or 
 Ares 
 
 ISq 
 Inch= 
 1 Square 
 Foot= 
 1 Square 
 Yard= 
 
 6.451484 
 929.013728 
 8361.123554 
 
 .06451484 
 9.29013728 
 83.61123554 
 
 .0006451484 
 .0929013728 
 .8361123554 
 
 .000929013728 
 .008361123554 
 
 'See "Conversion Tables," page 40, by Prof. Thureton, 
 and Trautwine's "Civil Engineer's Pocket Book", page 78, 
 Rankine's "Rules and Tables," p. p. 110-114.
 
 CHAPTER V 
 
 Of Water Powers, Power Mains and Pipe Lines. 
 
 Work is expressed in units of weight lifted through one 
 unit of height; as in pounds lifted one foot, called foot pounds. 
 Here there is no reference to the units of time consumed 
 Power is expressed in units of work done in one unit of time; 
 as in pounds lifted one foot in one second of time, called foot 
 pounds per second. 
 
 One horse power is a conventional quantity equal to 550 
 foot pounds per second, or to 550 pounds lifted one foot in 
 one second, or to one pound lifted 550 feet per second. 
 
 As there are 60 seconds in one minute of time, theexpres 
 ion of horse power in terms of foot pounds per minute would 
 be 550X60=33,000. or in foot pounds per hour it woud be 33,- 
 000X60=1,980,000. 
 
 One pound of water falling one foot does work equal to 
 that of raising one pound one foot high. Hence the number 
 of pounds of water falling in one second multiplied by the 
 distance fallen in feet will equal the number of foot pounds 
 per second, and as 550 foot pounds per second equal one horse 
 power, the totil number of foot pounds per second divided by 
 550 will equal the horse power of the water. Expressed as a 
 formula, we have 
 
 cubic f eet per Bec.X weight of one cubic footX Head or fall in feet. 
 H ' P - = - 550 
 
 The weight of one cubic foot of water at its maximum 
 density is 62.5 Ibs. This is the weight always assigned, in or- 
 dinary cases, to one cubic foot of water. The formula may 
 therefore be written 
 
 62 5 
 H. P.= --Xcubic feet per second X head or fall in feet. 
 
 62 5 
 If we take the quotient of -- =.3136363, we have,
 
 SULLIVAN'S NEW HYDRAULICS. 169 
 
 - H. P.=.1136363Xhead in feetXcubic feet per second.. .97 
 
 61. Formula for Cubic Feet Per Second Required to 
 Generate a Given Horse Power. 
 
 When the net head or fall in feet is given, then the cubic 
 feet per second required to develop any required horse power 
 will be 
 
 Horse Power Desired 
 
 Cubicfeet per sec.= jll36ae3xHeBd in Feet < 98 > 
 
 62. Formula for Net Head or Fall in Feet Required 
 to Develop a Given Net Horse Power. 
 
 The efficiency of a water wheel or other machine is the 
 ratio of effective power recovered from it to the total power 
 applied to it. To find the efficiency, divide the effective pow- 
 er delivered by the machine, by the total power applied to it. 
 The quotient is the efficiency. If a water fall of 100 horse 
 power is applied to a turbine and the turbine develops 80 
 
 horse power, then the efficiency of the turbine is E= j^ = 80 
 per cent. 
 
 The efficiency of the motor being given, then the net head 
 or fall in feet required to develop a given net horse power, 
 will be 
 
 Desired net H. P.-nper cent efficiency of motor 
 .1136363XCubic Feet per Second, 
 
 (99) 
 
 63. Head of Water Defined. By the term head is 
 meant the difference of level between the surface of the water 
 in the reservoir or head race, and the water surface in the tail 
 race, to which must be added the head due to the mean vel- 
 ocity of flow in the head race or stream above the fall. 
 
 The head due to the velocity in the head race is H= 
 
 (See formula (7) Chap. I.) In a pipe or power main the total 
 head is equal to the difference of level between the water sur- 
 face at the intake end of the pipe and the upper surface of 
 the jet at discharge, and the net head is equal to the total
 
 170 SULLIVAN'S NEW HYDRAULICS. 
 
 head lees the amount of head neutralized by friction or re- 
 sistance in the pipe. Hence in a pipe or power main the loss 
 of head by friction must be first deducted from the total 
 head in order to ascertain the effective head at discharge. 
 
 64. To Find the Diameter in Feet of Pipe Required 
 to Carry a Given Quantity of Water with a Given loss 
 of Head in Feet, 
 
 Where the total head is known, and it is desired to lay a 
 pipe of such diameter as will convey a given number of cubic 
 feet per second with a predetermined loss of head by friction, 
 so that a given net head will be secured at discharge, such di- 
 ameter in feet may be found as follows: 
 
 x ' ....................... (32) 
 
 For ordinary clean cast iron pipe n=.0003938 in terms of 
 diameter in feet. 
 
 Hence the formula reduces to 
 
 and, 
 
 '.. whence. 
 
 h" 
 
 4X <1 S (100) 
 
 h" 
 
 If it is an asphaltum coated pipe, then take n=00032 in 
 terms of diameter in feet, and the formula for finding the di- 
 ameter required to carry a given quantity in cubic feet per 
 second with a given total loss of head in feet by friction in 
 the entire length of pipe line, will be 
 11 
 
 V 
 
 In these formulas 
 
 d=diameter of required pipe in feet 
 q=cubic feet per second it is to discharge 
 Z=total length of pipe in feet 
 h"=head in feet lost by friction in total length, I,
 
 SULLIVAN'S NEW HYDRAULICS. 171 
 
 EXAMPLE OF THE USE OF THESE FORMULAS. 
 
 There is a total fall of 100 feet in a distance of 3,000 faet. 
 A diameter of asphaltum coated pipe is desired, which will 
 convey one cubic foot of water per second with a loss of head 
 not exceeding 6 feet, so that there shall remain an effective 
 head of 94 feet, at discharge while one cubic foot per second 
 is being drawn from the pipe at its lower end. By the above 
 formula 
 
 d= ll/ .000000269X J X9000000 _ 11 
 V 36 V 
 
 feet, 
 
 This diameter has an area =d 2 X-7 p 54=.48078 square feet. 
 The mean velocity required to discharge one cubic foot per 
 
 second in this diameter would be, v= ~ 48078 ~ 2.08 feet 
 
 per second. 
 
 The resu't may therefore be tested by the formula for 
 loss of head, 
 
 And we have, 
 
 .00032 
 h"= 692 X3000X4.3264-6.00 feet head lost. 
 
 It will be understood that the area at discharge is such 
 that it will admit of no greater discharge under the given net 
 head than the quantity q. The manner of discharge may be 
 through other small pipes tapped into the main if it is a 
 water works system, or the discharge may be through a re- 
 ducer or nozzle if the pipe is used as a power main for driv- 
 ing water wheels, or the discharge maybe full and the total 
 head lost except the velocity head, as may be desired. 
 
 65. To Find the Area and Diameter of the Nozzle 
 Tip or Aperture Required to Discharge a Given Quantity. 
 
 If there is a simple tip on the end of the pipe made in 
 the form of the contracted vein which reduces the diameter
 
 172 SULLIVAN'S NEW HYDRAULICS. 
 
 at discharge, there will be a very small loss of head by 
 friction in efflux from the tip. The area in square feet of the 
 required aperture in such tip will be found as follows: As- 
 sume the diameter of the pipe to be .7824 feet, and net head 
 at discharge to be 94 feet, as in the preceding section, and the 
 quantity to be disharged as one cubic foot per second. 
 
 The velocity that will be generated by this net head at 
 discharge will be 
 
 v = 1 /iTgTl=8.025 1 /94~~=77.8052 f ee t per second. 
 
 Now, q= areaX velocity ^ay^g H. Whence a = 
 
 q 10 
 
 1/2 H = 77 8052~ = ' Q128526 8< l uare feet - The diameter in feet 
 
 is then 
 
 =' 128 foot = 1 636 inchee diam ' 
 
 = .7854 
 
 eter. 
 
 See table No. 27, 58. 
 
 If the discharge is to be through a nozzle or reducer of 
 several feet length, there will be considerable loss of head by 
 friction in such nozzle or reducer, for which allowance must 
 be made. This loss will depend upon the length of the con- 
 vergent reducer or nozzle and its mean or average diameter as 
 well as its smoothness of internal circumference, and the 
 square of the velocity through it. We have seen heretofore 
 (37, 39) that the loss by friction in a convergent or conical 
 pipe is nine times as great as the loss in a pipe of uniform 
 diameter equal to the mean diameter of the convergent pipe. 
 It is therefore evident that such convergent pipes, reducers 
 or nozzles should be as short as possible.provided they do not 
 converge more rapidly than one inch in a length 2.33 inches, 
 which would make them conform to the form of the con- 
 tracted vein. Assuming the diameter of the base of the noz- 
 zle to be the same as the diameter of the pipe it is to join, and 
 that the net head at the base of the nozzle is 94 feet, and 
 that the reducer or nozzle is to be 6 feet in length, and is re- 
 quired to discharge one cubic foot per second under this net
 
 SULLIVAN'S NEW HYDRAULICS. 173 
 
 head at the base, the problem now is to determine the area 
 and diameter of the small, or discharge end of the nozzle so 
 that it shall discharge this given quantity per second under 
 the given head at its base. 
 
 This will require one or more approximations, for the 
 reason that as the mean diameter of the proposed nozzle is 
 yet unknown we have no means of knowing the friction loss 
 that will occur in the nozzle, and hence do not kuow the value 
 of the net effective head at the point of final discharge from 
 the nozzle. 
 
 For first approximation assume that there will be three 
 feet head lost in the nozzle, leaving an assumed effective 
 head at discharge of 943=91 feet. The velocity of dis- 
 charge under the net head of 91 feet will be ^8.025/91= 
 76.5535 feet per second. Then the area in square feet re- 
 quired to discharge the quantity q, in cubic feet per second, 
 
 will be a=^!=g=: 7^35 = .01306276 square feet. The di- 
 ameter in feet answering to this area in square feet is 
 
 eter in inches is therefore .129X12=1 548 inches. (See 58. 
 Table 27). 
 
 For first approximation we have then the following di- 
 mensions of the nozzle: Greatest, or butt diameterr=.7824 
 foot =9.388 inches. Smallest, or discharge diameter =.129 
 foot=l 548 inches. Total length of nozzle 6 feet. The 
 average or mean diameter of the nozzle is therefore, 
 
 Mean d=' " "*"' - = .4557 foot, or 5.4684 inches. 
 
 Now, two tests must be applied to this nozzle in order to 
 ascertain whether or not it will fulfill the required 
 conditions: 
 
 (1) It must be tested by the formula (39) for friction lose 
 in nozzles in order to ascertain the actual loss of head that 
 will occur while discharging the given quantity. 
 
 (2) It must then be tested to ascertain whether or not
 
 174 SULLIVAN'S NEW HYDRAULICS. 
 
 it will discharge the given quantity under the conditions 
 actually existing. If it fails to meet the requirements, fur- 
 ther approximation must be made. 
 
 (1) TEST FOR LOSS BY FRICTION. 
 
 The formula for loss of head in feet by friction in conver- 
 gent pipes and nozzles is 
 
 h"= X/X9V. (See 37,39). 
 
 In which 
 
 h"=head in teet lost by friction 
 i=rlength in feet of convergent pipe or nozzle* 
 d average or mean diameter of nozzle 
 v=mean velocity in the mean diameter of the nozzle 
 In the nozzle we are now considering the mean diameter 
 is .4557 foot, and the nozzle is required to discharge one 
 cubic foot per second. Hence the required mean velocity in 
 feet per second through this mean diameter to cause the dis- 
 charge of one cubic foot per second will be 
 
 v=-9_= -- - = _ L_=6.1312 feet per second. 
 a (.4557) s X-7854 .1631 
 
 Assuming the nozzle to be made of very dense, solid 
 smooth cast iron, the friction coefficient will be n .0003623 in 
 terms of diameter in feet. Applying the above formula for loss 
 by friction in this nozzle while discharging one cubic foot per 
 second, the velocity in the mean diameter being 6.1312 feet 
 per second, and we find the actual loss of head in the nozzle 
 to be 
 
 Hence at the point of discharge the effective head would 
 be 942.40=91.60 feet, whereas we had assumed that it 
 would be probably 91.00 feet. But as the assumed loss of head 
 (3 feet) and the actual loss (2.40 feet) are BO nearly equal, we 
 will now apply the test for quantity discharged under the 
 actual conditions. For this purpose we have the following: 
 
 Area of smallest diameter at discharge=.01306276 square 
 feet.
 
 SULLIVAN'S NEW HYDRAULICS. 175 
 
 Effective head at point of discharge from nozzle 91.60 
 feet. 
 
 Velocity due to this net head, v=!/2gH. = 8.025 v /91.b p = 
 76.807275 feet per second. Quantity discharged q, will be 
 
 q=a v^.01306276=76.807275=:1.003315 cubic feet per sec- 
 ond. 
 
 If a closer result is desired, the smallest diameter may be 
 reduced by 1-16 inch and all the foregoing tests be again ap- 
 plied to the new proportions of the nozzle thus changed. 
 Table No. 21, 40, will be of assistance in such calculations. 
 
 66. Pipe Lines of Irregular Diameter. Where the head 
 or pressure is due to the slope or inclination of a pipe line, 
 and not to a pump, there will be very little pressure within 
 the pipe in the upper portion of the line. In such cases 
 large diameters with thin shells may be adopted in the 
 upper part of the line where the pressure is small. As the line 
 proceeds down the slope and the pressure increases, the di- 
 ameter is diminished and the pipe shell increased in thickness 
 in proportion to the increase of pressure. 
 
 If a pipe line is of uniform diameter and is laid on a uni- 
 form grade and has a full and free discharge, there will be no 
 radial pressure in the pipe at any point except the 
 very small pressure due to the vertical depth of the diameter. 
 In this cas? there is no object in increasing the thickness of 
 pipe shell at its lower end, because the total head or pressure, 
 under these conditions, will be converted into velocity of flow, 
 with the exception of the amount of head lost by friction, and 
 as the velocity head or velocity pressure is always parallel 
 to the pipe walls, it does not tend to burst the pipe. 
 
 Where a given pressure or head is to be maintained at 
 the lower end of the pipe,or at any point along its length, while 
 a given supply of water is being drawn from it for domestic 
 purposes, or for driving water wheels, the capacity of the 
 pipe must be such that the mean velocity of flow in it while 
 delivering the given supply, will not cause a loss of head by 
 friction exceeding a predetermined amount. The discharge 
 permitted from such pipe must therefore bo regulated by
 
 176 SULLIVAN'S NEW HYDRAULICS. 
 
 the area of discharge BO that it will not exceed the givea 
 quantity. If the lower end of a pipe line be entirely closed 
 so there can be no discharge from it and no velocity within 
 it.the pressure at any point along the line will be that due to 
 the total head up to that point, which will be equal to the 
 difference in level between the given point in the pipe and 
 the water surface in the reservoir or source of supply. The 
 pressure at the lower end will be that due to the total head 
 in the pipe line. If a small orifice be opened in the lower end 
 of the pipe, it will at first discharge with a velocity due to the 
 total head, but this discharge will cause a small velocity to 
 be generated throughout the length of the entire pipe, and 
 this velocity will cause a small friction with the pipe walls 
 which will reduce the head by the amount of the friction 
 thus generated, and thus slightly check the velocity of dis- 
 charge through the orifice. The smaller the orifice relatively 
 to the area and capacity of the pipe, the smaller will be the 
 velocity in the body of the pipe to supply the quantity being 
 discharged; and as the loss of head by friction is as the square 
 of the velocity, the smaller the velocity becomes, the smaller 
 the loss by friction will become. If the orifice is enlarged so 
 that it may discharge a greater quantity per second, then 
 the velocity in the body of the pipe must increase proportion- 
 ately and loss of head or pressure will also increase as the 
 square of this greater velocity. If the entire end of the pipe 
 be opened so that the discharge is entirely free, then the 
 total head will be lost in friction due to the consequent high 
 velocity, except the small portion of the total head which re- 
 
 mains to generate the velocity, and which is h v=g^|. It is 
 
 evident then that if head or pressure is to be preserved the di- 
 ameter and area of the pipe must be sufficient to convey the re- 
 quired quantity at a low velocity, and the pipe must not be 
 permitted to discharge at anything like its full capacity. As 
 loss of head or pressure is directly as the roughness of the 
 pipe, and directly as the length, and inversely as j/d 3 , it is 
 necessary to take into account not only the diameter and ve-
 
 SULLIVAN'S NEW HYDRAULICS. 177 
 
 locity but also the length of pipe, and the nature of the pipe 
 walls with regard to smoothness or roughness, and probable 
 future deterioration. The chemical qualities of the water 
 which is to flow through a pipe, and the effect they have upon 
 different classes of pipe and pipe coatings should be care- 
 fully ascertained before the pipe is selected. Some waters, 
 apparently almost pure, will corrode a pipe in a very short 
 time to such an extent as to reduce its capacity by nearly one 
 half. A pipe line made up of different diameters, gradually 
 decreasing as the slope increases, designed to convey a given 
 quantity and to maintain a given pressure, is some- 
 times less expensive than a pipe line of uniform 
 diameter. The velocities in the different diametera 
 of such irregular pipe lines will be inversely as the 
 areas of the different diameters and the friction loss in 
 each section will be as the square of the velocity in that sec- 
 tion and inversely as ;/d 8 . The loss of head in such a line 
 must be calculated separately for each different diameter. 
 In case the line is divided into divisions of equal lengths, and 
 each division is of a constant diameter but of a different di- 
 ameter from the rest of the line, the mean diameter of the 
 whole line cannot be adopted for such calculations, because 
 the mean of all the velocities in the different diameters will 
 greatly exceed the mean velocity in a pipe of uniform diameter 
 equal to the mean diameter of the line composed of different 
 diameters. As the friction is as the square of the velocity, it 
 is evident that it will be much greater in the line of decreas- 
 ing diameters than in a pipe of uniform diameter equal to the 
 mean diameter of the former. Where the saving of head or 
 pressure is a principal object there are only a few cases in 
 which it is cheaper or advisable to adopt large diameters for 
 the upper portion of the line and smaller ones for the lower 
 portion. What is saved in the cost of constructing such line 
 is lost in head or pressure, which maybe of more value than 
 the difference in cost between the two kinds of pipe line. For 
 example a pipe line 5,000 feet in length, made of lap welded 
 
 Sipe and thoroughly coated with asphaltum, in which the 
 ret 1,000 feet length has a diameter of three feet, the second
 
 178 SULLIVAN'S NEW HYDRAULICS. 
 
 1,000 feet has a diameter of 2.75 feet, the third 1,000 feet has a 
 diameter of 2.5 feet, the fourth a diameter of 2 feet, and the 
 fifth a diameter of 1.5 feet, while discharging 8 cubic feet per 
 second, will have velocities and losses of head in the different 
 diameters as follows: 
 
 In section No. 1, =_!.=: ^=1.1178 feet, h"= .072 feet 
 a 7.069 
 
 In section No. 2, v=-*L = *L_ =1.3470 feet, h"= .119" 
 a 594 
 
 In section No. 3, v=-3_=-JL=1.6300 feet, h"= .202 " 
 a, 4 909 
 
 In section No. 4, v=-5-=_ =2.5400 f eet, h"= .680 " 
 a 3.1416 
 
 In section No. 5, v=^L= 8 =4.5200 feet, h"= 3.350 " 
 a 1767 
 
 4.423 
 
 The loss of head for this small discharge will be 4.423 feet 
 in the line of different diameters, and the mean of all the 
 velocities in the different diameters will be 2 2771 feet per sec- 
 ond. 
 
 Now if the sum of these five different diameters is divided 
 by 5 we have the mean diameter 2.35 feet. The area 
 of this mean diameter=4.3374 square feet. Conse- 
 quently if the entire pipe line had been of the uniform diam- 
 eter of 2.35 feet, the necessary velocity through it to cause a 
 discharge of 8 cubic feet per second would be 
 
 1.84442 feet, and the total loss of head 
 
 _ 
 4.3374 
 
 would have been h" =1.424 feet. (For this class of pipe n= 
 .0003). As the friction is inversely as i/d 8 , and also directly 
 as v 2 , it is apparent that a small increase of the discharge 
 would greatly increase the loss by friction in sections No. 4 
 and 5 of the irregular diameter. 
 
 67 A Power Main with Nozzle, and Water Wheel to 
 Run at a Given Speed and Develop a Given Power. 
 
 In mountainous regions are many small torrents, the
 
 SULLIVAN'S NEW HYDRAULICS. 179 
 
 sources of which are at such great altitudes as to afford 
 almost any head desired when the stream is confined within 
 a pipe or power main so as to preserve the head or pressure 
 by regulating the velocity of flow. Where the quantity of 
 water is small and the head is great, an impulse and re- 
 action water wheel will be much more efficient and satisfac- 
 tory than a turbine. The loss of head in a power main de- 
 pends upon the velocity of flow through it and upon its 
 length, diameter and smoothness and freedom from bends. 
 The velocity is governed by the quantity of wate'r the main is 
 permitted to discharge, and the quantity discharged is gov- 
 erned by the area of discharge at the point of the nozzle and 
 by the effective head at discharge. 
 
 The greater the length of the pipe line, the smaller the 
 velocity must be, for the loss of head by friction is directly as 
 the length and as the square of the velocity. Such power 
 mains or pipelines are usually constructed of riveted pipe 
 made of steel or wrought iron plate. The pipe is made in any 
 convenient lengths for transportation, or is made on the 
 ground where it is to be laid. After it is riveted into lengths 
 it is thoroughly coated by being submerged in a tank of hot 
 coating compound composed of 80 per cent asphaltum and 20 
 per cent crude petroleum which is maintained at a tempera- 
 ture of about 300 degrees Fahr. The pipe is allowed to re- 
 main submerged in the hot bath until the pipe metal attains 
 the same temperature as the bath. It is then withdrawn 
 from the bath and allowed to cool. In some cases coal tar 
 45 per cent and asphaltum 55 per cent is used as a coating 
 with fair results. 
 
 The quality or purity of the asphaltum used will deter- 
 mine the best proportion of asphaitum to crude petroleum to 
 use in the compound. The per cent of petroleum required 
 varies from 15 to 20. After the compound has been heated 
 and thoroughly mixed and incorporated it should be tested 
 by dipping into it a small sheet of the pipe metal and allow- 
 ing it to remain for ten minutes in the hot bath. It is then 
 withdrawn and placed in a large vessel of cold water and al-
 
 180 SULLIVAN'S NEW HYDRAULICS. 
 
 lowed to cool. If the coating is too soft after cooling and has 
 a tendency to run or wrinkle, there is too much oil in it, and 
 the quantity of asp laltuin should be increased. If it is a mix- 
 ture of coal tar and asphaltum the coating will be too brittle 
 and easily knocked off with a hammer if the proportion of tar 
 is too great to that of asphaltum. 
 
 In any case the coating should be tough and elastic and 
 should adhere to the metal similar to paint. If the bath is 
 too hot, the coating will wrinkle on the inside of the pipe 
 when it is withdrawn and laid aside to cool. The lengths of 
 pipe are put together like stove pipe, by wrapping a cloth 
 around the end of one length and driving it into the end of 
 the length below, the laying always being started at the lower 
 end of the pipe line. This is called a slip joint. In cases 
 where the pressure is considerable a sleeve joint is used. A 
 sleeve joint consists of slipping an iron sleeve over the ends 
 where two pipe lengths join or are butted, and running in 
 melted lead between the sleeve and the pipe, having first 
 packed the joint sufficiently to prevent the lead from running 
 into the pipe where the ends come together. 
 
 In rocky, mountainous localities where trenching would 
 be quite expensive, the pipe is usually laid on the surface 
 without any trenching except where it is necessary to secure 
 a substantial bearing or foundation for the pipe. 
 
 In very cold weather the pipe is allowed to discharge 
 constantly, which prevents freezing within the pipe, or the 
 water is prevented from entering the pipe and the line left 
 empty when not in use. 
 
 Suppose a stream affords 10 cubic feet per second and 
 has a fall of 400 feet per mile, and it is required to construct 
 a water power plant that will develop 200 net horee power, 
 using a water wheel of 85 per cent efficiency. What head 
 will be required and what diameter and length of pipe, and 
 what will be the proportions of the discharge nozzle required? 
 
 By formula (99) 62, the net head required will be, 
 200-=- 85
 
 SULLIVAN'S NEW HYDRAULICS. 181 
 
 As there is a fall of 400 feet per mile, it is seen that the 
 line will be a little longer than oce-half mile. The fall per 
 
 H 400 
 
 foot length will be S= -j-= 528Q = .075757575, and the 
 
 length in which there is a fall of one foot is Z=-~-= - ,-_ 
 
 =13.20 feet. 
 
 Hence the length of pipe required, not making allowance 
 for friction loss, will be 207.065X13.20=2733.258 feet of pipe. 
 
 But as there will be loss of head by friction in the pipe 
 line and also in the nozzle, and it is required to have 207.065 
 feet net head at discharge from the nozzle, we must lengthen 
 the pipe line until the total head will cover these losses and 
 still leave the net head of 207.065 feet at discharge. If the 
 nozzle is to be 8 feet long we will assume that the loss of 
 head in the nozzle will be 6 feet while discharging 10 cubic 
 feet per second, and we will design the pipe line so that the 
 loss of head in the line by friction will be 6 feet also. Hence 
 the line must be extended further down the hill until we 
 have a total head in the whole length of the line including 
 the nozzle=207 .065+12=210.065 feet. In order to gain this 
 additional 12 feet head the line will have to be extended in 
 length by 158.40 feet, including the nozzle. The nozzle is to 
 be 8 feet in length, and therefore the pipe line without the 
 nozzle will be (2733.258+158 40) 8=2883.66 feet in length. 
 It is to be double riveted, asphaltum coated, slip joiL.t pipe, 
 and the total loss of bead in the whole line without the noz- 
 zle is to be 6 feet while discharging 10 cubic feet per second. 
 What diameter will be required? 
 
 By formula (101) 64, the diameter required will be 
 d= U/ .000000269Xq^ X ^ =1 . 795 f ee t=21.54 inches di- 
 
 ameter. 
 
 We have a net head now at the junction of the pipe line 
 with the nozzle of 213.065 feet. The next step is to ascertain 
 the required dimensions of the nozzle to discharge 10 cubic 
 feet per second under these conditions with a loss of head
 
 182 S'ULLI VAN'S NEW HYDRAULICS. 
 
 not to exceed six feet in the nozzle. The method of doing 
 this is explained in 65. For this calculation we have the 
 length of the nozzle and itB butt or greatest diameter, and 
 the effective head at the butt of the nozzle. Now if we as- 
 sume that there will be probably a loss of 6 feet head in the 
 nozzle itself, the net head at discharge would be equal to the 
 head at the butt, le-s the amount lost in the nozzle, or 2 ] 8.065 
 6=207.065 feet. Hence by the rules given heretofore (65) 
 the area in square feet of the least diameter at discharge of 
 the nozzle will be 
 
 q 10. 
 
 = - 0866 8quare ' 66t 
 
 The diameter answering to this area is A.-*/ 1 
 
 v .7854 
 
 .11026 foot=1.323 inches 
 
 1.795+.11026 
 The mean diameter of the nozzle is= ^ 
 
 .95263 foot. 
 
 Now we must test this nozzle to ascertain what the ac- 
 tual loss of head will be in it while it is discharging 10 cubic 
 feet per second. If the loss is not so great as six feet, as we 
 have assumed in the nozzle, then we mav shorten the pipe 
 line to some extent, or we may reduce the diameter of the 
 pipe line very slightly, and still obtain the required head and 
 power at discharge. 
 
 The velocity through the mean diameter of this nozzle in 
 order to discharge ten cubic feet per second would be 
 
 q _ 10 
 
 v= ~a" (.95263)"X.7854 = 14 ' 03 feet per Becond ' 
 
 The actual loss of head by friction in the nozzle under 
 these conditions would be ( 37, 39, 65). 
 
 n 1 9 v 2 _ .0003623X8X9X ' 96.841 
 
 .9298 
 
 =55224feet. 
 
 As the net head at the base of nozzle is 213.065 feet, and 
 the loss in the nozzle is 5.5224 feet, we have a net head at
 
 SULLIVAN'S NEW HYDRAULICS. 183 
 
 point of discharge from the nozzle of 207.5426 feet. The 
 required net head was 207.065 feet. Hence we have 
 .4776 foot head in excess of exact requirements, which 
 Is near enough the desired result. 
 
 TEST FOR QUANTITY DISCHARGED. 
 
 The area of smallest diameter of nozzle at discharge is 
 .0866 square foot ae above found, and the net head at dis- 
 charge ia 207.5426 feet. 
 
 Hence the quantity that will be discharged is q=a v, or 
 
 q=.OS66X8.025 1 /207.54 =10.000568 cubic feet per second. 
 
 Now the velocity of discharge from the nozzle is v= 
 8.025/26T5T =115.48 feet per second or 115.48X60= 6,928.80 
 feet per minute. 
 
 It has been established by experiment and experience 
 that the velocity of greatest efficiency of the circumference 
 of an impulse and reaction water wheel is about one-half the 
 velocity of discharge upon the wheel. The number of revo- 
 lutions per minute of the water wheel will depend upon its 
 circumference from center to center of the buckets taken as 
 its diameter. The circumference equals the diameter in feet 
 from center to center of buckets multiplied by 3.1416. 
 
 The circumference of the wheel when the load is on 
 should travel at one- half the velocity of the discharging 
 water. Hence the diameter of the wheel may be so propor- 
 tioned to the velocity of discharge as to run any desired num- 
 ber f revolutions per minute. Where high speed is desired 
 under a low head, two or more water wheels of equal diam- 
 eter may be placed upon one shaft and have separate nozzles. 
 In this way very small diameters of the wheels may be used 
 to secure high speed, and the water divided so as to avoid 
 placing very large buckets on small wheels and to also pre- 
 vent flooding the wheel. The power developed does not de- 
 pend upon the diameter of the water wheel, but depends up- 
 on its speed with reference to its diameter. 
 
 The point of the nozzle should be firmly set beyond the 
 possibility of slipping against the wheel, and should be as 
 close to the buckets as possible not to strike them or to have
 
 184 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 the jet re-acted upon from the buckets. The distance between 
 the point of the nozzle and the center of the bucket on the 
 wheel will depend upon the diameter at discharge of the noz- 
 zle and the velocity of discharge upon the wheel. It should 
 not be so close that the jet will react upon itself on striking 
 the buckets. 
 
 68. Table of Eleventh Roots to Facilitate Calcula- 
 tions of Diameter Required to Discharge Given Quan- 
 tities. 
 
 The following table covers diameters from one inch to 
 32 inches both inclusive, and will be convenient in conjunction 
 with formulas for ascertaining the diameter in feet required 
 to generate a given discharge (formulas 28, 43, 65, 81, 100, 101) 
 or to cause a given discharge with a given loss of head. 
 TABLE No. 36. 
 
 Number 
 
 llth. Root 
 
 Number 
 
 llth. Root 
 
 .OOOOOOOOOU01345 
 .0000*002762 
 
 .08333 
 .1667 
 
 46.24 
 86.50 
 
 .417 
 .5 
 
 .000000^384 
 
 .25 
 
 156.40 
 
 583 
 
 .000005638 
 
 .3333 
 
 276.20 
 
 .667 
 
 .00006578 
 
 .4167 
 
 471.50 
 
 .75 
 
 .0004883 
 
 .5 
 
 784.80 
 
 
 .002659 
 
 .5833 
 
 1285.00 
 
 ^917 
 
 .01157 
 
 .6667 
 
 2048.00 
 
 2.000 
 
 .04223 
 
 .75 
 
 3203. 00 
 
 2 083 
 
 .1345 
 
 .8333 
 
 4948.00 
 
 2.167 
 
 .3842 
 
 .9167 
 
 7482.00 
 
 2.25 
 
 1.0000 
 
 1.000 
 
 11150.00 
 
 
 2.404 
 
 1.083 
 
 16370.00 
 
 2^416 
 
 5.467 
 
 1.167 
 
 23840.00 
 
 2 5 
 
 11.64 
 
 1.250 
 
 31300. (0 
 
 2.584 
 
 23.62 
 
 1.333 
 
 48560.00 
 
 2.667 
 
 REMARK 1. Where the pipe is to be of uniform diameter 
 and to have free discharge, as in the case of a pipe conveying 
 water from one reservoir to another, there is no object in pre- 
 serving the head by throttling the discharge, and in such case 
 the total head is consumed in balancing the resistance to flow 
 except that part of the head which is converted into velocity. 
 The diameter of a pipe which is required to convey a given 
 quantity of water per second under such conditions will be 
 
 .3805 H 2
 
 SULLIVAN'S NEW HYDRAULICS. /85 
 
 m=coefficient of velocity in terms of diameter in fe*-t. 
 
 q=cubic feet per second that pipe is to discharge. 
 total head in feet 
 
 S =total length in feet= Bine of elo P 6 
 
 H=total head in feet. 
 
 REMARK 2 Where the pipe must convey a given quantity 
 per second to a given point and must maintain a given head 
 or pressure at that point while the given quantity is being 
 drawn from it, then the diameter required will be found as 
 pointed out in G4, or by the following general formula. 
 
 i 
 
 
 
 .38u5Xh" 8 
 
 This diameter will convey a given quantity with a given 
 loss of head which is pre-determined according to require- 
 ments. 
 
 In which, 
 
 h"=head in feet to be lost in friction. 
 
 n=coefficient of resistance applicable to class of pipe. 
 
 q cubic feet per second pipe is to discharge. 
 
 I =length of pipe in feet. 
 
 REMARK 3. The results of experiments by the writer on 
 "Converse Patent Lock Joint Pipe" made of wrought iron in 
 lengths of from 15 to 20 feet and lap welded, and coated with 
 asphaltum gave an average value of n=.000299 in terms of 
 diameter in feet. The small value of the coefficient of re- 
 sistance n, in this pipe is to be attributed to its uniformity of 
 diameter, and to the fact that it is made in long lengths BO 
 there are fewer joints per mile of pipe, and the joints are so 
 arranged as to present a continuous and uniform surface to 
 the flow. For this class of pipe take n=.0003 and m=: .00030472 
 in terms of diameter in feet. These values of the coeffi- 
 cients do not allow for future deposits in the pipe, if such 
 should occur, nor for deteriorationinthe pipe coating. It is not 
 probable that a first class asphaltum coating will deteriorate 
 to any considerable extent for a great number of years. This 
 remark has no reference to coatings made of coal tar com- 
 pounds. 
 
 The diameter (inside) in feet of Converse pipe, asphaltum 
 coated, required to convey a given quantity with a given loss 
 of head, would be
 
 186 SULLIVAN'S NEW HYDRAULICS. 
 
 f q 4 
 
 Or if the discharge is to be free and full bore, and no at- 
 tempt made to preserve the head or pressure, the diameter 
 required to carry a given quantity will be 
 
 'a* m 2 11/m 2 11 
 
 = V >< l 
 
 11/m 2 I 2 q 4 11 / I s q 4 
 
 d =T/ :s805^-=- 25055 i/ -IP- 
 
 ll/ q 4 
 For riveted asphaltum coated pipe d =.2o41i/ - 
 
 69. Head Lost by Friction at Bends in Water Pipes. 
 
 The amount of the loss of head produced by a bend in a 
 pipe will depend upon the velocity of flow and the radius of 
 the central arc of the bend, and also upon the number of de- 
 grees included in the arc- of the bend. Whether the addi- 
 tional head required to overcome the resistance of a bend will 
 be proportional to the square or to the cube of the velocity is 
 doubtful. Weisbach's formula, which is most generally used 
 for determining the resistance of bends, gives results un- 
 doubtedly too low in all cases except for a bend of 90 with a 
 radius of central arc of bend equal to one half the diameter. 
 
 The resistance at a bend in a pipe or in an open channel 
 is caused by the change of direction of the flow. The more 
 abrupt the change, and the greater the amount of the change 
 in direction, the greater will the resistance be. It is evident 
 therefore that the resistance will be directly as the number 
 of degrees included in the central arc of the bend and in- 
 versely as the radius of that arc.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 187 
 
 FIG.B. 
 
 Fig. A Bhowe a bend of 90, the radius c a, of the central 
 arc of the bend being equal 6 times the radius a b, of the 
 pipe, or equal three diameters of the pipe. Fig. B shows a 
 bend of 90 with the radius c e of the central arc of the bend 
 equal the radius of the pipe, or equal 12 diameter of pipe. 
 
 When the radius c a of the central arc of the bend is 
 only equal to the radius of the pipe, or to one half the diam- 
 eter, then the resistance or amount of head lost at such bend 
 will equal the head in feet which generates the velocity of 
 
 V s 
 
 flow, or h"=gj. For example suppose the velocity to be 3 
 
 feet per second through the pipe, and the bend is as shown 
 in Fig. B, then the head in feet lost by resistance at the bend 
 
 _ (3) 2 
 
 ~~ 
 
 will be h"= 
 
 = - U foot 
 
 For a bend of 90 or any other constant number of de- 
 grees, the amount of change in the direction of the flow will 
 be the same for any length of radius c a, of the arc of the 
 bend, but the distance in which this change is effected will 
 be directly as the len th c a, of the radius of the bend. 
 Hence the shorter the radius of the bend the more 
 abrupt will be the change in direction of flow, and con- 
 sequently the greater the resistance. The central arc, a ed, 
 of the bend increases in length or becomes more gradual 
 directly as the radius of the bend c a increases in length and 
 hence the longer this radius c a becomes the more gradual 
 will be the change effected in the direction of the flow. The
 
 183 SULLIVAN'S NEW HYDRAULICS. 
 
 resistance at a bend will therefore be directly as the number 
 of degrees included by the central arc of the bend, and in- 
 versely as the length of the radius of the bend and will in- 
 crease as v 2 (or possibly as v 8 ). The formula will therefore be 
 
 , __ Ay, r v v a _ A .5 v v 8 A .5 y v 2 
 ~ 90 A R A -2g 90 A R A 64 4 90 X 64 4 A R 
 
 Which reduces to 
 
 In this formula (102) 
 r=$4 diameter of pipe=.5 
 R= radius of central arc o f bend in diameters of 
 
 the pipe and is to be expressed as 1, 2, 3 etc di- 
 
 ameters. 
 A number of degrees of the arc of bend as 30, 90, 
 
 180, etc, 
 v=mean velocity of flow through the pipe. 
 
 EXAMPLE OF THE USE OP THE FORMULA. 
 
 It is required to find the resistance at a bend of 180 in 
 an eight inch pipe where the mean velocity is 3 feet per sec- 
 ond and the radius of the central arc of the bend is equal 3 
 diameters. 
 
 ,.._ A v* .007764 _ 180X9X.OQ7764 _ n4fifiju fflflf head 
 90 R 90X3 
 
 REMARK 1. The resistance at a bend is in addition to the 
 ordinary frictional resistances of the pipe walls. Hence for a 
 pipe which contains a bend, first calculate the loss of head by 
 friction as for a straight pipe, and then add the loss of head 
 due to the bend. 
 
 REMARK 2 It is assumed in all formulas for resistance 
 at bends that the resistance is independent of the diameter of 
 the pipe or width of the open channel, and that the resis- 
 tance of a bend depends solely upon the velocity, the radius 
 of the bend and the number of degrees included in the 
 central arc of the bend. It is doubtful whether the diameter 
 of a pipe exerts an influence on the resistance at a bend or 
 not. It probably does.
 
 SULLIVAN'S NEW HYDRAULICS. 189 
 
 REMARK 3 The force exerted by a column of water im- 
 pinging upon a fixed surface is as the product of the quantity 
 of water by its head. The quantity ip directly as the velocity 
 and the head is as the square of the velocity. Consequently 
 the product is vXv 8 =v 3 . It is therefore possible that the 
 force or head or energy absorbed at a bend will vary as v in- 
 stead of v 8 . 
 
 70 Formulas of Weisbach and of Rankine for Resis 
 tance at Bends in Pipes. 
 
 The formula for resistance at bends proposed by Weis- 
 bach is 
 
 h'=.l31+1.847 (-LVx-^-X 
 
 In which 
 
 r=radius of pipe in feet=^ diameter in feet. 
 
 R=radius of axis of bend in feet. 
 
 A=central angle of bend in degrees. 
 
 2g=effect of gravity=64.4. 
 
 Professor W. J. M. Rankine's formula is simply a change 
 in form of Weisbach's formula, and is as follows: 
 
 In which 
 
 A=angle of bend in degrees 
 
 d=diameter in feet of pipe 
 
 r=radius of central arc of bend 
 To simplify Weisbach's formula, place the coefficient, 
 
 .131+1.847(-^-)*=Z. Then 
 V R / 
 
 , ., A ^, v 8 Av a Z y / A v 2 \ 
 =ZX T80 X 60 = -11592- = Z \TI592 ) 
 
 Remembering that in Weisbach's formula, r= half the 
 diameter of the pipe in feet, and R= radius of the central arc 
 of the bend in feet, the following table of values of Z will be 
 readily understood and applied:-
 
 190 SULLIVAN'S NEW HYDRAULICS. 
 
 Value of Z in Weisbach's Formula. 
 
 r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .1 
 
 .15 
 
 .2 
 
 .225 
 
 .25 
 
 .275 
 
 .3 
 
 .325 
 
 .35 
 
 .375 
 
 .4 
 
 .425 
 
 Z= 
 
 .131 
 
 .133 
 
 .138 
 
 .145 
 
 .15 
 
 .155 
 
 .16 
 
 .17 
 
 .18 
 
 .195 
 
 ,20i ; 
 
 .225 
 
 r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .45 
 
 .475 
 
 .5 
 
 .525 
 
 .55 
 
 .575 
 
 .6 
 
 .625 
 
 .65 
 
 .675 
 
 .7 
 
 .725 
 
 Z= 
 
 .244 
 
 .264 
 
 .294 
 
 .32 
 
 .35 
 
 .39 
 
 .44 
 
 .49 
 
 .54 
 
 .60 
 
 .661 
 
 .73 
 
 r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .75 
 
 .775 
 
 .80 
 
 .825 
 
 .85 
 
 .875 
 
 .9 
 
 .925 
 
 .95 
 
 .975 
 
 l.(X) 
 
 
 Z= 
 
 .806 
 
 .880 
 
 .98 
 
 1.0- 
 
 Ujj 
 
 1. 29L 41 
 
 1.51 
 
 1.68ll.8:r2.00 l 
 
 USE OP ABOVE TABLE. The velocity iu feet per second 
 through an eight inch pipe is 3 feet. There is a bend of 90 
 with a radius of bend equal 4 inches or half the diameter. 
 What is the loss of head in feet caused by the bend? 
 
 We see that as the radius of the central arc of the bend 
 
 is equal to half the diameter of the pipe; that -D-=1.00. Re- 
 
 ferring to the above table, and it is seen that when^s- = 1.00, 
 then Z=2.00. Hence by the formula, 
 
 h " =z - 
 
 The radius in feet of an 8 inch pipe=.3333 foot. 
 The diameter in feet of an 8 inch pipe=.6666foot. 
 Suppose the radius of the above bend R=.66G6 foot or 
 equal the diameter, and the radius of the pipe is .3333 foot. 
 
 - .6666 ~- 5 
 
 From the above table it is seen that when-p~ = -5, then 
 Z=.294. And in this case Weisbach's formula would give the 
 loss for 3 feet velocity of flow as 
 
 =.^[ggf-]==.(*feet 
 
 h " =Z 111592 
 
 This latter result is altogether too small.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 191 
 
 71. Comparison of the Results by Weisbach's Formula 
 and by the Formula Herein proposed, for Bends of 90 with 
 Radii Varying form /?= y z d t o R= 3d, and Different Veloci- 
 ties. 
 
 In the following table the lose of head by friction has been 
 computed by our formula (102) and also by Weisbach's for- 
 mula for various velocities of flow through a bend of 90 in 
 which the radius of the central arc of the bend varies from R 
 =^ d to R=3d. It is possible that the results by either for- 
 mula are too small for the reason suggested in remark 3, 69 
 
 TABLE No. 38. 
 Table of computed results for comparison. 
 
 
 2 
 
 g 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 
 Velocities 
 
 Feet 
 
 Feet 
 
 Feet 
 
 Feet 
 
 Feet 
 
 Feet 
 
 Feet 
 
 
 
 .062 
 
 .14 
 
 .248 
 
 388 
 
 56 
 
 .761 
 
 .994 
 
 ( Formula (102) 
 
 
 .0621 
 
 .14 
 
 .248 
 
 .388 
 
 .56 
 
 .761 
 
 .994 
 
 1 Weisbach 
 
 fld < 
 
 .031 
 .009 
 
 .07 
 02 
 
 .124 
 .026 
 
 .198 
 .056 
 
 .28 
 081 
 
 .38 
 .11 
 
 .497 
 .144 
 
 i Formula (102) 
 1 Weisbach 
 
 R=2d \ 
 
 .0155 
 .005 
 
 .035 
 .011 
 
 .072 
 .(19 
 
 .C97 
 .029 
 
 .14 
 
 .042 
 
 .19 
 .057 
 
 .248 
 .074 
 
 j Formula (102) 
 1 Weisbach 
 
 j 
 
 .0103 
 
 0233 
 
 .0413 
 
 .'646 
 
 .093 
 
 
 .1656 
 
 j Formula (102) 
 
 
 .001 
 
 .01 
 
 .017 
 
 .027 
 
 .038 
 
 .052 
 
 .069 
 
 1 Weisbach 
 
 It would appear from au inspection of the results by 
 Weisbach's formula that there is little to be gained by mak- 
 ing the radius of the bend greater Iban twice the diameter of 
 the pipe. This is not true, however, in practice. The radius 
 of a becd should be made as great as the circumstances will 
 permit unless the velocity of flow through the pipe is to be 
 very small. The velocity should be the controlling feature 
 in determining the radius of the bend. 
 
 Fanning says ''Our bends should have a radius, at axis, 
 equal at least to 4 diameters." Trautwine advises a radius of 
 bend equal to 5 diameters length, or as much longer as it can 
 be made. If the velocity does not exceed 5 feet per second, 
 then a radius of 3 diameters will reduce the loss of head to 
 .0646 foot at a 90 bend.
 
 192 SULLIVAN'S NEW HYDRAULICS. 
 
 72. Resistance at Bends. Rennie's Fxperiments. 
 
 While the results of experiments by Bennie on leaden 
 pipe one half inch diameter are not of great value as estab- 
 lishing any law of resistance at bends, yet they indicate 
 very clearly that the results by Weisbach's formula are too 
 low. 
 
 Bennie experimented with a leaden pipe 15 feet in length 
 and half inch in diameter under a total head of 4 feet. He ob. 
 tained the following results; 
 
 The straight pipe before being bent discharged .00699 
 cubic feet per second. 
 
 With one bend at right angles near the end, 00556 
 
 cubic feet per second. 
 
 With 24 right angle bends 00253 
 
 cubic feet per second. 
 
 It will be noted that the bends are described as right 
 angled. This may have crushed the pipe out of form and re- 
 duced the area at the bends, This would materially affect the 
 velocity and the resistance through the bend. Whether this 
 occured or not is not stated, Prom the area in square feet 
 of this half inch pipe and the quantity in cubic feet per sec- 
 ond it discharged we find that the velocities of discharge were 
 as follows: 
 
 Before the pipe was bent, v = JL= 06 ^ 9 =5 feet per sec- 
 ond. 
 
 With one right angle bend, v =-S_= - 00556 = 3.971 feet 
 per second. 
 
 With 24 right angled bends, v=-i-=-^HL= 1.80 feet 
 
 per second. 
 
 In order to prevent confusing the resistance of the pipe 
 walls with that of the bends, we will first find the value of 
 the coefficient of resistance n, of the pipe before it was bent. 
 
 The total head was 4 feet, and while the pipe was straight 
 the velocity of discharge was 5 feet per eecond. The head in 
 feet lost by friction along the walls of the straight pipe under 
 this velocity was equal the total head minus the head due to 
 the velocity of discharge, or was
 
 SULLIVAN'S NEW HYDRAULICS. 193 
 
 4 ^f=4. .3882=3.6118 feet. 
 
 After one bend was made in the pipe, the total head re- 
 maining 4: feet, the velocity of discharge was only 3.971 feet 
 per second. Now from the data of flow in the straight pipe 
 before the bend was introduced we find the value of D to be 
 
 = Jv* 15X25 =- 000082 - 
 
 After one bend had been introduced the velocity was re- 
 duced to 3.971 feet per second, so the friction of the pipe walls 
 exclusive of the resistance of the bend was now 
 
 nlv"_.000082Xl5X15.76884 
 h =-/oT- .0085 
 
 But the total loss of head due to pipe walls and one bend 
 combined was equal the total head of 4 feet minus the ve- 
 locity head, or equal 
 /o 971 \ 
 
 4 644 =* .244842=3.755158 feet. 
 
 If we deduct from this total loss the loss due to pipe 
 walls we have 3.7551582.2818=1.473358 feet head lost by the 
 resistance at the bend; which is equal 6 times the head gen- 
 erating the velocity. This would indicate that the resistance 
 at a bend is more nearly proportional to v* than to v*. as inti- 
 mated in remark 3, 69. The resistance at a bend in a very 
 small pipe is probably greater than in large pipes, 
 
 The total head remaining 4 feet, after 24 right angled 
 bends were made in this 15 foot length of half inch lead pipe 
 the velocity was 1.80 feet per second as determined from the 
 quantity discharged. The loss of head due to friction of pipe 
 walls, exclusive of the bends, was, for this velocity. 
 
 h , = nZv = . 000082X15X3.24 = mB feet head> 
 v 'd 3 .0085 
 
 The total loss of head due both to the 24 bends and the 
 
 friction of pipe wall wae H_ lL= 4. .05031=3.94969 feet. 
 
 *& 
 
 The loss due to the 24 bends alone was therefore equal
 
 194 SULLIVAN'S NEW HYDRAULICS. 
 
 the total loss minus the loss due to pipe walls=3.94969 .4688 
 =3.48 feet. 
 
 If the loss was equal at each bend, then h= 3 J 48 = 
 
 .145 foot head lost at each bend for a velocity of 1.80 feet per 
 second. In this caee the head lost at each bend was only 
 equal 2.88 times the head generating the velocity. It must 
 be remembered that all these bends are described as right 
 angled bends, It is probable that serious contractions of the 
 area of the pipe were produced at each such bend and that 
 the velocity of flow through the contractions was greater 
 than 1.80 feet per second. 
 
 Because of the direct action and equal reaction of the 
 water impinging upon the pipe wall at a right angled bend 
 the lose of head at such bend could not be less than twice 
 
 v 2 
 the head producing velocity, or h" = 2-sr- According to the 
 
 above results of Ronnie's experiments with 24 right angled 
 bends it appears that the loss at each bend was equal nearly 
 
 three times the head producing the velocity or h"=2.88 -| 
 
 But it is doubtful what the actual velocity was in the bends 
 as the areas were probably contracted. 
 
 Right angled bends or shoulders are, however, never in- 
 troduced into a water pipe, but the bends are always circular. 
 As a true right angled bend cannot be made without cutting 
 and fitting, or casting, it is probable that Rennie's pipe was 
 bent like Fig. B, 69. 
 
 73. Relation of Thickness of Pipe Shell to Pressure, 
 Diameter and Tensile Strength of Pipe Metal 
 
 When a pipe is filled with water and is closed at dis- 
 charge end so there can be no flow in it, the radial pressure 
 within the pipe tending to burst it will vary as the head of 
 water above any given point along the pipe, and at any
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 195 
 
 given point will be equal HX.434=lbs. pressure on each 
 square inch of the internal circumference. 
 A E F 
 
 In the Figure let R represent a reservoir, the water level 
 in which is A, and a pipe C D G, is laid from it ov*r hills and 
 depressions. When the pipe is closed at G, the pressure 
 within the pipe which tends to burst it will vary as the ver- 
 tical distance C E, D F, between the given point in the pipe 
 and the level of the water A E F B, in the reservoir. Hence 
 the thickness and strength of the pipe shell must be pro- 
 portion according to the position it is to occupy in the pipe 
 line. If the vertical distance CE is J30 feet then the pressure 
 at C on each squara inch of the internal circumference of the 
 pipe will be 130X .434=56.42 Ibs. But the pipe passing over the 
 hill at D is only 80 feet below the level of the water in the 
 reservoir, and consequently the pressure within the pipe at D 
 is equal 80X.434=34.7'2 Ibs. per square inch. A profile of the 
 pipe line showing the distance at all rises and depressions 
 along the line between the pipe and the level A E F B should 
 always be made before the thickness of pipe shell is calcula- 
 ted for any portion of the line. With such profile the thick- 
 ness and strength of the pipe for each division of the line 
 may be calculated so as to conform to the pressure it must 
 sustain. 
 
 The inclined line A, G, is the hydraulic grade line, or line 
 which indicates the hydraulic or running pressure in the 
 pipe when the pipe is open at G and discharging freely. 
 
 The hydraulic or running pressure within the pipe at any 
 given point along the pipe line is equal to the distance in- 
 feet, measured vertically, from the given point in the pipe to
 
 196 SULLIVAN'S NEW HYDRAULICS. 
 
 the hydraulic grade line, A G., multiplied by .431. Thus, the 
 running pressure at C in the pipe ia equal the vertical dis- 
 tance C H in feet multiplied by .434. The difference in feet 
 between C E and C H shows the loss of head in feet by fric- 
 tion between the reservoir and C. If the pipe were laid on 
 the hydraulic grade line A, G, there would be no pressure in 
 it at all when discharging freely except that due to the depth 
 of the diameter. The pipe must be so laid that no part of it 
 will rise above the hydraulic grade line. If the pipe at D 
 should rise above the line A G, to K, then the line would re- 
 quire to be divided into two divisions, A K, and K G, both as 
 to diameter of pipe and as to the hydraulic grade line. The 
 diameter KG, if the same as A K, would not run full, for the 
 reason that K G would have a greater fall per foot length 
 than A K. Assuming the pipe to be laid as shown by C D G, 
 and that it is closed at G so there is no discharge, then the 
 internal pressure on each square inch at any given point in 
 the pipe will equal the vertical head in feet between the 
 given point in the|pipe and the line A E P B, multiplied by .434, 
 and the number of square inches subject to this pressure will 
 be directly as the diameter in inches of the pipe, because the 
 circumference is equal dX3.1416. 
 
 The total pressure on the inner circumference will there- 
 fore be HX.434XdX3.U16. 
 
 The pressure of quiet water is equal in all directions. In 
 a circular pipe the pressure radiates from the axis of the pipe 
 to every point in the circumference. The resultant of the 
 pressure on one half the circumference acts through the 
 center of gravity of that half, and equals the products of the 
 pressure into the projection ofjthat half circumference. The 
 projection of half the circumference equals the diameter of 
 the pipe. An equal resultant acts in the opposite direction 
 through the center of gravity of the other half circumference. 
 The resulting strain on the pipe shell at any point in the cir- 
 cumference is equal to the sum of these opposing resultants. 
 If therefore, the thickness and strength of the pipe shell is to 
 be lound simply in terms of the pressure resultant of one half
 
 SULLIVAN'oQ NEW HYDRAULICS. 197 
 
 the circumference, due to the total head, it is evident that the 
 thickness and strength must equal twice this resultant, or, 
 2tS=PXd (103) 
 
 t= thickness of pipe shell in inches. 
 
 S= tensile strength in Ibs. per square inch of pipe metals. 
 
 P= pressure in Ibs. per square inch - H.X-434. 
 
 d= inside diameter of pipe ininches. 
 
 This gives a thickness and strength just sufficient to 
 equal or balance the pressure of the quiet water, as 
 
 t ^g- OM) 
 
 To be sufficiently strong to withstand the violent shocks 
 and sudden strains caused by water ram, and to provide for 
 defects in casting or in riveting, and to prevent breakage in 
 handling and from unequal settlement of the pipe in the 
 trench, it is necessary to make cast iron pipe very much 
 thicker and heavier than theory would indicate, and wrought 
 iron and steel pipe from three to six times as thick as the 
 quiet pressure alone would actually require. For these rea- 
 sons the formula (104) must have added to it another factor 
 called the factor of safety, and it then becomes 
 
 * Pd -XF (105) 
 
 2S 
 
 The factor of safety F, may be equal 2, 3, 4 etc. according 
 to the service the wrought iron or steel pipe is to be put to. 
 
 This formula is not used for cast iron pipe for the reason 
 that cast iron pipe is BO brittle that it is necessary to give it 
 heavy dimensions regardless of the pressure it is to with- 
 stand, Wrought iron and steel pipe being flexible and 
 tough, does not require high factors of safety, but if laid as 
 a permanent line, the shell should be sufficiently thick to 
 prevent pitting through in case the coating is knocked off. 
 The factor of safety of a pipe is found by the formula 
 
 (106). 
 
 The value of S depends on the net strength of a riveted 
 joint, (See 74)
 
 198 SULLIVAN'S NEW HYDRAULICS. 
 
 Many steel pipes have been in successful use under high 
 pressure for many years with factors of safety as low as 2. 
 These small factors of safety were used, however, where the 
 pipe was not subject to water ram. 
 
 For the reason heretofore mentioned, the formulas for 
 the thickness of cast iron pipe are necessarily arbitrary and 
 empirical. 
 
 For thickness in inches'of cast iron pipe of diameters of 
 less than 60 inches 
 
 t=(P+100)X.OOOH2Xd+.33(l. .01 d) 
 
 For thickness in inches of cast iron pipe of 60 inches di- 
 ameter or greater, 
 
 t=(P-r-100)X-OOOU2Xd. 
 
 t=thickness of pipe shell in inches. 
 
 P=pressure in pounds per square inch. 
 
 d=diameter (inside) of pipe in inches. 
 
 The tensile strength of cast iron pipe is ordinarily taken 
 as equal to 18,000 pounds per square inch. If made of the 
 best quality of iron and remelted four times, and cast verti- 
 cally with bell end down, the pipe would have a tensile 
 strength as great as 30,000 pounds per square inch, and would 
 be tough, so that a large part of its superfluous weight might 
 be dispensed with, and the thickness of shell greatly reduced 
 thus reducing the cost of freight, hauling and laying. 
 
 74. Values of S in Water Pipe~ t Formulas.The value 
 of S to be used in the formula (105) for determining the re- 
 quired thickness and strength of pipe shell depends on the 
 the nature of the pipe, whether steel or iron, and whether 
 welded or riveted, and if riveted, then whether single or 
 double riveted. The net strength of a riveted joint depends 
 on the ratio of shearing strength of rivets to tensile strength 
 of the plate, and also upon whether the riveting is done by 
 hand or by hydraulic power. In hand riveting the work is done 
 with cold rivets and the rivet boles are made from 1-32 to 1-16 
 jnch larger than the diameter of the rivet, and the effect of the
 
 SULLIVAN'S NEW HYDRAULICS. 199 
 
 hammer in upsetting the rivet is not sufficient to swell the 
 rivet to its full length so as to completely fill the rivet hole. 
 Hand riveting does not leave as substantial a head on the 
 rivet as machine riveting and is inferior to machine riveting 
 in many respects. A formula for fixing the pitch of rivets in 
 a joint is necessarily based on the ratio of the given shearing 
 strength per square inch of the rivet metal to the given ten 
 sile strength of the plate metal. The formula must be varied 
 at these factors vary. The tensile strength of wrought iron 
 plates varies from 44,000 to 57,000 Ibs per square inch. A 
 good average wrought iron plate should have a tensile 
 strength of 50,000 pounds per square inch before the rivet 
 holee are made in it. The tensile strength of solid steel plate 
 varies from 56,000 to 108,000 Ibs per square inch. 
 
 The best iron rivets have a shearing strength of only 
 45,000 Ibs. per square inch. The results of a great many ex- 
 periments made by the Research Committee of the Institu- 
 tion of Mechanical Engineers (London, 1881) showed that the 
 ultimate shearing resistance of steel rivets was 49,280 Ibs. 
 per square inch for single riveted joints, and 53,760 Ibs. per 
 square inch for double riveted lap joints. It is very proba- 
 ble that iron rivets would not have a greater ultimate shear- 
 ing resistance than 40,000 Ibs. per square inch of livet area in 
 a single riveted joint riveted by hand. Very high steel of 
 great shearing strength is too brittle for rivets, although riv- 
 eted hot. Hence there is no advantage in adopting plates of 
 greater tensile strength than rivets of suitable shearing 
 strength can be found for. A steel plate of about 66,000 to 
 70,000 Ibs. per square inch tensile strength is as high as suit- 
 able rivets can be obtained for, and plates of this class will 
 require steel rivets of best quality. The value of S to be 
 used in the formula (105) should be the net strength of the 
 joint or pipe shell. We will first give the formula for propor- 
 tions of riveted joints, and then for testing the strength of 
 such joints. By these 'means the value of S must he deter- 
 mined in each case. (See 75 80.)
 
 200 SULLIVAN'S NEW HYDRAULICS. 
 
 75. Riveted Steel Pipe For riveting cold, the best 
 grade of steel plate is open hearth mild steel of about 60,000 
 Ibs. per square inch tensile strength to be riveted with best 
 quality swede iron rivets of 45,000 Ibs, per square inch shear- 
 resistance. We have then 4500 =75 per cent as the ratio 
 oOOOO 
 
 of shearing strength of rivets to tensile strength of plates. In 
 this case 1 =1.33, is the ratio of area of rivets to net plate 
 
 required to balance the tensile strength of the plate. When 
 the rivet holes are made in the plate it is weakened as a whole 
 by a percentage found thus: 
 
 Let S=Original tensile strength :>f plate, unperforated. 
 
 S'=tensile strength of plate after holes are made. 
 
 P=pitch, inches, center to center of rivets In one 
 row. 
 
 d=diameter in inches of rivet hole (not of rivet). 
 
 t= thickness of plate in inches. 
 
 Then the per cent strength of the punched plate S' , to 
 the original unpunched plate will be 
 
 S' = P ~ d =per centS 
 
 The numerical value of S' will 
 
 r p j -\ 
 Q' "I * *-* I v/Qx/4 
 
 O = ?s X&XI 
 
 We have just seen that in order to make the shearing 
 strength of the rivets equal to the tensile strengh of the plate 
 ; in this case, the combined area of the rivets must equal 1.33 
 times the net plate area between holes. The plate area be- 
 tween the rivets holes is 
 (P-d)t 
 
 The area of the rivets is d 8 X. 7854. Hence the equation 
 (P d)Xt X 1.33=d*X .7854 
 From which
 
 SULLIVAN'S NEW HYDRAULICS. 201 
 
 And 
 p= d.7854x2 +d=L20 -^L+d, for double riveted 
 
 joint, 
 
 But eupose the rivets had been steel rivets of 50,000 plbs. 
 shearing strength, and the plates as above, that is, of 60,000 
 Ibs. per square inch tensile strength. Then the pitch formu- 
 la would be worked out as follows: 
 
 50,000 Ibs. shearing strength 
 
 60,000 Ibs. tensile strength = ' 833 P er 
 
 Hence,- 030= 1-20. That is, the combined area of rivets 
 
 must be 1.20 times the net plate area between holes. 
 Then, 
 
 (P_d)tXl.20=d* .7854 
 Prom which, 
 
 p= [ d t xi 8 2o ] + d =- 6545 -r~+ d > for Bin * le riveted 
 
 And 
 
 d=1 .3094-+d, for double riveted 
 
 Observe that d=diameter of rivet hole, which is always 
 from 1 32 to 1-16 inch larger than the rivet before the rivet 
 is upset. 
 
 We are restricted to the use of the market sizes of rivets, 
 and should select a diameter of rivet equal to from 1.70 to 2.33 
 thicknesses of the plate. When the diameter of rivet is select- 
 ed then add 1-32 (.03125 inch) for value of d in the pitch formula 
 
 If steel plate of 70,000 Ibs. per square inch tensile 
 strength is used, then the best quality of steel rivets of not 
 less than 53,000 Ibs. per square inch shearing resistance 
 should be adopted. In this case the combined area of the 
 rivets must exceed the area of the net plate metal between 
 rivet holes by .32075 per cent, as below shown. 
 70000 
 
 '53000~ = per
 
 202 SULLIVAN'S NEW HYDRAULICS. 
 
 Then, 
 
 (P d)tX 1.32075=d 2 .7854=total area of rivets. 
 
 And, 
 
 itXl.320?5 ] +d=-5946-^+d, for single riveted 
 
 joints 
 And 
 
 P= + d=1 - 19 -+ d ' for double riveted 
 
 joints. 
 
 If the pipe is to sustain an extremely high pressure, or is 
 subject to frequent water ram, it should be triple riveted 
 with a ribbon of lead 1-32 inch thick placed between the lap 
 of the plates. Then for a triple riveted joint with rivets and 
 plates of the above strengths, the pitch formula would be 
 
 P= [tx 1.32075 J +d=1.784 +d, center to center, in 
 
 one row. 
 
 After many tests of riveted joints (steel plates and steel 
 rivets) the Research Committee of the Institution of Mechan- 
 ical Engineers (London, 1881) reported that: "To attain the 
 maximum strength of joint the breadth of lap must be such 
 as to prevent it from breaking zig-zag. It has been 
 found that the net metal measured zig-zag should be 
 from 30 to 35 per cent in excess of that measured straight 
 across, JQ order to insure a straight fracture. This corres- 
 
 2 d 
 
 ponds to a diagonal pitch of -5- P -f-~ o~ if P be the straight 
 
 pitch and d=diameter of rivet hole To find the proper 
 breadth of lap for a double riveted joint it is probably best 
 to proceed by first setting this pitch off, and then finding 
 from it the longitudinal pitch, or distance between the cen- 
 ters of the two rivet lines running parallel across the plate." 
 If the net metal between two rows of rivet holes is equal 
 to twice the diameter of the rivet hole, the joint will be safe.
 
 SULLIVAN'S NEW HYDRAULICS. 203 
 
 The distance of the rivet holes from edge of plate should be 
 equal to two diameters of the rivet hole. 
 
 In the experiments of the Research Committee they 
 found that a single riveted joint, riveted by hand, (steel rivets 
 and plate) would begin to slip or give when the stress or load 
 per rivet amounted to 6,600 Ibs. The plates were 3-8 inch 
 thick and rivets one inch diameter. A similar hand riveted, 
 double riveted joint, began to slip or give when the load per 
 rivet reached 7,840 Ibs. whereas a machine riveted joint of 
 similar proportions did not begin to slip until the load per 
 rivet was double that at which the hand riveted joints began 
 to give. 
 
 The value of hydraulic riveting is in the fact that.it holds 
 the plates more tightly together, and thus doubles the load 
 at which the slip in a joint commences. The size of rivet 
 heads and ends was found of great importance in single 
 riveted joints. An increase of one-third in the weight of 
 the rivets (all the excess weight being in the rivet heads and 
 ends) was found to add 8 1-2 per cent to the resistance of the 
 joint, for the reason that the large heads and ends held the 
 plates firmly together and prevented them from cocking so as 
 to place a tensile strain on the rivets. The committee also 
 found that the effect of punching instead of drilling the rivet 
 holes was to weaken the plates from 5 to 10 per cent in soft 
 wrought iron, and 20 to 25 per cent in hard wrought iron 
 plates, and 20 to 28 per cent in steel plates. This weakening, 
 of coursrf, extended only to the metal immediately around the 
 hole. They also found that the metal between the rivet holes 
 in mild steel plate has a considerably greater tensile strength 
 per square inch than the unperforated metal. The excess 
 tensile strength amounted to from 8 to 20 per cent, being 
 largest where the distance between rivet holes was least. 
 
 "A riveted joint may yield in three ways after being 
 properly proportioned, namely, by the shearing of its rivets; 
 or by the pulling apart of the net plate between the rive* 
 holes; or by the crippling (a kind of compression, mashing or 
 crumpling) of the plates by the rivets when the two are too
 
 204 SULLIVAN'S NEW HYDRAULICS. 
 
 forcibly pulled against each other. It also compresses the 
 rivets themselves transversely at a less strain than a shearing 
 one; and this partial yielding of both plates and rivets al- 
 lows the joint to stretch considerably before there is any 
 danger of actual fracture. Or in steam or water joints it may 
 cause leaks without further inconvenience or danger." 
 Trautwine. 
 
 In view of the results of the experiments as to the slip- 
 ping, or giving or "crippling" of joints, as shown by the re 
 port of the Research Committee, it is evident that if an ab 
 solutely water tight joint is to be made to stand high pres- 
 sure, the pitch of the rivets must be less than would be in- 
 dicated by the theory of simply equalizing the shearing 
 strength of rivets and the tensile strength of plates. The 
 crushing or mashing load, within elastic, limits, must be 
 observed. 
 
 76. Table ot Proportions of Single and Double Riv- 
 eted Joint, Mild Steel, Water Pipe Joints. The pitch of 
 the rivets iu the following table is for sheet steel of 60,000 Ibs. 
 per square inch tensile strength, and for Swede Iron rivets 
 of 45,000 Ibs. per square inch shearing strength. The lap for 
 any class or strength of plate in the straight seams should 
 equal 5 diameters of the rivet hole in single riveted joints, 
 aid 8 diameters of the rivet hole in double riveted joints. 
 This gives two diameters distance between edge of rivet hole 
 and edge of plate in both single and double riv- 
 eted joints, and in double riveted joints also gives 
 two diameters (straight distance) between the two rows 
 of li vets, or three diameters straight across from one pitch 
 line to the other. Such lap gives more friction between the 
 plates, is more rigid and less straining on the rivets, and may 
 be scarped down better than a smaller lap. The round seams 
 should have a lap of three times the diameter of the rivet 
 ho!e, and pitch as for single riveted joint.
 
 SULLIVAN'S NEW HYDRAULICS. 
 TABLE No. 39. 
 
 205 
 
 
 
 
 
 
 
 - 
 
 . 
 
 8 
 
 "o 
 
 "S 
 
 | 
 
 5 
 
 
 r 
 
 |o 
 
 
 
 .2 
 "3 
 
 1 
 
 S 
 o> 
 a 
 
 2 
 
 JL 
 
 <D 
 
 g 
 
 S 
 
 D 
 
 ja 
 
 1 
 
 "o 
 
 *o,2 
 
 
 "S-2 
 
 o 
 
 S-s 
 
 2xl 
 
 . 
 
 
 is 
 
 is 
 
 35 
 
 si 
 
 Q 
 
 .2+J 
 
 II 
 
 1 
 
 i 
 
 HW 
 
 
 
 
 
 
 
 
 
 W . 
 
 G.No. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 5. 
 
 0.220 
 
 7-16 
 
 .46875 
 
 .21972656 
 
 1.06875 
 
 1.66725 
 
 2.11-32 
 
 3.34 
 
 6. 
 
 .203 
 
 3-8 
 
 .40625 
 
 lt)r>03906 
 
 0.89405 
 
 1.38185 
 
 2.1-32 
 
 3.14 
 
 7. 
 
 .180 
 
 3-8 
 
 .40625 
 
 .1650:i90t5 
 
 0.95638 
 
 1.50651 
 
 2.1-32 
 
 3.14 
 
 8. 
 
 .165 
 
 3-8 
 
 .40325 
 
 .16503906 
 
 1.00000 
 
 1.64285 
 
 2.1-32 
 
 3.14 
 
 9. 
 
 .148 
 
 14 
 
 .28125 
 
 .07910256 
 
 0.6019r> 
 
 0.92262 
 
 .13-32 
 
 2.1-4 
 
 10- 
 
 .134 
 
 1-4 
 
 .2^12') 
 
 .07910256 
 
 0.63545 
 
 0.98963 
 
 .13-32 
 
 2.1-4 
 
 11. 
 
 .120 
 
 1-4 
 
 .28125 
 
 .07910256 
 
 0.67676 
 
 1.07227 
 
 .13-32 
 
 2.114 
 
 12. 
 
 .109 
 
 3-16 
 
 .21875 
 
 .04785156 
 
 0.48215 
 
 0.74555 
 
 .3-32 
 
 .3-4 
 
 13. 
 
 .095 
 
 3-16 
 
 21871 
 
 .04785156 
 
 0.52097 
 
 0.82319 
 
 .332 
 
 .34 
 
 14. 
 
 .083 
 
 3-16 
 
 .21875 
 
 .04785156 
 
 0.5646} 
 
 0.91058 
 
 .3-32 
 
 .34 
 
 15. 
 
 .072 
 
 1-8 
 
 .1562^ 
 
 .02441400 
 
 0.35970 
 
 O.F6315 
 
 0.25-32 
 
 .14 
 
 16. 
 
 .065 
 
 18 
 
 .15625 
 
 .02*41406 
 
 0.38161 
 
 0.60697 
 
 0.25-32 
 
 .14 
 
 77 Table of Decimal Equivalents to Fractional Parts 
 of an Inch. 
 
 The following table will greatly facilitate calculations of 
 of riveted joints. 
 
 TABLE No. 40. 
 
 1-32=. 03125 
 1-16=. 0625 
 3-32=. 09375 
 1-8=. 125 
 1-8 +1-32=. 15625 
 1-8+116=. 1875 
 1-8 +3-32=. 21875 
 1-4= 25 
 14+1-32=. 28125 
 14+1 16=. 3125 
 
 1-4+3-32=. 34375 
 3-8=. 375 
 3-8+1 32=. 40625 
 3-8 + 1-16=. 4375 
 38+332=46875 
 1-2=. 50 
 1-2 +1-32=. 53125 
 1-2 +1-16=. 5625 
 1-2+3:52=. 59375 
 5-8=. 625 
 
 5-8 +1-32=. 65625 
 5-8+1-16---. 6875 
 58+3-2=.71875 
 34=. 75 
 3-4 +1-32=. 78125 
 34+1-16=. 8125 
 34 +3-32=. 84375 
 7-8=. 875 
 7-8 +1-32=. 90625 
 7-8 +1-16=. 9375 
 7-8+3-82=. 96875
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 78. Weight of Each Thickness, Per Square Foot, of 
 Sheet Iron and Steel 
 
 TABLE No. 40 A . 
 
 CT 1 
 
 02 
 
 Thickness 
 Inches 
 
 02 
 
 0.300 
 .284 
 .259 
 .238 
 .220 
 .203 
 .180 
 .165 
 .148 
 
 . 
 
 11.48 lb.- 
 10. 47 Ibs 
 9.6191bt 
 
 8.8921b< 
 8.2051b t 
 7.2751bt 
 
 5.9811bs 
 
 11.591bt 
 10.571b' 
 9.7151b^ 
 
 8.981 ]b 
 8.287)bt 
 7. 348 Ibs 
 6.736 Ibf 
 6.041 Jhi- 
 
 0.134 
 .120 
 
 .083 
 .072 
 .065 
 .058 
 .049 
 
 4.8501bs 
 4. 405 Ibs 
 3 840 Ibs 
 3. 3551 be 
 2.9!01bs 
 2. 627 Ibs 
 2. 344 Ibs 
 l 
 
 5. 470 Ibs 
 4. 899 Ibs 
 4. 449 Ibs 
 3. 878 Ibs 
 3.3881b8 
 2. 939 Ibs 
 2. 653 Ibs 
 2. 367 Ibs 
 1. 
 
 79.- Calculating Weight of Lap- Joint Riveted Pipe. 
 
 In measuring the length of a sheet of metal to make a circle 
 of given inside diameter, allowance must be made for the 
 contraction or compression of the metal in bending, This 
 contraction or shortening of the plate in bending equals the 
 thickness of the plate to be bent. Consequently the length 
 of plate required to make a lap riveted pipe of a given inside 
 diameter in inches must be equal to (d+t)X3.14164- required 
 lap In inches. d= required inside diameter in inches, and 
 t= thickness of plate to be bent, in inches. The weight of 
 the metal punched or drilled out in making the rivet 
 holes for straight and round seams is about equal to 25 per 
 cent of the weight of the rivets. Consequently take the 
 weight of the solid plate of required dimensions (Table No. 
 40A) and add 75 per cent of total weight of rivets required. 
 If the pipe is to be coated or flanged, this 1 must also be added 
 to the weight. Allow for lap of each round seam as much 
 loss of length of pipe off each sheet of metal as six times the 
 diameter in inches of the rivet hole, except for the two 
 sheets forming the ends of a length of pipe which will be 
 
 For the straight seams the lap should be 
 Lap=dX8. for double riveted pipe joints.
 
 SULLIVAN'S NEW HYDRAULICS. 207 
 
 Lap=dx5, for single riveted pipe joints. 
 
 And for round seams dx3=lap at each end of each 
 sheet. 
 
 Observe that d= diameter of rivet hole in calculating 
 lap, and in calculating the pitch of the rivets. 
 
 80. Tests for the Strength of a Riveted Lap Joint- 
 
 To ascertain the actual net strength of a riveted lap joint pro- 
 ceed as follows: 
 
 Let S^tensile strength per square inch of plate before 
 punched. 
 
 S' tensile strength of plate per square inch after 
 punched. 
 
 t=thickness of plate in inches or decimals of an inch. 
 
 d=diameter in inches of rivet hole. 
 
 P=pitch, or distance from center to center of rivets in 
 one row. 
 
 Then the net tensile strength of the punched plate will 
 
 EXAMPLE. 
 
 The original unpunched plate had a tensile strength of 
 say 60,000 Ibs. per square inch, or S=60,000. 
 
 The plate was of No. llguage steel and .12 inch thick, 
 or t=.12. 
 
 The diameter of rivet hole was d=.28125. 
 
 It was double riveted and the pitch of the rivets in one 
 row was P=1.07227. 
 
 Then, 
 
 The strength before the rivet holes were made was 
 S=SSXt-60,000=.12X7,200 Ibs. 
 
 Then the actual value of S to be used in the formula for 
 thickness and strength of pipe shell (105) would be 
 
 =- 7377 P er cent of S > or 60,OOOX-7377.
 
 208 SULLIVAN'S NEW HYDRAULICS. 
 
 The test for actual strength of plate between rivet holes 
 in one row being satisfactory, we then test the joint for its 
 resistance to shearing of rivets. The area of net plate be- 
 tween two holes in one row was 
 
 f P d 1 
 Net plate = [-p J Xt. 
 
 But as the shearing resistance per square inch of rivet 
 metal was only 75 per cent of the tensile strength of the plate 
 
 60,000 
 metal, we made the rivet area = ^ QQQ=I 33 times the 
 
 net plate area. 
 
 Then, if R= resistance to shear of rivets, we have 
 
 R= [ p J XtXl-333X45,000=5311.48 Ibs. 
 
 This shows the tensile and shearing strength to be equal. 
 As to test for "crippling strength of joint, we have Traut- 
 wine's rule. N=number of rivets in one inch length of joint. 
 
 1 2 
 
 N -p- for single riveted joint, and N=-p- for dou- 
 
 joint. In this double riveted joint N= 
 =1.86522. 
 
 Then, 
 
 Crippling strength=NX2 tXdX60,000=7,554 Ibs. 
 
 The value of S to be used in formula (105) should be the 
 smallest of the three values above found if the pipe is to be 
 absolutely water tight, which in this case was S=60,000 X 
 .7377 per cent. 
 
 81. Testing Plates for Internal Defects. The quality 
 of iron or steel as to density will of courpe be determined by 
 the weight per cubic unit of the metal. Light weight indi- 
 cates weakness and impurities in the metal. Internal lamin- 
 ations may be detected by standing the plate on edge and 
 tapping it all over with a light hammer. If the sound is dull.
 
 SULLIVAN'S NEW HYDRAULICS. 209 
 
 the plate is laminated internally, but if the ring IB clear and 
 sharp the plate is sound. Another test is to place supports 
 under the four corners of the plate and throw a thin layer 
 of dry fine sand upon the plate, and tap it lightly with a 
 hammer. If the plate is defective, the sand will collect over 
 the defective places, but if the plate IB sound the vibrations 
 will throw the sand off the plate. 
 
 82. Different Methods of Joining Pipe Lengths. 
 Cast iron pipe is usually made in lengths of 12 feet, having 
 an enlargement at one end of each length called a bell or hub, 
 to receive the spigot end of the next length. After the spigot 
 is inserted into the bell and adjusted so as to fit up closely at 
 the end and bring the pipe into line, a piece of jute, old rope, 
 or gasket cut long enough to reach around the pipe with a 
 small lap, is forced into the joint to prevent the melted lead 
 from running into the pipe. A fire-clay roll with a rope 
 centar is now wrapped around the pipe cloae to the bell with 
 its two ends turned out along the top of the pipe to guide the 
 melted lead into the joint. The lead is made sufficiently hot 
 to flow freely, and is poured in until the joint is full. The 
 lead is then calked back into the joint all around the pipe 
 with a calking tool. 
 
 Lap welded pipe, such as the converse lock joint pipe 
 have hubs similar to cast iron pipe, and the lead is poured by 
 the use of a pouring clamp. Lap welded and riveted pipe are 
 sometimes joined by a butt sleeve joint, In this case the 
 ends of two pipe lengths are butted evenly against each other 
 and an iron or steel sleeve somewhat thicker than the pipe 
 shell, is drawn over the joint, leaving a epace of % inch be- 
 tween the sleeve and pipe. A little packing is then inserted 
 to prevent the lead from running into the pipe, and the space 
 between the sleeve and pipe is then run full of melted lead. 
 
 When there is too much water in the trench to permit of 
 pouring hot lead in pipe joints, several pipe lengths may be 
 joined together on the surface and afterward lowered into 
 the trench by the use of several derricks, and these compound 
 lengths may be jointed in the trench by forcing small lead
 
 210 SULLIVAN'S NEW HYDRAULICS. 
 
 pipe into the joint and setting it up firmly with a calking tool. 
 The method of making a slip joint was described in K7. 
 
 83. Reducers for Joining Pipe Lengths of Different 
 Diameters. 
 
 Where a pipe line is made up of different diameters, or 
 where a small pipe is to be connected to a larger pipe, a re- 
 ducer should be used which is simply a short length of pipe 
 converging from the larger to the smaller diameter. In the 
 investigation of friction in nozzles and converging pipes it 
 was shown that the friction in a converging pipe is much 
 greater than in a uniform pipe whose diameter is equal to 
 the mean or average diameter of the converging pipe. The 
 friction in a converging pipe depends upon its length and 
 mean diameter. Its mean diameter should be as great as 
 possible and its length as short as possible provided it does 
 not converge more rapidly or at a greater angle than the form 
 of the vena contracta or contracted vein. If d is the inside 
 diameter of the larger pipe, then in a length of the reducer 
 
 equal-o~, the diameter should converge to d'=dX-7854. For 
 example a pipe of 20 inches diameter is to be joined to a pips 
 of 3 inches diameter, and it. is required to find the length of 
 the reducer in inches. 
 
 Let d = diameter in inches of the large pipe=20. 
 
 d'=diameter in inches of the small pipe=3. 
 d 20 
 
 Then, in a length=-^- =~2~ = 1 inches, the reducer 
 
 must converge to a diameter=dX.7854 = 20 X -7854 = 15.708 
 inches. Hence total amount of convergence is d d'=20 
 15.708=4.295 inches in a length of 10 inches, or the rate of 
 
 convergence per inch length of the reducer is ,Q* J =.4292 of 
 an inch per inch length. Or the diameter will converge 1 
 inch in a length of ^92 = 2 -33 inches. It shoutd there- 
 fore converge from 20 to 3 inches diameter in a length I = 
 (d d')X2.33=(20 3)X2.33=39.61 inches. If a diameter of
 
 SULLIVAN'S NEW HYDRAULICS. 211 
 
 one foot is to be joined to a diameter of .7854 foot, then the 
 length in feet of the reducer should be I s= (d d') X 2.33= 
 (1. .7854)X2.33= .5 foot. 
 
 In this latter case d and d' are expressed in feet. All 
 reducers and all nozzles for fire streams or power mains, and 
 conical pipes in general should conform to the foregoing pro- 
 portions where the most effective delivery and smallest loss 
 by friction and contraction are desired. 
 
 The rate of convergence is one inch in 2.33 inches length 
 or one foot in 2.33 feet length of the converging pipe and 
 hence the length of the convergent pipe or reducer will be 
 found by the general formula 
 
 f=(d d')X2.33 (107) 
 
 If I is expressed in inches then d and d* must be in inches 
 
 If l=is in feet, then d and d' must be in feet. 
 
 d=largest diameter. 
 
 d'=smallest diameter.
 
 CHAPTER VI. 
 
 Plow in Open Channels of Uniform Cross Section. 
 
 84. Permanent and Uniform Flow. Permanent flow 
 may .occur in a channel either of uniform or non-uniform 
 cross section. The flow is said to be permanent when an 
 equal quantity flows through each cross section in equal 
 timea. If the cross sections of the channel are of unequal 
 area the velocities will be inversely as the areas, in the case 
 of permanent flow. Uniform flow can only occur in a chan- 
 nel of uniform cross-section and grade. By uniform flow is 
 meant that both the mean velocity and the quantity are 
 equal at all places along the channel. In this case the slope 
 of the water surface and the slope of the bottom of the chan- 
 nel are necessarily the same, otherwise the velocities or quan- 
 tities passing different points would not be equal. In natural 
 streams with firm beds which are not undergoing scour and 
 fill, the flow will become permanent if the supply of water is 
 constant and uniform. These conditions can scarcely occur 
 in large streams of great length, but may occur in email riv- 
 ers or creeks. In artificial channels such as irrigation canals 
 and mill races where the area of cross section and grade are 
 uniform, and where the quantify admitted into the canal is 
 constant and uniform, both permanent and uniform flow will 
 occur after sufficient time has elapsed for equilibrium to be 
 established between the acceleration of gravity and the re- 
 sistances to flow, provided seepage and evaporation are not 
 appreciably great, as sometimes they are. 
 
 If different portions of a canal are all of uniform sectional 
 area but the slope is different in the different divisions, the 
 flow may become permanent, but cannot become uniform un- 
 less the roughness and resistances in the portions of greatest 
 slope happen to be just enough greater than in the other divis- 
 ions to equalize the velocity head in all. In such
 
 SULLIVAN'S NEW HYDRAULICS. 213 
 
 case each division might be considered separately 
 and the flow might be called uniform in and for 
 any given division of the canal in which the 
 area and slope are uniform. With the exception of flumes 
 aqueducts, and canals lined with masonry, there are few open 
 channels in which uniform flow takes place. The variations 
 in grade, area of cross-section and roughness of perimeter 
 may each be slight and yet the effect is marked. In uni- 
 form flow the resistances and accelerations of gravity must 
 be constantly equal to each other. If the slope varies the 
 head will be greater in one division than in another. If the 
 sectional area varies the resistances will be inversely as y'r 8 , 
 and will also be increased by cross currents and re actions of 
 the particles of water which impinge upon the irregularities 
 of the perimeter and react therefrom. The resistances due 
 to mere irregularities of perimeter are similar to the resist- 
 ances of a bend in a pipe or open chancel . They deflect the 
 particles of water impinging upon them and thus destroy an 
 amount of head depending upon the angle of deflection and 
 the velocity of the particles affected. 
 
 Where the width of a channel is alternately small and 
 then greater, the resistances are similar to these in a con- 
 vergent or divergent pipe, and will vary with the mean value 
 of i/r 3 for a given convergent length of channel and with the 
 mean velocity through the section having the mean value of 
 r for the given length considered. It is apparent, therefore, 
 that a coefficient which would apply at one station or to one 
 given short length of a non-uniform channel, will not apply 
 at another station or to another given length unless the same 
 conditions of roughness and convergence of banks obtain at 
 both. 
 
 In natural streams containing bende of varying grade, 
 depth and width, there will be what may be termed velocity 
 of approach in many of its divisions which will cause veloci- 
 ties in short straight reaches of the channel which are ap- 
 parently greater than the velocity due to the apparent slope. 
 A coefficient of velocity C, developed from the data of flow
 
 214 SULLIVAN'S NEW HYDRAULICS. 
 
 observed at such places will be much too high to be appli- 
 cable at any other reach or to any other conditions of flow. 
 Such conditions are most common at low water stages, and 
 may not obtain at the same place during medium and high 
 stages of water. In natural and non-uniform channels the 
 areas for different depths of flow and the various angles 
 made by the banks at different heights, and the varying de- 
 grees of roughness of the banks above the usual depth of 
 flow, so complicate the conditions for different depths of flow 
 at any given station that it is necessary to find the value of C 
 for the given station under each separate set of conditions. 
 In Section 13 an approximate method of determining C under 
 such conditions has been pointed out. It will require a con- 
 sideration of the form of the channel above and below the 
 observation station as well as at the station. No one formula 
 without the aid of auxiliary formulas, such as suggested 
 in 13, supplemented by experience and sound judgment, 
 can be made to apply to the conditions of flow in rivers and 
 irregular channels. With all attainable aids, we can only 
 expect fairly approximate results in such cases. We shall 
 therefore consider the flow in artificial channels of uuiform 
 grade and sectional area, or channels in which, by courtesy, 
 these conditions are said to be approximated. It would be 
 closer the truth to say that the flow is permanent to a degree 
 approaching uniform flow in each division of uniform slope. 
 
 The closer the actual conditions approach to uniform 
 flow the closer will be the computed results by the formula 
 for flow. 
 
 85. Resistances and Net Mean Head In Open Chan- 
 nels. In channels of uniform grade and cross section the re- 
 sistances to flow consist in the friction of the liquid in contact 
 with the perimeter and the internal resistances among the 
 particles of water themselves. The internal resistances are 
 caused by the distortion of the onward course of some of the 
 particles of water causing them to collide with and distort the 
 course of other particles. 
 
 These distortions have their origin in the small inoquali-
 
 SULLIVAN'S NEW HYDRAULICS. 215 
 
 ties or roughnesses along the sides and bottom of the channel 
 against which the moving particles flow, and from which 
 they are hurled off in eddies angling across the path of the 
 parallel flow. Difference in the temperature of different par- 
 ticles of water, which may be caused in part by impact and 
 velocity, also causes upward and downward movements 
 among the particles of water. If each particle of water 
 moved uniformly in a course parallel to the bottom and sides 
 the term resistance to flow would include no element of any 
 importance except what is called the friction of the liquid 
 with the solid perimeter. The results of experiments estab- 
 lish the fact, however, that the sum total of all the resist- 
 ances whether internal or of friction at the perimeter, are 
 proportional to the extent of wetted perimeter, in channels of 
 uniform cross section and slope. The internal resistances 
 among the particles of water are not caused by friction of one 
 particle with another, but by the collisions and reactions of 
 particles travelling in different directions. There can be no 
 friction as between the particles themselves for they have no 
 roughnesses to interlock or by which they can take hold on 
 each other. 
 
 The molecules are independent, free bodies which act 
 upon each other by impact only, and not by friction. 
 
 If the flow could occur without any resistance of any 
 nature the effect of gravity would accelerate the flow so that 
 the rate of velocity at any given point down a uniform grade 
 would equal the square root of the total fall in feet between 
 the origin of flow and *he given point. The velocity on a uni- 
 form grade would therefore constantly increase each second. 
 As this result does not actually occur, but on the contrary 
 the mean velocity becomes uniform throughout the length 
 of such grade, it is evident that the acceleration of gravity 
 has been balanced by and is equal to the combined resist 
 ances to flow. It is equally evident that the resistances are 
 as the square of the velocity or are equal to the total head in 
 each foot length. If this were not true there would be a gain 
 in unresisted head in each foot length of channel, and to this 
 extent the acceleration of gravity would cause the velocity to
 
 216 SULLIVAN'S NEW HYDRAULICS. 
 
 increase in each foot length of channel, and there could be no 
 such thing as uniform flow under any conditions, and all for- 
 mulas based upon the theory of uniform flow would necessar- 
 ily fail .Attention was called to this in the discussion of coeffi- 
 cients and the law of variation of coefficients. It is mentioned 
 again here because some hydraalicians of eminent ability 
 contend that the coefficient of friction or rather of resistance 
 will decrease with an increase in the velocity, which means 
 that the acceleration of gravity is greater than the combined 
 resistances to flow. If that contention can be established it 
 must be admitted that uniform flow is an impossibility either 
 in pipes or in channels of uniform grade and cross section. 
 The writer is not yet ready to make that admission. The law 
 governing the flow in pipes of uniform diameter is the same 
 which governs the flow in all uniform channels. The theory 
 of flow and resistance to flow was discussed in general hereto- 
 fore (3 to 7 inclusive) and need not be repeated here. 
 
 It is evident that the velocity of any given film or parti- 
 cle of water will depend upon the net unresisted head of such 
 film or particle after the resistances to its flow have been 
 balanced. It is equally evident that the mean of all the dif- 
 ferent velocities in a cross section will depend upon the 
 mean net head of all the particles. If the mean net head in- 
 creases more rapidly than the resistances, it follows that the 
 rate of velocity will increase in every successive foot length 
 of channel; which we know is not the case. In channels of 
 uniform grade and cross section the sum of the resistances 
 per foot length of channel is equal to the head included in 
 each foot length, and tbus leave the net unresisted head, or 
 velocity head, a uniform and constant quantity, and the uni- 
 form mean velocity is as the square root of this constant net 
 mean head. 
 
 There is no friction between the molecules of the atmos- 
 phere and the molecules of water at the surface. Before fric- 
 tion can occur between two independent bodies it is neces- 
 sary that both of the bodies should have projections or rough- 
 nesses which would interlock, and require force to separate.
 
 SULLIVAN'S NEW HYDRAULICS. 217 
 
 When winds occur, the molecules of air are hurled against 
 the molecules of water and thus create resistance by distort- 
 ing the course of the water from its direct path, if the direc- 
 tion of the wind if not the same as that of the flow,but if the 
 wind follows the direction of the flow of the water with a 
 downward sweep it does not resist, but assists the flow. The 
 small bombardment of the water surface by molecules of air 
 caused by difference in temperature of different air strata 
 does not cause any appreciable resistance to or distortion of 
 the flow. In truth, it may be said that none of the resist- 
 ances to flow are due to pure friction, but are all due to 
 changes in direction of the courses of different molecules 
 which produces internal collisions and reactions as well as 
 collisions with and reactions from the solid perimeter. The 
 projections and inequalities along the perimeter, however 
 small they may be, distort the course of the molecules of 
 water impinging upon them, and the reaction sends them ed- 
 dying across the path of the adjacent molecules causing fur- 
 ther distortions and reactions among the molecules them- 
 selves. Roughnesses along the bottom of a channel cause 
 whirls and boils and vertical currents which spend their en- 
 ergies in reaching the water surface and there spread out in- 
 ert and without direction or velocity. For this reason the ve- 
 locity at the surface is less than it is below the surface, which 
 fact has led some persons to believe that there is friction be- 
 tween the atmosphere and the water surface. 
 
 Such boils rise above the surface of the water on the 
 same principle that water rhes above the surf ace in a Pitot 
 tube, and when it reaches the height due to its velocity, its 
 energy is spent, and it spreads out in all directions upon the 
 surface. Abrupt bends or changes in the direction of flow 
 produce impact and reaction and cause the formation of 
 whirls and cross currents which are finally overcome by con- 
 tact with the onward flow at the expense of considerable head, 
 the amount of which will depend upon the angle and the 
 radius of the bend. These remarks in connection with the 
 laws of resistance given at -. and the discussion of the re-
 
 218 SULLIVAN'S NEW HYDRAULICS. 
 
 lationsof area to wetted perimeter and the resulting relations 
 between acceleration and resistance discussed in 3 to 7 
 both inclusive, it is believed will cover all the important fea- 
 tures relating to flow and resistance to flow in channels of 
 uniform grade and sectional area. There are, however 
 certain ratios and relations of surface, to mean and bottom 
 velocities in open channels which demand a separate and 
 more special investigation, as the knowledge of these re- 
 lations has always been involved in much uncertainty. The 
 writer's theory of these relations is entirely original, and is 
 based upon his theory of coefficients of resistance and upon 
 observation and experiment. 
 
 86. There is no Constant Ratio Between the Surface, 
 the Mean and the Bottom Velocities. 
 
 It cannot be denied that the velocity of flow of any given 
 particle of water will depend wholly upon the net unresisted 
 head of such particle. 
 
 The conditions under which the motion of any given par- 
 ticle takes place will vary with the relative position of the 
 particle in the cross section with reference to the perimeter, 
 which is the original place of impact and reaction. The dis- 
 tance that a rebounding particle will be projected into and 
 across the flow will depend upon the difference in the velocity 
 along and near the perimeter and the velocity at the center 
 and surface of the cross section, or the difference in the 
 velocity of the rebounding particle and that of the particles 
 with which it comes in collision. The action of a particle of 
 water is similar to that of a billiard ball. When it impinges 
 upon a projection along the perimeter its course is changed 
 so that it travels diagonally toward the opposite bank or 
 surface, but instantly meets the opposition of the particles 
 having a direction of flow parallel to the perimeter. 
 
 The force and direction of the reaction is changed and 
 reduced with each successive collision as the rebounding 
 particle travels across the parallel flow, until its direction 
 also becomes parallel and the resistances and collision cease 
 as to that particle.
 
 SULLIVAN'S NEW HYDRAULICS 219 
 
 These impingements and reactions along the sides and 
 bottom are in continual progress and are naturally stronger 
 at the place of their origin along the perimeter than else- 
 where and grow weaker and weaker as they approach the 
 center of the volume of flow. The number of these reactions 
 will be directly as the roughness of the perimeter. If the 
 bottom of the channel is corrugated transversely the entire 
 volume of water will rise and fall and reproduce the corru- 
 gations on the surface, thus agitating the entire volume of 
 flow. 
 
 In such case there will be only a small difference in the 
 surface velocity and that at mid-depth, but the bottom ve- 
 locity will be almost nothing. If the sides and bottom of the 
 channel are fairly uniform and smooth there will be very 
 little disturbance at the surface and a small number of re- 
 actions from the bottom and sides, and the bottom velocity 
 will be proportionately much greater, which will result in in- 
 creasing the mean velocity. It is well known that the mean 
 velocity will increase very rapidly in uniform channels or di- 
 ameters, simply by increasing the hydraulic mean radius 
 without increasing the slope. This is accounted for by the 
 fact that as diameter or hydraulic mean radius increases, the 
 area of cross section of the column of water gains very rap- 
 idly on solid perimeter aud there will be a very large rela- 
 tive quantity passed which, in smooth, uniform channels of 
 large radius, will not come in contact with the perimeter nor 
 any other retarding influence. The result ie to increase the 
 rate of mean velocity, not by increasing the bottom velocity 
 but by increasing the area or section of the unretarded por- 
 tion of the vein, or the number of particles of water having 
 an unresisted head. An increase in hydraulic mean radius or 
 of diameter can not affect the velocity of the water in con- 
 tact with the perim iter or affected thereby. It do '8 not re- 
 move the resistance nor add anything to the net head or 
 freedom of flow of these particles. An increase in hydraulic 
 radius or diameter cannot relieve the roughness ol the peri- 
 meter nor the reactions therefrom, nor does it ad I anything
 
 220 SULLIVAN'S NEW HYDRAULICS. 
 
 to their head. There is no conceivable reaeon.therefore, why 
 the bottom velocity should increase or decrease with changes 
 in hydraulic mean depth or diameter, because it will be af- 
 fected by the same retarding influences and resistances re- 
 gardless of the value of the diameter or hydraulic radius. 
 The velocity along the sides and bottom of a channel will 
 therefore depend solely upon thd degree of roughness of the 
 wetted perimeter and the slope of the channel, and will in no 
 manner be affected by an increaee in the hydraulic radius or 
 size of the channel. It cannot be maintained that the rapid 
 movement of the upper central core of the liquid vein will 
 assist the flow at the sides and bottom, because the minute 
 globules of water are independent of each other anJ are 
 without friction among themselves. There are no rough- 
 nesses upon these globules of water by which they can take 
 the slightest hold on each other. If there were any rough- 
 nesses upon them they would interlock and the flow would 
 become uniform and as great at the perimeter as at the cen- 
 ter, or would be brought to rest entirely by friction with the 
 perimeter. There is nothing to affect the velocity of flow 
 of any particular portion of the vein except the constant 
 net head it has remaining after the resistances to its flow 
 have been balanced. As an increase in hydraulic mean rad- 
 ius cannot relieve the roughness and reaction at the peri- 
 meter and the consequent loss of head to the portion of the 
 vein thus affected, it cannot therefore increase its velocity 
 which must depend solely upon the inclination of the chan- 
 nel and roughness of perimeter The velocity of the water 
 affected by the perimeter will be the same for the same slope 
 and same degree of roughness regardless of the sizj of the 
 channel and regardless of the mean and surface velocity. 
 This is directly confirmed by the fact that very high mean 
 and surface velocities may be permitted in large canals with- 
 out damage by erosion of the bed, while such mean velocity 
 in a small canal would rapidly destroy its bed. The 
 reason is that the small canal would require a steep slope 
 to generate a high mean velocity because the whole volume
 
 SULLIVAN'S NEW HYDRAULICS. 221 
 
 of water in a small canal is affected by the resistance of 
 and reactions from the perimeter, and consequently the bot- 
 tom velocity which is controlled by the slope, would be dis- 
 astrously high. 
 
 The smoother the perimeter, the fewer the reactions and 
 disturbances, and the greater the area of cross section un- 
 affected by retarding influences, and as the area of unresisted 
 section increases, the mean velocity will increase. In such 
 case the ratio of surface to mean velocity will be small but 
 the ratio of bottom to mean or surface velocity will be great. 
 The mean velocity is apparently largely controlled by the 
 ratio of area to perimeter as well as by smoothness of peri- 
 meter and slope of channel. 
 
 The bottom velocity is controlled entirely by the slope and 
 the roughness of perimeter. After the depth of flow is sufficient 
 to remove the water surface from the small reaction from the 
 bottom in a fairly smooth channel, the surface velocity de- 
 pends only upon the slope and nothing else. 
 
 It is evident that there is no fixed ratio between any two 
 of these three velocities. The different velocities are.'dependi 
 ent upon separate and distinctly different conditions. The 
 mean velocity gains as area gains over perimeter without any 
 increase of slope, not because the maximum velocity gains, but 
 because a greater number of particles are set free from the 
 retarding influences of the perimeter and thus increase the 
 sectional area of the vein having the higher velocity. This 
 does not affect the bottom velocity because there is no 
 change of slope. If the channel is comparatively deep and 
 has a smooth bottom, a further increase in hydraulic mean 
 depth would not affect the maximum surface velocity which, 
 under these circumstances would be removed from the 
 effects of reactions from the bottom and would therefore 
 only be increased by an increase of slope simply. It is evi- 
 dent that the relation of the maximum surface velocity to 
 the bottom velocity is more constant than the relation of 
 surface to mean or of mean to bottom velocity, and it is also 
 evident that there are so many different influences affecting 
 the one which does not affect the other to an appreciable 
 degree, that it cannot be said that there is any given ratio or 
 relation between any two of them.
 
 222 SULLIVAN'S NEW HYDRAULICS. 
 
 The relation between them will be very different in a 
 shallow rough, stony channel from what it will be in a deep 
 smooth channel, and the relation will change in any given 
 channel with changes in depth of flow. It has been demon- 
 strated that the mean velocity will increase as /r 3 while all 
 other conditions remain constant. The increase in r does 
 not affect the bottom velocity at all. An increase in r may or 
 may not increase the maximum surface velocity. The 
 various empirical formulas for deducing the mean or the 
 bottom velocity from the surface velocity are therefore 
 totally unreliable, for such a formula can only apply to one 
 set of given conditions. If such formula would apply to a 
 wooden trough two feet wide and one foot deep, it would not 
 apply to a canal five feet wide and three feet deep. If it 
 would apply to a canal with smooth and uniform perimeter 
 it would not apply to a rough canal of like dimensions. Such 
 formulas are therefore not of sufficient importance to de- 
 mand discussion. 
 
 87. The Eroding Velocity in Unpaved Channels in 
 Earth. 
 
 In irrigation engineering there is no one feature of greater 
 importance than the proper adjustment of the eroding 
 velocity, or velocity adjacent to the sides and bottom, to the 
 character of the soil which must form the perimeter of the 
 canal. There is one particular bed velocity best adapted to 
 each different class of earth. From considerations of econ- 
 omy it is desirable to maintain as high a velocity as the 
 nature of the material forming the canal bed will stand 
 without damage by erosion. 
 
 The stability of the bed of a canal will depend upon (1) 
 the nature of the material forming the bed, (2) the alignment 
 of the canal. (3) the angle made by the side slopes, (4) the vel- 
 ocity of flow of that portion of the vein adjacent to the sides 
 and bottom, (5) the action of frost, or climatic influences. 
 
 The destruction of the side slopes depends as much or 
 more upon the angle made by them as upon the velocity of 
 flow in contact with and adjacent to them. In cold climates
 
 SULLIVAN'S NEW HYDRAULICS. 223 
 
 where frost penetrates the earth to a depth of several feet 
 the side slopes should be much flatter for the same nature of 
 material than in climates not subject to frost. 
 
 The eroding velocity in a majority of cases is only the 
 partial agent of destruction of the bed. Bad alignment and 
 side slopes too steep to withstand the disintegrating action 
 of alternate freezings and thawings are the principal factors 
 in destroying the uniformity and efficiency of the canal. 
 
 In a canal of uniform section with direct alignment the 
 only velocity which tends to erode the perimeter is the vel- 
 ocity of the water which is in contact with it, which velocity 
 is governed entirely by the slope and roughness of peri- 
 meter and is not affected by the value of the hydraulic mean 
 depth. 
 
 On the contrary if the canal has bends and curves, then 
 the surface, mean and bottom, and all intermediate vel- 
 ocities, become eroding velocities at all places where the 
 direction of flow is changed. The outer bank of the curve 
 must form the resistance which forces the change in direc- 
 tion of flow. The amount of this resistance will depend upon 
 the amount of change in direction of flow and the time or 
 distance in which the change is finally effected. It requires 
 work and power, (see 60) The resistance will therefore be 
 distributed along the outer curves over a distance depending 
 upon the abruptness of the curve or upon the distance in 
 which the total curvature is effected. The power expended 
 upon each square unit of area of the outer curve will there- 
 fore be directly as the radius of the curve. This is the 
 measure of resistance which each unit of area must be 
 sufficiently stable to offer, otherwise it will be eroded and 
 removed. 
 
 A comparison of the coefficients for straight flumes with 
 the coefficient of the crooked Highlme flume (Group No. 5) 
 would indicate that the resistance of a bend of 90 with a 
 radius equal one-half the width of the channel would amount 
 to at least twice the head iu feet generating the mean velocity 
 of flow. If this ratio of resistance holds good in channels of
 
 224 SULLIVAN'S NEW HYDRAULICS 
 
 all widths then the resistance (which is equal to the head 
 required to balance it) would be 
 
 A 2v*X. 007764 AX2v 2 X.OQ776* 
 
 ^go^X ~~R~~ 9oxR (108) 
 
 In which 
 
 A=angle in degrees included in central arc of bend. 
 R=radius of central arc of bend in widths of the 
 channel, not feet. 
 
 For further discussion see 69 et seq., where the for- 
 mula is explained in detail. 
 
 In channels with converging banks the resistance, which 
 they must be sufficiently stable to offer and withstand is 
 similar to that in a conical or convergent pipe( 37,39), and 
 therefore will vary as (3Xv) s , when v= the mean velocity 
 through the section of the convergent length at the point 
 where the value of r is the mean or average value of r for the 
 whole length of the convergent channel. If the channel is 
 both curved and convergent at the same place, then the 
 banks must be able to withstand the resistances due to both 
 causes. The necessity of direct alignment and of uniformity 
 of cross-section is therefore apparent, if we would avoid 
 erosion and yet maintain a reasonably high mean velocity. 
 In large rivers which have small slope and frequent bends 
 with cross-sections alternately wide and shallow and then 
 deep and narrow, all the velocities become eroding velocities 
 and their forces vary inversely as !/r 8 . The work done by 
 the impinging water is in the direction of straightening the 
 bends and trimming the sides so the width will be uniform, 
 and in bringing the slope of the bottom to uniform grade. 
 Unfortunately the banks and bends cave in and form new 
 resistances which divert the energies and directions of the 
 water to new quarters, and thus its work is self destructive. 
 In artifical channels this work should be done in advance so 
 that the energies of the water may be employed in a profit- 
 able way, and not wasted in building and destroying bars and 
 bends.
 
 SULLIVAN'S NEW HYDRAULICS. 225 
 
 88. Eroding Velocity in Straight Canals of Uniform 
 
 Section. Theory and observation both indicate that a depth 
 of flow of one foot upon the perimeter of a straight canal of 
 uniform section will cause as great erosion as a flow of ten 
 feet depth or any greater depth. The power of erosion in a 
 straight, uniform canal varies with the square of the bottom 
 velocity, or as the square of the velocity in contact with the 
 sides and bottom. It has been shown that the velocity along 
 the sides and bottom is controlled by the slope and degree of 
 roughness of perimeter, in straight uniform channels, and that 
 this velocity cannot be affected in such channels by any 
 change in hydraulic mean radius. 
 
 As this bed velocity is not affected by the size of the chan- 
 nel, but is the same for the same slope of channel bed and 
 roughness of perimeter without regard to hydraulic mean 
 radius of the channel, we may conceive, for the purpose of de- 
 termining the eroding velocity in such straight uniform chan- 
 nel, that the central portion of the liquid vein has been re- 
 moved so that there remains only one foot depth of water 
 upon the sides and bottom of the channel. 
 
 Then find the sectional area of this layer of water in 
 square feet, and the length in lineal feet of the wet girth or 
 perimeter. 
 
 Then, 
 area in square feet of the layer of w*ter__ rnr hydraul - c 
 
 Wet girth in lineal feet 
 depth, so far as this one foot layer of water is concerned. 
 
 Then the velocity of flow of this layer of water one foot 
 depth upon the sides and bottom will be 
 
 In channels where the actual depth of flow exceeds one 
 foot, no matter how greatly, the value of r determined as above 
 will be less than unity, but will approach unity. In order to 
 err on the safe side and as a matter of convenience, we as-
 
 226 SULLIVAN'S NEW HYDRAULICS. 
 
 eurne that r is a constant equal unity in channels where the 
 depth of flow is one foot or greater; and under these con- 
 ditions the eroding velocity or velocity of this layer of water 
 is 
 
 < 109 > 
 
 If the channel is so small that the actual value of r for 
 the whole volume of flow is less than rr=1.00, then the mean 
 velocity and all other velocities may be considered as equal 
 and may be found by the formula for mean velocity in chan- 
 nels of the given degree of roughness. In either case the ac- 
 tual eroding velocity will not exceed the computed eroding 
 velocity, and the computed result will be a safe guide in de- 
 termining the grade of the canal. 
 
 89. Slope or Grade of Canal to Generate a Qiven 
 Bottom or Eroding Velocity. The stability of the material 
 which forms the perimeter of the canal must be the controll- 
 ing factor in determining the grade or elope of the canal. 
 Very light soil will not stand a bottom velocity greater than 
 one half foot per second without serious erosion, while other 
 classes of soil will stand much higher bottom velocities with- 
 out damage. When it has been determined what bottom ve- 
 locity is best adapted to the material forming the perimeter, 
 then the slope or grade of the canal (without reference to its 
 size) which will be required to generate that given bottom ve- 
 locity will be 
 
 S=m v* ........................................ (110) 
 
 In which, 
 
 v 2 =the square of the proposed bottom velocity in feet 
 per second. 
 
 m=coefficient of velocity applicable to roughness of peri- 
 meter. 
 
 S=Slope required to generate the given bottom velocity. 
 
 If the channel is so small that the value of r for the en- 
 tire volume of flow is less than r=i.OO, then 
 
 S = :/7F> and tlie mean and bottom velocities will be 
 practically the same.
 
 SULLIVAN'S NEW HYDRAULICS. 227 
 
 If the bottom velocity =.J-L has been decid6dt then 
 the mean velocity for any value of r will equal the bottom ve- 
 locity multiplied by fr 8 , or v=f/r 3 X -/ 
 
 V m 
 
 The value of m may be selected from the groups of data 
 of flow in open channels heretofore given. 
 
 90. Stability of Channel Bed Materials, According 
 to the observations of Du Buat a bottom velocity of 3 inches 
 per second will just begin to work upon fine clay fit for pot- 
 tery; a bottom velocity of 6 inches per second will lift fine 
 sand; 8 inches per second will lift sand coarse as linseed; 12 
 inches per second will sweep along fine gravel. 24 inches per 
 second will roll along rounded pebbles an inch in diameter; 
 a bottom velocity of 3 feet per second will sweep along shiv- 
 ery, angular stones as large as eggs. Professor Rankine give a 
 the following table of the greatest velocities close to the 
 bed which are consistant with the stability of the materials 
 mentioned :- 
 
 Soft clay 0.25 feet per second . 
 
 Fine sand 0.50 " " 
 
 Course sand, and gravel as large as peas. .0.70 ' " " 
 
 Gravel as large as French beans 1.00 " " " 
 
 Gravel one inch diameter 2 25 " " " 
 
 Pebbles 1} inches diameter ,3.33 " " 
 
 Heavy shingle 4.00 " " " 
 
 Soft rock, brick, earthenware ,450 " " " 
 
 Rock, various kinds 6.00 and upwards. 
 
 See also "Civil Engineer's Pocket Book" by Trautwine, 
 pp. 563, 570, and "Irrigation Engineering" by H. M.Wilson 
 page 86, and Fanning, page 622. 
 
 The experiments of Du Buat were in a small wooden 
 trough with a smooth bottom so there was little friction be- 
 tween the moving particles of the material and the bottom of 
 the trough. Loose material on a smooth uniform floor 
 would be moved by a smaller bottom velocity than if it were
 
 228 . SULLIVAN'S NEW HYDRAULICS. 
 
 incorporated in the bed of an earthen channel. It is probable 
 that in ordinary earth the bottom velocity should be about 
 .70 foot per second, and the slope should be S=tn v* = .00031X 
 (.70)* =.0001519. 
 
 91 Adjustment of Slope Or Grade, Bottom Velocities 
 and Side Slopes of Canals, to the Material Forming the 
 Bed. In order to preserve the efficiency and delivery of a ca 
 nal, its cross-section must be uniform, sy metrical and free of 
 deposits and plant growth. Caving and sliding banks, due to 
 the action of frost upon side slopes steeper than the natural 
 angle of repose of the material forming the sides of the canal, 
 when such material is reduced to powder by frost in winter 
 when the canal is empty, not only causes the filling up of the 
 canal, but also leaves the banks rough, irregular and ragged, 
 and greatly reduces its area, while it increases and roughens 
 the perimeter. The efficiency or delivery of a canal may be 
 reduced fully one third during one winter from this one cause 
 alone. The extent of damage thus done will not be fully dis- 
 covered until the water has again been admitted to the canal. 
 All the loose, disintegrated material will then be washed off 
 the sides and deposited in the bottom in irregular heaps. 
 These heaps will be acted upon by the mean velocity in the 
 same manner that a bridge pile or pier is attacked by the 
 flow, and will thus be cut away and redeposited on one side 
 where the velocity is not sufficiently great to keep the mater- 
 ial in suspension and in transit. This will change the direc- 
 tion of the current to the deepest part of the cross section 
 next the opposite bank which produces an undercutting and 
 caving at that point and a further deposit on the side oppo- 
 site the cutting. The thread of the current is caused to cross 
 from one side to the other and thus the energy of the stream 
 is expended in destroying the banks and in transporting ma- 
 terial from one point to another. There are few instances 
 in which the bottom of a canal has been scoured and eroded 
 to a serious extent. The silt and deposits nearly always come 
 from the banks which clearly indicates that the side slopes
 
 SULLIVAN'S NEW HYDRAULICS. 220 
 
 are too steep for the material and for the climate, or that the 
 alignment is bad, for if the alignment IB bad and the ve- 
 locity too high, all the velocities are eroding velocities at 
 the bends, and consequently a very low mean velocity must 
 be adopted or the banks must be protected by paving or 
 otherwise.else the annual expense of cleaning and repairs will 
 be excessive. The proper side slopes of a canal will depend 
 upon the nature of the material forming the perimeter. The 
 side slope should never be steeper, in climates subject to 
 frost, than the natural angle of repose of the material when 
 thrown up in considerable heaps, loose and dry. In climates 
 subject to frost the side slopes will be thoroughly pulverized 
 by alternate freezing and thawing when the canal is empty 
 in winter, or above the water level if the water is not turned 
 out in winter. Under these conditions, if the side slope is 
 steeper than the natural angle of repose of the material 
 when it is perfectly loose and dry, the result is that the ma- 
 terial thus pulverized by frost will roll down into the canal 
 at each thawing until the slope finally reaches its natural an- 
 gle of repose in a rough and irregular way. The method of 
 determining the angle of repose is not by reference to pub- 
 lished tables of such angles for different materials, but by 
 throwing up a large heap of the material to be dealt with and 
 allowing it to assume any angle it will. The angle thus as- 
 sumed by the sides of the heap is as steep as the side slopes 
 of the canal should be in that class of material. The angle 
 of repose will be found to vary widely for different classes of 
 earthy material, and for most kinds the angle will be much 
 steeper if the material is damp or moderately wet than if it is 
 either dry or saturated. Hence the angle should be found 
 when the material is perfectly dry and loose. 
 
 The side slopes having been made to conform to the 
 angle of repose thus found, and due attention having been 
 given to the alignment, it is then necessary to so adjust the 
 slope of the bottom of the canal as to cause a bottom velocity 
 of flow most suitable to the material of the perimeter. If the 
 canal is to be of considerable width and to have a depth of
 
 230 SULLIVAN'S NEW HYDRAULICS. 
 
 flow exceeding one foot, then the grade or slope should be 
 
 S=mv 8 . 
 
 Here m is to be selected from the values of m developed 
 for canals in like condition and in like material, given in the 
 groups of data of flow in open channels. 
 
 The value of v will depend upon the bottom velocity 
 which the given material of the perimeter will stand without 
 erosion. The suggestions heretofore (87) given may assist in 
 determining what value should be assigned to v in the above 
 formula. 
 
 If the canal is to be comparatively deep and narrow, as 
 it should be where practicable, then the grade should be 
 mv 8 mv a 
 
 But in this formula the value of r is found not by taking 
 the quotient of the total cross-sectional area of the column of 
 water by the wetted perimeter, but by assuming that there 
 is one foot depth of water adhering to the sides and bottom, 
 the area of which is to be divided by the total wet girth in 
 lineal feet. The resulting value of r is that which is to be 
 used in determining the slope to generate the given bottom 
 velocity. 
 
 If the value of r is the true value for total area divided 
 by wet perimeter, and v represents the desired mean velocity, 
 then the last formula will give the required slope to gener- 
 ate the given mean velocity, without reference to bottom 
 velocity. 
 
 In very light soil mixed with fine sand the action of waves 
 will reduce the side slopes much flatter than the angle of re- 
 pose of the material when dry or only damp. If fluming, pud- 
 dling, or paving cannot be resorted to where the canal passes 
 through such material, then the canal should have a cross- 
 section elliptical in form, and the bottom or scouring velocity 
 should not exceed .45 foot per second, and great care must be 
 taken to avoid bad alignment. 
 
 The grade of the canal having been determined with 
 reference to the greatest bottom velocity the material of the
 
 SULLIVAN'S NEW HYDRAULICS 231 
 
 bed will safely stand, it then becomes necessary to determine 
 the dimensions of the canal with that given grade which will 
 cause the discharge or carriage of the required quantity of 
 water. 
 
 92. Dimensions of Canals to Carry Given Quantities. 
 
 In the case of canals with side slopes of about 2 horizontal 
 to 1 vertical, and of considerable capacity, the value of the 
 
 hyd aulic mean depth , may be approximately found by 
 formula (64) which is 
 
 In this connection see 19 and 3. The required value of r 
 being thus found in terms of cubic feet per second q, then, 
 
 a=r 8 Xl2- 566 * and wet perimeter, P=_ a _. For reasons here- 
 tofore pointed out these formulas are not generally applicable 
 to all forms of cross-section and capacities of open channels, 
 and when the values of a, p, and r have been calculated in 
 this manner, the general formula for velocity should be ap- 
 plied as a check. When the mean velocity is thus found, 
 then q=aXv. 
 
 For example suppose the grade decided upon for a canal 
 is S=.0002754=l in 3631.08, and the value of m applicable to 
 the class of gravelly earth is m=.00034. What area in square 
 feet and what wet perimeter and what value of r would be 
 required to cause the canal to discharge 1,000 cubic feet per 
 second, the side slopes being 2 to 1? In the first place find the 
 required value of r by formula (64) which will be r=5.121. 
 
 Then required area in square feet, a=r a X12.5664=329.554. 
 
 The required wet perimeter =JL= 32 ^f =64.353. 
 r 5.121 
 
 Taking 33.1668 feet of the wet perimeter as the bottom 
 width of the canal, there will have to be a depth at center 
 sufficient to take up the remaining 31.1862 feet of wet peri- 
 meter which is to be divided equally between the two side
 
 232 SULLIVAN'S NEW HYDRAULICS. 
 
 elopes. Then the wet perimeter of one side slope will be= 
 31.1862 
 
 As the side slopes are 2 horizontal to 1 vertical, a verti- 
 cal depth of water equal about one half the length of one 
 side slope, or about 7 feet in this case, will be required. So 
 making the depth of water at the center equal 7 feet, and the 
 bottom width as above, equal 33.1668 feet, and the side slopes 
 2 to 1, we have the length of one side slope =-/ 7* +14* =15.65 
 feet. Then total wet perimeter =15.65+15.65-(-33.1668= 
 64.466 feet. 
 
 The actual area will be 330.1676 feet. The actual value of 
 
 r will be = 330 - 1676 =5.121. Now as a check on this calcu- 
 04.460 
 
 lation we must apply the general formula for mean velocity 
 to the slope and dimensions above found, and we have 
 
 .064. And the 
 
 quantity in cubic feet per second which will be discharged 
 will be q=areaXvelocity=330.1 676X3.064=1011.63 cubic feet, 
 
 ,-Q 
 
 Tho bottom velocity in this canal would be v=.J = 
 
 Vm 
 
 While it is seen that the dimensions of a canal of this 
 form of cross section and capacity ruaybe closely ascertained 
 by the formulas for r, a and p, as above shown, yet these 
 particular formulas do not apply to small canals nor to rec- 
 tangular canals, with any degree of accuracy. These parti- 
 cular formulas do apply, however, with exactness to pipes or 
 circular closed channels running full. 
 
 93. Allowance In Cross Section of Canals For Leak- 
 age and Evaporation. The amount of loss by leakage and 
 evaporation from a canal will depend upon the climate, th e 
 nature of the soil, the length of the canal, the depth of flow, 
 and above all the position of the canal with reference to the
 
 SULLIVAN'S NEW HYDRAULICS 233 
 
 elevations and depressions of the surface of the surrounding 
 country. 
 
 If the canal is constructed upon the highest line of the 
 land through which it passes, the leakage from it will be 
 great, and because of its elevated position it can never regain 
 any part of this loss by return seepage. Such location also 
 exposes the water surface to the action of the sun and wind, 
 and thus large losses occur by evaporation, especially if the 
 canal is wide and shallow. In arid regions where irrigation 
 is not general and abundant, the sub-surface water level i<3 at 
 considerable depth below the surface, but after irrigation has 
 been practiced for several years, the earth becomes saturated 
 and the sub-surface water level rises near to the surface. Un- 
 til this occurs the loss from new canals in such regions will 
 be very great. After irrigation has been practiced for a num- 
 ber of years, and has become general in the given locality, the 
 canals situated along side hills and skirting the valleys will 
 gain vastly more by seepage into the canal than will be lost 
 by leakage and evapoiation combined. In some canals in 
 Colorado the gain by seepage into the canal is as great as 
 two thirds the total original quantity admitted into the canal 
 at its head. This occurs only in canals located where irri- 
 gation has been practiced for years, and in canals so situated 
 on side hills or along the foot of the hill, as to admit of the 
 seepage flowing into the canal. 
 
 The loss by leakage and evaporation from new canals in 
 arid regions varies from 20 to 75 per cent of the quantity ad- 
 mitted into the canal, according to the nature of the soil and 
 the length of the canal. As the canal becomes silted and the 
 sub-surface water level rises, the leakage will decrease, and if 
 the canal is so located as to admit of it, the gain by return 
 seepage will, in the course of a lew years, more than balance 
 the loss by leakage and evaporation. 
 
 In regions where the rainfall is great it is probable that 
 the seepage into a new canal will offset the leakage from the 
 first opening of the canal, because the sub-surface water level 
 is already very close to the surface of the ground.
 
 234 SULLIVAN'S NEW HYDRAULICS. 
 
 In making allowance in cross-sectional area of a canal 
 to cover these losses, it should be by way of extra depth. 
 
 94. Where a Flume Forms Part of a Canal. Where 
 
 the course of a canal would pass around on a very steep side 
 hill, or through stretches of very porous earth, or across low 
 depressions, flumes are frequently adopted as portions of the 
 canal for such reaches. In this event the question arises as 
 to the proper ratio of flume cross section to that of the canal, 
 of which the flume forms a part. The determination of this 
 question involves a consideration of the relative degree of 
 roughness of the two classes of channel, and the difference in 
 slope or grade of the flume and the canal, as well as the length 
 of the flume and its alignment. If the flume is short and 
 upon the same grade as that of the canal, and has no vertical 
 fall at its lower end, the water will not acquire a velocity in 
 such short flumes much greater than that in the canal, and 
 therefore the area of the flume under such conditions cannot 
 be reduced much below that of the wetted area of the canal. 
 While the velocity of flow will usually be greater in a flume 
 than in a canal of equal slope, yet at the entry to the flume 
 the water has only the velocity of the canal, and the head due 
 to that velocity. It must flow a sufficient distance in the 
 flume to acquire the greater velocity due to the smoother peri- 
 meter before the depth and area of the flume can be materi- 
 ally reduced from that of the connecting canal, otherwise 
 there will be an overflow at the upper junction of the flume 
 with the canal. The flume should converge from the mean 
 width oi the canal at the junction, to the standard section 
 adopted for the flume, in a length varying from 50 to 200 feet 
 according to the difference in slope and in roughness of the 
 flume and the canal. The value of C might be 56 for the canal 
 and anywhere from 70 to 130 for the flume, according to 
 the method and materials adopted in its construction and 
 alignment. 
 
 A straight canal in firm, dense earth and in best condi- 
 tion develops C 75.00, while a rough, crooked flume with 
 battens on the inside develops C 70.00. In such cases as
 
 SULLIVAN'S NEW HYDRAULICS, 235 
 
 this the flume would require an area slightly in excess of 
 that of the canal, or would require an equal area and steeper 
 grade. On the other hand the value of C for a rough canal 
 may be as low as 40, while the value of C for a very smooth 
 well jointed hard wood flume of good alignment might be as 
 high as 130. 
 
 The slopes being equal, the velocities will be as f/r* in 
 the one is to J/r 3 in the other, as modified by the respective 
 values of C, or viviiCJ/r^CJ/r 3 . If the slopes are different 
 then v:v:: C/rVS:Cf/rVS 
 
 The value of C may be taken from the data of like 
 flumes and channels given in the groups, Chapter 2. 
 
 95 Mean Velocity In Uniform Sections of Canals 
 Found by Floats. 
 
 In straight sections of canals of uniform cross-section 
 where the thread of the greatest velocity is midway between 
 banks and just beneath the water surface, the place of mean 
 velocity will be found at .50 of total depth at a point midway 
 between the center of the canal and the bank, unless the 
 depth of flow is less than two feet, in which case the place 
 of mean velocity will be at or just above mid-depth at a point 
 midway between the bank and the middle of the canal, as- 
 Burning that the sides and bottom of the canal are fairly 
 smooth. In shallow canals with gravel and pebbles along 
 the bottom the place of mean velocity is very near mid-depth, 
 aometimes slightly above, and at one-fourth the width of the 
 canal from the bank. A large tin bucket loaded with gravel 
 and covered, may be suspended by a fine wire at this depth 
 and connected to a flat circular float on the surface no larger 
 than is absolutely necessary to support the submerged bucket 
 at proper depth. This double float is to be placed at some 
 distance above the upper end of a measured length of the 
 canal, and adjusted to proper position with reference to the 
 bank or width of the canal, and with reference to depth, and 
 allowed to travel over the given course a number of 
 times. The average time required for its passage over the 
 given number of feet length of the canal will closely approxi-
 
 236 SULLIVAN'S NEW HYDRAULICS. 
 
 mate the rate of mean velocity. The difficulty of ascertain- 
 ing the exact number of seconds which elapse between the 
 time the float crosses the line at the upper station and arrives 
 exactly at the line of the lower station, will probably cause a 
 slight error in the final determination of the mean velocity. 
 For this reason the measured course should be several hun- 
 dred feet in length. If the channel is rough and winding the 
 float will be cast either too near the bank or into mid-cur- 
 rent, and the result is without value. Float measurement of 
 mean velocity is practicable only in channels of uniform 
 width and depth. The surface velocity has no particular re- 
 lation to the mean velocity, and it is therefore impossible to 
 deduce the mean from the surface velocity. The ratio be- 
 tween surface and mean velocity varies with the form of 
 cross-section, roughness of perimeter, uniformity of cross- 
 section, variation in slope, depth of flow and hydraulic radius 
 and alignment of the channel. 
 
 The surface velocity depends mainly on the slope, while 
 the mean velocity depends upon the value of {/r 3 as well as up- 
 on the roughness and slope of the channel. In rough, stony 
 channels of varying cross-section and small depth of flow 
 there is scarcely any difference between surface and mean 
 velocity.
 
 CORRECTION OF TEXT. 
 
 It is probable that no one ever turned his manuscript 
 over to the printer without a lively sense of its probable de- 
 merits when it shall stare one in the face from the printed 
 page. 
 
 The greater part of the book was written several years 
 ago. and portions of it were published in various journals in 
 1894 and 1895, While the ultimate conclusions reached and 
 formulas deduced, as appear in the text, are correct, yet some 
 of the reasoning is at fault, and not clear. The author would 
 be glad to stop the press and re -write the entire book after 
 having seen half the printed "proof," but it ie too late. 
 
 He must therefore resort to the alternative of writing 
 a criticism of his own work, and thus forstall the other 
 fellow. 
 
 The three important principles which are sought to be 
 established are:- 
 
 (I) That it is the effective value of the head or slope which 
 varies with some function of the diameter or hydraulic 
 mean radius, or mean depth, and not the coefficient 
 that varies. 
 
 (II) That for any given class of wet perimeter, or any given 
 degree of roughness, the coefficient is necessarily a con- 
 stant for all heads, slopes, velocities, diameters or mean 
 hydraulic radii. 
 
 (Ill) That the value of the coefficient is governed absolutely 
 by the roughness of wet perimeter, and by nothing else, 
 and is therefore an absolutely reliable index of the 
 roughness of perimeter. 
 
 FIRST PROPOSITION. 
 
 That the Effective Value of a Constant Head or Slope 
 Varies With Some Function d/d 8 , or /R 8 ) of the Diam-
 
 238 SULLIVAN'S NEW HYDRAULICS. 
 
 eter, or of the Hydraulic Mean Radius, and that the Coe* 
 ficient does not Vary with the Diameter or Hydraulic Mean 
 Radius at all. 
 
 If a series of pipes or open channels of exactly equal 
 roughness of perimeter, but of different diameters, or differ- 
 ent hydraulic mean radii, have exactly the same head or 
 slope per foot length, it ia well known that the pipe having 
 the greatest diameter, or the open channel having the great- 
 est hydraulic mean depth (R), will generate the greatest 
 velocity of flow, and the pipe having the least diameter, or 
 the open channel having the least mean hydraulic depth, will 
 generate the least velocity of flow. As all these pipes, or all 
 these channels, are of equal roughness, and all have exactly 
 equal heads or slopes, it is evident that the velocity would be 
 the same in each of them if the constant head or slope were 
 not made more effective with an increase in diameter or hy- 
 draulic mean depth. This being true, the next inquiry is, 
 what is the ratio of increase in the effectiveness of the given 
 head or slope as diameter or hydraulic mean depth increases? 
 
 To solve this problem we must appeal both to the laws 
 of friction or resistance, and of gravity. The resistance, or 
 head lost by resistance, will be directly as the roughness of 
 perimeter, and directly as the extent of perimeter, and also 
 directly as the square of the velocity. 
 
 As demonstrated in the text the wet perimeter or extent 
 ot friction surface, varies exactly with d or r. (See pp. 3 
 36,39,40.) 
 
 But if there were no friction or resistance, then the velocity 
 would be the same for the same actual slope regardless of the 
 value of d or r. While the friction surface and consequently 
 the absolute loss of head by resistance, increases only as d or 
 r, the cross section of the column of water increases as d 8 or 
 r, or as the sectional area. 
 
 The absolute head or slope therefore increases as the area, 
 or as d 8 or r 2 , while the absolute loss of head increases only 
 as d or r. It is evident then, that the absolute head or slope, 
 which varies as d 8 or r*, must be modified by the absolute 
 loss of head or slope which varies as d orr. Then the mean.
 
 SULLIVAN'S NEW HYDRAULICS. 239 
 
 head, or relative head, of all the^ particles of water in the 
 croBB section will vary with d* as modified byd, or with r 1 as 
 modified by r. As r* must not be increased by r, but must be 
 modified by i, we must reduce both d and d, or r and r 1 , in 
 the same ratio, in order to obtain a reducing or modifying 
 multiplier. To accomplish this result, we say that j/d bears 
 the same relation to d that d bears to d 2 , or that y/r bears 
 the same relation to r that r bears to r*. In other words to 
 maintain the ratio, of r to r*, or d to d, and at the same time 
 obtain a multiplier which will give the combined net effects 
 of d and d 2 . or r and r s , upon the value of H or S, it is neces- 
 sary to take the square root of both d and d 8 , or of both r 
 and r*. We then say that, relatively, the area or absolute 
 head (d" or r 2 ) varies with y'd*=J,or with ^/r*=r, while the 
 friction surface or absolute loss of head varies with -/d or y'r. 
 and consequently the relative mean head of all the particles in 
 the cross section will vary with the resultant of these two 
 effects, which will be as d^/d, or as R^/R. Thus we obtain 
 the modifying multiplier j/d, or y/r, while we maintain the 
 correct ratio of friction surface to area, or of loss of head 
 to gain in head as d or r varies for a constant head or 
 slope. 
 
 It is evident then that the constant head or slope be- 
 comes more effective or less effective as dy/d=>/d 8 , or \/r*, 
 increases or decreases. 
 
 SECOND PROPOSITION. 
 
 That for any Given Degree of Roughness of Wet Peri- 
 meter, the Coefficient is a Constant for all Heads, Slopes, 
 Velocities, Diameters or Hydraulic Mean Depths. 
 
 It was shown in the foregoing discussion that the effect- 
 ive value of the head or slope varies with y / d 3 ory / r 3 . By the 
 law of gravity the square of the velocity must always be pro 
 portional to the head or slope in any given pipe or channel, 
 or v a =2gH. As a necessary consequence of this law, it is 
 obvious that anything which affects the effective value of the 
 head or slope must at the same time equally affect the value 
 of v s .
 
 240 SULLIVAN'S NEW HYDRAULICS. 
 
 When we write m= ^3 and remember that the 
 
 effective value of S increases with i/r*, and that any increase 
 in the effective value of S must a'so increase v in the same 
 ratio, it is evident that as both dividend and divisor increase 
 aliKb the quoti?nt, m, will continue a constant for all values 
 of r, Sand v*. Their relation is such that we cannot increase 
 the effective value of S without also increasing the value of 
 v 1 in the same ratio. Hence m is necessarily a constant. 
 
 THIRD PROPOSITION. 
 
 That the Value ot the Coefficient is Governed Abso- 
 lutely by the Roughness ot the Wet Perimeter, and by 
 Nothing Else, and is Consequently an Absolutely Corrrect 
 Index of the Roughness. 
 
 When we inspect the formula for the coefficient, m= y8 
 
 it is apparent that m is simply the expression for the ratio of 
 effective slope to the square of the velocity. If the pipe or 
 channel is rough it will require a large value of the effective 
 slope, Sy/r 8 , to generate a small value of v*. Consequently 
 the ratio, m, of effective slope to v*,will be large in rough 
 channels. But if the channel is uniform in area, and smooth 
 then a small effective value of slope, Sy'r 3 , will generate a 
 relatively large value of v s , and hence the ratio, m, will be 
 small for smooth perimeters. As m is simply the expression 
 for this ratio, and as this ratio depends exclusively on the 
 roughness of perimeter, it is obvious that m will vary only 
 with the roughness. 
 
 The coefficient, C= A I y2 , is simply the square root of 
 
 VSyr 8 
 
 the reciprocal of m, and will consequently be a constant, like 
 m, for any given degree of roughness. But being the square 
 root of the reciprocal of m, C will vary with the roughness in 
 the exact opposite way from m that is, C will be large for 
 smooth perimeters and small for rough perimeters, while m 
 will be large for rough perimeters and small for smooth peri- 
 meters.
 
 SULLIVAN'S NEW HYDRAULICS. 241 
 
 As either of the coefficients vary only with the rough- 
 ness of wet perimeter, but is very sensitive to uny change in 
 roughness, it will be found that C will decrease as depth of 
 flow increases in all channels where the sides are rougher 
 than the bottom, and will increase with increase of depth of 
 flow in all channels where the sides are smoother and more 
 uniform than the bottom. In other words C will vary as the 
 mean of the roughness varies. See in this connection 13 
 page 58, and also p p. 27, 28, 29, 41, 42. 
 
 The best form of the formula for general use is, 
 
 This form of the formula also shows by mere inspection 
 that the effective value of S varies with ^/r*. 
 
 If the formula is written, v=C V r * l/S, the actual result 
 would be the same whether we say that C or \/S varies with 
 * V r 3 , but as C insists on being constant, it is evident that it 
 is the effective value of S that varies with v/r 8 , and the writer 
 desires to correct all statements to the contrary, It is some- 
 what absurd to insist that the coefficient is a constant and at 
 the same time to claim that it varies. The coefficient in our 
 formula can vary only as the average of roughness of the en- 
 tire wet perimeter. In the Chezy or Kutter form 
 of formula, the coefficient must vary as the roughness 
 and also as {/r. (See pp. 6, 7, 42, 44.) Hoping that this ab- 
 surdity is fully corrected in this explanatory note, and asking 
 pardon for having committed such a glaring fault, the author 
 commits the work to the hands of the profession with the 
 further hope that its merits may outweigh its faults. 
 
 MARVIN E. SULLIVAN. 
 Longmont, Colorado, 
 
 November, 1st, 1899.
 
 APPENDIX 1 
 
 Suggestions Relating to Weir and Orifice Measurements of 
 Flowing Water. 
 
 96 Remarks in Relation to Weir Coefficients. In the 
 
 third remark under Group No. 2 14, a general form of Weir 
 formula was suggested. It is not here intended to discuss the 
 well known theory of flow over measuring weirs with sharp 
 crests and full or partial contraction, any further than to 
 point out what the writer believes would be an improved 
 method of application which is believed would reduce the 
 errors in such determinations. From the nature of a meas- 
 uring weir it is impossible that the head or depth upon the 
 weir should ever be great, and consequently the velocities are 
 never very high, even in the cases where there is velocity of 
 approach. The amount of resistance to flow (being as v) 
 offered by the edges or perimeter of the notch is therefore a 
 small factor in the sum total of the coefficient of discharge. 
 The important factor is the coefficient of contraction. It is 
 usual to combine the coefficient of resistance with the coeffi- 
 of contraction and their product forms the coefficient of dis- 
 charge, which is usually assigned a mean value of .62. For 
 the reason that these two independent coefficients which 
 combined form the usual weir coefficient of discharge, do not 
 vary in the same manner under similar conditions, it has 
 been found necessary to find their combined value for each 
 given depth upon the weir and for each given length of notch, 
 and for each form of notch. If the length of weir notch re- 
 mains constant, a small change in depth upon the weir will 
 greatly affect the value of the combined coefficient, or coeffi- 
 cient of discharge. This cannot be attributed, except in very 
 small part, to the resistance at the edges of the notch, for 
 a small change in depth upon the weir does not greatly affect 
 the ratio of area to perimeter of the notch, which may be
 
 SULLIVAN'S NEW HYDRAULICS. 24:'. 
 
 regarded as a very small fractional length of open channel. 
 The effect upon the combined coefficient of varying the depth 
 upon the weir must therefore be accounted for in the factor 
 representing contraction of the discharge. It is evident from 
 the discussion of coefficients of flow in pipes and open chan- 
 nels ( 3 to 7) that the resistance to flow offered by the edges 
 of the notch will vary as H and \/r a . But the coefficient of 
 contraction which is the controlling and important factor has 
 no known relation to the value of r. The coefficient of contrac- 
 tion is affected greatly by the position of the weir, the depth 
 upon the weir, the distance from the crest to the bottom of the 
 channel, the distance between the shoulders of the notch and 
 the banks of the channel, and the velocity of flow through the 
 notch. 
 
 The experiments of Mr. J. B. Francis upon the same weir 
 of constant length, and where all conditions were constant ex- 
 cept the depth upon the weir, show that a change of depth 
 alone upon any given sharp crested weir of the usual form 
 will greatly affect the value of the coefficient of discharge, 
 and further show that the variations of the coefficient of con- 
 traction apparently follow no law. The coefficient will de- 
 crease as depth increases until a certain depth is reached 
 (depending upon the proportions of the notch) and then in- 
 creases with a further increase in depth up to a certain point 
 where it will again begin to decrease to a small extent until 
 it becomes nearly constant for great depths (if such were 
 practicable). 
 
 To make the usual weir coefficients apply with any de- 
 gree of accuracy is not a simple matter by any means, for the 
 conditions must be identical with those under which the 
 given coefficient was determined, The ratio of area of notch 
 to area of channel, the depth or height of overfall, the height 
 of crest above the bottom of the channel on the upstream side 
 of the weir, the position of the weir, whether at right angles 
 to the thread of the channel, and vertical, and rigidly straight 
 or allowed to bend under pressure, all affect the coefficient of 
 contraction, in addition to the influence of varying the depth 
 upon the weir. There are so many different influences bear-
 
 244 SULLIVAN'S NEW HYDRAULICS. 
 
 ing upon the coefficient of contraction that we can never be 
 certain of its value except under given favorable conditions 
 which do not often occur in actual practice. It is therefore 
 suggested that it would be safer practice where careful de- 
 terminations are to be made to avoid all these uncertainties 
 by suppressing all contraction. When this is done there re- 
 mains only the coefficient of resistance of the edges of the 
 notch to be dealt with, and the law of its variation is known. 
 In order to suppress contraction it is suggested that the 
 notch, whether rectangular, triangular or trapezoidal, should 
 be chamfered on the upstream side of the notch to the form 
 of the vena contracta^instead of placing the chamfered side 
 downstream. As illustrating the desultory manner or vari- 
 ation of the coefficient of discharge of a sharp crested weir 
 the first three columns I, H, and q, quoted by Fanning from 
 Francis' experimental data (Table 68, page 288 Water Supply 
 Engineering) are given in the following table, and the column 
 
 v was computed by the formula v=-^L, and from these data 
 
 the resulting values of m were computed, 
 
 The fundamental formula for flow over weirs with sharp 
 crests may be written 
 
 v= %-\l - > or v m %V 2gH=5.35 m^/H. 
 V m 
 
 Whence 
 
 m= 28 - 622 5H ^ . f m is U8ed as adiviBor> 
 
 v* 
 Or 
 
 m= - =- / v , if m is used as a multiplier. 
 
 5.35^ V 28.6225H ' 
 
 , or q=AreaX5.35 m^E
 
 SULLIVAN'S NEW HYDRAULICS. 
 TABLE. No. 41 Table of Weir Data. 
 
 245 
 
 L 
 
 Feet 
 
 H 
 
 Feet 
 
 Cubic 
 Feet 
 Sec. 
 
 A 
 
 Feet 
 
 V 
 
 Feet 
 Sec. 
 
 V 2 
 
 Feet 
 Sec. 
 
 R 
 Feet 
 
 Coefficient 
 "5.35T/H 
 
 9.997 
 9.997 
 9.997 
 9.997 
 
 0.62 
 
 S:i 
 
 1.56 
 
 16.2148 
 23.4304 
 45 5654 
 626019 
 
 6.198 
 7.997 
 12.496 
 15595 
 
 2.610 
 2.929 
 3.648 
 4014 
 
 6.8121 
 8.5790 
 13.2875 
 161122 
 
 0.5515 
 0.6900 
 1.000 
 
 1.188U 
 
 .6195 
 .6121 
 .6046 
 .6007 
 
 L= length in feet of notch. 
 H= depth in feet upon the weir. 
 q= cubic feet per second actually discharged. 
 A=LXH=Area in square feet=depth of water upon the 
 irXlength of notch. 
 
 v=-S-=mean velocity in feet per second. 
 R= hydraulic radius in feet of notch=-2_ 
 
 m=Coefficient of discharge: 
 
 v 
 5.35/H' 
 
 In these experiments the conditions all remained con* 
 stant except the depth H, upon the weir. 
 
 In the formula 
 v=5.35 m v/H 
 
 if we combine the value of m with the constant 5.35=%\/2g, 
 the following values of the coefficient C result:- 
 
 fl=.62, m=.6195, 5.35Xm=C=3.3143. 
 
 H=.80, m=.6121, 5.35Xm=C=3.2747. 
 
 H=1.25, m=.6096, 5.35Xm=C=3.2613. 
 
 H=1.56, m=.6007, 5.35Xm=C=3.2137. 
 
 Whence, 
 
 q=AreaX<V H=C(LX H )/ H 
 
 It is evident, even for different depths upon the same 
 weir, that if the constant value C=3.33 is used, the results 
 must be erroneous. Suppose the velocity of approach is consid- 
 erable, as on mountain streams, and that the weir notch (rec- 
 tangular) is nearly as long as the stream is wide, as often
 
 246 SULLIVAN'S NEW HYDRAULICS. 
 
 becomes necessary, then the eloping banks will approach the 
 submerged corners of the notch and greatly affect the coeffi- 
 cient of contraction, but to what extent, is merely surmise. 
 It is frequently the case that in order to stop the leaks under 
 and around the weir, earth, straw and brush are banked 
 against its upper side, thus training the flow upon the notch 
 and also preventing full contraction. This affects both the 
 real value of H or v z and the contraction of the discharge. 
 
 The range of experimental coefficients as determined by 
 Francis was very small, being mostly for weirs about 10 feet 
 length with depth upon the weir varying from about six 
 inches to 1.60 feet. The variation of the coefficient of contrac- 
 tion was found so fitful and irregular as the ratio of length to 
 depth was changed and with different depths upon any given 
 length of weir, that Mr. Francis advised caution in the appli- 
 cation of his formula and coefficients in cases not falling di- 
 rectly within the experimental conditions. It is assumed that 
 the contraction of the discharge over a sharp crested weir in 
 full contraction is analogous to the contraction of the jet 
 from a sharp edged orifice in thin plate. If the numerous 
 tables of experimental orifice coefficients determined under 
 various heads above the center, and under various proportions 
 of height to width of orifice be investigated, it will be found 
 that each form of orifice, or each ratio of height to width, 
 develops a distinct series of values of the coefficient as the 
 head varies. 
 
 The coefficient for an orifice will either decrease or in- 
 crease with the head upon the center in an irregular and 
 alternating manner which apparently depends upon the ratio 
 of height to length of orifice, as indicated in the following 
 table of experimental coefficients for square edged orifices in 
 thin plate and with full contraction, which were determined 
 by Poncelet and Lesbros. 
 
 Coefficients of discharge for square edged orifices in thin 
 plate and with full contraction.
 
 SULLIVAN'S NEW HYDRAULICS. 247 
 
 TABLE No. 42 Table from Ponoelot and Lesbros. 
 
 Dimensions of Orifice in Inches. 
 
 Head above 
 
 
 
 
 
 
 
 
 Center 
 
 8 X 8 
 
 6X8 
 
 4X8 
 
 3X8 
 
 2X8 
 
 1X8 
 
 0.4X8 
 
 In Inches 
 
 
 
 
 
 
 
 
 0.4 
 
 
 
 
 
 
 
 .70 
 
 0.8 
 
 
 
 
 
 
 .65 
 
 .69 
 
 1.0 
 
 
 
 
 
 
 .64 
 
 .68 
 
 1.5 
 
 
 
 
 
 .61 
 
 .64 
 
 .68 
 
 2.0 
 
 
 
 
 .60 
 
 .62 
 
 .64 
 
 .68 
 
 2.5 
 
 
 
 .59 
 
 .61 
 
 .62 
 
 .64 
 
 .67 
 
 3.0 
 
 
 
 .60 
 
 .61 
 
 .62 
 
 .64 
 
 .67 
 
 3.5 
 
 
 .57 
 
 .60 
 
 .61 
 
 .62 
 
 .64 
 
 .66 
 
 4.0 
 
 m 
 
 .58 
 
 .60 
 
 .61 
 
 .63 
 
 .64 
 
 .66 
 
 4.5 
 
 .56 
 
 .59 
 
 .60 
 
 .61 
 
 .63 
 
 .64 
 
 .66 
 
 5.0 
 
 .57 
 
 .59 
 
 .61 
 
 .62 
 
 .63 
 
 .64 
 
 .66 
 
 8.0 
 
 .59 
 
 .60 
 
 .61 
 
 .62 
 
 .63 
 
 .64 
 
 .65 
 
 12.0 
 
 .60 
 
 .60 
 
 .61 
 
 .62 
 
 .63 
 
 .63 
 
 .64 
 
 36.0 
 
 .60 
 
 .60 
 
 .61 
 
 .62 
 
 .62 
 
 .63 
 
 .63 
 
 60.0 
 
 .60 
 
 .60 
 
 .61 
 
 .61 
 
 
 .62 
 
 .62 
 
 120.0 
 
 .60 
 
 .60 
 
 .60 
 
 .60 
 
 '.60 
 
 .61 
 
 .61 
 
 TABLE No. 43 Table From George Rennie. 
 
 Head above 
 
 
 
 Center 
 
 Dimensions of Orifice. 
 
 Coefficient 
 
 In Feet 
 
 
 
 1.0 
 
 1 inch diameter, circular. 
 
 .633 
 
 1.0 
 
 1X1 inches, square. 
 
 617 
 
 1.0 
 
 2.0 
 
 1 square inch area, triangular. 
 1 inch diameter, circular. 
 
 !596 
 .619 
 
 2.0 
 
 1X1 inch, square. 
 
 .635 
 
 2.0 
 3.0 
 
 1 square inch area, triangular. 
 1 inch diameter, circular. 
 
 .577 
 .628 
 
 3.0 
 
 1X1 inch, square. 
 
 .606 
 
 3.0 
 4.0 
 
 1 square inch area, triangular. 
 1 square inch area, triangular. 
 
 .572 
 .53 
 
 4.0 
 
 1X1 inch, square. 
 
 .M
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE No. 44 Table from Gen. Ellis. 
 
 Coefficients of discharge for square edged.circular Orifices 
 in iron plate one half inch thick. 
 
 Head above 
 Center 
 In Feet 
 
 Diameter of Orifice in Feet. 
 
 Coefficient 
 
 2.1516 
 9.0600 
 17.2650 
 1.1470 
 10.8819 
 17.7400 
 1.7677 
 5.8269 
 9.6381 
 
 0.50 
 0.50 
 0.50 
 1.00 
 1.00 
 
 ft 
 
 2.00 
 2.00 
 
 .60025 
 .60191 
 .59626 
 .5T<73 
 .59431 
 .59994 
 .58829 
 .60915 
 .61530 
 
 TABLE No. 45. 
 
 Coefficients for square orifice 1X1 foot with curved en- 
 trance and discharge slightly submerged. (Gen. Ellis.) 
 
 Head above 
 Center 
 In Feet 
 
 Dimensions of Orifice. 
 
 Coefficient 
 
 3.0416 
 10.5398 
 18.2180 
 
 Square, 1X1 Feet 
 Square, 1X1 Feet 
 Square, 1X1 Feet 
 
 .95118 
 .9*246 
 .94364 
 
 In these last experiments if the orifice had been in the 
 'orm of the vena contracta, and the discharge had been en- 
 tirely free instead of being partially under water, it is proba- 
 ble that the coefficient would have reached .98, and would 
 not have been affected in any manner except by the slight re- 
 sistance of efflux offered by the perimeter of the orifice. The 
 curving entrance had almost suppressed all contraction of 
 the jet in the above experiments. 
 
 The object of these tables and suggestions is to point out 
 the fact that all these uncertainties in the application of weir 
 and orifice coefficients may be easily avoided by so chamfer- 
 ing the inner edges of the weir notch or orifice as to make 
 them conform as nearly as possible to the form of the vena 
 contracta. 
 
 In many cases of the practical application of the ordinary
 
 SULLIVAN'S NEW HYDRAULICS. 249 
 
 weir and orifice coefficients the conditions are such that com- 
 plete contraction cannot be obtained. In almost any case it 
 is much more convenient to suppress all contraction than to 
 obtain complete contraction, and when contraction is sup- 
 pressed there is no limit to the range of the remaining coeffi- 
 cient which should be determined in the same manner as the 
 value of m for pipes or open channels. When contraction is 
 suppressed (as pointed out 83). Then for a submerged 
 orifice. 
 
 v =A /IZL=8.025 J3Z1 ; m- 6 ^ H 
 
 q =AreaX8.025j H * /r> = 
 
 v m 
 
 And for weirs, 
 
 28.6225 H r/r 
 = 
 
 And. 
 
 m 
 
 When the numerical value of m is ascertained for any 
 thickness of plate it will apply to any shape or size of orifice or 
 
 weir notch, and the square root of its reciprocal^/ , may 
 
 then be taken and combined with the constant 8.025 or 5.35 as 
 the case may be. 
 
 APPENDIX II. 
 
 Useful Data and Tables Relating to Water Works and the 
 Water Supply of Cities and Towns. 
 
 97. Purposes to Which City Water is Applied. 
 
 In planning a water works system for town or city sup- 
 ply, the nature of the chief occupation of the inhabitants 
 must be considered as well as the number of inhabitants at
 
 250 SULLIVAN'S NEW HYDRAULICS. 
 
 present, and the probable increase in population within the 
 next fifteen or twenty years. The purposes to which city 
 water will be applied will depend upon the humidity of the 
 climate. In the arid portion of the West the city water is 
 demanded for all purposes to which water is applied, such as 
 irrigation of lawns and gardens, and shade trees, street 
 sprinkling, carriage washing, watering horses and cows, 
 water for steam boilers and hydraulic motors, hydraulic lifts 
 or elevators, steam laundries, drinking fountains, ornamental 
 fountains, manufacturing purposes, extinguishment of fires 
 and ordinary household uses. Where manufacturing is the 
 chief business of a town the demand for water will be two or 
 three hundred per cent greater than in towns of equal size and 
 in like climates which are not manufacturing centers. In 
 some manufacturing towns situated on rivers the factories 
 have their own private water supply, and in such cases the 
 city water works is called upon only for water for ordinary 
 purposes. The coast states, and the Eastern and Southern 
 states, have frequent and large rainfalls and except at manu 
 facturing centers, the city water works in these states will 
 not be called upon except for ordinary purposes. In the arid 
 portion of the West the demand on the city water supply is 
 from fifty to one hundred per cent greater than in towns of 
 like population in other parts of the United States. 
 
 In non-manufacturing towns in such climates as in Ar- 
 kansas, Mississipi and Louis&na, the demand for all purposes 
 will not exceed 60 gallons per capita per 24 hours, while in 
 Colorado and other arid states the demand in small non- 
 manufacturing towns is from 110 to 150 gallons per capita 
 per 24 hours, and in older and larger cities the demand is 
 from 150 to 200 gallons per capita. Should an essentially 
 manufacturing city spring up in the arid West, it is probable 
 that the demand for water would reach 400 gallons per capita 
 per 24 hours. 
 
 98. Quantity of Water per Capita Required The 
 
 quantity of water required per capita per 24 hours for the 
 .present given number of inhabitants, and for all purposes,
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 251 
 
 depends upon the bection of the country and the chief occu- 
 pation of the inhabitants, as just pointed out. But in plan- 
 ning a water supply, the very rapid increase in the popula- 
 tion of towns and cities in the United States must be amply 
 allowed for. The U. S. census of 1890 shows that our popu- 
 lation is f aet gathering into the towns and cities. The popu- 
 lation of towns and cities, taken collectively, throughout the 
 United States, increa sed by 61.10 per cent from 1880 to 1890, 
 while the total population of town and country increased 
 only 24.85 per cent. The following table is valuable in this 
 connection. 
 
 TABLE No. 46. 
 
 Growth of population in cities and in the United States. 
 
 Cen- 
 sus 
 Year 
 
 Total Pop. 
 U.S. 
 
 Population 
 in Cities 
 
 Increase 
 in total 
 pop. per 
 cent 
 
 Per cent 
 total pop 
 in citie 
 
 of the 
 living 
 s. 
 
 1800 
 
 5,308,483 
 
 210,873 
 
 
 
 
 1810 
 
 7,239,881 
 
 356,920 
 
 36.28 
 
 4.93 
 
 
 1820 
 
 9,633,822 
 
 475,135 
 
 33.66 
 
 4.93 
 
 
 1830 
 
 12,866020 
 
 1,864509 
 
 32.51 
 
 6.72 
 
 
 1840 
 1850 
 
 17,069,453 
 23191,876 
 
 1,453.994 
 2,897,586 
 
 32.52 
 35.83 
 
 8.52 
 12.49 
 
 
 1860 
 
 31,443,321 
 
 5,072,256 
 
 35.11 
 
 16.13 
 
 
 1870 
 1880 
 
 38,558,371 
 50,155,783 
 
 8,071,875 
 11,318,547 
 
 22.65 
 30.08 
 
 20.93 
 22.57 
 
 
 1890 
 
 62,622,250 
 
 18,238,672 
 
 24.85 
 
 29.12 
 
 
 99. Table Showing the Consumption of Water Per 
 Capita Per 24 Hours in Various Cities and Towns, and 
 the Cost to the Consumer Per 1,000 Gallons, and the in- 
 crease In Population in Each City in 20 Years. 
 
 The foregoing table shows that the general average in- 
 crease of population in the towns and cities of the United 
 States was 61.10 per cent from 1880 to 1890. But the rate of 
 increase varies in different sections of the country and 
 also in different classes of cities and towns. The railroad 
 and general manufacturing centers increase most rapidly in 
 all parts of the country, while tho general growth of all cli 
 of towns increases most rapidly in the Western states.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE No. 47. 
 
 
 
 
 
 
 a 
 
 P 
 
 
 
 
 
 
 cCt 
 
 So 
 
 
 
 1 
 
 l-H 
 
 1 
 
 II 
 
 11 
 
 s 
 
 
 
 
 i 
 
 
 
 gg 
 
 s 
 
 
 
 
 a 
 
 a 
 
 
 
 00 
 
 O 
 
 <3 
 
 6 
 
 S 
 
 o 
 
 OS 
 
 Alabama 
 
 Birmingham 
 
 
 
 400 
 
 26,241 
 
 155 
 
 8c to 30 c 
 
 Gala. 
 
 Los Angeles 
 
 5,758 
 
 11,183 
 
 50,394 
 
 175 
 
 20c 
 
 Colo. 
 
 Denver 
 
 4,759 
 
 35,629 
 
 106,670 
 
 200 
 
 
 Conn. 
 
 New Britain 
 
 9840 
 
 11,800 
 
 19,010 
 
 87 
 
 10 c 
 
 Conn. 
 Conn. 
 
 Norwich 
 Hartford 
 
 16,653 
 37,180 
 
 15.112 
 42,015 
 
 16,195 
 53,182 
 
 50 
 125 
 
 15 c ;o 30 c 
 7Hcto30c 
 
 Conn. 
 
 New Haven 
 
 50840 
 
 62882 
 
 85,981 
 
 130 
 
 fV4cto30o 
 
 Georgia 
 Georgia 
 
 Atlanta 
 Augusta 
 
 21,789 
 15,389 
 
 37,409 
 21,891 
 
 65.515 
 33,1' 2 
 
 164 
 106 
 
 10 c 
 
 Georgia 
 
 Macon 
 
 10,810 
 
 12,479 
 
 22,698 
 
 70 
 
 6 c to 30 c 
 
 Illinois 
 
 Aurora 
 
 11.162 
 
 11,873 
 
 19,634 
 
 60 
 
 
 Illinois 
 Illinois 
 
 as? 80 
 
 298,977 
 5441 
 
 503,185 
 
 8,787 
 
 1,098,576 
 17,429 
 
 131& 
 70 
 
 8 c to 10 c 
 3c to8c 
 
 Illinois 
 
 Streator 
 
 1,486 
 
 5,157 
 
 6.671 
 
 120 
 
 10 c to25c 
 
 Illinois 
 Illinois 
 Indiana 
 
 Freeport 
 LaSalle 
 Indianopolis 
 
 7,889 
 5,200 
 48,224 
 
 8,516 
 
 7,847 
 75,056 
 
 10,159 
 11,610 
 107,445 
 
 46 
 70 
 90 
 
 10 c to 50 c 
 8 c to \~> c 
 6 c to 30 o 
 
 Indiana 
 Iowa 
 
 Richmond 
 Cedar Rapid* 
 
 9,445 
 5,940 
 
 12,472 
 10,104 
 
 16,845 
 17,997 
 
 74 
 68 
 
 5 c to 25 c 
 lOctoSOc 
 
 Iowa 
 
 Sioux City 
 
 3,401 
 
 7,366 
 
 37,862 
 
 43 
 
 10 c to 25 c 
 
 Iowa 
 
 Des Moines 
 
 5,241 
 
 22408 
 
 50,067 
 
 43 
 
 20cto 40 o 
 
 Kansas 
 
 Atchison 
 
 
 15,105 
 
 14,122 
 
 90 
 
 10 c to 50 c 
 
 Kansas 
 
 Minneapolis 
 
 
 
 2,000* 
 
 200 
 
 35 c 
 
 Kansas 
 
 Arkansas Citj 
 
 
 
 3,347 
 
 46 
 
 lOcto 40c 
 
 Ky. 
 
 Louisville 
 
 100,752 
 
 123,758 
 
 161,005 
 
 JO 
 
 6 c to 15 c 
 
 Ky. 
 
 Lexington 
 
 14.801 
 
 16,656 
 
 22,355 
 
 40 
 
 10 c to 25 c 
 
 Ky. 
 
 Frankfort 
 
 5,396 
 
 6.958 
 
 8,500 
 
 100 
 
 6 c to 15 c 
 
 Ky. 
 
 Fulton 
 
 
 
 4,500* 
 
 200 
 
 
 Md. 
 
 Hagerstown 
 
 5.779 
 
 6,627 
 
 11,698 
 
 115 
 
 8 c to 40c 
 
 Mass. 
 
 Adams 
 
 12,090 
 
 5,591 
 
 9,206 
 
 84 
 
 
 Mass. 
 
 Fall River 
 
 26.766 
 
 48,961 
 
 74,351 
 
 28 
 
 
 Mass. 
 
 Holyoke 
 
 10,733 
 
 21,915 
 
 35,528 
 
 78 
 
 5 c to 15 c 
 
 Mass. 
 S ass. 
 
 Lowell 
 New Bedford 
 
 40,928 
 21,320 
 
 59,475 
 26845 
 
 77,605 
 40,705 
 
 75 
 113 
 
 2 1/, ctolSc 
 
 ass. 
 
 Newton 
 
 12,825 
 
 16,995 
 
 24,357 
 
 53 
 
 12cto35o 
 
 Mass. 
 Mich. 
 
 Springfield 
 Battle Creek 
 
 26,703 
 
 5,838 
 
 33,340 
 7,063 
 
 44,164 
 13,190 
 
 87 
 31 
 
 30c 
 
 Mich. 
 
 Bay City 
 
 7,064 
 
 20,693 
 
 27,836 
 
 80 
 
 5 c to 10 c 
 
 Mich. 
 
 Detroit 
 
 79,577 
 
 116,340 
 
 205,669 
 
 140 
 
 3%c 
 
 Mich. 
 
 Miss. 
 
 Sagnaw 
 Vicksburg 
 
 7,460 
 12,443 
 
 10,525 
 11,814 
 
 46,215 
 13,298 
 
 100 
 43 
 
 6 c to 11 c 
 6 c to 35 c 
 
 Missouri 
 
 
 5,555 
 
 6.522 
 
 21.842 
 
 SO 
 
 25 c 
 
 Missouri 
 
 sfEolis 
 
 310,864 
 
 350,518 
 
 460,357 
 
 75 
 
 10 c to 30 c
 
 SULLIVAN'S NEW HYDRAULICS. 
 TABLE No. 47 CONTINUED. 
 
 253 
 
 
 
 
 
 
 !i 
 
 |l 
 
 
 
 S 
 
 
 
 ot 
 
 
 OQ 
 
 
 
 00 
 
 00 
 
 CO 
 
 (2 
 
 O 
 
 
 
 
 p 
 ' 
 
 i 
 
 a 
 
 at 
 
 P 
 
 0) 
 
 1> 
 
 s * 
 
 OQ 
 
 
 
 6 
 
 Q 
 
 
 
 
 i* 
 
 Missouri 
 N. Hamp 
 
 Butler 
 Nashua 
 
 10,543 
 
 13 397 
 
 4,000* 
 19,266 
 
 25 
 150 
 
 6cto60c 
 10 c to 20 o 
 
 N. Hamp 
 
 Manchester 
 
 23,536 
 
 32,630 
 
 43,983 
 
 50 
 
 20 c 
 
 N.' Y. 
 
 Bayonne 
 Portland 
 
 3.834 
 3066 
 
 9.372 
 4050 
 
 18,996 
 8,561 
 
 7? 
 90 
 
 13 & c-23*c 
 
 10 c 
 
 N . Y. 
 
 Elmira 
 
 15863 
 
 20541 
 
 28.070 
 
 86 
 
 1% c to 45 o 
 
 N . Y. 
 
 Kingston 
 
 6,315 
 
 18,344 
 
 21,181 
 
 80 
 
 8cto30c 
 
 N. Y. 
 
 Olean 
 
 
 
 7,3S8 
 
 75 
 
 10 c to 40 c 
 
 N. Y, 
 
 Syracuse 
 
 43051 
 
 51.792 
 
 87.877 
 
 300 
 
 6 c to 25 c 
 
 N. Y. 
 N. Y. 
 N. Y. 
 
 Brooklyn 
 \ewYorkCity 
 
 396,099 
 12.733 
 
 942,292 
 
 566,663 
 
 18,892 
 1,206,299 
 
 804,377 
 31.942 
 1,513.501 
 
 100 
 70 
 92 
 
 IVt C-11& o 
 4 c to 25 c 
 
 Ohio 
 
 Dayton 
 
 30,473 
 
 33678 
 
 58,868 
 
 53 
 
 *c 
 
 Ohio 
 
 Findlay 
 
 3,315 
 
 4.633 
 
 18,672 
 
 48 
 
 6 c to 12 c 
 
 Ohio 
 
 Oberlin 
 Sanduskj 
 
 13,000 
 
 15,838 
 
 4,000 
 19,234 
 
 20 
 154 
 
 30 c 
 4 c to 15 c 
 
 Ohio 
 Ohio 
 Ohio 
 
 Springfield 
 Toledo 
 Cincinnati 
 
 12,652 
 31,584 
 216.239 
 
 20,730 
 50.137 
 255,139 
 
 32,135 
 82,652 
 296.309 
 
 90 
 70 
 124 
 
 10 c to 40 c 
 SotolOc 
 17 c 
 
 Oregon 
 Penn. 
 
 Salem 
 Ml City 
 
 2276 
 
 7,315 
 
 10,943 
 
 100 
 230 
 
 15 c to 25 c 
 6c to25c 
 
 Penn. 
 Penn. 
 
 tfcKeesport 
 Williamsport 
 
 2,523 
 16,030 
 
 8,212 
 18,934 
 
 20,711 
 27,107 
 
 110 
 
 200 
 
 4!4cto30c 
 SctolOc 
 
 Penn. 
 
 ^larrisburg 
 
 23,104 
 
 30,762 
 
 40,164 
 
 130 
 
 2!4 c to lOc 
 
 Penn. 
 
 Philadelphia 
 
 674 022 
 
 847.170 
 
 1,046.252 
 
 143 
 
 \o 
 
 R I. 
 
 iVoonsocket 
 
 11527 
 
 16,050 
 
 20,759 
 
 22 y* 
 
 10 c to 80 c 
 
 Texas 
 
 Pawtucket 
 Laredo 
 
 6,619 
 2,046 
 
 19,0 
 3,321 
 
 2>, 502 
 11,313 
 
 79 
 150 
 
 tic. to 30 c 
 60 c 
 
 Texas 
 
 ?ort Worth 
 
 
 
 6,663 
 
 20.725 130 
 
 20 c to 65 o 
 
 Va. 
 
 Richmond 
 
 51.038 
 
 66,600 
 
 80,388 ' 151 
 
 7 c to 15 o 
 
 *Estimated Population. 
 
 The above table will be useful in determining the quan- 
 tity of water required per 24 hours per person, and in de- 
 termining what extia capacity of reservoirs and conduits 
 should be provided for the increase in population during the 
 coming 20 years. The capacity of a water supply system 
 should not be based on the present number of inhabitants, 
 but upon the probable number of inhabitants 20 years hence.
 
 254 SULLIVAN'S NEW HYDRAULICS. 
 
 What the increase of population will be in any given town or 
 city within any given number of years is a matter which 
 must be considered in the light of the local conditions and 
 surroundings of each given town or city. There are very 
 few cities or towns in the United States which do not increase 
 by 50 per cent within 20 years, and some increase by from 300 
 to 600 per cent within ten years. The general average increase 
 of population in all cities and towns in the United States for 
 the 10 years, 1880-1890, was 61.10 per cent. 
 
 100.~Formulas and Tables for Determining the Diam- 
 eter of the Conduit or Pipe Required to Convey any 
 Given Number of Gallons Per 24 Hours. -When the total 
 supply of water in gallons per 24 hours has been decided 
 upon, then the required diameter in feet of the circular brick 
 conduit or pipe, or other circular water way, may be at once 
 found by the formula 
 
 In this formula the value of m varies with the class or 
 roughness of the internal circumference of the waterway, 
 and the value of m must be in terms of diameter in feet. 
 The value of m for any class of wet perimeter will be found 
 by referring to the different groups of pipes and channels. If 
 the value of m, when found, is in terms of R in feet, it may 
 be converted to terms of d in teet as shown at section 10. 
 
 In the above formula q=cubic feet per second, and S 
 
 TT 
 
 =the sine of the inclination of the waterway= -j-. 
 
 For a constant degree of roughness of perimeter, the 
 
 11 /m 2 
 value of ~yf ~^^ is a constant, and the formula may be 
 
 simplified accordingly. Thus, if we are going to adopt a
 
 SULLIVAN'S NEW HYDRAULICS. 255 
 
 double riveted asphaltum coated Bteel pipe, then m=.00033, 
 
 11 /m 8 
 and j/ ogQg =0.2541, and the formula for any pipe in this 
 
 11 / Q 4 
 class reduces to d=.2541-| / / -g^. If we adopt an ordinary 
 
 uncoated, cast iron pipe, then m=.0004, and the formula re- 
 duces to 
 
 d= l 
 
 If the pipe is to convey water from the distributing res- 
 ervoir to the street mains, its capacity or diameter should be 
 such as to enable the pipe to maintain a given pressure in Ibs. 
 per square inch at the point of juncture with the street sys- 
 tem while it is supplying the given quantity of water in cubic 
 feet per second. It is also well to remember that the total 
 supply per 24 hours is usually drawn between 6 o'clock a. m 
 and 9 o'clock p. m., and for this reason the city supply pipe 
 leading from the distributing reservoir to the city must have 
 such diameter as will pass the entire 24 hours' supply within 
 12 hours' time, and also maintain a given pressure while so 
 discharging. In other words this pipe must carry a given 
 quantity of water within a given time with a given loss of 
 pressure or head at a given point. The formula for finding 
 the required diameter to carry a given quantity with a given 
 or pre-determined loss of head has already been given and 
 discussed . (See 64, 63.) The following tables will greatly 
 facilitate all such calculations, and show at once the value of 
 q, or cubic feet per second, corresponding to any supply in 
 gallons per 24 hours. (See also 102) .
 
 256 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE No. 48.* 
 
 Gallons pei 
 24 hours= 
 
 Cub feet 
 per sec- 
 ond q 
 
 Loga 
 rithm 
 of q 
 
 Value of q 4 
 
 l. 
 
 .00000154667 
 
 6.189397 
 
 .000,000,000,000,000,000,0 0,005,722,563,8T)0,675 
 
 10. 
 
 .0000154667 
 
 5.189397 
 
 .000,000,000,000,000,000,057,225,638,506,75 
 
 100. 
 
 .000154667 
 
 4.189397 
 
 . 030,000,000,000,0 X),572,256,335.067 .5 
 
 1,000. 
 
 .00154667 
 
 3.189397 
 
 .000,000,000,005,722,563,850,675 
 
 10,000. 
 
 .0151667 
 
 2.189397 
 
 000,000,057,225,638,506,75 
 
 100,000 
 
 .154667 
 
 1.189397 
 
 .000,572,256,335,067,5 
 
 1,000,000. 
 
 1.54667 
 
 0.189397 
 
 5.722,568,850,675 
 
 10,000,000. 
 
 15.4667 
 
 1.189297 
 
 57,225.638,506,75 
 
 100,000,000. 
 
 ir,4.667 
 
 2.189397 
 
 572,256,385.067,5 
 
 1,000,000,000. 
 
 1546.67 
 
 1. 189397 
 
 5,722,563,850,675.034,2 
 
 10.000,000,000. 
 
 15466.70 
 
 4.189397 
 
 57,225,638,506,750,342.032,1 
 
 100,000,000000. 
 
 154667.00 
 
 5.189397 
 
 572,256,385,067,503,420,321 .00 
 
 *One cubic foot=7.48 gallons. One gallon=23l cubic 
 inches. 
 
 TABLE No. 49. 
 
 Gal. per 
 24 hours 
 
 Cub. feet 
 per sec- 
 ond q 
 
 Loga- 
 rithm of 
 
 q 
 
 Value of q 4 
 
 
 10 
 
 .0000154667 
 
 5.1893 r 8 
 
 .000,000,000,000,000,000,057,225,638,508.75 
 
 
 20 
 
 .0000309334 
 
 5.490427 
 
 .000,000,000,000,000,000,915,720,15 
 
 
 25 
 
 .00003866675 
 
 5.587337 
 
 .000,000,000,000,000,002,235,678,513 
 
 
 30 
 
 .0000464001 
 
 5.666518 
 
 .000,000.000,000,000,004,63) 
 
 
 40 
 
 .0000618668 
 
 5.791458 
 
 . 000,000,000,000,000,014,65 
 
 
 50 
 
 .0(00773835 
 
 5.888367 
 
 . 000,000,000,000,000,035,77 
 
 
 60 
 
 .0000928002 
 
 5.967549 
 
 . 000,000,000,000,000,074,26
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE No. 49 Continued. 
 
 257 
 
 Gal. per 
 24 houre 
 
 Cub. feet 
 per sec- 
 ond q 
 
 Loga- 
 rithm of 
 
 q 
 
 Value of q*. 
 
 70 
 
 .00 1082669 
 
 4.034495 
 
 .000,000,000,000,000.137,398,72 
 
 80 
 
 .0001237336 
 
 4.092488 
 
 .000,000,000,000,000,234,396,1 
 
 90 
 
 .0001392003 
 
 4.1436399 
 
 .000,000,000,000,000,375,457,278 
 
 100 
 
 .000154667 
 
 4.189398 
 
 .000,000,000,000,000.572,^56,385,067.5 
 
 200 
 
 .000309334 
 
 4.490427 
 
 .000,000,000,000,009,157,201,5 
 
 250 
 
 .0003866675 
 
 4.587337 
 
 .000,000,000,000,022,356,735.513 
 
 300 
 
 .000464001 
 
 4.666518 
 
 . 000,000,000,000,046,350 
 
 400 
 
 .000618668 
 
 4.791458 
 
 . 000,000,000,000,146,500 
 
 500 
 
 .000773335 
 
 4.888367 
 
 . 000,000,000,000,357,700 
 
 600 
 
 .000928002 
 
 4.967549 
 
 . 000,000,000,000,742,600 
 
 700 
 
 .001082669 
 
 3.034496 
 
 .000,000,000,001,373,987,200 
 
 800 
 
 .001237336 
 
 3.092488 
 
 .000,OOU,000,002,343,96l,00 
 
 900 
 
 .001392003 
 
 8.1436399 
 
 .000,000,000,003,754,572,780 
 
 1,000 
 
 .00154667 
 
 3.189398 
 
 .000,000,000,005,722,563,850,675 
 
 2,000 
 
 .00309334 
 
 3.493427 
 
 .000,000,000,091,572,015 
 
 2,500 
 
 .003866675 
 
 3.587337 
 
 .000,000,000,223,-567,351,3 
 
 3,000 
 
 .00464001 
 
 3.666518 
 
 .000,000,000,463,5 
 
 4,000 
 
 .00618668 
 
 3.791458 
 
 .000,000,001,465 
 
 5,000 
 
 .00773335 
 
 3.888367 
 
 .000,000,003,577 
 
 6,000 
 
 .00928002 
 
 3.967549 
 
 .000,000,007,426 
 
 7,000 
 
 .01082669 
 
 2.034495 
 
 .000,000,013,739,872 
 
 8,000 
 
 .01237336 
 
 2.092488 
 
 .000,000,023,439,610 
 
 9,000 
 
 .01392003 
 
 2.5745399 
 
 .000,000,037,545,727,800 
 
 10,000 
 
 .0154667 
 
 2.189398 
 
 .000,000,057,225,638,506,750 
 
 20,000 
 
 .0309334 J2.490427 
 
 .000,000,915,720,015 
 
 25.000 
 
 .03866675 
 
 2.587337 
 
 .000,002,223,567,351,3 
 
 30,000 
 
 .0464001 
 
 2.666518 
 
 .000,004,635
 
 258 SULLIVAN'S NEW HYDRAULICS 
 
 TABLE No. 49 Continued. 
 
 Gal. per 
 24 hours 
 
 Cub. feet 
 per sec- 
 ond q 
 
 Loga- 
 rithm of 
 
 q 
 
 Value of q* 
 
 40,000 
 
 .0618668 
 
 2.791458 
 
 .000,014,650 
 
 50,000 
 
 .0773335 
 
 2.888367 
 
 .000,035,770 
 
 60.000 
 
 .0928002 
 
 2.967549 
 
 .000,074,260 
 
 70,000 
 
 .1082669 
 
 1.034495 
 
 .000,137,398,720 
 
 80,000 
 
 .1237336 
 
 1.092488 
 
 .000,234,396,100 
 
 90,000 
 
 .1392003 
 
 1.5745399 
 
 .000,375,457,278 
 
 100000 
 
 .154667 
 
 1.189398 
 
 .000,572,256,385,067,5 
 
 200,000 
 
 .309334 
 
 1.490427 
 
 .(09,157,201,5 
 
 250,000 
 
 .3866675 
 
 1.587337 
 
 .022,356,735,130 
 
 300,000 
 
 .464001 
 
 1.666518 
 
 .046,35 
 
 400,000 
 
 .618668 
 
 1.791458 
 
 .146,5 
 
 500,001 
 
 .773335 
 
 1.888367 
 
 .357,7 
 
 600,000 
 
 .928002 
 
 1.967549 
 
 .742,6 
 
 700000 
 
 1.082669 
 
 0.034495 
 
 1.373,987,2 
 
 800,000 
 
 1.237336 
 
 0.092488 
 
 2.343,961 
 
 900,000 
 
 1.392003 
 
 0.1436399 
 
 3.754.572,78 
 
 1,000,000 
 
 1.54667 
 
 0.189398 
 
 5.722,563,850,675 
 
 2,000,000 3.09334 
 
 0.490427 
 
 91.572,015 
 
 2,500,000 
 
 3.866675 
 
 0.587337 
 
 223.567,351,3 
 
 3,000,000 
 
 4.64001 
 
 0-666518 
 
 463.500 
 
 4,000,000 
 
 6.18668 
 
 0.791458 
 
 1465.00 
 
 5,000000 
 
 7.73335 
 
 0.888367 
 
 3577.00 
 
 6,000,000 
 
 9.28002 
 
 0.967549 
 
 7426.00 
 
 7,000,000 
 
 10.82669 
 
 1.034495 
 
 13939.872 
 
 8,000.000 
 
 12.37336 
 
 1.092488 
 
 23439.61 
 
 9,000,000 
 
 13.92003 
 
 1.1436399 
 
 37545.727,8
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE 49 Continued. 
 
 259 
 
 Gal. per 
 24 hours 
 
 Cub. feet 
 per sec- 
 ond q 
 
 Loga- 
 rithm of 
 
 q 
 
 Value of q*. 
 
 10.000,000 
 
 15.4667 
 
 1.189398 
 
 57225.638,506,75 
 
 20,000,000 
 
 30.9334 
 
 1.490427 
 
 915720.16 
 
 25,000,000 
 
 38.66675 
 
 1.587337 
 
 2235673.513,03 
 
 30,000,000 
 
 46.4001 
 
 1.666518 
 
 46350' 0.00 
 
 40,000000 
 
 61.8668 
 
 1.791458 
 
 14650000.00 
 
 50,000,000 
 
 77.3335 
 
 1.888367 
 
 35770000.00 
 
 60,000,000 
 
 92.8002 
 
 1.967549 
 
 74260000.00 
 
 70000,000 
 
 108.2669 
 
 2.034495 
 
 137398720.00 
 
 80,000,000 
 
 123.7336 
 
 2.092488 
 
 234396100.00 
 
 90.000,000 
 
 139.2003 
 
 2.1436399 
 
 375457278.00 
 
 100000,000 
 
 154.667 
 
 2.189398 
 
 572256385.067,5 
 
 200,000,000 
 
 309.334 
 
 2.490427 
 
 9157201500.000 
 
 250,000,000 
 
 386.6675 
 
 2.587337 
 
 22356735130.30 
 
 101. To Find the Diameter in Feet of a Circular Con- 
 duit or Pipe With Free Discharge, as From One Reservoir 
 Into Another, which is required to Discharge a given quan- 
 tity in Cubic Feet Per Second, the Total Head or ths Slope 
 Being Known: 
 
 The general formula for finding the required diameter in 
 feet will be 
 
 Simplifying the formula as pointed out heretofore (100) 
 and for the following classes or degrees of roughness of peri- 
 meter we have, 
 
 (1) For ancoated clean cast iron pipe,m=.0004, and
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 (2) For uncoated steel or wrought iron, m=.00038, and 
 
 (3) For uncoated wooden stave pipe, made of dressed 
 hard wood, and closely jointed, m=.00048, and 
 
 (4) For cement mortar lined pipe, one third sand and two 
 thirds cement, m-. 000424, and 
 
 (5) For riveted pipe, thoroughly dipped and coated with 
 asphaltum and crude petroleum, m=. 000325, and 
 
 (6) For cast iron or welded pipes thoroughly asphaltum 
 coated and carefully laid and jointed, m=r.000305, and 
 
 For brick perimeters see 24. Always make an extra al- 
 lowance in the diameter of pip > or conduit for future deteri- 
 oration and for deposits. 
 
 102. To Find the Diameter in Feet of a Circular Con- 
 duit or pipe which is Required to carry a Given Quantity in 
 Cubic Feet Per Second to a Given Point and Maintain a 
 Given Head or Pressure at That Point while Delivering the 
 Required Quantity: 
 
 This formula is very important in designing power mains 
 for water wheels.'in which it is required to maintain a given 
 pressure or head at the base of the nozzle which discharges 
 upon the wheel or motor It applies equally well to hydraulic 
 giants used in placer mining, and to fire hose with nozzle at- 
 tached, and to all other cases where the discharge is partially
 
 SULLIVAN'S NEW HYDRAULICS. 26l 
 
 throttled, as in the case of a supply pipe leading from the 
 distributing reservoir of a water works system to the street 
 mains. In the latter case it is desirable to so proportion the 
 diameter that it will convey the required quantity of water 
 and at the some time maintain not less than a given head 
 pressure at the point of its juncture with the street mains. 
 The general formula will be 
 
 In which, 
 
 h" = total head in feet to be lost in friction in the length I. 
 
 n=coefficient of resistance, and varies with different 
 classes of wet perimeter. 
 
 Simplifying the formula for given classes of perimeters 
 as heretofore pointed out ( 64, 68) and 
 
 (1) For uncoated clean cast iron, n=.0003938. and 
 
 (2) For uncoated clean steel orwrought iron, n=.00037411 
 and 
 
 (3) For uncoated wooden stave pipe, made of dressed 
 hard wood and closely jointed, n=.00047256, and 
 
 (4) For cement mortar lined pipe, one-third sand and 
 two-thirds cement, n=.0004175, and 
 
 d= .2653 11
 
 262 SULLIVAN'S NEW HYDRAULICS. 
 
 (5) For riveted pipe, thoroughly dipped and coated with 
 asphaltum and crude petroleum, n=.00032, and 
 
 (6) For cast iron and welded pipes, thoroughly coated 
 with asphaltum and oil, and carefully laid and jointed, n= 
 .00030, and 
 
 REMAKK. For any given class of perimeter n=mX-9845, 
 and m=-qgT^, and the difference in value between 
 
 H/' m* 11 /~~n*~ 
 y ogQc and ./ qgnc for any given roughness is equal .0008. 
 
 That is to say, 
 
 y 1 OQQ5 is .0008 less than the corresponding ualue of 
 
 n / m 
 ^ ^805- 
 
 11 / m*~ 11 /~n*~~ 
 
 If ,/ -oon^- =-2608, then 1 / / ^ ? ^=.2600, and soon. 
 
 V .OoUD V .ooUO 
 
 While the difference in value of m and n is small, yet it 
 must be remembered that m=the head per foot length of 
 pipe to balance the resistance and generate the mean velocity 
 of flow, and n is equal the friction head only, per foot length 
 of pipe. In a pipe of considerable length the difference be- 
 comes very considerable. (See, in this connection, 4 and 5) 
 
 Formulae (43) and (45) given in 17 may be adopted in- 
 stead of the above but in that event the value of m or n must 
 be converted to terms of P as in 17.
 
 SULLIVAN'S NEW HYDRAULICS. 263 
 
 103 Velocities, Discharge and Friction Heads for 
 Slopes and Diameters. 
 
 The slope required to generate a velocity of one foot per 
 second in any given diameter with full and free discharge is 
 
 The slope required to generate any other velocity, either 
 greater or less than one foot per second, is 
 
 In the latter formula v must equal the square of the de- 
 aired velocity in feet per second. Having found the value of 
 S for v^l.OO in any given diameter, then the required value 
 of S to generate any other velocity in the given diameter, 
 will equal the value of S for v = 1.00 multiplied by the square 
 of the proposed velocity . The distance or length in feet i, of 
 pipe, in which there is a fall of one foot is 
 
 As the value of S shows the total head per foot length of 
 pipe, the fall in feet per 100 feet length is found by moving 
 the decimal point in the value of S two places to the right. 
 The friction head per foot length in any given uniform diam- 
 eter with full and free discharge is .9845 per cent of the value 
 of S for that pipe. The friction head may therefore be easily 
 found from the value of S. The friction head per 100 feet 
 length of pipe will be 
 
 h*=SX98.45, or h ' =(SX 100) (SX100X -0155). 
 
 When the friction head per 100 feet is ascertained for a 
 given diameter with v=1.00, then the friction head per 100 
 feet in the given diameter for any other velocity will equal 
 that for v=1.00 multiplied by the square of the proposed vel- 
 ocity. The following table (No. 50) is based on m=.0004 for 
 all clean iron pipes.
 
 264 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 TABLE No. 50. 
 
 Velocities, Discharge and friction heads for given slopes 
 and diameters. 
 
 d;/d 
 
 
 
 
 g 
 
 8 
 
 h 
 
 
 u 
 
 
 
 06 
 
 * 
 
 a& 
 
 8,1 
 
 If 
 
 ?! 
 
 h 
 
 50 
 
 si^ 
 
 >fc 
 
 ||| 
 
 U| 
 all 
 
 Dischar 
 Cubic t 
 Second. 
 
 3 inches 
 
 
 
 
 
 
 
 .25 feet 
 
 0.500 
 
 .0008 
 
 0.50 
 
 .07876 
 
 11.01804 
 
 .02455 
 
 
 
 .0032 
 
 1.00 
 
 .31504 
 
 22.03608 
 
 .04910 
 
 
 
 .0072 
 
 1.50 
 
 .70*84 
 
 33.05412 
 
 .07365 
 
 
 
 .0128 
 
 2.00 
 
 1.26016 
 
 44.07216 
 
 .09820 
 
 
 
 .0200 
 
 2.50 
 
 1.96900 
 
 55.09020 
 
 .12275 
 
 
 
 .0288 
 
 3.00 
 
 2.83536 
 
 66.10824 
 
 .14730 
 
 
 
 .0392 
 
 3.50 
 
 3.85928 
 
 77.12628 
 
 .17185 
 
 
 
 .0512 
 
 4.00 
 
 5.04070 
 
 88 14432 
 
 .19640 
 
 
 
 .0648 
 
 4.50 
 
 6.37964 
 
 99.16236 
 
 .22095 
 
 
 
 .0800 
 
 . 5.00 
 
 7.87600 
 
 110.18040 
 
 .24550 
 
 
 
 .0968 
 
 5.50 
 
 9.53008 
 
 121.19844 
 
 .27005 
 
 
 
 .1152 
 
 6.00 
 
 11.34158 
 
 132.21648 
 
 .29460 
 
 
 
 .1352 
 
 6.50 
 
 13.31060 
 
 143.23452 
 
 .31915 
 
 
 
 .1568 
 
 7.00 
 
 15.43715 
 
 154.25256 
 
 .34370 
 
 
 
 .2048 
 
 8.00 
 
 20.16281 
 
 176.28864 
 
 .39280 
 
 
 
 .3200 
 
 10.00 
 
 31.50400 
 
 220.36080 
 
 .49100 
 
 4 inches 
 
 
 
 
 
 
 
 .3333 feet 
 
 0.579 
 
 .00207850 
 
 1.00 
 
 .204625 
 
 39.18024 
 
 .08730 
 
 
 
 .00466662 
 
 1.50 
 
 .459428 
 
 58.77036 
 
 .13095 
 
 
 
 .0083140 
 
 2.00 
 
 .8185133 
 
 78.36048 
 
 .17460 
 
 
 
 .0129906 
 
 2.50 
 
 1.278924 
 
 97.95060 
 
 .21825 
 
 
 
 .0187065 
 
 3.00 
 
 1.811655 
 
 117.54080 
 
 .26190 
 
 
 
 .0254616 
 
 3.50 
 
 2.506694 
 
 136.72096 
 
 .30555 
 
 
 
 .0332560 
 
 4.00 
 
 3.254053 
 
 155.90120 
 
 .34920 
 
 
 
 .0420896 
 
 4.50 
 
 4.143721 
 
 175.08144 
 
 .392S5 
 
 
 
 .0519625 
 
 5.00 
 
 5.115708 
 
 194.26168 
 
 .43650 
 
 
 
 .0628746 
 
 5.50 
 
 6.190004 
 
 213.44192 
 
 .48015 
 
 
 
 .0748260 
 
 6.00 
 
 7.368619 
 
 232.62216 
 
 .52380 
 
 
 
 
 6.50 8.645544 
 
 251.80240 
 
 .56745 
 
 
 
 .'1018465 
 
 7.00 10.026788 
 
 270.98264 
 
 .61110
 
 SULLIVAN'S NEW HYDRAULICS. 
 TABLE 50. Continued. 
 
 
 
 
 o 
 
 
 8 
 
 u 
 
 ^ 
 
 !* 
 
 
 
 02 
 
 g| 
 
 Is* 
 
 lo-S 
 
 
 
 ^^ 
 
 O> 
 
 O *** 
 
 v> *^ ^ 
 
 g.2 o 
 
 J' 
 
 .s 
 
 ?! 
 
 002 
 02 
 
 ?!1 
 
 ill 
 
 .1-5.2 
 
 fiu S 
 
 
 5 inches 
 
 
 
 
 
 
 
 4167 feet 
 
 0.645 
 
 .00148120 
 
 1.00 
 
 .14651329 
 
 61.17144 
 
 .13630 
 
 
 
 .00334845 
 
 1.50 
 
 .32965490 
 
 91.757160 
 
 .20445 
 
 
 
 :()05952<SO 
 
 2.00 
 
 .58605316 
 
 122.342880 
 
 .27260 
 
 
 
 .00930125 
 
 2.50 
 
 .91570806 
 
 152.92860 
 
 .34075 
 
 
 
 ! "1339380 
 
 3.00 
 
 1.31861961 
 
 183.51432 
 
 .40890 
 
 
 
 .01823045 
 
 8.50 
 
 1.79276780 
 
 214.10004 
 
 .47705 
 
 
 
 .02381120 
 
 4.00 
 
 2.34421264 
 
 244.68576 
 
 .54520 
 
 
 
 .03013605 
 
 .03720500 
 
 4.50 
 5.00 
 
 2.96989412 
 3.66283225 
 
 275.27148 
 305.85720 
 
 .61335 
 .68150 
 
 
 
 .04501805 
 
 5.50 
 
 4.43202702 
 
 336.44292 
 
 .74965 
 
 
 
 .05357520 
 
 6.00 
 
 5.27447844 
 
 367.02864 
 
 .81780 
 
 6 inches 
 
 
 
 
 
 
 
 .50 foot 
 
 0.7071 
 
 .001131156 
 
 1 00 
 
 .1113623 
 
 88.14432 
 
 .1964 
 
 
 
 .002543101 
 
 1 50 
 
 .2503683 
 
 132.21648 
 
 .2946 
 
 
 
 .004524624 
 .007%9725 
 
 2.00 
 2 50 
 
 .4454492 
 .6960144 
 
 176.28864 
 
 .3928 
 .4910 
 
 
 
 .010180404 
 
 3 00 
 
 1 002260 
 
 264 [43296 
 
 .5892 
 
 
 
 .013*56051 
 .DIM 19*49(5 
 .022905909 
 .028278900 
 
 3.50 
 4.00 
 4.50 
 5.00 
 
 1.364198 
 1.781796 
 2.255086 
 2.784057 
 
 308.50512 
 352.57728 
 396.64944 
 440.72160 
 
 .6874 
 .7856 
 8838 
 .9820 
 
 
 
 .03J217469 
 
 5 50 
 
 3.368709 
 
 484.79376 
 
 [.0802 
 
 
 
 .040721616 
 
 6 00 
 
 4.008903 
 
 5?8. 86592 
 
 [ 1784 
 
 7 inches 
 
 
 .047791341 
 
 6.50 
 
 4.705057 
 
 572.93808 
 
 [.2766 
 
 .5833 feet 
 
 0.764 
 
 .000897583 
 
 1 '0 
 
 .088367 
 
 119.96424 
 
 .26730 
 
 
 
 .002019561 
 .003590332 
 
 1.50 
 200 
 
 .198825 
 .&5346S 
 
 179.94636 
 
 239.92J4S 
 
 .40095 
 .53460 
 
 
 
 .Ol)560lHt3 
 
 2 50 
 
 .552294 
 
 299 91060 
 
 .66825 
 
 
 
 .00-078247 
 
 3.00 
 
 795303 
 
 359.89272 
 
 .80190 
 
 
 
 .010995391 
 .013961328 
 .018176055 
 
 3.50 
 4.00 
 4.50 
 
 1.081996 
 1.374493 
 1.789433 
 
 419.87484 
 479.85(596 
 539.83908 
 
 .93555 
 1.06920 
 
 1.20285 
 
 8 inches 
 
 
 .022439575 
 027151885 
 
 5^50 
 
 2.209176 
 2.673103 
 
 599.82120 
 659.80332 
 
 1.33650 
 1.47015 
 
 .6667 feet 
 
 0.817 
 
 .000734357 
 
 1 00 
 
 .0722975 
 
 156.67608 
 
 .3491 
 
 
 
 .002937428 
 .006609213 
 .011749712 
 .018358925 
 .026436852 
 .035983493 
 .046998848 
 
 2:00 
 
 3.00 
 4.00 
 5.00 
 6.00 
 7.00 
 8 00 
 
 ! 287 1888 
 .6506771 
 1.1567592 
 1.8074362 
 2.6027091 
 3 5425749 
 4 6270366 
 
 313.35216 
 
 470.02824 
 626.70432 
 783.38040 
 940.05648 
 1096.73256 
 
 .6982 
 1.0473 
 1.3964 
 1.7455 
 2.0946 
 2.4437 
 2.7928 
 
 
 
 .059482917 
 .073435700 
 
 9 00 
 10.00 
 
 5.8560932 
 7.2297500 
 
 li"li> !(472 
 1566.76080 
 
 3.1419 
 3.4910
 
 SULLIVAN'S NEW HYDRAULICS 
 TABLE No. 50 CONTINUED. 
 
 
 
 
 1 
 
 as "to 
 * 
 
 O Jo 
 
 <D "S 
 
 M 
 
 1 
 
 fc 
 
 a 
 
 -PH O 
 
 P 
 
 lit 
 
 fcfcS 
 
 
 V 
 
 I 33 
 
 
 
 li 
 
 3i 
 
 S3l 
 
 inches 
 .75 Foot 
 
 0.866 
 
 .00061585835 
 
 1.00 
 
 .060631255 
 
 198.27984 
 
 .4418 
 
 
 
 .00246343340 
 
 2.00 
 
 .242525020 
 
 396.55968 
 
 .8836 
 
 
 
 .00554272415 
 
 3.00 
 
 .545681193 
 
 594.83952 
 
 1.3254 
 
 
 
 .<HMS53733tiO 
 
 4.00 
 
 .970100080 
 
 793.11936 
 
 1.7672 
 
 
 
 .01529f.45.s75 
 
 5.00 
 
 1.505936364 
 
 991.39920 
 
 2.2090 
 
 
 
 .02217090060 
 
 6.00 
 
 2.182725170 
 
 1189.67904 
 
 2.6508 
 
 
 
 .030177U:>915 
 
 7.00 
 
 2.970931474 
 
 1387.95888 
 
 3.0926 
 
 
 
 .03941493440 
 
 8.00 
 
 3.880400300 
 
 1586.23872 
 
 3.5344 
 
 
 
 .0498S452635 
 
 9.00 
 
 4.911131620 
 
 1784.51856 
 
 3.9762 
 
 
 
 .06158583500 
 
 10.00 
 
 6.063125500 
 
 1982.79840 
 
 4.4180 
 
 
 
 .07451886035 
 
 11. fO 
 
 7.336381802 
 
 2181.07824 
 
 4.8598 
 
 
 
 .08868360240 
 
 12.00 
 
 8.730900660 
 
 2379.35808 
 
 5.3016 
 
 10 inches 
 
 
 
 
 
 
 
 .8333 Ft 
 
 0.913 
 
 .00052576237 
 
 1.00 
 
 .051761306 
 
 244.77552 
 
 .5454 
 
 
 
 .00210304948 
 
 2.00 
 
 .207045222 
 
 489.55104 
 
 1.0908 
 
 
 
 .00473186133 
 
 3.00 
 
 465851748 
 
 734.32656 
 
 1.6 62 
 
 
 
 .00841219792 
 
 4.00 
 
 .828180886 
 
 979.10208 
 
 2.1816 
 
 
 
 .01314405925 
 
 5.00 
 
 1.294 32634 
 
 1223.87760 
 
 2.7270 
 
 
 
 .01892744532 
 
 6 00 
 
 i.,s'->:uor,992 
 
 1468.65312 
 
 3.2724 
 
 
 
 .02576235613 
 
 7.00 
 
 2.5363039H1 
 
 1713.42864 
 
 3.8178 
 
 
 
 .03364879168 
 
 8.00 
 
 3.312723541 
 
 1958.20416 
 
 4.3632 
 
 
 
 .04258675197 
 
 9.00 
 
 4.192665732 
 
 2202.97968 
 
 4.9086 
 
 
 
 .05257623700 
 
 10.00 
 
 5.176130600 
 
 2447.75520 
 
 5.4540 
 
 
 
 .06361724677 
 
 11.00 
 
 6.263117945 
 
 2692.53072 
 
 5.9994 
 
 12 inches 
 
 
 
 
 
 
 
 1.00 Feot. 
 
 1.00 
 
 .00040000000 
 
 1.00 
 
 03938 
 
 352.48752 
 
 .7854 
 
 
 
 .0016 
 
 2.00 
 
 ; 15752 
 
 704.97504 
 
 1.5708 
 
 
 
 .0036 
 
 3.00 
 
 .35442 
 
 1057.46256 
 
 2.3562 
 
 
 
 .0064 
 
 4.00 
 
 .63008 
 
 1409.95(X'8 
 
 3.1416 
 
 
 
 .0100 
 
 5.00 
 
 .98450 
 
 1762.43760 
 
 3.9270 
 
 
 
 .0144 
 
 6.00 
 
 1.41768 
 
 2114.92512 
 
 4.7124 
 
 
 
 .0196 
 
 7.00 
 
 1.92962 
 
 2467.41264 
 
 5.4978 
 
 
 
 .0256 
 
 8.00 
 
 2.52032 
 
 2819.90016 
 
 6.2832 
 
 
 
 .0324 
 
 9.00 
 
 3.18978 
 
 3172! 38768 
 
 7.0686 
 
 
 
 .0400 
 
 10.00 
 
 3.94800 
 
 3524.87520 
 
 7.8540 
 
 
 
 .0484 
 
 11.00 
 
 4.76498 
 
 3877.36272 
 
 8.6394 
 
 14 inches 
 
 
 
 
 
 
 
 1.167 Feet 
 
 1.080 
 
 .00031736964 
 
 1.00 
 
 .026817735 
 
 479.7672 
 
 1.069 
 
 
 
 00126947856 
 .00285632676 
 
 2.00 
 3.00 
 
 .1249*0165 
 .281205370 
 
 959.5344 
 1439.3016 
 
 2.138 
 3.207 
 
 
 
 .00507791424 
 
 4.00 
 
 .49! 1920,558 
 
 1919.UC.NS 
 
 4.276 
 
 
 
 .00793424100 
 
 5.00 
 
 .78U26000 
 
 2398.8360 
 
 5.345 
 
 
 
 .01142o30704 
 
 6.00 
 
 1.1248208115 
 
 2878.6032 
 
 6.414 
 
 
 
 .01555111236 
 
 7.00 
 
 1.531007012 
 
 3358.3704 
 
 7.483 
 
 
 
 .02031165696 
 
 8.00 
 
 1.999682628 
 
 3838.1376 
 
 8.552 
 
 
 
 .02570694084 
 
 9.00 
 
 2.569280203 
 
 4317.9048 
 
 9.621 
 
 
 
 .TO! 73696400 
 
 10.00 
 
 3.124504100 
 
 4797.6720 
 
 10.690 
 
 
 
 .03840172844 
 
 11.00 
 
 3.790649969 
 
 5277.4892 
 
 11.759
 
 SULLIVAN'S NEW HYDRAULICS. 
 TABLE 50 Continued. 
 
 267 
 
 
 
 
 o 
 
 1' 
 
 
 
 m 
 
 
 
 ? 
 
 
 ||. 
 
 &! 
 
 I 4 
 
 Is 
 S-s 
 
 ?! 
 
 Jh. 
 
 02 
 
 Ill 
 
 111 
 
 C Q m 
 
 fcWfe 
 
 11! 
 
 Q OS 
 
 ill 
 
 QOra 
 
 16 Inches 
 
 
 
 
 
 
 
 1.333 feet 
 
 1.155 
 
 00025980521 
 
 1.00 
 
 .025577823 
 
 626.5248 
 
 1.396 
 
 
 
 00103922084 
 
 2.00 
 
 .103350513 
 
 1253.0496 
 
 2.792 
 
 
 
 (X 1233,^24(^9 
 
 3.00 
 
 .23020 407 
 
 1879.5744 
 
 4.188 
 
 
 
 '415688336 
 
 4.00 
 
 .409245167 
 
 2506.0992 
 
 5.584 
 
 
 
 00649513025 
 
 5.00 
 
 .639445574 
 
 3132.6240 
 
 6.980 
 
 
 
 00935298756 
 
 6.00 
 
 .920801626 
 
 3759.1488 
 
 8.376 
 
 
 
 01273045529 
 
 7.00 
 
 1.253313324 
 
 4385.6736 
 
 9.772 
 
 
 
 01662753344 
 
 8.10 
 
 1.636980668 
 
 5012.1984 
 
 11.168 
 
 
 
 02104422201 
 
 9.00 
 
 1.971803657 
 
 5638.7232 
 
 12.564 
 
 
 
 02598052100 
 
 10.00 
 
 2.5577823 
 
 6265.2480 
 
 13.960 
 
 
 
 03143643041 
 
 11.00 
 
 3.126353005 
 
 6891.7728 
 
 15.356 
 
 18 inches 
 
 
 
 
 
 
 
 1.50 feet 
 
 1.224 
 
 0002124183 
 
 1.00 
 
 .02091259 
 
 793.0296 
 
 1.767 
 
 
 
 0008496732 
 
 2.00 
 
 .08365033 
 
 1588.0592 
 
 3.534 
 
 
 
 0019117737 
 
 3.00 
 
 .18821413 
 
 2379 0888 
 
 5.301 
 
 
 
 0'>339;?6928 
 
 4.00 
 
 .33460131 
 
 3172.1184 
 
 7.068 
 
 
 
 0053104575 
 
 5.00 
 
 .52281455 
 
 3965.1480 
 
 8.835 
 
 
 
 0076470588 
 
 6.00 
 
 .75284194 
 
 4758.1776 
 
 10.602 
 
 
 
 01' 140-4967 
 
 7.00 
 
 1.02471651 
 
 5551.2072 
 
 12.369 
 
 
 
 0135947712 
 
 8.00 
 
 1.33840523 
 
 6344.2368 
 
 14.136 
 
 
 
 0172"5S823 
 
 9 00 
 
 1.69391912 
 
 7137.2664 
 
 15.903 
 
 
 
 0212418300 
 
 10.00 
 
 2.0912590 
 
 7930.2960 
 
 17.670 
 
 
 
 0257026143 
 
 11.00 
 
 2.53 42238 
 
 8723.3256 
 
 19.437 
 
 20 inches 
 
 
 
 
 
 
 
 1.667 feet 
 
 1.291 
 
 000185865228 
 
 1 00 
 
 .0182984317 
 
 979.2816 
 
 2.182 
 
 
 
 000743460912 
 
 2.00 
 
 .0731937268 
 
 1958.5632 
 
 4.364 
 
 
 
 001672787052 
 
 3 00 
 
 .1646858853 
 
 2937.8448 
 
 6.546 
 
 
 
 002973843648 
 004646630700 
 
 4.00 
 5.00 
 
 .2927749072 
 .4574610000 
 
 3917.1264 
 4896. 40SO 
 
 8.728 
 10.910 
 
 
 
 (X)tit.i9114.>20> 
 009107396172 
 
 6.00 
 7 01 
 
 .6587435411 
 
 >9(231532 
 
 5875.6896 
 6854.9712 
 
 13.092 
 15.274 
 
 
 
 011895374592 
 015055083468 
 
 8.00 
 9.00 
 
 1.17109962*6 
 1.4821729675 
 
 -7834.2528 
 8813.5344 
 
 17.456 
 19.638 
 
 
 
 
 10 00 
 
 1 82984317 
 
 
 21.820 
 
 
 
 022489692588 
 
 11.00 
 
 2.2141102353 
 
 10772:0976 
 
 24.002 
 
 24 inches 
 
 
 
 
 
 
 
 2.00 feet 
 
 1.4142 
 
 .0001414227124 
 
 000565690849* 
 
 1.00 
 2.00 
 
 013923055 
 
 055692220 
 
 1409.35008 
 
 2818.70016 
 
 3.1416 
 6.2832 
 
 
 
 ! 0012728044116 
 .0022623633984 
 .0035355678100 
 .0050912176464 
 
 4^00 
 5.00 
 6.00 
 7 00 
 
 .125307495 
 
 ! 5012299 -i 
 
 .t;>222'.t')95 
 
 4228.06024 
 
 5637.40032 
 7046.75040 
 8456.10048 
 9S65. 45046 
 
 9.4248 
 12.5664 
 15.7080 
 18.8496 
 21.9912 
 
 
 
 ! 009061051899 
 
 .0114552397044 
 
 s'.oo 
 
 9.00 
 
 l' 127767455 
 
 11274.80084 
 12684.15072 
 
 25.128S 
 
 2-S.2744 
 
 
 
 0141422712400 
 .0171121482004 
 
 10.00 
 11.00 
 
 1.39230550 
 1.684689655 
 
 1-1 CM. 500SO 
 15502.85088 
 
 31.4160 
 34.5578
 
 SULLIVAN'S NEW HYDRAULICS 
 TABLE No. 50 CONCLUDED. 
 
 5-31 
 
 xl 
 
 27 inches 
 2.25 Feet 
 
 30 inches 
 2.50 Feet 
 
 1.581 
 
 .00047407 4C740 
 
 .01)29(529629625 
 .0042671671660 
 .OJ5807 4074065 
 .0375851851840 
 
 0118518518500 
 0143407407385 
 
 .0001012018 
 .0004048072 
 
 0016192288 
 0:)25 300450 
 0036432648 
 
 0064769152 
 0081973458 
 0101218000 
 0122454178 
 
 .0000769823 
 
 0005928407 
 .0012317168 
 0019245575 
 0027713628 
 .0037721327 
 0049268672 
 
 1.00 
 2.00 
 8.00 
 4.00 
 5.00 
 6.00 
 7.00 
 8.00 
 9.00 
 10.00 
 11.00 
 
 1.00 
 2.00 
 3.00 
 4.00 
 5.00 
 6.00 
 7.00 
 8.00 
 9.00 
 10.00 
 11.00 
 
 1.00 
 2.00 
 3.00 
 4.00 
 5.00 
 6.00 
 7.00 
 8.00 
 
 .011721478 
 
 .046885912 
 .105493302 
 .187543648 
 
 .421973208 
 .574352422 
 .750174592 
 .949439718 
 1.17214780 
 
 .1L941312 
 .24908300 
 .35867952 
 
 .63765248 
 
 1.20556172 
 
 .00757891 
 .03131564 
 
 .18947275 
 .27284076 
 
 CO! 13148583 
 
 .48505024 
 .61389171 
 .75789100 
 .91704811 
 
 1724.4288 
 3448.8576 
 5173.2864 
 6897.7152 
 8622.1440 
 10346.5728 
 12071.0016 
 13795.4304 
 15519.8592 
 17244.2880 
 
 2203.1592 
 4406.3184 
 6609.4776 
 
 11015.7960 
 13218.9552 
 15422.1144 
 17625.2736 
 
 19828.4328 
 22031.5920 
 24234.7512 
 
 3172.5672 
 6345.1844 
 9517.7016 
 
 15862.8360 
 19035.4032 
 22207.9704 
 25380.5376 
 28553.1048 
 31725.6720 
 34898.2492 
 
 3.976 
 7.952 
 11.928 
 15.904 
 19.880 
 
 31 ! 808 
 35.784 
 39.760 
 43.736 
 
 14.727 
 19.636 
 24.545 
 29.454 
 34.363 
 39.272 
 44.181 
 
 54.000 
 
 7.069 
 14.138 
 21.201 
 
 35.345 
 42.414 
 49.483 
 56.552 
 63.621 
 
 77.759 
 
 104. Thickness and Weight of Cast Iron Pipe. There 
 is a great want of uniformity in regard to the thickness of 
 cast iron pipe for any given pressure. Every city seems to 
 have adopted different thicknesses of pipe. The leading for- 
 mulas for thickness give greatly differing results for the same 
 conditions.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 t=(.000058hd) +.0152d+.312 (J.B.Francis 
 
 t=(.0016 n d) +.013 d+.32 (M. Dupuit 
 
 t=(.00238 n d) +.34 (Julius Weisbach 
 
 The following formula gives thickness of cast iron pipe 
 as adopted in recent practice, 
 
 t=(p+100) .000142 d+.33 (1 .01 d) (110) 
 
 In the above formulas, 
 t=thickness of pipe shell in inches 
 d=inside diameter in inches 
 h=head of water in feet 
 p=pressure of water=HX-434 
 n=number atmospheres pressure at 33 feet each. 
 Fannings formula for the weight per lineal foot of cast 
 iron pipe, including the weight of the bell or hub is, for 12 
 foot pipes, 
 
 W=12 (d+t) Xl-08 tX3.1416X.2604 
 
 By a 12 foot pipe is meant a pipe which will actually lay 
 12 feet, or is 12 feet from bottom of bell to end of spigot. The 
 bell or hub adds about 1% per cent to the weight of a length 
 of pipe. The above formula allows for the extra weight of 
 bell. For more on weight of pipes, see "Gregory's Practical 
 Mathematics." 
 
 105 Dimensions and Weight ot Cast Iron Pipe Made 
 by The Colorado Fuel and Iron Company of Denver, for 
 100 Ibs. Pressure. 
 
 TABLE No. 51. By W. F. McCue 
 
 I 
 
 1 
 
 1 
 
 1 
 I 
 
 Length over all. 
 Feet Inches. 
 
 "3 
 
 
 
 s 
 
 a I 
 !l 
 
 Will Lay 
 Feet Inches 
 
 Thickness of 
 Shell Inches* 
 
 Inside Diameter 
 of Bell Inches 
 
 s| 
 
 is 
 
 3 
 
 0*0 
 
 Outside Diam. 
 of Spigot. 
 
 i 
 
 fe 
 
 M 
 
 A 3 
 
 9& 
 
 *.s 
 
 3 
 4 
 
 6 
 8 
 10 
 12 
 16 
 20 
 
 12-4 
 124 
 324 
 124 
 124 
 124 
 124 
 124 
 
 3 
 3 
 3 
 3V4 
 3K 
 4 
 4 
 
 121 
 12-1 
 12-1 
 12 Vt 
 
 1I-* 
 
 12 
 12 
 
 1332 
 7-16 
 1-2 
 17-32 
 1932 
 5-8 
 34 
 2732 
 
 4 1-2 
 5 1-2 
 
 7 5-8 
 9 7-8 
 11 7-8 
 133-1 
 18 
 22 1-8 
 
 7 
 81-4 
 10 7-8 
 13 38 
 15 5-8 
 17 3-4 
 22 1-2 
 26 7-8 
 
 43-8 
 5 3-8 
 7 1-2 
 9 3-4 
 11 3-4 
 13 5-8 
 17 7-8 
 22 
 
 15 1-2 
 
 33 
 44 
 
 63 
 
 ,1 
 
 175 
 
 *Sce Table No. 27. 58 fo- fractional inches in equivalent 
 decimals.
 
 270 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 Packing (Jute Hemp) and Lead Required Per Joint For 
 Above Pipe. 
 
 Diameters =* 
 
 3" 
 
 4' 
 
 6" 
 
 8" 
 
 10" 
 
 12" 
 
 16' 
 
 20" 
 
 Lead, Ibs. Per 
 
 
 
 
 
 
 
 
 
 Joint 
 
 4 1-2 
 
 5 1-2 
 
 7 
 
 10 
 
 12 1-2 
 
 17 
 
 20 1-2 
 
 29 
 
 Packing, ozs 
 
 3 
 
 3 1-2 
 
 5 
 
 7 
 
 91-2 
 
 12 
 
 20 
 
 26 
 
 106 Weight Per Foot Length of Cast Iron Pipe For 150 
 and 200 Ibs. Pressure, as Made by Colorado Fuel and Iron 
 Co. of Denver, Colorado. 
 
 Diameters 
 
 3" 1 4' 
 
 6" 
 
 8- 
 
 10" 
 
 12" 
 
 16" 
 
 20" 
 
 Wt.Pei.ft. 
 
 
 
 
 
 
 
 
 150 pounds 
 Pressure 
 
 17 Ibs 23V, Ibe 
 
 361b< 
 
 48Jbs 
 
 70 Ibs 
 
 85 Ibs 
 
 140 Ibs 
 
 210 Ibs 
 
 Wt. Per. ft. 
 
 
 
 
 
 
 
 
 200 pounds 
 Pressure 
 
 1 
 19 lbs|26 Ibs 
 
 421bi 
 
 55 Ibs 
 
 78 Ibs 
 
 94 Ibs 
 
 15b Ibs 
 
 222 Ibs 
 
 REMARK The market prices of pig iron, cast iron and 
 lead and other metals fluctuate so rapidly that tables for esti- 
 mating the cost of pipe and laying are of no great value ex 
 cept in so far as such tables furnish the data as to the quan- 
 tity and weight required. The price of pig iron May 12th, 
 1898, was $6.65, and on July 28th, 1899, the price was $15.25. 
 
 The present price of cast iron pipe (August 2nd, 1899) is 
 $33.00 per ton of 2,000 Ibs., and of lead, $5.00 per 100 Ibs. in 
 Denver. 
 
 107 Manufacturers' Standard Casllron Water Pipe 
 For 100 Ibs. Pressure Per Square Inch. 
 
 TABLE No. 52. 
 
 Diameters In. 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 10 
 
 18 20 
 
 24 
 
 30 
 
 36 
 
 48 
 
 Thickness, In* 
 
 1-2 
 
 1-2 
 
 1-2 
 
 9-lfi 
 
 9-16 
 
 8-4 
 
 8-4 
 
 7 8 15-16 
 
 1 
 
 11-813-8 
 
 11-2 
 
 Wt. per. ft. Ib. 
 
 22 
 
 88 
 
 45 
 
 ro 
 
 75 
 
 117 
 
 125 
 
 167 200 
 
 251 
 
 350 
 
 475 
 
 775 
 
 Wt.per. 12ft. 
 
 2ti4 
 
 ;*; 
 
 540 
 
 720 
 
 900 
 
 nm 
 
 1500 
 
 200012400 
 
 no 
 
 4200 
 
 5700 
 
 B800 
 
 *See Table No. 27, 58 for fractional inches in equivalent 
 decimals. 
 
 108 Cost Per 100 Feet Length, For Labor and Ma- 
 terial in Laying Cast Iron Water Pipe in Denver, Colorado, 
 in 1890. 
 
 The conditions were: Top of pipe 5 feet below surface. 
 Depth of trench 5 feet, plus outside diameter of pipe. Easy
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 271 
 
 trenching in sandy loam, Wages, foreman $3.00, calkere 12.50 
 laborers $1.75 per day of 10 hours, teams 83.00 per day, pipe 
 $33.00 per ton of 2000 Ibs.. lead $4.15 per 100 Ibs., packing 6 
 cents per Ib. No pavements to tear up. Backfilling done by 
 teams and scrapers. Average water pressure 80 Ibs. Thick- 
 ness of pipe for 120 Ibs. hydraulic pressure. Hemp packing. 
 Hauling pipe 60 cents per ton. 
 
 TABLE No. 53* Cost per 100 feet. 
 
 I 
 
 s, 
 
 
 If 
 
 22 
 82 
 
 4:, 
 80 
 
 7fi 
 117 
 125 
 
 170 
 'iJO 
 
 a-,u 
 r.oo 
 no 
 
 $86.30 
 
 52.80 
 74.25 
 99.00 
 123.75 
 193.05 
 206.25 
 280. EO 
 412.50 
 577.50 
 825.00 
 1155.00 
 
 10.20 
 
 .94 
 1.28 
 1.88 
 2.63 
 4.50 
 6.30 
 
 $ 0.66 $0. 
 
 1.05 
 
 1.35 
 
 1.80 
 
 2.25 
 
 3.50 
 
 3.75 
 
 5.10 
 
 7. tO 
 10. EO 
 IB. 00 
 21.00 
 
 $ 2.15 
 
 3.13 
 
 4.03 
 
 4.14 
 
 5.36 
 
 8.07 
 
 9.30 
 
 11.17 
 
 14.96 
 
 16.15 
 
 23.75 
 
 49.87 
 
 $0.20 
 .20 
 
 .20 
 .'JO 
 .20 
 
 $0.15 
 ..15 
 .15 
 .20 
 .20 
 .25 
 .25 
 
 :! 
 
 .60 
 
 .70 
 
 1.00 
 
 15.00 
 16.00 
 20.00 
 31.00 
 32.00 
 38.00 
 44.00 
 50.00 
 60.00 
 75.00 
 
 *Allow 440 joints per mile when ebtimating cost of lay- 
 ing cast iron pipe. Wrought iron and steel pipe is made in 
 lengths of 15 to 27 feet according to conditions to be met. 
 Cast iron pipe is in lengths of 12 feet. See Remark under 
 Table No. 55. 
 
 109 Cost of Pipe Per Foot Laid in Boston. 
 
 Axis of pipe is 5 feet below surface. Labor $2.00 per 
 day. Cost of pipe 1^ cents per Ib., or $30.00 per ton of 2000 
 Ibs. Special castings 3 cents, lead 5 cents per Ib. Cost of 
 excavating rock $3.50 to $5,50 per cubic yard, measured to 
 neat lines. 
 
 This table is transcribed from "Details of Water Works 
 etc.", by W, R. Billings.
 
 272 SULLIVAN'S NEW HYDRAULICS 
 
 TABLE No. 54. Cast Iron Pipe. 
 
 . 
 
 d 
 
 
 | 
 
 1 11* 
 
 
 5 
 
 
 t 1 
 
 
 
 | 
 
 fc| 
 
 "1 r-i 
 
 
 "t 
 
 _^ 
 
 1 
 
 | 
 
 Jj] 
 
 -J 
 
 &. 
 
 t3 
 
 M . 
 
 &gj 
 
 111 
 
 bi 
 a 
 
 2 o 
 
 J4^3 
 jjfl 
 
 ~ 
 
 s 
 
 .2 
 
 i 
 
 CUD" 
 'S u. 
 
 
 
 T3 a 
 a P 
 go 
 Hft 
 
 I' 3 ! 
 
 O*0 CO 
 
 M *- 
 
 UT3 I- 
 
 
 
 1 
 
 H.S 
 
 a- 
 
 4 
 
 6 
 
 0.45 
 0.50 
 
 21.7 
 85.0 
 
 -0.70 
 1.00 
 
 $0.38 
 0.57 
 
 ^S 
 
 $0.02 
 .08 
 
 $0.25 
 0.27 
 
 $0.70 
 .93 
 
 8 
 
 0.55 
 
 50.0 
 
 1.85 
 
 0.83 
 
 .08 
 
 .05 
 
 0.30 
 
 1.26 
 
 10 
 
 0.60 
 
 68.0 
 
 1.70 
 
 1.10 
 
 .10 
 
 .06 
 
 0.34 
 
 1.60 
 
 12 
 12 
 
 0.58 
 0.65 
 
 S:S 
 
 2.00 
 2.00 
 
 1.27 
 1.42 
 
 .13 
 .13 
 
 .07 
 
 .07 
 
 0.37 
 0.37 
 
 1.84 
 1.99 
 
 16 
 
 0.66 
 
 118.0 
 
 2.70 
 
 1.87 
 
 .17 
 
 .08 
 
 0.45 
 
 2.57 
 
 16 
 
 0.75 
 
 185.0 
 
 2.70 
 
 2.12 
 
 .17 
 
 .08 
 
 0.45 
 
 2.82 
 
 20 
 
 0.73 
 
 162.0 
 
 3.35 
 
 2.55 
 
 .21 
 
 .09 
 
 0.55 
 
 3.40 
 
 20 
 
 0.85 
 
 183.0 
 
 3.35 
 
 2.94 
 
 .21 
 
 .09 
 
 0.55 
 
 8.79 
 
 24 
 
 0.81 
 
 216.0 
 
 4.00 
 
 3.44 
 
 .25 
 
 .10 
 
 0.68 
 
 4.47 
 
 24 
 
 0.94 
 
 250.0 
 
 4.00 
 
 3.95 
 
 .25 
 
 .10 
 
 0.68 
 
 4.98 
 
 80 
 
 0.93 
 
 308.0 
 
 5.00 
 
 4.92 
 
 .29 
 
 .11 
 
 0.80 
 
 6.12 
 
 36 
 
 1.04 
 
 410.0 
 
 6.00 
 
 6.58 
 
 .34 
 
 .12 
 
 1.00 
 
 8.04 
 
 40 
 
 1.12 
 
 490.0 
 
 6.70 
 
 7.80 
 
 .40 
 
 .15 
 
 1.30 
 
 9.65 
 
 48 
 
 1.25 
 
 660.0 
 
 8.00 
 
 10.40 
 
 .48 
 
 .20 
 
 1.75 
 
 12.83 
 
 REMARK From the high cost of trenching and the ref- 
 erence to rock excavation, the ground must have been very 
 "hard digging." Compare cost of trenching with that at 
 Omaha for like diameters. 
 
 IIOCost of Trenching, Laying, Calking and Back- 
 filling in Omaha, 1889, With wages of Foreman $2.50, 
 Calkers $2.25, Laborers $1.75 Per Day of 10 Hours. (W. 
 
 F. McCue, C. E., of Colorado Fuel & Iron Co.) 
 
 TABLE No. 55. Cast Iron Pipe. 
 
 Diam. 
 of Pipe 
 
 Width 
 of 
 trench 
 feet 
 
 Depth of 
 trench, 
 feet 
 
 Cost of 
 trench, 
 lineal 
 foot 
 
 Laying, 
 calking, 
 backfilling, 
 lineal foot. 
 
 Cost of 
 labor per 
 lineal foot 
 complete. 
 
 4' 
 
 6 
 8 
 10 
 12 
 16 
 
 1.75 
 1.75 
 1.75 
 2.00 
 2.00 
 2.33 
 
 5.666 
 6.000 
 6.000 
 6.083 
 6.250 
 7.333 
 
 $0.104 
 0.10.1 
 0.107 
 0.126. 
 0.126 
 0.175 
 
 $0.036 
 0.036 
 0.043 
 0.053 
 0.056 
 0.063 
 
 $0.140 
 0.141 
 0.150 
 0.179 
 0.182 
 0.238 
 
 REMARK Mr. McCue lias been in charge of the con- 
 struction of nearly 700 miles of pipe line in the Eastern and
 
 SULLIVAN'S NEW HYDRAULICS. 273 
 
 Western states, In a letter to the writer he says: "We gen- 
 erally employed 60 to 70 men in a gang enough laborers to 
 excavate the trench ahead of the layers. In laying 4 to 12 
 inch pipe, we had one yarner aud one calker. In laying pipe 
 16 inches diameter or larger, we had two yarners and two 
 calkers. In laying pipe larger than 12 inches diameter it is 
 necessary to use a derrick for lowering the pipe into the 
 trench. 
 
 One yarner and one calker will make about CO joints per 
 day of 10 hours in laying 4 or 6 inch cast iron pipe, and about 
 50 joints of 8 inch, 45 joints of 10 inch and 40 joints of 12 
 inch pipe. In laying pipe larger than 12 inchs, a derrick is 
 required, and progress is much less. Most of the backfilling 
 is done by team and scraper. The largest days work I ever 
 had done was 80 joints of 8 inch pipe yarned by one man and 
 calked by one man. In 1893, I took one yarner and one 
 calker, the fastest I ever saw, and laid and calked 272 joints 
 of 6 inch pipe in 35 hours. The cost was 1^ cents per lineal 
 foot including foreman, kettlemen, and 3 to lay pipe in the 
 trench. We use Jute hemp for packing." 
 
 IIIWeston's Tables for Estimating Cost of Lay lag 
 Cast Iron Pipe. 
 
 The following tables by E. B. Weston, C. E., of Provi- 
 dence, Rhode Island, were published in Engineering News, 
 June 21, 1890, together with other valuable data of like char- 
 acter. The elements of cost entering these tables are: 
 
 Wages, foreman $3.00, calkers $2.25, laborers $1.50, per 
 day. Teams $2.25 per day. Carting $1.00 per ton of 2240 
 Ibs. Depth of trench 4.67 feet plus one-half the outside 
 diameter of pipe. Lead, 5 cents per pound. Tools, blocks 
 and wedges 7 2 10 to 16 1-10 per cent of cost of trenching, 
 laying and backfilling the trench. In the tables the word 
 "trenching" includes excavation and backfilling. "Medium" 
 digging is ground equivalent to gravel and sand. "Hard" 
 digging id ground equivalent to hard or moist clay. Cost of 
 engineering and inspection not included in tables.
 
 274 
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 s, 
 
 g 8 
 
 I 
 
 " 
 
 g 
 
 1 1 
 
 I I 
 
 3 | 
 
 *H ei 
 
 
 
 S 
 
 111 
 
 SSSS 
 
 s i 1 i 3 
 
 -H o O O O O O 
 
 S8SSS 
 
 3 i 
 
 3 e 
 
 ifllilll
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 275 
 
 112 Cubic Yards of Excavation in Trench Per Lineal 
 Boot, Vertical Sides Bell Holes Mot Included. 
 
 TABLE No. 57. 
 
 Depth of Trench in Feet. 
 
 10 11 
 
 5.50 
 6. 
 
 8. JO 
 9. 
 
 77S 
 
 0.370 
 0.444 
 0.518 
 
 3.740 
 0.815 
 1.888 
 1.968 
 
 [.037 
 1.111 
 
 [.185 
 [.259 
 :.333 
 1.407 
 
 0.926 
 015 
 111 
 
 0.888 
 .000 
 
 .111 
 
 0.388 0.444 
 
 0.518 0.592 
 
 0.644 0.740 
 
 0.777 0.888 
 0.876 
 
 3.000 
 3.166 
 
 i. :,:,:, 
 0.740 
 a. 926 
 1.111 
 296 
 1.481 
 1.666 
 1.851 
 2.037 
 2.222 
 2.407 
 2.592 
 2.777 
 2.963 
 J.148 
 3.333 
 3.518 
 
 0.611 
 0.815 
 1.018 
 1.222 
 1.425 
 628 
 833 
 2.037 
 2.237 
 2.444 
 2.647 
 2.851 
 i. or,:, 
 3.258 
 3.462 
 3.666 
 3.870 
 
 0.666 
 0.888 
 1.111 
 
 1.333 
 1 . 555 
 
 1.777 
 2.000 
 
 2' 222 
 
 3.611 
 3.851 
 4.092 
 4.000 4.333 
 4.222 U.573 
 
 0.722 
 
 0.962 
 
 203 
 
 444 
 
 2.648 
 
 0.777 
 037 
 
 2.S8 
 
 r,r,r> 
 
 074 
 
 2.852 
 
 3.111 
 
 .370 
 
 4.148 
 
 406 
 
 4.666 
 
 4.924 
 
 REMARK. The foregoing table (No. 57) will be useful in 
 estimating the cost of sewer work as well as in estimates of 
 cost of pipe laying. It is also the custom of some engineers 
 to excavate irrigation canals with vertical sides and allow for 
 the caving and sliding of the banks until they assume the 
 natural angle of repose. There is nothing to commend this 
 practice, but still it is followed to a considerable extent. In 
 sewer work where the ground is firm, the trench is excavated 
 in alternate sections, and tunnels driven through the short 
 blocks of ground between the excavated sections. This re- 
 duces the amount of excavation by about 30 per cent, and 
 saves the cost of sheeting and bracing. In estimating cost 
 of excavation in earth or rock, see Trautwine's "Engineers 
 Pocket Book." 
 
 113. -Bell Holes in Trench for Cast Iron Pipes. in 
 
 order that the "yarner" and the calker may have room to get
 
 276 SULLIVAN'S NEW HYDRAULICS. 
 
 at all parts of the joint, the trench should be dug out 8 inches 
 deeper for a distance of four feet in front of the bell or hub, 
 and 8 inches wider on either side for the same distance to 
 give shoulder and striking room. This adds materially to the 
 cost of excavation, especially where the ground has a tendency 
 to cave and slide, or is very wet. 
 
 114 Depth of Trenches for Pipe. Pipes in which there 
 is a constant flow of water are in little danger from freezing 
 even if laid on the surface of the ground, but in the distribu- 
 tion or street system the flow id almost if not entirely stopped 
 during certain hours of the night when little or no water is 
 being drawn by consumers. 
 
 Pipes supplying reservoirs and having a constant dis- 
 charge may be covered to any convenient depth simply for 
 the protection of the pipe from injury by wagons, falling trees 
 etc., and to prevent too great expansion by heat or con- 
 traction by cold, and to get the pipe out of the way. 
 
 The general rule in the New England States is to make 
 the trenches for street pipes of such depth as will place the 
 center or axis of th3 pipe five feet under cover. That is, the 
 trench is five feet plus one half the outside diameter of the 
 pipe. The depth that a street pipe should be covered depends 
 on the climate, the nature of the ground and the diameter of 
 the pipe. Where the temperature gets down to from 25 to 40 
 degrees below zero (Fahr.) for two or three days at a time, 4 
 and 6 inch pipes will freeze solid when five feet under cover 
 in sandy and gravelly loam. This occurred in many towns in 
 Colorado in February, 1899. If the earth id dense and free 
 from stones and gravel it is not probable that frost will pene- 
 trate to a depth exceeding four and a half feet. Small pipes 
 laid in open, gravelly soil, should have the top of the pipe at 
 least six feet under cover. 
 
 115. Amount of Trenching and Pipe Laying Per Day 
 Per Man. The number of cubic yards of excavation done 
 per man per day will be less in deep trenchee than in com-
 
 SULLIVAN'S NEW HYDRAULICS. 277 
 
 paratively shallow ones because of the extra effort required 
 to throw the dirt out of deep trenches. The nature of the 
 earth or rock to be excavated will, of course, be a controlling 
 element in determining the amount of excavation that can be 
 accomplished per day, by an average laborer. Quicksand, 
 water and caving banks may also be large items of expense 
 and prevent rapid progress. There are so many elements of 
 uncertainty invol/ed in making an estimate of the work that 
 one man will accomplish in a given time that it is best to as- 
 certain what has been actually accomplished under like con- 
 ditions in the past. By analysis of statements of work 
 actually done in a given time by a given number of men, we 
 can approximate the time required and the cost of doing 
 similar work. Mr. W. R. Billings, superintendent of the 
 Taunton, Mass., Water Works (1887) says*: 
 
 "The following notes of actual work are offered, not in 
 any sense as instances of model performance, but as simple 
 illustrations: Time July 6th 1887; gang 60 men, 16 inch pipe, 
 2 yarners, 2 calkers, 4 to 10 men digging bell holes, 30 boll 
 holes per day, 400 feet of pipe laid and jointed in 10 hours." 
 
 These notes are somewhat incomplete in that they do not 
 disclose the following items: (1) nature of earth excavated; 
 (2) depth of trench; (3) width of trench; (4) what part of the 
 total 400 feet length of trench and bell holes made on July 
 6th. (5) Was the trench back-filled for 400 feet on July 6th. 
 (6) How many of the 60 men were in the derrick gang. (7) 
 Did the derrick gang assist in excavating a part of the 400 
 feet of trench before beginning to lay pipe, or was a part of 
 the trench and bell holes made on the day before. Mr. Bil- 
 lings statement shows that 4 to 10 men working 10 hours 
 made 30 bell holes for 16 inch pipe. 30 bell holes would ac- 
 commodate only 360 feet of 12 foot pipes. He states that 400 
 feet were laid. It is therefore evident that some part (at 
 least 40 feet) of trench and bell holes must have been made on 
 some other day. 
 
 *Details of Water Works Construction, p. 55. (Published by "Engi- 
 neering Record" N. Y.)
 
 278 SULLIVAN'S NEW HYDRAULICS 
 
 In another chapter of Mr. Billings work we find some 
 "Notes on the construction of two miles of 16 inch water 
 main," in 1887. The date shows that it is the same pipe above 
 referred to. From these notes we gather the following facts: 
 The pipe was hauled an average distance of 1)^ miles over 
 good roads for 64 cents per ton of 2240 Ibs. The first division 
 of the pipe line was 2,927 feet in length. The trenching was 
 in good ground except a short stretch of quicksand and water 
 The total cost of labor for this division of the line was 32.30 
 cents per lineal foot, including all labor charged on the time 
 book from foreman to water boy, in a gang of 60 men. An- 
 other division of 2,100 feet length furnished sandy digging 
 with some tendency to caving. A brook had to be crossed 
 and a blow-off located which required the trench to be 10 or 
 12 feet deep for 100 feet length. An old 8 inch pipe had to 
 be removed, and 18 services furnished with a temporary sup- 
 ply. The cost of labor per lineal foot for this division was 
 
 34.7 cents. In the next division the digging was dry and 
 sandy, and caving of the trench was almost constant. An old 
 8 inch pipe had to be taken up, and a temporary supply main- 
 tained for 53 services. The cost of labor on this division was 
 
 41.8 cents per lineal foot. 
 
 In the next division the digging was wet and dirty. Old 
 pipe had to be taken up, and temporary supply maintained 
 for 30 services, and four connections made for a manufactur- 
 ing company. The cost of labor in this division was 47.4 
 cents per lineal foot. The mill connections being the princi- 
 pal cause of the increased expense. 
 
 Mr. Billings states that a detachment of the same gang 
 of men laid 2,000 feet of 8 inch pipe in new ground, good dig- 
 ging, at a cost of 17.3 cents per lineal foot for all labor, and 
 1060 feet of 4 inch pipe at a cost of 13.10 cents per foot, and 
 600 fee't of 6 inch pipe at 15.38 cents per lineal foot. 
 
 While the depth and width of trench and daily wages 
 paid are not stated, it will be near enough to assume that the 
 trenches were 5 feet plus one half the diameter (outside) of 
 the pipe to be laid, and the width of trench 2.333 to 3.00 feet,
 
 SULLIVAN'S NEW HYDRAULICS. 279 
 
 according to size of pipe (4*, 6", 8" and 16" diameters). For 
 amount of excavation in bell holes, refer to paragraph 
 110, ante. 
 
 Assume wages as follows: Foreman $3, Calkers and 
 yarners $2.25, Derrick gang (6 to 10 men) $1.75, laborers $1.50 
 per day of 10 hours. A gang of six men is sufficient to 
 handle the 4, 6, and 8 inch pipe, together with one yarner and 
 one calker. For the 16 inch pipe it will require 2 yarners 
 and 2 calkers and 10 men in the derrick gang. The remain- 
 der of the gang of 60 men will be laborers digging trench 
 and bell-holes ahead of the derrick gang. Subtracting the 
 number of calkers and yarnere and derrick gang and the 
 foreman from 60, the remainder shows the number of men en- 
 gaged in trenching and digging bell-holes. The length of 
 trench and bell-holes completed in 10 hours gives a basis of 
 calculating the cubic yards excavated by each man per day, 
 and the wages paid him per day furnishes the data for find- 
 ing the cost per cubic yard of excavation. In fairly good 
 digging it will be found that one man will make from 5.60 to 
 6.25 cubic yards of excavation per day of 10 hours. In ex- 
 cavating rock the average will be from, .50 to 1.50 cubic yards 
 of excavation per man per day, depending on the nature of 
 the rock. The excavation of deep, narrow trenches is very 
 much more expensive per cubic yard than railroad and canal 
 work in like earth or rock. See "Remark" under table No. 55, 
 Section 107. With labor at $2 per day the cost of excavation 
 in rock was $3.50 to $5.50 per cubic yard, measured in place, 
 in the City of Boston. This was an average of from .3636 to 
 .57 cubic yard of excavation in rock per man per day. In 
 very wet trenches the digging of sumps, sheet piling and 
 bracing, and pumping out of water is a heavy expense in ad- 
 dition to the ordinary cost, and will amount to from 40 cents 
 to $1.00 per lineal foot. 
 
 By reference to table No. 56, it will be seen that the cost 
 of laying 4", 6% 8" and 16" pipe as given above by Mr. Billings, 
 is about the same as given in Weston'a Table for "medium" 
 digging, and also about the same as shown in table No. 53 for
 
 280 SULLIVAN'S NEW HYDRAULICS. 
 
 cost of laying pipe in Denver, in sandy loam. Referring to 
 cost of trenching in Omaha (table No. 55) with wages of 
 laborers at $1.75 per day, and we find that a trench, in good 
 digging, 5.666 feet deep and 1.75 feet wide, cost .10^ cents per 
 lineal foot. In a lineal foot of this trench there were 5.666X 
 
 1.75-i-27=.36724 cubic yards of excavation, or l =2.723 lin- 
 eal feet of trench to the cubic yard of excavation. With the 
 cost at .104 cents per lineal foot of trench, and 2,723 lineal 
 feet to the cubic yard, the cost per cubic yard of excavation 
 was 2.723 X.104=.284 cents. 
 
 With wages at $1.75 per day of 10 hours, the average work 
 done by one man in one day was ' =6.162 cubic yards. 
 
 One man would therefore average 2.723x6.162=16.779 feet 
 length of trench of those dimensions and in that kind of 
 ground, per day. If wages were reduced to $1.50 per day, the 
 cost of trench would be \ part less, or .24343 cents per cubic 
 yard of excavation. In stiff clay or cemented gravel, one man 
 will average about 4.50 cubic yards of excavation per day, and 
 the cost at $1.50 per day wages, will be 33% cents per cubic 
 yard, or if wages are $1.75 per day, the cost will be .39 cents 
 per cubic yard of excavation. Hence in stiff clay or cemented 
 gravel the average progress per man per day would be 
 12.25 lineal feet of trench 5.666 feet deep by 1.75 feet wide. 
 Trenches for larger diameters than 8 inches would be both 
 deeper and wider, and the cubic yards of excavation per 
 lineal foot would be increased in proportion. 
 
 One yarner and one calker will joint cast iron pipe about 
 as follows, in an average days work: 720 feet of 4 inch pipe, 
 or 660 feet of 6 inch, or 600 feet of 8 inch, or 540 feet of 10 inch, 
 or 480 feet of 12 inch, or 360 feet of 14 inch, or 200 feet of 16 
 inch pipe.
 
 SULLIVAN'S NEW HYDRAULICS. 281 
 
 The number of joints made will depend on whether the 
 trench is wet or dry or stands up well or caves. The wages of 
 calkers and yarners are usually from 50 to 75 cents per day 
 more than the wages paid to ordinary laborers. 
 
 In estimating the cost of completing a cast iron pipe sys- 
 tem add five per cent to cost of the pipe in order to allow for 
 breakage. Also add the cost of engineering and inspection. 
 
 116 Lead Required Per Joint For Cast Iron Pipe. 
 
 The quantity of lead required per joint for cast iron pipe 
 depends on the dimensions of the lead space between the 
 bell and spigot, and also upon the manner in which the joint 
 is yarned or packed. There is no uniform rule observed in 
 the manufacture of cast iron pipe as to the dimensions of the 
 lead space, and consequently no rule can be framed for de- 
 termining the quantity of lead required per joint. The in- 
 ner diameter of some bells is uniform while in others it con- 
 verges. Inside of some bells there is a groove, semi-circular 
 in form, extending around the inner circumference of the 
 bell. Others are plain without grooves. Different foundries 
 adopt different depths and slopes of the lead space, and some 
 yarners will put twice as much yarn into a joint as others. 
 Some engineers adopt the rule of estimating 2 Ibs. of lead 
 for each inch diameter, as being approximately the quantity 
 required per joint. The result of this rule is too much for 
 small diameters and not enough for large diameters. The 
 amount of lead per joint used in recent practice is from one. 
 third to one-half less than formerly, and the tendency is to 
 reduce the quantity still more. 
 
 In laying 6", 8" and 16" pipe in Taunton, Mass., in 1887, 
 Mr. Billings used 7.68 Ibs. per joint for 6 inch pipe, 9.12 Iba., 
 per joint for 8 inch and 21 Ibs. per joint for 16 inch pipe.
 
 282 
 
 SULLIVAN'S NEW HYDRAULICS 
 
 
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 Diam. 
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 11 
 
 II 
 
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 Diameter 
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 s 
 
 If belle and lead spaces were designed and specified by 
 engineers with regard to flexibility of joint and economy in 
 the quantity of lead and packing required, one third the lead 
 now used would be saved and the joints would be equally 
 strong and much more flexible and satisfactory. It is gen-
 
 SULLIVAN'S NEW HYDRAULICS. 283 
 
 orally agreed that the calking tool does not affect or set up 
 the lead to a greater depth than one inch, and the lead be- 
 yond this is worse than wasted, for it only stiffens the joint, 
 which is really an element of weakness. 
 
 AB the circumference of a pipe increases directly as the 
 diameter, and as there is no sufficient reason for increasing 
 the depth of bell as the diameter increases, there is no reason 
 why the quantity of lead required per joint should not vary 
 directly with the diameter if the bell and spigot were prop- 
 erly designed. 
 
 Three inches is an ample depth of bell for any diameter, 
 and greater than necessary. Unequal settlement in the 
 trench must be prevented by proper laying anyway.
 
 SULLIVAN'S NEW HYDRAULICS. 
 
 INDEX. 
 
 A 
 
 PAGE. 
 
 Abbot, Gen. H. L., discussion of data 84, Bee also 23, 30, 54, 98, 97 
 
 Abbot, Humphreys and, River Formula, , 11 
 
 Abrasion of Banks by frost and flow gl, 121,189. 222, 229 
 
 Acceleration of gravity 21,22,31, 32,60, 61,62,66,99,215,216 
 
 Acre, area of, in square feet 166 
 
 Action and reaction at bends 194,217,223 
 
 Action of frost on canal banks 81, 121, 222, 223, 228, 229 
 
 Adjustment of side slopes of canals 228,231 
 
 Air, friction of, at water surface 216, 217 
 
 Alignment of canal or flume 69, 96, 97, 124, 125, 223, 224, 229, 234, 235 
 
 Altitude affect 3 g in the formula 99 
 
 Amount of pipe laid per day 276,277, 281 
 
 Angle of bend in canals 186, 187, 189, 213, 217, 223, 224, 229 
 
 Angleof bend in pipes 186, 187,188,189 
 
 Angle of repose of earth 229, 230 
 
 Appendix I. New Orifice and Weir formulas 242, 249 
 
 Appendix II . Water works general data and f 01 mulas 249, ' 
 
 Application and limitation of formulas 6,36,37,101,105,232 
 
 Aqueducts 27, 28,29,09,70,96, 97,124,125 
 
 Area of canal, how found 119, 120 
 
 Area of canals, tables of 121,125 
 
 Area of egg-shaped sewers 112, 113 
 
 Area of nozzle discharge; how determined 171, 173, 182 
 
 Area, of one acre in square feet 166 
 
 Area of rivets to net pipe metal 200 201, 202 
 
 Area of channel varies with square of friction surface, 34, 36, 39, 40, 49 
 
 104,105, 238, 239 
 
 Ashlar masonry, coefficient 69, 70, 74. See 28, 29, 58, 240, 241 
 
 Asphaltum, density of 57 
 
 Asphaltum coated cast iron pipes, coefficient 63, 61, 67, 151, 15:5, 260, 262 
 
 Asphaltum coated riveted pipe, coefficient, 63, 64, 67, 110, 111, 151, 152, 153, 
 
 186, 197. 260, 262 
 
 Asphaltnm coated welded pipe, coefilcient 64, 185, 197, 260, 262 
 
 Asphaltum coating, how made and applied Ill, 179, 185 
 
 Average consumption of water in towns and cities 249, 252 
 
 Average of roughness of perimeter 28,58, 80,81, 240,241 
 
 Average value of C for irregular perimeter 28, 48, 58, 75, 76, 81, 210, 241 
 
 Banks of channel, density of, affects coefficient 1..54, 96, 97 
 
 convergent and irregular, 6, 28, 29, 58, 76, 81, 84, 212, 213 
 
 ......I........ .....214, 224, 236 
 
 Bazin's formula 10 
 
 Bell holes in pipe, trench 275,276 
 
 Bends in open channels 186, 188, 189, 213, 217, 223, 224, 229 
 
 Bends in pipes 186, 187,188
 
 INDEX. 285 
 
 PAGE. 
 
 BlackwelTs formula 9 
 
 Bodies, law of falling 31,32.60,61.62,66 
 
 Boston, cost of pipe laying in 271, 272 
 
 Bottom velocity, controlled by grade 220, 221, 223, 225 
 
 grade required for 226,228,230 
 
 formula for 225,226,228,230 
 
 which erodes and moves material 227 
 
 value of R does not affect 219, 220,223, 225 
 
 ratio to other velocities 218, 219. 220, 22(5, 236 
 
 Brahms & Eytelwein's formula 10 
 
 Brass fire nozzles 140 143 
 
 Brass pipes, coefficient .".'.' .'.'.'.'l4i,'l42, 144 
 
 Brick conduits 27,28,29,70, 71,72,73,111,112 
 
 Brick /ewers HI, 112,113,114 
 
 Bursting pressure 52,195,196 
 
 Calculating weight of riveted pipes 206, 207 
 
 Canal, area of cross-section, how found 119, 120 
 
 areas of. table 121,125 
 
 alignment 69, 96. 97, 124, 125, 223, 224, 229, 234, 235 
 
 banks, affected by frost 81, 121, 222, 223. 228, 229 
 
 banks, convergent and irregular . ..6, 12, 27, 28, 58, 213, 221, 240, 241 
 
 banks, density of, affects coefficient 54, 55, 56, 57, 67, 96, 97, 124 
 
 benda in 69, 96, 97, 124, 186, 188, 189, 213, 217, 223, 22 1, 229 
 
 bed, stability of 222,226,227,230 
 
 bottom velocity in, controlled by grade 220, 221, 223, 225 
 
 bottom velocity, eroding power 227 
 
 bottom velocity, formula for 225, 226, 228, 230 
 
 bottom velocity, grade required for given 226, 228, 230 
 
 bottom velocity, no ratio to others 218,219,220, 226,236 
 
 bottom velocity, size of canal does not affect 219, 220, 223, 225 
 
 Coefficients, tables of ....87,96 
 
 coefficients vary with mean roughness, 27, 28, 29, 80, 58, 75, 76. 81 240 
 
 dimensions of, how found . Ill " II" "II 1 1 II 1 1 II II I .'I . iJ9, i20J 121, 125 
 
 djmensions to carry given flow 231,232 
 
 dimensioi s, formulas for R, p and a. . 231,232 
 
 effective value of grade or sk pe 237, 238, 239, 241 
 
 efficiency of 
 
 erod ng velocity in 222,223,224,229 
 
 evaporation and leakage 232,233 
 
 excavation, table 275 
 
 See also 121,125 
 
 float measurement of velocity in 68, 96, 97, 235, 236 
 
 See also ....24,25 
 
 flow in 212,236 
 
 See also r.8, 210, 241, 121, 125 
 
 flume fo mirgpart of 234 
 
 See also 07, 68, 69, 96, 97, 124,125 
 
 formula for flow 105,241 
 
 Seeabo 124,125 
 
 grade for bottom velocity 226,228,230 
 
 grade for mean velocity 120, 121,128 
 
 grade, value of, varies with y'l 3 237, 239, 211 
 
 hj dran ic mean depth, how 1'ound 119, 120, 121, 231, 232 
 
 length in which is on., loot fall 121, 125, 128, 181 
 
 mean velocity formulas 52,53,98,105,124, J2r>, 241 
 
 mean velocity in 221, 222, 235,23.1
 
 286 SULLIVAN,S NEW HYDRAULICS. 
 
 PAGE. 
 
 Canal, new, flow in 92.232,233 
 
 new losses from 232,233 
 
 perimeter, how found 120, 231, 232 
 
 perimeter, roughness defined 96, 97 
 
 Seeal-o 27,28,29,58,240.241 
 
 quantity discharged by 121, 125, 235, 236 
 
 ratio of velocities in 218, 219, 236 
 
 See also 25 
 
 reaction ae bends ia 189,217, 223 
 
 reactions at perimeter 218, 221 
 
 return seepage 233 
 
 Bide slopes 222, 223,228,229,230 
 
 slope of, for bottom velocity 226, 228, 2EO 
 
 slope of, for mean velocity 120, lv;l, 128 
 
 slope or grade varies in value with -j/r 3 237.239,241 
 
 slope, scouring velocity depends on 220, 227 
 
 surface velocity 216,217, 221, 222, 236 
 
 stability of bed 222,226,227,230 
 
 whirls and boi's in 217 
 
 wind, effect on flow 217 
 
 Capacity, relative, of pipes 101 
 
 Cast iron, specific gravity of 57 
 
 Cast iron nozzles and giants 140, 171, 180, 181, 182, 183, 210, 211 
 
 Cast iron pipes, densit y of affects coefficient 54, 57 
 
 cost of laying 270.281 
 
 dimensions and weight 269, 270, 271 
 
 dimensions and contents 162, 163 
 
 joints 209,270,281.282,283 
 
 tensile strength 198 
 
 thickness of eht-li 197,198,268,269 
 
 weight of 269, 270, 271 
 
 Cement joints, vitrified pipes 161, 162 
 
 Cement linings, coefficient 55, 66, 69, 71 
 
 Cement mortar linings, coefficient 55, 66, 67 
 
 Census of cities, water supply 249, 252 
 
 Circle, properties of, 34, 35 
 
 ( ' i ties, water supplied to various 219, 252 
 
 Cities, cost of water in 251,252 
 
 Clay roll for running lead joints 209 
 
 Coating for water pipes 111,179,180,185 
 
 Coefficients, of entry 7,59.60,62 
 
 flow, or velocity 38, 51, 54, 67, 99, 101, 102, 259, 260 
 
 friction or resistance. . . .37, 48, 54, 98, )01, 102, 261, 262 
 Coefficients, are constant, 29, 30, 37. 38, 39, 42, 47, 48. 58, 62, 65. 66, 138, 240, 
 
 241 
 
 are correct index of roughness 42. 47, 48, 240, 241 
 
 conversion of 51,53,101, 128, 155,162 
 
 density of perimeter affects 54,96,124,125 
 
 discussion of 237,241 
 
 Seeaho 34 to 54 
 
 in Chezy or Kutter formula 6, 7, 42, 43, 44, 81, 241 
 
 in terms of cubic feet 51, 100 
 
 in terms of diameter in feet and head 98,106 
 
 in terms of diameter in inches 51, 118 
 
 in terms of diameter and pressure 101 , 102 
 
 in terms of gallons per minute 51, 137 
 
 in terms of hydraulic m< an depth 103, 104, 106, 107 
 
 orifice 7, 96,97,246.247,248, 249 
 
 reverse variation of 27 : 28, 29, 30, 58, 240, 241
 
 INDEX. 287 
 
 PAGE. 
 
 Coefficients, varies only with roughness 240, 241 
 
 See also 58,23,29 
 
 for aqueducts.... 27. 28, 29, 58, 67,68. 69, 70, 71, 124, 125,240, 241 
 
 asphaltum coated cast iron pipes 260, 262 
 
 See also 63,64 
 
 asphaltum coated riveted pipe 57, 67, 144, 151, 260, 262 
 
 brass fire nozzles 142, 143. 144, 210, 211 
 
 brass pipes 141,142.144 
 
 brick conduits, 27, 28, 29, 58, 69, 70, 71, 72, 73, 111, 112, 113, 
 
 124, 125 
 
 cast iron pipes 52, 54, 55, 64, C5, 67, 108, 150, 260, 262 
 
 cast iron nozzles 6,146,210.211 
 
 cement lined pipe 55,66.69,71 
 
 cement mortar lined pipe 55, 66, 67, 260, 261 
 
 convergent pipes 142, 143, 146, 210, 211 
 
 converse lock-joint pipe 185, 186, 209 
 
 concrete conduits 73 
 
 conduits of wood 07, 68, 69, lt>0, 161, 124. 125 
 
 cansls 87,96 
 
 See 27,28,29,58,240,241 
 
 different depths of How 28, 29, 58, 240, 241 
 
 earthenware pipes 161, 162 
 
 flumes 67, 68, C9, fc6, 124, 125, 234 
 
 hammer dressed btor.e 70, 75 
 
 lead pipes 57,59.67,193 
 
 rivers 58, fcl, 96, 240, 241 
 
 rough masomy 74, 75, 76, 86 
 
 rubble masonry 76.77, 78, 92 
 
 rubber fire hobo 137,138,140 
 
 rubber pipes 144 
 
 vitrifiu d pipes 161,162 
 
 wooden pipes 67,68,69,160,161,124,125 
 
 wiers and oiific's 242,249 
 
 Combination of different roughnesses .f verimeter, 27, 28, 29,30, 58, 240, 
 
 Common properties of pipes and open channels 36. 37, 104, 105, 231, 232 
 
 Concrete conduits 73 
 
 Conical pipes, friction in 140, 146, 172, 181, 182, 183, 210, 211 
 
 Consumption of water in citits 251,252 
 
 Contents of pipe per foot 162, 163 
 
 Contracted vein, form of 143,210,211 
 
 Convergent pipes, nozzles and reducers 143, 146, 210, 211 
 
 See 163,171,180 
 
 Conversion of coefficient s 51, 53, 101, 128, 155, 162 
 
 Conversion of U. S. to Metrical measures 165,166 
 
 Correction of text 237,238,239,240,241 
 
 Cost of pipe laying in Boston 271, 272 
 
 Denver 270,271 
 
 Omaha 272,273 
 
 Weston's tables for 273,274 
 
 Cost of trenching i 270, 276, 281 
 
 Cost of water per 10CO gallons 251,252 
 
 Cox's formula ' 
 
 Cubic foot of water 167 
 
 Cubic measure 16 < 
 
 Cubic feet in equivalent gallons 256, 259 
 
 Cubic feet per second, logarithms of 2at>, >9 
 
 Cubic yards of excavation per man 276, 277, 281 
 
 Cubic yards of excavation, table of 273 
 
 Current meters.... 24,71,96,97
 
 SULLIVAN'S NEW HYDRAULICS 
 
 PAGE. 
 
 D'Arcy's formula 8,11 
 
 D' Arcy & Bazin's formula 11, 22, 23 
 
 D'Arcy Pitot tube gaugings 68,74 
 
 Data of flow defective 23 to 30, 58, 60, 61, 62,66, 72,81, 84, 96, 97 
 
 Data of flow forming basis of author's formula 65, 137. 138 
 
 Data of flow, how to test 60, 61, (Compare with 65, 138) 
 
 Data of flow in pipes, conduits and rivers 58 to 96 
 
 Data of water supply in cities 249,252 
 
 Data of water works construction 249,283 
 
 D'Aubuieson's formula 9, 11 
 
 Days work of one man '. 276, 277,281 
 
 Decimal parts of inch and f iot 164,205 
 
 Defects in old formulas for fl . w, 3, 8, 23, 37, 3<, 43, 44, 48, 61, 62, 66, 237, 241 
 
 Defects in sheot metal, how detected 208 
 
 Defects in weir aud orifice formulas 6, 7, 64, 68, 96, 97, 242 to 249 
 
 Density of perimeter affects coefficient 54, 57, 95,97,124,125 
 
 Denver, Colorado, cost of pipe laying in 270, 271 
 
 Depth, hydraulic mean, of canal, how found i20, 231,232 
 
 egg-shaped sewers 112, 113 
 
 Depth of penetration of frost 276 
 
 Depth of pipe trench 276 
 
 Diameter found from area 171, 172, 173 
 
 Diameter of giant, nozzle, or orifice, how found, 171,172,173,210 211 
 
 (Sao 140 to 148) 
 
 Diameter of cast iron pipe for given discharge, 100, 108, 109, 136, 149. 161, 
 
 184,254,259260,263 
 
 Diameter of coated pipe forgiven discharge 100, 102, 110,260 
 
 Diameter of cement mortar lined pipe for given discharge 260 
 
 Diameter of earthenware pipe for given discharge 161, 162 
 
 Diameter of steel pipes forgiven discharge 260 
 
 Diameter of welded pipes for given discharge 260 
 
 Diameter of wooden pipes forgiven discharge 260 
 
 See 160, 161, and 67.68 
 
 Diameter of pressure or power mains 170, 171, 181. 185, 186, 261. 262 
 
 (Sen 100, 149, 150) 
 
 Dimensions of canals 120, 124, 125, 23', 232 
 
 cast iron pipes 162, 163, 269, 270, 271 
 
 cast iron gi-mts 146, 210,211 
 
 fire nozzles 140. 143. 210, 211 
 
 flames 124.125 
 
 reducers 210,211 
 
 sheet metal for given diimeter 2 6 
 
 sewers : Ill, 112,113 
 
 Discharge area of nozzle 171, 173, 182 
 
 brick sewers 112,113 
 
 canals 121,124 
 
 cast iron pipes 108, 109, 127, 129. J50, 151, 268, 264, 268 
 
 coated riveted pipes 110, 111, 151, 152, 153, 2BO 
 
 cement lined pipes 260 
 
 See T.:. 55,66,67,69,71 
 
 earthenware pipes Ml, 162 
 
 flumes 124, 125,234 
 
 wooden pipes 67, 68, 69, 160, 162, 124, 125, 260 
 
 E 
 
 Earth, angle of repose 229,230
 
 INDEX. 289 
 
 PAGE. 
 
 canals in 87,96,121,124,212 
 
 ,_ (See 12, 54, 57, 58, 241) 
 
 Earthenware pipes 161,162 
 
 Effective value of the slop- 48,237,241 
 
 Efficiency of canal 228 
 
 Efficiency of water wheel 169,183 
 
 Egg-shaped sewers Ill, 112. 113 
 
 Elementary dimensions of pipes 162, 183 
 
 Eleventh roots and powers 184 
 
 Entry, resistance to 7. 59. 60, 62 
 
 Equilibrium of gravity and resistance 22,24,27,28, 37, b2, 215, 216 
 
 Eroding velocity 222,223,227,229 
 
 Erroneous data of flow, example of 60, 6l, 62 
 
 See 23 to 30 
 
 Errors in formulas for flow 3, 8, 13, 23, 37, 42, 44, 61, 62, 6<j, 2*7, 241 
 
 Errors in orifice and weir formulas 6, 7, 64, 68, 96, 97, 242, 249 
 
 Evaporation and leakaee from canals 232,233 
 
 Excavating pipe trenches, cost 270 to 281 
 
 Excavation, table of 275 
 
 Experiments forming basis of our formula 65,138 
 
 F 
 
 Factor of safety 197 
 
 Fall, distance for one foot 121, 125, 128, 181 
 
 Fall, head, or slope 99,128,157,158,161,169,180 
 
 Fulling bodies, law of 31,32 
 
 Kire hose 137,146 
 
 Fire hydrant presi-ure 139, 154,155, 164 
 
 Fire nozzles 140, 146,210,211 
 
 Floats, d-.uble 25,96,17,235.236 
 
 surface 25,96,97 
 
 Flow, discus ion of '. 34, to 58,212, 237, 241 
 
 S*e21to30 
 
 generwl formulas for 98, JOS, 241, 259, 2 0, 261. 262 
 
 in silted conduits 27, 28, 29, 30, 58, 237, 241 
 
 in canals and river- 21, 30. 48. 54, 57, 58, 81, 212, 237, 241 
 
 permanent and uniform 27, 37, 212 
 
 of a par icle of water 218 
 
 resi=t nee to. directly as roughness, 22, 23, 32, 33, 48, 58, 237, 239, 241 
 
 resistance to, inversely as^/r 8 40, 41, 42, 48, 49, 237, 241 
 
 Fumes 67,68,69,96,97,124,125,234 
 
 H oot au.-l inch, decimals 164, 205 
 
 Foot, cubic 167,256,259 
 
 Foot pound 168 
 
 Form of nozzles and reducers 143,210,211 
 
 vena contracta 143,210,211 
 
 Formula, affected by great altitude 99 
 
 basis of the writer's 31, 32, 33, 34, 35, 36, 54, 65, 138, 237, 241 
 
 for area of egg. shaped conduits 113, 114 
 
 area of nozzle discharge ....172, 173, 182 
 
 area of rivets , 202 
 
 area of trapezoidal canals 119 
 
 bends 187,190, 213,217,223,224,229 
 
 bottom velocity 225, 226, 228. 230 
 
 C 42,43,46,48,53,56,58,106 107,241 
 
 capacity of nozzle 173, 174, 182 
 
 Chezy or Kutter coefficient 6. 7. 42. 44, 81, 2U 
 
 coefficient of flow 38,51,53.99,101.102
 
 290 SULLIVAN'S NEW HYDRAULICS. 
 
 PAGE. 
 
 Formula for coeffici ntof friction 37,48,98,101, 102 
 
 combination perimeters 58, 241. (See 27, 28, 29) 
 
 convergent pipes 143, 146, 210, 211 
 
 conversion of coefficient 51, 53, 301,128,155,162 
 
 contracted vein 143, 146,210,211 
 
 cubic feet required for power 169 
 
 diameter of conduit 114,259, 260 
 
 diameter cf cast iruu pipe, 1 0,102,104, 106, 107,136,149,254, 
 
 259,260 
 
 diameter of coated cast iron pipe 260 
 
 diameter of cemen t mortar lined pipe 26U 
 
 diameter of earthenware pipe 161, 162 
 
 diameter of riveted, coated pipe 110,111, 260 
 
 diameter of uucoated steel pipe 260 
 
 diameter of wooden pipe 160, 161, 260 
 
 diameter of pressure mains 170, 171, 181, 185,261,262 
 
 diameter of nozzle discharge 172, 173, 182 
 
 dimensions of canals 119, 120, 124. J25, 231, 232, (See 104, 105) 
 
 reducers 143, 146, 210, 211 
 
 sheet metal 206 
 
 discharge from head or slope 154 
 
 losaof head 153, 154 
 
 loss of p ; esbure 157 
 
 pressure 156 
 
 discharge of nozzle 172, 175, 183 
 
 efficiency of a machine 169 
 
 effective head 169, 180 
 
 entry head 60 
 
 factor of safety 197 
 
 fall or grade 99, J01, 102, 103, 104, 103, 107, 128, 1C9, 180, 181 
 
 falling bodies 32 
 
 rinding head or (dope 157, 158, 161. 169, 180, 263 
 
 finding pressure required 139, 154, 155 
 
 finding n from m 50, 51, 152, 157, 262 
 
 friction at bends 187. 190 
 
 friction coefficient 37,48 
 
 friction head SO, 98, 101. 104, 130, 132,133,149,150 
 
 friction in gints 146, 148, 173, 1U, 182, 210, 211 
 
 friction in reducers 210, 211 
 
 grade of canal, bottom velocity 226, 228, 230 
 
 grade of canal, mpan velocity 121,125,128 
 
 horse power 168, 19, 170, 181, 185, 186 
 
 hydrant pressure required 139, 154, 155, 164 
 
 hydraulic mean depth of canal 119, 120, 121, 231, 232 
 
 ,sVl04,105) 
 
 hydraulic mean depth of epg-shaptd sewer 112.113 
 
 hydraulic moan radius of pipe 35, lot 108 
 
 inclination of pipe 99, 127. 129, 136, 149, 157, 159. 263 
 
 jet velocity 172,175,183 
 
 length and fall 128,181,263 
 
 mean velocity 42, 52, 53, 65, 9, 102, 103, 105. 108, 110, 112, 241 
 
 net rffective head 169,180 
 
 nozzle area 172,173,182 
 
 iiozzle diameter 172.173,182,210,211 
 
 nozzle discharge 172,175, 183 
 
 nozzle proportions 143, 146, 210, 21 1 
 
 nozzle testing 173, 174,182, 183 
 
 orifice coefficient 246, 249 
 
 orifice discharge 249
 
 INDEX. 291 
 
 PAGE. 
 
 Formula for perimeter 35, 112, 113, 119, 120, 231, 232, (104, 105) 
 
 pitch of rivets 200,201,202 
 
 power nozzles H6, 171, 180. 183,210,211 
 
 power mains 170,171,181,185,186,261, 262 
 
 pump pressure 139, 154, 155 
 
 pressure 101, 102, 103, 105, 139, 154. 155, 156, 194, 195, 196 
 
 pressure lost, in nozzle 142, 146 
 
 pressure lost in hose 137, 138, 140 
 
 pressure lost in pipes 102, 103,156,157 
 
 proportions of nozzles 143,146,210,211 
 
 proportions of sheet metal 206 
 
 proportions of reducers 210, 211 
 
 proportions of riveted joints 200, 205 
 
 quantity discharged, canals 124, 125 
 
 quantity discharged, egg-shaped sewers 113, 114 
 
 quantity discharged, giants or nozzles 172, 174, 182, 183 
 
 quantity discharged, pipes.. .153, 154, 155, 156, 157, [108, 110, 264] 
 
 ratio of rivet to plate area 200,201 
 
 resistance at bends 186,189 
 
 resistance at entry 60 
 
 resistance in convergent pipe 142, 146, 210, 211 
 
 resistance to flow 41, 48, 49, 50, 98, 101, 102, 103, 104 
 
 rivet area 202 
 
 riveted joints 200, 208 
 
 slope, bottom velocity 226,228, 230 
 
 slope, mean velocity 114,121,128,129,136,149, 181, 263 
 
 strength of riveted joint 207,208 
 
 supply pipe, rtiameter 255. 261, 262 
 
 testing capacity of nozzle 173, 174 182, 183 
 
 testing friction loss in nozzles 173, 174, 182 
 
 test ing strength of pipe 197, 207, 208 
 
 thickness of cast iron pipe 198, 268,280 
 
 thickness of ductile pipe 197 
 
 total head 99, 100. 103, 104, 106, 107, 149, 151, 157, 158, 180 
 
 total pressure 198 
 
 total pressure lost 102, 103,156, 157 
 
 velocity along the bottom i25, 226, 228, 230 
 
 velocity head 32.49. 61,146,169 
 
 velocity pressure in firehose 139 
 
 velocity t ressure in fire nozzle 141 
 
 velocity of nozzle discharge 172,175,183 
 
 velocity in vertical pipes 107 
 
 venaconiracta 143,210,211 
 
 watT p-wer 168,169,180 
 
 weight of cast iron pipe 269, 270, 271 
 
 weir coefficients 242,249 
 
 weir discharge 64, 242,249 
 
 wetperimeter, canals 36,104,106,119,120,231,232 
 
 wet perimeter, eeg-shaped conduit 112, 113 
 
 Formulas, a...., 
 
 oldw ir ................. 6, 7,61,68,96,97,242,249 
 
 ::::iw4ft, 
 
 of other writers ............... 8, 9, 10, 11, 23. 189, 190, 24', 244, 246 
 
 Foundation of the formula .......... 21, 31, 32, 33, 84, 35, 36, 65, 138, 237, 241 
 
 Francis, J. B^weTr^periments'.'.V. V.'.'.V.'.'. V. '.'.'.'.'.'. V.'.V.V.'.'.V.'.'.242V244; 246 
 Freezng of canal banks .............................. 81,121,222,223,228,229
 
 292 SULLIVA.N.S NEW HYDRAULICS. 
 
 PAGE. 
 
 Freezing of pipes ....180,276 
 
 Friction, laws of ... 3288 
 
 Friction coefficient, defined 87 
 
 how determined 48 
 
 is a constant 37, 48, 61, 62, 66, 138,237, 241 
 
 formula for, 41, 50, M, 98, 101, 103, 1C4, 130, 132, 152, 157, 
 
 170,261, 262 
 
 head, formula for 50,98, 101,104,130, 132, 133, 149, 150,263 
 
 varies inversely with^ r s 39, 40, 41, 49, 50, 237, 241 
 
 surface always varies with y/area.. ..34, 36, 39, 49, 104, 105, 240, 241 
 
 pressure in lea her fire hose 140 
 
 in rubber fire hose 137, J38 
 
 in pipes 102,103,156,157 
 
 in convergent pipes 142, 143, 146, 163, 173, 174, 182, 210, 211 
 
 of a>r with water surface 216, 217 
 
 at bends in pipes 187, 190 
 
 Frost, depth of, in earth 276 
 
 G 
 
 Gallons of water required 249,256,259 
 
 Gauges and weights of sheet metal 206 
 
 Ganging, by current meter 71, 96, 97 
 
 by D'Arcy Pitot tube 68, 74 
 
 by floats 23,24,25,68,96,97, 235, 236 
 
 by weir and orifice 6,7,64,68,96,97,242,249 
 
 Gaugings, data of 58 to 96, 137, 138, 146, 148 
 
 General formulas 52,53,54,98,105,241,259,260,262 
 
 water works data 249,283 
 
 Giants and nozzles for power 143, 146, 163, 171, 173, 180, 183, 1< W 4, 210, 211 
 
 Grade of canal, for bottom velocity 226,228,230 
 
 formran velocity 121,125, 128.230 
 
 conduit for mean velocity 114 121, 125, 126, 127 
 
 Gradient, hydraulic 194,195.196 
 
 Granular metal, resistance of to How 55 
 
 Gravity, law of 31,32,99 
 
 acceleration and resistance, 21, 22, 23, 27, 28, 33, 36, 3?. 40, 42, 48, 
 
 60, 62,215,216,237,241 
 
 specific, affects coefficient 54, 55, 57, 96, 97, 124, 125 
 
 of' various materials 57 
 
 Grouped data of flow 58 to 97, 137, 138 
 
 experimental coefficients 58 to 97, 137, 138, 146, 148 
 
 Growth of cities 251 
 
 Gunter's chain 166 
 
 H 
 
 Head due to velocity 32 
 
 effective 169,180,183 
 
 effective, varies with y/r* 42. 48,237,239, 241 
 
 entry 7,59, 60,62 
 
 forgiven horsepower 169, 180,183 
 
 friction, formula 50, 98, 101, 104, 130, 132, 133, 149, 150, 263 
 
 friction, varies inversely with ^/r 39, 40, 41, 49, 50, 237, 239 
 
 pressure 101,102,139,154,194,196 
 
 loss of, in coated pipes 134,135,151,152,153 
 
 loss of, in cast iron pipes 130,132,150,151,263,264 
 
 loss of , in fire hose 137,145 
 
 loss of in fire nozzles 140,143
 
 INDEX. 293 
 
 PAGE. 
 
 Head loss of in giants 146,148,171,182,210 
 
 lost at bends 186,189,217,221,223 
 
 lost in conical pipes 140,143, 146,210 
 
 to force given discharge 99,103,139,148,149,154 
 
 velocity 32,41,49, 61,146,169 
 
 vertical pipes 107 
 
 Hose, leather 140 
 
 rubberlined.. 137,138,145 
 
 stream 164 
 
 Horse power of wa tar 168,169,170,180,183 
 
 Hydrant, size of pipe to supply 164 
 
 pressure required, 139, 154,155 
 
 Hydraulic giants, 143,146,170,182, 183,210,211 
 
 grade line 194,195,196 
 
 mean depth (R), 35,36, 104,106,119,120,112,113 
 
 mean depth, (R), formula 99,231,232 
 
 mean radius . . 35 
 
 Impulse water wheels 168,180,183 
 
 Inch and foot, decimals of 164,205 
 
 Inclination of open channels 121, 125, 128, 226, 228, 237, 241 
 
 pipes 127. 129, 157,159,263 
 
 sewers 114,121,128.161,162 
 
 sewers to prevent deposit 161, 162 
 
 Inhabitant, water supply per .' 249, 252 
 
 Iron and steel, tensile strength 198, 199 
 
 density of 54,57 
 
 >' weight of sheet 206. 207 
 
 pipes, thickness of 197, 198 
 
 Irregular channel roughness 6, 27. 28. 10, 58. 213, 236,241 
 
 Irregular diameter pipe lines 175, 176, 177, 178, 210, 211 
 
 J 
 
 Jet, velocity 172,175,183 
 
 Joining small to larger pipes 210,211 
 
 Joining pipe lengths 161, 162, 180.209 
 
 Joints, packing required IfcO, 209, 2.70 
 
 lead required 270, 281, 282, 283 
 
 testing riveted 207, 208 
 
 proportions of riveted 204, 205 
 
 K 
 
 Kilograms, equivalent pounds 167 
 
 Kilometers, equivalent square yards 166 
 
 Kutter's formula 6,7,9,10,23,42,44,81,82.241 
 
 L 
 
 Land measure, U, S . and metric 165 
 
 Lap of riveted joints 206,207 
 
 Law of friction 32, 33, 37, 42, 48, 237, 238, 241 
 
 Law of gravity 31,82,37,42,48,237,238,241 
 
 Laying pipe 180,270,281 
 
 Leadfointe 209.270,281,283 
 
 Lead pipes, coefficient 57,59, 67,193 
 
 Leakage from canals 232, 233 
 
 Leather firehose 140
 
 294 SULLIVAN'S NEW HYDRAULICS 
 
 PAGE. 
 
 Length for one foot fall 121,128,181,263 
 
 Length of reducer 210,211 
 
 Length of a sheet of metal 206 
 
 Limitation of the formula 6, 28,104,105,232 
 
 Lineal measure, U.S. and metric 165 
 
 Local slope 28 
 
 Location of canal 23S 
 
 Lock-joint pipe 185,186,209 
 
 Logarithms of q 256,259 
 
 Loss of head at bends 187, 190,191,213,217,223,229 
 
 diameter for given 10 J, 149, 170, 180, 261, 262, 264 
 
 discharge found from 153,154 
 
 for given discharge 132, 133, 150, 151, 153, 263, 265 
 
 e for given discharge 156, 157 
 
 discharge found from 157 
 
 M 
 
 Mains, power or pressure 170, 175, 181, 185, 186, 194, 261, 262 
 
 Man, work of per day 276,277,281 
 
 Masonry conduits 27, 28, 29, 69, 70. 71, 72, 76, 112, 113, 124. See 58, 241 
 
 Mean, surface and bottom velocity ratios ... 25, 218, 226, 236 
 
 Mean hydraulic depth 5, 36, 104, 106. 112, 119, 120,231, 232 
 
 Mean roughness 12, 27,28,29, 30,58,238,241 
 
 Mean velocity, open channels 104, 121, 124, 221, 235, 236 
 
 Measures, U. S. and Metric...*. 165,166 
 
 Metal, sheet, tests of 208 
 
 specific gravity of 57 
 
 weight of sheet 206 
 
 Meters, current 71. 96, 97 
 
 Metric Measures 165,166 
 
 N 
 
 Net horse power, cubic feet required 169 
 
 diameter required 170,180, 181, 185,186,261,262 
 
 head required 168, 169, 180. 181 
 
 New canals, flow in 92, See 78,79 
 
 losses from 232,233 
 
 Notation used 34. 35, 36 
 
 Nozzles 143,146,172,173,174,182,183,184,210,211 
 
 o 
 
 Omaha, cost of laying pipes at 272, 273 
 
 Open channels and rivers 12, 22, 28, 56, 58, 96, 97, 121. 212, 237. 239, 241 
 
 coefficients 27, 28, 29, SO, 58, 96, 97, 241 
 
 Orifice, area for given discharge 172, 173, 182 
 
 coefficients 7, 64, 96,97.246,249 
 
 formulas 7,64,249 
 
 P 
 
 Packing for pipe joints 180,209,270 
 
 Per capita water supply 249,251,252 
 
 Perimeter, action of frost on 81. 121, 222, 223, 228, 229 
 
 average of roughness 28, 29, 30, J8, 58- 75, 76, 80, 81, 96, 241 
 
 classification of necessary 12, 51, 55, 56 
 
 classified 58 to 97 
 
 density of, affects flow 54,57,96,97,124,125
 
 INDEX. 295 
 
 PAGE. 
 
 Perimeter, different class es of, combined 28, 29, 30, 58 241 
 
 formulas for 112,113,119 120 231 232 
 
 irregular 6, 28, 29, 48, 58, 75, 76, 81, 84, 96, 9?! 2)2,' 2U, 224* 236 
 
 ratio of area to...., 34, 35,86,89, 40.41,42, 48, 104, 105, 237,238,241 
 
 resistance of 21, 22, 23, 82, 33, 48, 58, 81, 96, 97, 212, 237, 241 
 
 roughness of, defined f 4, 96. 97, 124, 125 
 
 roughnef s governs coefficient 22, 23, 28, 32, 33, 48, 58, 240 
 
 scour and fill 26,82,83,224 
 
 stability of 121, 222, 224, 226, 22T, 280 
 
 variation of C 48, f 8. 240, 241. See 27, Z8, 80 
 
 varies with d, R or y/area .... 34, 36. 39, 40, 48, 49, 104, 105, 237, 241 
 
 Pipe, area of, formula 35 
 
 areas and diamenters. tabl ] 62, 163, See 109, 110, 1 12 
 
 diameter found from area 171, 172, 173 
 
 depth of trench 180,276 
 
 dimensions and weight 197, 269, 270, 271 
 
 joints, cast 209, 210, 211, 270, 281, 2e2, 283 
 
 joints, ductile 180, 209, 2iO 
 
 mean radius of 35 
 
 metals, specific gravity 54,55.57 
 
 metals, gauges and weights 206 
 
 resistance at entry to 7, 59, 60. 62 
 
 shell, cast thickness 194, 197, 198, 2*8, 2t 9, 270, 271 
 
 shell, sheet metal, thickness 196,197,198,206,207 
 
 test for strength of riveted 207, 208 
 
 Pipes, brass 57,141,142, 144 
 
 cast, coating for 56,57, 111,179,180,185 
 
 coefficient /or large, thick 109, 110 
 
 for coated 151,152,260 
 
 for clean, uucoated, 52, 54, 55, 57, 64, 65, 67, 108, 150 
 
 259.260,264 
 
 for convergent 6, 146, 210, 211 
 
 of resistance 37, 48, 98, 150, 151. 152, 261, 262, 264 
 
 of velocity 38, 41, 51 , 98, 150, 152, 254, 255, 259, 260 
 
 varies with roughness only 42, 48, 240, 241 
 
 cost of laving 180,270,271,272, 281 
 
 depth of trench 180,276 
 
 diameter for free discharge, 200, 106, 136, 149, 161, 18t, 254, 255 
 
 diameter for pressure.. ... .7. ........ .V. . ...... 100, 255J 261, 262 
 
 digging bell holes 275,276 
 
 discharge tables 108, 1(9, 263, to 268 
 
 discharge from loss of head 153, 154 
 
 discharge from loss of pressure 157 
 
 discharge from pressure 156 
 
 discharge from sh>pe 154 
 
 elementary dimonfcions 162, 163 
 
 friction head, formula 50,98,101,104,130,132, 149, 150 
 
 friction at bends 186,188.193 
 
 friction in conical 143,146,210,211 
 
 friction loss tables 131, 133, 151, 263, 264, 268 
 
 E">ns discharged by 264. 268 
 for given discharge 100. 148, 149, 157, 159, 160, 161 
 forgiven velocity 128, 129 
 
 pressure in 52,175,176,178,180,181,195, 196 
 
 pressure for given discharge 154.155 
 
 pressure lost for given discharge ..156, 157 
 
 pressure lost by friction 101,102,103
 
 296 SULLIVAN'S NEW HYDRAULICS. 
 
 PAGE. 
 
 Pipes cast, preservation of pressure.... .' 176 
 
 pressure, static 194,195, 196 
 
 pressure coefficient 101, 102, 103 
 
 quantity discharged 264, 268 
 
 slope for any velocity 99, 127,129 136 
 
 slopes and )/d, tables 125,127 
 
 thickness 194, 198, 268, 271 
 
 yalueof^d, j/d 8 , t/d 3 115,119 
 
 value of ^/d 11 133 
 
 value of q* 256,259 
 
 cement mortar lined 55, 66,67,260,261 
 
 earthenware 161, 162 
 
 lead 57, 59, 67, 193 
 
 sheet metal 57, 180, 194, 209, 260, 261, 262 
 
 woodn 67,68,124,125,160,161, 260,262 
 
 weight of riveted 206,207 
 
 Pipelines of irregular diameter 175, 178 
 
 with nozzles 178,179,183,184 
 
 Pitting, or rust ecal-s 197 
 
 Pitch of rivets '. 200', 2t2 
 
 Plate metal 57,197,198,203,206,208 
 
 Power, horse, formula 168 
 
 cubic feet required 169 
 
 head required 169 
 
 pipe required 170,181,185, 186,261,262 
 
 Power mains and nozzles 168, 178, 179, 180, 181, 182, 183, 184, 194 
 
 Power nozzles, dimensions 146, 148, 210, 211 
 
 friction in 146,171,173,160,181,183 
 
 Properties common to all channels 36,37, 104,105 
 
 Properties of the circle 34, 35 
 
 Proportions of nozzles 143,146,210,211 
 
 Proportions of reducers 210, 211 
 
 Proportions of riveted joints 204, 205 
 
 Proportions of metal sheet for pipe 206 
 
 Pressure, bursting 52,175, 176,180,194,196 
 
 coefficient iu terms of 101, 102, 103 
 
 forgiven discharge 154, 155 
 
 discharge for given 156 
 
 discharge for given loss of 157 
 
 hydrant 139 
 
 hydraulic 52,195,196 
 
 in kilograms 167 
 
 loss of by f rici ion 101, 102. 103 
 
 no effect on fn'ctiou 22, 33 
 
 Pump, power forgiven dischaige 139, 154,155 
 
 Q 
 
 q, formula for 1M, 101, 104, 106, 110, 133,157,172,175 
 
 q. logarithms of 256, 259 
 
 i*, value of 256, 259 
 
 e aantity per capita.... 249,252 
 
 Quantity discharged pipes, 263, 268, See 106, 109, 110, 111, 153, 154, 155, 156 
 
 Quantity 'in 'cubic feeVand'ga'lions .'.'.'. .'.'.'.'.'.'.'.'.'.'256,' 259, 263, 268 
 
 Quantity of canal discharge 120, 124, 125, 232, See 104. 105
 
 INDEX. 297 
 
 PAGE. 
 Quantity of flame discharge ...................... .............. 125,234 
 
 Quantity of nozzle discharge ............................ 143, 146, 172, 17M83 
 
 Quantity of sewer discharge ..................... . . . ...... 112,113 
 
 Quantity discharged, diameter for. ... 100, 102, 104, 106, 136, 149, 170, 260, 262 
 
 Quantity of lead per joint .................................. 270,281,282,283 
 
 Quantity of packing per joint .................................... 269,270,281 
 
 Quantity of water for power ................................. 168, 169, 180, 181 
 
 R 
 
 R, v/R 3 , fc/R 3 values of .................................... 115,119.133,184 
 
 Radii of conduits ..................................................... 112,113 
 
 of pipes ...................................................... 35, 104,107 
 
 Ratio, area to friction surface ................. 34, 36, 39, 41, 49, 237. 238, 239 
 
 bottom and other velocities..- .......................... 25, 218, 226, 236 
 
 rough to smooth perimeter ........... 28, 29, 30, 48, 58, 237, 238, 239, 241 
 
 rivet to plate area ................................................. 202 
 
 Reaction at bends, open channels .......................... 189, 217, 221, 223 
 
 in pipes ............................................ 187, 193 
 
 water wheels .......................................... 168, 180, 183 
 
 Rectangular channels ................................................ 124,125 
 
 Reducers .......................................................... 146,210,211 
 
 Relative capacities of pipes ............................................. 101 
 
 Reservoir supply pipe ....................................... 254, 255, 259, 260 
 
 Reservoir to street system ....................................... 260,261,262 
 
 Resistance at bpnds ..................................... 186, 189, 217. 221, 223 
 
 at entry of pipe ........................................ 7,59,60,62 
 
 coefficient ............................................ 37,48,98,262 
 
 mean, in cross-section ........ 23, 33, 37, 39, 40, 48, 50. 237, 238, 241 
 
 varies inversely with i/r 3 ..... 40, 41, 42, 48, 49, 50. 237, 241 
 
 varies directly as roughness, 22, 23, 28,29,32,33,48,58 
 
 not affected by presbure.... .. ........................ 22,33 
 
 in nozzles ......................................... 143,146,210,211 
 
 in fire hose ................................................ 137,145 
 
 in reducers ................................................ 146,210 
 
 to flow in open channels .................................. 212. 236 
 
 Return seepage t_> canal ................................ ............... 233 
 
 Reverse variation of C ................................... 27,28,29,30,58,241 
 
 Revolutions of water wheel ............................................. 183 
 
 Rip-rap, linings of, coefficient .................................... 76, 77, 78 
 
 River coefficients .......................................... 6,58.81,96,97,241 
 
 formula, local slope ................................................ 28 
 
 Rivers, flow io ..................... 6, 22, 23, 28, 56, 58, 98, 212. 224, 229, 237, 241 
 
 gauging of ......................................... 23,24,58,59.96,97 
 
 and canals, grouped data .................................... 69, 96 
 
 Rivet area ............................................................ 199, 202 
 
 Riveted joint, may fail, how ..................................... 203.204,207 
 
 how tested ...................................... .' ...... 207,208 
 
 proportions of .......................................... 204,205 
 
 pitch formula- .................. ; ...................... 200,202 
 
 length of sheet ............................................ 208 
 
 Rivets, shearing strength ....................................... 198,199,207 
 
 Riveting, hand, hydraulic ............................................ 198,203 
 
 h masony lnings ......................... 74, 75, 76, 86, See 27. 28, 29, 58 
 
 rubble linings ............................................. 76,77,78,92
 
 298 SULLIVAN'S NEW HYDRAULICS. 
 
 PAGE. 
 
 Roughness of perimeter 12, 27, 28, 29, 42, 48, 54, 57, 58, 96, 124, 238, 241 
 
 mean of 27, 28, 29, 58, 241 
 
 indezof 48,237,239,241 
 
 of large cast iron pipes 109, 110, See 54, 57 
 
 Bubber pipe, coefficient 144 
 
 lined fire hose 137,145 
 
 Bust spots in pipe 197 
 
 s 
 
 Safety, factor of 197 
 
 Seepage in canals 232, 233 
 
 Sewer, circular brick 112 
 
 gg-shaped brick 113 
 
 i trifled pipe 161,162 
 
 egg-shaped brick 113 
 
 vitrified pipe... 
 slope or grade . 
 
 trenches 275 
 
 Shell, thickness of cast pipe 197,198,268,269,270 
 
 ductile 194,195, 196 
 
 Ering of rivets 198, 199. 207 
 slopes of canals 121,222, 223,228,230 
 _ le riveted pipe 200, 202,201,205,207 
 
 Size of sheet for given diameter 206 
 
 Size of pipe to supply hydrant 164 
 
 from reservoir to street 255, 260, 261, 262 
 
 Sleeve joints 180,209 
 
 Slip joints 180 
 
 Slope, for bottom velocity 226,228,230 
 
 mean velocity 103,104,121,128 
 
 of conduit 114,121, 125 
 
 formulas 99, 101, 106, 107, 128, 129. 133, 136, 149, 154, 180 
 
 of pipe for given discharge 100, 148, 149, 157, 161, 169, IfcO, 264 
 
 diameter found from 149 
 
 discharge found from 154, 157, 158 
 
 forgiven velocity 127, 128, 136, 264, 268 
 
 discharge for given 264, 268 
 
 does not affect coefficient 23, 37, 39, 42, 48, 239, 240 
 
 effective value varies with ^r 3 42, 48, 237, 238, 239 
 
 local, in formulas 28 
 
 of sewrs 162 
 
 and y'S, table 125,127 
 
 Special formula, vertical pipes 107 
 
 Speed of water wheel 183 
 
 Specific gravity, effect on C 54,57,67,96,97, 124,125 
 
 of materials 57 
 
 Square metric measure 166 
 
 Steamer pressure 139, 154, 155 
 
 Stability of channel bed 121,222,226,227, 230 
 
 Steel pipe....: 180,186, 197,198,200,209 
 
 Strength of pipe joints 207, 208 
 
 Strength of pipe metals 198, 199. 200,207 
 
 Suggestion of new weir formula 64, 242,249 
 
 orifice formula 249 
 
 fupply per capita of water 249, 252 
 npply pipes 254,255,259,260,264 
 
 for fire hydrant 164 
 
 Surface velocity 25,218,226,236
 
 INDEX. 299 
 
 T 
 
 TABLES. 
 
 PAQB. 
 
 For conversion of U. S. and Metric weights and measures 165, 169 
 
 Of data of flow and experimental coefficients 58 to 97 
 
 No. 1. Velocity and discharge, cast iron pipes 108, 109, 264, 268 
 
 No. 2. Velocity and discharge, coated pipes 110, 111 
 
 No. 3. Velocity and discharge, circular brick sewers 112 
 
 No. 4. Velocity and discharge, egg-shaped brick sewers 113 
 
 No. 5. Valuesof y'd, T/d 8 , $/d 3 115,119 
 
 No.5. Valuesofj/r, \/r 3 , tyt* 115,119 
 
 No . 6 . to No . 13 . Velocity and discharge, trapezoidal canals 121, 124 
 
 No . 14 . Velocity and discharg e, flumes, rectangular channels 125 
 
 No. 15. Values of slopes and ^/S 125,127 
 
 No. 16. Slopes for any velocity, cast iron pipes 127,129,264,268 
 
 No. 17. Loss of head for any velocity, cast iron pipes.... 130, 131,264,268 
 
 No. 18. Loss of head in any pipe for given discharge 132,133 
 
 No. 18. Valuesof ^/d 11 133 
 
 No. 19. Loss of head in coated pipe for any velocity 134, 135 
 
 No. 20. Friction loss in tire nozzles 143 
 
 No. 21. Friction loss in power nozzles and giants 148 
 
 No. 22. Loss of head in cast iron pipe for given discharge, 150,151,264 
 
 268 
 
 No . 23 . Loss of head in coated pipes for given discharge 152, 153 
 
 No. 24. Head or slope of cast iron pipe for given discuarge, 157, 159, 264 
 
 No. 25. Area, diameter in feet, and contents of pipes ................. 162 
 
 No . 26 . Area, diameter in inches, and contents of pipes .............. 163 
 
 No. 27. Inch and foot in decimal parts ................................ 164 
 
 No. 28 to 35. For conversion of U. S. and Metric weights and measures, 
 
 No. 36'.' ''Eleventh roots'.'.".'.' .'.'.'.'.'.'.'.'..'.'.'.''.'.'.'.'.'.' .'.'.'.'.'.'.'.'.'.".'.'.' .'.'.'.'.'.'.'.'....' 184 
 No. 37. Value of Z in Weisbach's bend formula ....................... 190 
 
 No. 38. Lofasof head at b^nds ........................................ 191 
 
 No. 39. Proportions of riveted pipe joints ......................... 204,205 
 
 No. 40. inchin decimals ................................................ 205 
 
 No. 40 A. (inages and weights of sheet metal ......................... 206 
 
 No. 41. Weir data ....................................................... 245 
 
 No. 42. Orifice coefficients ............................................. 247 
 
 No. 43 . Orifice coefficients .............................................. 247 
 
 No. 44. Orifice coefficients .............................................. 248 
 
 No. 45. Orifice coefficients .............................................. 248 
 
 No. 46. Increase of population by decades ........................... 251 
 
 No. 47. Increase of population and water supply .................. 252, 253 
 
 No. 48. Gallons per 24 Hours in cubic feet per second .................. 256 
 
 No. 48. Cubic feet per second, q, logarithms of q, value of q4, ...... 256 
 
 No. 49. Same as 48 continued ........................................ 2o6, 259 
 
 No. 50. Velocities, discharges, friction heads, clean iron pipes .... <#3, 268 
 
 No. 51. Dimensions and weight of cast iron pipes ..................... 269 
 
 No. 52. Manufacturers' standard cast iron pipes ...................... 270 
 
 No. 53. Cost of laying pipe in Denver, Colorado ....................... 271 
 
 No. 54. Cost of laying pipe in Boston, Mass ............................ 272 
 
 No. 55. Cost of laying pipe in Omaha, Neb ............................. 272 
 
 No. 56. Weston's tables of cost of pipe laying ..................... 273,274 
 
 No. 57. Cubic yards of excavation of trench ........................... 275 
 
 No. 5S. Lead required for cast iron pipe joints ...... .... ,.i,. ......... 282
 
 300 SULLIVAN.S NEW HYDRAULICS. 
 
 PAGE. 
 
 Tenacities of metals 198, 199 
 
 Tenths of a foot in inches 164 
 
 Test of coating compound 179, 180 
 
 Test of data of flow 6), 61. (compare 138) 
 
 Test of discharge and friction loss in nozzles 173, 175, 182, 183 
 
 Test of sheet metal for defects 208 
 
 Test of strength of riveted joints 207, 2o8 
 
 Text, correction of 237,241 
 
 Thick, large, cast iron pipes, coefficient 109, 110, (See 54, 57) 
 
 Thickness of cast iron pipes 197, 198, 268,269, 270 
 
 Thickness of sheet metal pipes 194, 195,196 
 
 Thickness, weights and guages of sheet metal 20ft 
 
 Total head defined 16 
 
 Total head for given discharge 157, 159 
 
 Total pressure due to hear) ; 175, 176, 194, 195, 196 
 
 Total pressure for given discharge 101,102,139,154,155 
 
 Trapezoidal canals 119,124 
 
 Trench, bell holes in 275,276 
 
 depth required 180,276 
 
 excavation table 275 
 
 Trenching, cost of 180, 270 to 281 
 
 Triple riveted pipe 202 
 
 Uniform flow 27, 37,62,71,72, 212,236 
 
 Unplaned lumber, flames and conduits 68,69, 124, 234 
 
 ept 
 3 
 
 Value of C for different depths of flow ..................... 28, 29,30,58, 241 
 
 115 - " 
 133 
 
 256,259 
 
 T/r, i/r s , t/r* ............................................ 115,119 
 
 8 in thickness formula for pipes .............................. 198 
 
 S and ys .................................................. 125,127 
 
 Z in Weisbach's bend formula .............................. 190 
 
 Variation of coefficient, 22, 23, 28, 29, 36, 37, 38, 39, 42, 48, 54, 55, 58, 62, 96, 
 
 effective head or'slope. ............. ....... .42, 48, 237,' 23S,' 240 
 
 resistance to flow is inversely as ,/r 3 , 39, 40,41, 49, 50, 237, 
 .................... . ................................. 239,241 
 
 weir coefficients ..................................... 64, 242, 249 
 
 wet perimeter with y^area ......... 36, 37, 39, 40, 48, 49, 104, 105 
 
 Velocity, defined ........................................................ 31,32 
 
 bottom ...................................................... 2.9,230 
 
 coefficient .............................................. 38,51, 53,99 
 
 due to head .................................................. 32,172 
 
 eroding ...................................................... 222.229 
 
 greatest efficiency, water wheel ............................... 183 
 
 head ........................................... 32,41,49,61,146,169 
 
 nozzle discharge ...................................... 172, 175,183 
 
 pressure ............................................ 102,139,141,175 
 
 sewers .......................................................... 162 
 
 surface .......................................... 25, 217 221, 222, 236
 
 INDEX. 301 
 
 PAGE. 
 
 Velocities and discharges of canal* 120,124,125 
 
 pipes 263,268 
 
 sewers 112, 113,161, 162 
 
 Velocities, ratio of 25,218,226,236 
 
 Vena Contracts . 62, 143,210,211 
 
 Vertical pipes, flow in 107 
 
 Vitrified pipes 161, 162 
 
 w 
 
 Water, consumption of 249 253 
 
 contained in pipes 162, 163 
 
 cost of, 1000 gallons 251. 252 
 
 cubic feet per second in gallons 256, 259, 2^:4, 268 
 
 cubic foot of 167 
 
 flow of a particle 218 
 
 pipes, cost of laying 180,209,270,283 
 
 pipes, diameter for given free di charge 259,260,264 268 
 
 pipes, diameter for power or pressure 170, 175, 181, 255, 261, 262 
 
 power of 168, 169, 183 
 
 powers and pipe lines.... 168, 175, 180, 181, 194, 197, 209, 255, 261, 262 
 
 required for given power 169 
 
 supply per capita 249. 253 
 
 supply pipes 255,261, 262 
 
 wheels, efficiency of 169,183 
 
 wheels, power of .... 183 
 
 wheels, revolutions 183 
 
 wheel plant 180,183 
 
 wheels and power mains 168tol7 
 
 works data 249 to 283 
 
 Weight of cast iron pipes 197,268,270 
 
 Weight of pipe metals 57.206 
 
 riveted pipes 206, 207 
 
 Weights and measures, U. S. and metric 165, 167 
 
 Weirformula 6 1. 242, 249 
 
 Weir and orifice gangings 6, 7,64,55,68,98,97,242,249 
 
 Weisbach's bend formula 189 
 
 Welded pipes 180,209,260, 262 
 
 Weeton's table of cost of pipe laying 273,274 
 
 Wet perimeter, how found 35, 104, 106, 112, 113, 120, 231, 232 
 
 Wet trenches 209 
 
 Whirls and boils 25,217 
 
 Wind, effect on flow 217 
 
 Wooden flumes 67,68,69,124,125.234 
 
 pipes 67,68,160,161 
 
 Work, definition of . 1< 
 
 done por man i 7o ^77, iol 
 
 Wrought iron and steel pipes 5*. 57, 180, 197, 198,204, 209 
 
 Z, value of, in Weisbach's bend formula 189
 
 THE WEIGELE 
 
 Pipe Works. 
 
 ...Manufacturers Of... 
 
 For Water Powers, Town Water 
 
 Supply, Irrigation and Hy= 
 
 draulic Mining. 
 
 Our Riveted Pipe is unex- 
 celled for workmanship and 
 durability and is made to with- 
 stand pressure up to 500 Ibs. 
 per square inch. 
 
 Send for Catalogue. 
 2949-2951 Larimer St. 8SS&e.
 
 WATER WHEELS 
 
 For Heads of 3 Feet to 2OOO Feet. 
 
 WE GUARANTEE: 
 
 The Largest Power ever obtained from a wheel of the same 
 dimensions. The highest speed ever obtained for the same: 
 power. The highest mean efficiency ever realized when run- 
 ning from half to full gate. 
 
 State your Head and write for pamphlet. 
 
 JAMES LEFFEL & CO,, SPRINGFIELD, OHIO, U, S. A. 
 
 SCLLIVflN'S 
 
 I NEW HYDRAULICS. 
 
 S 
 
 v An absolutely new and original work giving new * 
 
 * and simple formulas and demonstrating the Law of jJJ 
 52 Variation of Coefficients. In this work many of the $ 
 
 * old standard theories are exploded and replaced by W 
 
 * new theories and formulas which are demonstrated and JJJ 
 
 shown to be both theoretically and practically correct, (ft 
 
 The work covers the subjects of flow in canals, rivers, * 
 
 sewers, wooden pipe, earthenware pipe, iron and steel S 
 
 52 pip e > flre hose, tire nozzles, hydraulic giants, water 4* 
 
 vfc power pipes, riveting and riveted pipe, pipe coating, * 
 
 * cost of trenching, laying and back-filling, cost of water 2 
 52 works, etc., and many other very practical and useful ifi 
 
 Sdetaila not to be found in any other book. This book jj 
 
 , does not follow any of the old ruts. Nothing is taken $ 
 
 J2 for granted but each position and each new formula is 41 
 
 ttj clearly demonstrated in a simple and convincing man- jj 
 
 % ner. It is written and explained in the simplest Ian- JjJ 
 
 guage possible in order that the merest novice may (fi 
 
 6 .? r _ __j ll_ . 1 J u __. _ i_ __jl 
 
 V 
 
 easily grasp and fully comprehend each principle and 
 its practical application . Price in cloth binding $3.00, 
 postpaid. In leather, 14.00, postpaid. PUBLISHED AND ji 
 FOR SALE BY Mining Reporter, Denver, Colo. W
 
 -THE 
 
 \jjolorado Fuel and |ron 
 
 GENERAL OFFICES 
 
 Boston B'ld'g., -- Denver, Colo. 
 
 Cast Iron, Water and Gas Pipe and 
 Specials, Steel Bands for Wooden Stave 
 Pipe. Also Manufacturers of the fol- 
 lowing: 
 
 949DAILY CAPACITY. * 
 
 Rails, Blooms and Billets 1000 Tons 
 
 Coal 
 
 Pig Iron and Spiegel 600 " 15,000 Tons 
 
 Bar Iron and Steel 150 " 
 
 Structural Iron 150 " Coke 
 
 Steel Plate 150 " 1650 Tons 
 
 Water and Gas Pipe 50 " ' 
 
 Bolts and Nuts 25 " Iron Ore 
 
 Spikes 25 " 1500 Tons 
 
 Special Castings 20 " 
 
 Lag Screws, Boat Spikes Lime Stone 
 
 Steel Shafting, R. E. Steel and Iron Tire 1000 Tone 
 
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 Average Number of Men Employed Over 
 
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 Write for Yest-Pocket Memorandum Book.
 
 STANDARD ORE CAR 
 
 WITH 
 
 ANACONDA SELF-OILING WHEELS AND AXLES. 
 
 SIDE AND END DUMPING. 
 
 THE BEST CAR BUILT. 
 
 CARS BUILT TO MEET ANY REQUIREMENTS. 
 
 AMERICAN ENGINEERING WORKS, 
 
 204 DEARBORN ST. CHICAGO, ILL.
 
 THE 
 
 HUG WATER WHEEL 
 
 Manufactured by 
 D. HUG, DENVER, COLO. 
 
 Test of 12-inch HUG WATER MOTOR by Prof. R. C Carpenter of 
 Cornell University, Ithaca, N. Y. 
 
 SIBLEY COLLEGE, DEPT. EXPERIMENTAL ENGINEERING, 
 
 CORNELL UNIVERSITY. R.C. CARPENTER. 
 
 ITHICA, N. Y., Sept. 7th, 1898 
 MB. OSOAH KNAPP, 
 207 Ross St. 
 
 Brooklyn, N. Y. 
 DEAR SIB : 
 
 I enclose with this letter a synopsis of the tests mane en the sec- 
 ond Hug Motor, together with diagrams showing the efficiencies when 
 working under two heads, the one corresponding to about 25 pounds 
 pressure, the other to about 80 pounds pressure. 
 
 The results of the test show very favorably for your motor. The 
 efficiency obtained with a bead of 182 feet corresponding to 86.5 per 
 cent. Yon will notice that the results are slightly higher with the 
 frame in position than with it out, but the difference is not a great 
 amount, running not far from 1-2 per cent under working conditions. 
 The last motor is a decided improvement over the one first tested 
 and considering its size, it has an exceedingly high efficiency. 
 
 You are certainly to be congratulated on the high efficiency which 
 has been attained by this second motor. 
 
 Yours very truly,
 
 MINING 
 
 REPORTER 
 
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