BROOKLYN WATER WORKS. ON THE POSITION OF THE Jill Engine J mt WITH NOTES OF CERTAIN EXPERIMENTS MADE ON THE WATER DELIVERIES OF PORTIONS OF THE CROTON AND THE JERSEY CITY PIPE MAINS. 18 5 8. NEW YORK: HOSFORD & CO, PRINTERS AND STATIONERS, 57 & 59 William Street. 1 8 58. Engineer's Office, Brooklyn Water Works, November 8th, 1858. JOHN H. PRENTICE, Esq., -* President: Sir-As it will soon become necessary to select a site for the Prospect Hill Engine House, 1 beg to make a statement of the reasoning which has assisted me in determining the height above tide water, at which I would propose to place it. The Pump Well of the Prospect Hill Engine House is to be supplied with water by a branch pipe from the 36 inch main which has just been laid in De Kalb Avenue; a part of this branch pipe will be of 30 inches diameter, and part of 20 inches. It is a difficult point to determine exactly the height on the Prospect Hill slope, at which the required amount of water (156,250 gallons per hour) for that secondary service can be delivered, under all the conditions of the city consumption. During the first or second season after the receipt of water into the city, when its use by the citizens will be comparatively limited, a difference of level of but 20 feet below the watqr of the Ridgewood Reservoir would probably secure the desired delivery on Prospect Hill; but this difference would become en- tirely insufficient, when the use of the water in the city became as general as it now is in the City of New York. I have assumed that the Prospect Hill Pump Well should be situated low enough to secure a sufficient delivery of water 4 there when the flow through the 36 inch main, laid from Ridge- wood Reservoir, is equal to the flow at this time through the same size of main into New York. From experiments made recently by Mr. G. S. Greene, with Mr. Craven's permission, on the New York Works, to ascer- tain, among other points, the delivery of the two 36 inch mains from the Receiving Reservoir at Eighty-sixth Street into the Distributing Reservoir at Forty-second Street (see Note 1), the flow into the city by each of the two effluent mains (36") which convey the water from the south side of the Distributing Res- ervoir for the city consumption, was ascertained to be 647,101.5 cubic feet during the eight hours between 10 A. M. and 6 P. M. of Saturday, the 10th of July, 1858, = 22.469 cubic feet per second. For the twelve hours of day between 6 A. M. and 6 P. M., assuming the same rate of delivery to prevail, This would give 970,652 cub, ft. For the twelve night hours, assume the con- sumption to be one fourth of the above, viz... 242,663 41 Total flow in 24 hours for this 36 inch pipe .. 1,213,315 " The Croton water is delivered from the Re- ceiving Reservoir aforesaid into New York by four mains, two of 36 inches diameter each, and two of 30 inches diameter. The aggregate consumption of the City of New York at the above rate would sum up as follows : The second 36 inch main1,213,315 " Flow through the two 30 inch mains, nearly in proportion to the areas of the 36 inch and 30 inch pipes, or more accurately, as 7ds 1,538,333 " Total daily consumption in cubic foot. .3,964,963 5 This is equal to 24,781,019 imperial gallons, or 30,976,273 New York gallons, in twenty-four hours. It has been shown that the delivery of the 36 inch main into New York during the twelve hours of the day, amounts to 970,652 cubic feet, = 7,583,219 New York gallons. * I will assume the 36 inch main from the Ridgewood Res- ervoir to be delivering at this rate into Brooklyn and Wil- liamsburg, when the Pump Well at Prospect Hill is receiving its quota of water. This would make the delivery per hour from Ridgewood Reservoir 631,935 gallons, say 632,000 New York gallons. Assuming one fourth of this quantity to pass on by the 30 inch branch main to Williamsburg, there would flow on into Brook- lyn proper a rate per hour of 474,000 gallons. The Prospect Hill pumping engine is required to be of suf- ficient capacity to raise 156,250 gallons per hour, and must con- sequently be supplied at that rate-call the rate 166,666 gallons per hour through its supply pipe, to allow for the effect of the two 12 inch branches upon this pipe, one at Gates Avenue and the other at Fulton Avenue. Applying the proper distances, wo have now the following data: 15,637 feet of 36 inch main, between Ridgewood Reservoir and the junction of De Kalb Avenue with Division Avenue, de- livering at the rate of 632,000 gallons per hour. 10,425 feet of 36 inch main, from the last mentioned point along De Kalb Avenue to the crossing of Washington Avenue, delivering at the rate of 474,000 gallons per hour. 4,600 feet of 30 inch and 20 inch main, from the last point to the supposed position of the pump well, delivering at the rate of 166,666 gallons per hour. Assuming, in the first place, the above mains or pipes to be straight and unbroken by branches, the following table will show the calculated head necessary to produce the rates of flow above indicated. 6 LOCATION. Length of Pipe, in feet. Diameter of Pipe, in inches. Rate of Flow, in N.Y. gallons per hour. Rate of Flow, in cubic feet per second. Calculated head to produce the given flow by the formula, h=0.00046749-( d v+0.391)8 Reservoir to De Kalb Avenue 15,637 36 632,000 22.471 31.160 feet. De Kalb Avenue to Wash- ing ton Avenue 10,425 36 474,000 16.853 12.5663 G Washington Avenue to Pump Well 3,000 30 166,666 5.9259 1.4437 G 1,600 20 166,666 5.9259 4.3497 G 30,662 49.5197 G The above formula is derived from a formula of Prony's, which has been altered in its constants, so as to correspond very nearly with the results of recent experiments on the ordinary deliveries of the connect- ing pipes of the New York Reservoirs and of the Jersey City Reservoirs. Table A. 7 The head required to produce, under the given circumstances, the necessary delivery at the Prospect Hill pump well, accord- ing to the New York and Jersey City experiments, is.49.52 feet. For the effect of the branch pipes to be connected hereafter with these mains, add 10.00 " Total head lost 59.52 " This last mentioned allowance of 10 feet will be adverted to again. The surface of Ridgewood Reservoir, when full, is 170 feet above mean high water of Brooklyn Harbor. Assume that the height of water in the Reservoir (except in extreme cases) is not allowed to fall below 164.0 feet. Deduct the head lost as above 59.5 " Height of water in Prospect Hill Pump Well above tide. 104.5 " The floor of the Engine House may be situated 12 or 15 feet above the water of the Pump Well, say.. 15.0 " Height of this floor above tide 119.5 " The ground for the site of the Engine House may be conven- iently 4 or 5 feet below the level of this floor, say 115 feet. This height of 119.5 feet, if our calculations are correct, should enable you to control a liberal supply of water at the Prospect Hill Engine House, when the delivery of the 36 inch main into Brooklyn is about its maximum in practice. Another line of similar pipe from the Reservoir will, in all probability, be laid before the rate of flow into the city, which has been assumed for this one, is exceeded. In the interim, the free delivery at the Prospect Hill Pump Well would begin, as already stated, by being much in excess of 8 the contract requirements, but would approximate with every additional year more nearly to our calculations. The excess of head during the early years can be controlled by the stop-cock, and might be used to assist the action of the engine and reduce the consumption of fuel. To enable me to understand how much to allow beyond the results which any calculations can well give for the confusing influences of the various connecting pipes hereafter to be ap- plied on this section of the city " distribution," I made, with Mr. Craven's permission, two experiments on the New York City mains, at points near the centre of the city. One of the 36 inch delivering mains of the Distributing Res- ervoir passes down the Fifth Avenue into Broadway, and down Broadway to opposite Houston Street, where it is reduced to a 30 inch main, which last continues down Broadway to about opposite the Hospital. At Canal Street a 20 inch pipe branches from the 30 inch main last mentioned. Upon this 20 inch pipe, within 12 feet of the 30 inch main, I placed an Ashcroft guage, and had its in- dications noted every quarter hour between 7 A. M., and 5 P. M., of the 23d of July last. The readings varied from 26 lbs. at 7 A. M., to 241 lbs. at 9 and 10 o'clock, A. M.; thence back to 26g lbs. at 5 P. M. The average and more general reading was 25 lbs., equal to a head of 57 feet. The distance of this point from the Distributing Reservoir is 13,130 feet, and from the Receiving Reservoir 24,430 feet, all of which length consists of 36 inch pipe, with the exception of about 2.300 feet of 30 inch pipe between Houston and Canal Streets. Between the Distributing Reservoir and Canal Street, (13,130 feet) branch pipes connect at intervals, as hereinafter enumerated. 9 The height of the Receiving Reservoir above tide, when full, as it was in this instance, is 114.0 feet. The height of the pipe in question at this point (Canal Street) above tide 4.5 " The difference in level, therefore 109.5 " Guage indication of head available at Canal Street. . 57.0 " Loss of head 52.5 " In this case 52| feet of head are absorbed in a distance of 4.63 miles. The distance between the Ridgewood Reservoir of the Brooklyn Water Works and the Prospect Hill Engine House is 5.81 miles. The other experiment was made on the 30 inch main in Avenue A, opposite Tompkins Square. This 30 inch main, after leaving the vaults of the Receiving Reservoir, follows down Fifth Avenue to Seventy-ninth Street, thence along Seventy-ninth Street to Third Avenue, along Third Avenue to Fourteenth Street, along Fourteenth Street to Ave- nue A, and along Avenue A to Tompkins Square. The distance along its line from the Receiving Reservoir to the point where the Ashcroft guage was applied, is 23,400 feet. The distributing pipes branching from it are shown in the ac- companying sketch. The guage indicated an average pressure of 25| lbs., equal to a head of 58 feet. The difference in level between the surface of the water in the Receiving Reservoir and the Pipe at this point is 102 feet. Average head, by the guage, available at Tompkins Square 58 " Loss of head 44 " 10 In this case 44 feet of head are absorbed in a distance of 4.43 miles. In Table D, I have divided that part of the Fifth Avenue and Broadway main, applicable to our experiment, into two sections, viz.: the portion between the two Reservoirs, and the portion between the Distributing Reservoir and Canal Street. The first length measures 11,217 feet, and the difference of level of the surface waters of the two Reservoirs averaged, during Mr. Greene's experiment, 20.215 feet. The second length measures 13,130 feet, and the difference of level between the surface of the water in the Receiving Reser- voir and the surface of the pipe in Canal Street, is 109.5 feet. In this Table, I have compared the actual head in practical use, as ascertained in the first section by levelling and in the second by the guage, with the calculated heads which some of the best formulas show, under the supposition of an unbroken pipe line and certain given deliveries. On the first section of the 36 inch main between the two Reservoirs, there were no side connections open to interfere with the regular flow in the pipe during the time of the experi- ment already mentioned (see Note 1). It will be observed that in this first section the calculated head (20.17) by the assumed formula "I" in column 8, necessary to pass the water which was delivered by each 36 inch main, agrees very nearly with the actual head 20.2, as obtained by levelling between the two surfaces. The well established formulas of columns 9 and 10, give 14.90 and 14.83 for the re- quisite head. The formula ("I") referred to, is derived from one of Prony's, the constants of which have been modified, so as to render it an exponent of the experiments made on the New York and the New Jersey mains, as will be further explained. In the portion of the main below the Distributing Reservoir, Tabular Statement in regard to the Experiments upon the New York Mains. D. 1 2 3 4 5 0 7 8 9 10 Head lost, in feet. How ascertained. Difference in level between the points, in feet. Delivery in N. Y. Gallons per hour. Delivery in cubic feet per second. Length of Pipe, in feet. Diameter of Pipe, in feet. Calculated head to produce the given flow, by the formula, 11=0.000467491 (v+0.397)s Calculated head to produce the given flow, by Prony's formula (2). Calculated head to produce the given flow, by Hawkes- ley's formula. W SECTION 1. Pipe Main between the Receiving Reservoir and the Distributing Reservoir. 20.215 By levelling between the Res- 20.215 596,352 21.2036 11,217 3 20.1670 20.1670 14.899 14,833 ervoir surfaces. SECTION 2. Pipe Main between the Distributing Reservoir (down Broadway) and Canal Street. The total distance is divided up. as in coininn 6, for convenience of calculation. 89.28 - 632,000 570,000 480.000 420,000 350.000 22.471 20.267 17.067 14.933 12.444 3,050 2,250 2,850 2,650 2,330 3 3 3 3 2.5 6.0778 3.7357 3.5103 2.6008 3.7461 4.5175 2.7371 2.5032 1.8113 2.6925 4.6938 2.8670 2.5389 1.8148 2.7792 52.5 By an Ashcroft 109.5 19.6707 19.6707 guage applied to - the pipe. 39.8377 Similar Statement for the Msan of Experiments upon the 20 inch Main of the Jersey City Water Works. How ascertained. Actual head, in feet. Delivery in N. Y. Gallons per hour. Delivery in cubic feet, per second. Length of Pipe, in feet. Diameter of Pipe, in feet. Calculated head to produce the given flow, bv the formula, h=0.000467494 (v+0.397)3 Calculated head to produce the given flow, by Prony's formula (2). Calculated head to produce the given flow, by Hawkes- ley's formula. (AJ 28.1285 By levelling between the Res- ervoir surfaces. 28.1285 88,231.5 3.13712 29,715 1.6667 28.064 17.921 16.056 Note (a.)-The first of the New York Mains has three right angled curves, of 90 feet radius, which are taken into account in the calculations. The Jersey City Main is enlarged, for a distance of 128 feet, to 24 inches diameter. Allowance is made, in the calculation, for this enlargement and the curves in the pipe. ♦ Note (b.)-The formula (Z) is used only as an exponent of the experimental delivery of the first section of the New York Mains, and also of the delivery by experiment of the Jersey City Main, to make a convenient application of their general results to a similar case in Brooklyn. Note (c.)-The Pipes branching from the 36 inch Main, situated in Fifth Avenue and Broadway, within the distance given in this table, are as follows: (See Sketch S.) At 29th Street, a 20 inch pipe branches East and West. " 20th " a 20 " " " East and West. " 10th " a 20 " " " West. " Houston St. a 20 " " " East and West. " Canal " a 20 " " " West. and a 6 " " " East. The flow of water into the Main at the point where it leaves the Distributing Reservoir, has been ascertained by experiment. The reduced flow, beyond the several points where the pipes above mentioned branch off, is assumed, and cannot be exactly determined. Formulas used in Table D. (Ji.) Hawkesley's h=0.0004338027 v8-XL+54dJ. (D.) Prony's (2) h=0.00040085y[ (v-|-0.15412)3-0.02375] (Z.) Expressing the mean result of the New York and the Jersey City experiments h=0.00046749-(v J-0.397)* Where v=Velocity, in feet per second. h=the Head, in feet. d=Diameter of the pipe, in feet. L=Length of the pipe, in feet. 11 where the distributing pipes for the city consumption radiate from it on either side, the actual head absorbed between this Reservoir and Canal Street, in producing the flow occurring there, is 32.28 feet. Assuming the pipe to be straight, and the quantities to be as in the table, the calculated head required to produce the same flow of water, is by formula "I" 19.67 feet- showing a difference of 12.61 feet. The difference by the other formulas is much greater. The great difference in this case between calculation and the guage indication, must be attributed largely to the effect of the many connecting pipes which occur on this section, involv- ing eddies inside the pipe, and confused action, which these formulas were not intended to express; but there must be other reasons growing out of circumstances connected with the condi- tion of the pipe, unknown to me, producing this large difference: these circumstances, however, might obtain on the Brooklyn pipe also, and it has been thought best, therefore, to make an allow- ance for them. The accompanying sketch S will show the position of the branching pipes known to me, as well as their sizes. There are five 20 inch pipes branching from the west side of this 36 inch main, and three from the east side, being eight 20 inch pipes in all, drawing their supplies from this main between the defined points. These eight pipes have a water area of 17.45 square feet. The delivery area of the main, when it leaves the Distribut- ing Reservoir, is 7.07 square feet: when it reaches Canal Street it has virtually increased to the united areas of one 30 inch pipe and eight 20 inch pipes, equal to 22.36 square feet of water space. The loss of head resulting from this rapid enlargement, in effect, of the original main, could be counteracted and to a cer- tain extent neutralized by a liberal addition of auxiliary mains 12 from the Reservoirs, and of cross mains throughout the small pipe distribution. This kind of correction of the difficulty has already been begun, but it will involve, probably, an increased expenditure of water. So far as the loss of head may result from accidental collec- tions of air in the pipes, it could to that extent be remedied by a more liberal supply and more frequent use of air-cocks. The reasons will now be understood which influenced me in making an allowance of 10 feet for the effect of branches, <fcc., in the calculations of head required to secure the Prospect Hill supply. The branchings in this case are not likely, for a very long time, to equal in extent those on the New York section referred to, and I have not. therefore, allowed as much. To recapitulate, 1st. In a distance of 4.63 miles on the Now York 36 inch main the head lost is feet. 2d. In a distance of 4.43 miles on the New York 30 inch main the head lost is 44 feet. (The guage varied considerably in this experiment on the 30 inch main. The morning readings would have given a much greater loss than the above.) 3d. In a distance of 5.81 miles of 36, 30, and 20 inch pipes in the Brooklyn case referred to, the loss of head will amount, it is calculated, to 56 feet, some five to ten years hence, when the use of the water has become very general throughout the city. The experiment made upon the two Croton Reservoirs, to as- certain the actual delivery of the two intervening 36 inch mains under a given head, gave results considerably below those which the usual formulas would have promised under the same conditions. The discrepancy may have grown out of various causes of 13 disturbance to which all lines of pipes are subject, some of these beyond the reach of correction, and others controllable by the exercise of constant care and attention. Among the first may be instanced the tubercular corrosion, which on these pipes is considerable, as I have ascertained by inspection. Among the second may be instanced the collection of air on the high points of the line, and some sedimentary deposits at low points. Both of these last causes might have been more or less got rid of by blowing off at the depressions when there exists the means of doing so, and by opening the air-cocks which are provided, and adding others where necessary. But the experiment was more interesting and pertinent to the case in point without such previous preparation of the pipes. It was desirable to understand the rate of flow under the ordi- nary condition and superintendence of the service, rather than under a special condition of it. To ascertain whether the discrepancy adverted to was excep- tional, or whether it arose more or less from some speciality in the character of this experiment, I have had, with the consent and assistance of Mr. G. H. Bailey, the Engineer of the Jersey City Water Works, a somewhat similar experiment made on the pipe which connects the two Reservoirs of these Water Works, the one situated near Belleville, the other in Hudson City. The length of the pipe connecting these two Reservoirs is 29,715 feet. The diameter is 20 inches, except at the crossing of the Hackensack River, where it is increased to 24 inches for 128 feet of its length. During the experiment no water was received into the Belle- ville Reservoir from the Pumping Engine. 14 At the beginning of the experiment the difference in level of the surface water of the two Reservoirs was 30.529 feet. At the end of the experiment it was 25.646 feet. The experiment was made on the 25th, 26th, and 27th of Sep- tember, 1858. Mr. C. W. Boynton, one of our assistant engineers, took the principal observations, and has made for me the calculations presented in Table J. In this Table we have brought together a number of well- known formulas, and compared the velocities which they give for the head and size of pipe, with the actual velocity as ob- tained from this experiment (see Note 2): the same comparison is there made witli the results of the Croton Reservoir experi- ment. It will be seen that in both cases all these formulas gave ve- locities considerably greater than the actual velocity which pre- vailed in each experiment. The Jersey Reservoir experiment, therefore, corroborates the Croton Reservoir experiment, in giving deliveries and velocities below the quantities which the formulas gave. Preferring to take these experiments for my guide, the cir- cumstances of which elucidate so well the case which is pre- sented on the Brooklyn Works, I have had one of Prony's formulas modified in its constants, to meet very nearly the re- sults of both experiments, and have used it as thus modified to ascertain the probable loss of head in the Brooklyn case al- ready detailed. This exceptional equation (given elsewhere) has also been transformed for our convenience so as to express the head re- quired under the conditions defined, instead of the velocity. The modified form of Prony's formula I do not introduce as applicable elsewhere, or as a correction of well-established Tabular Comparison of the New York and Jersey City Experiments. J. EXPERIMENTS: Where, and by whom, made. Diameter of the Pipe, in fen. Length of Pipe, in feet. Mean Heads under which the discharge occurred. VALUES OF THE VELOCITY, IN FEET 'ER SECOND. As deduced from the discharge. By Hawkesley's formula. MJ By Blackwell's formula. MJ By Prony's formula (1). (c.) By Prony's formula (2). (D.) By Eytelwein's brmula. mj By D'Aubuisson's formula (1). (F-) By D'Aubuisson's formula (2). MJ By Weisbach's formula. mj On the 20 inch Main between the Reservoirs ' . 1.6667 29,715 30.262 1.4924 1.97399 1.97624 1.9206 1.91068 1.97063 1.927302 1.92923 2.03255 of the Jersey City Water Works. \ 1.6667 29,715 29.758 1.51337 1.9575 1.9597 1.9039 1.89338 1.95416 1.9105 1.9123 2.01294 By G. H. Bailey and C. W. Boynton. ) 1.6667 29,715 29.317 1.44893 1.94293 1.94514 1.8891 1.87838 1.93963 1.8957 1.8976 1.99688 128 feet of this Main is 24 inches diameter. j 1.6667 29,715 28.365 1.45795 1.91112 1.9133 1.8570 • 1.8453 1.90789 1.8632 1.8650 1.95938 Allowance is made in the calculation for this / 1.6667 29,715 27.302 1.39107 1.8750 1.877115 1.8204 1.8077 1.87180 1.8263 1.8282 1.91797 enlargement, and the curves in the pipe. I 1.6667 29,715 26.325 1.381155 1.84115 1.84323 1.7861 1.7726 1.83801 1.7918 1.7936 1.87943 Jersey City Water Works. Mean result. 1.6667 29,715 28.1285 1.437 95 1.90031 1.9053 1.8489 1.837 1.8999 1.855 1.857 1.9502 New York 36 inch Main between Receiving and Distributing Reservoirs. By G. S. Greene. This pipe has three right angled curves of 90 feet radius, which are taken into account in the calculation. 3.0 11,217 20.215 2.99967 3.5016 3.5230 3.484 3.514 3.4917 3.4891 3.506 3.848 The formula, which very closely expresses the results of the New York and the Mean of the Jersey City Experiments, is: -0.397, whence, (v+0.397)8 Formulas used in Table J. (.7.) Hawkesley's. v=48.0125 I- vL4-54d See Civil Eng. and Architects' Journal, Vol. XVIII., p. 99, line 28. (B.) Blackwell's. v=47.913 This formula takes into acco', P , V L mt the curves of the pipe. See Hughes on Water Works. Formula (33j, p. 336. (C.) Prony's (1). 4-0.00665)-0.0816. See Prony's Recherches Physico-Mathematiuues sur la thiorie des Eaux „ Courantes, § 184. (D.) Prony's (2). ¥=^(2494.69^4-0.02375)-0.15412. See Prony's Recherches Physico-Mathimatiques sur la thtorie des Eaux „ Courantes, § 210. (22.) Eytelwein's. v=47.8731 / h(* v L4-54d See Memoires de V Academic des Sciences de Berlin, 1814 et 1815, p. 165. (F.) D'Aubnisson's (1). f() 015fl36]+ ? See E'Aubuisson's Hydraulics, (Bennett's translation,) p. 206, top. d+ ' 0.000417568-4-[0.015536] (G.) D'Aubuisson's (2). ¥=^(2394.82^4-0.00814)-0.090224. See Seville's Hyd. Formula (109J, p. 118. Simplification of [F], by omit). mg the constant [0.015536], and reducing. (H.) Weisbach's. h-0.015538v8 =0.015538-f 1552 ] d i See Julius Weisbach's Ingenieur und Maschinen Mechanik. Vol. I., p. 748 Where v=Velocity, in feet per second. h=the Head, in feet. d=Diameter of pipe, in feet. L=Length of pipe, in feet. Comparison of Calculations from Established Formulas, with the Results of Various Experiments on Pipes. M. EXPERIMENTS: WHERE, AND BY WHOM, MADE. 7 Character of the Water. Age of the Pipe laid, in years. Diameter of Pij in feet. )C, Length of Pipe, in feet. Head of Water, in feet. VELOCITIES, IN FEET PER SECOND. As taken from the Experiments. By Prony's formula (2). By D'Aubuisson's forrtiula (1.) (F.) By Hawkesley's formula. By Eytelwein's formula. rr.; Jersey City Water Works. Main from the Belleville Reservoir to the Hudson City Reservoir. By G. H. Bailey and C. W. Boynton. .■ Of this Main 128 ft. is 24 inches diameter. Correction for this enlargement, as also for the curves, is made in the calculation Soft. Soft. 4 20 in. = 1.6667 1.6667 29,715 29,715 30.262 29.758 1.4924 1.51337 1.91068 1.89338 1.927302 1.9105 1.97399 1.9575 1.97063 1.95416 Jersey City Water Works. Mean result Soft. 4 1.6667 29,715 28.1285 • 1.43795 1.837 1.855 1.90031 1.8999 Croton Aqueduct. Main from the Receiving Reservoir to the Distributing Res- ervoir. By G. S. Greene. There are in this Main three right angled curves of 90 ft. radius, for which allowance is made in the calculations Soft. 16 36 in.=3.0 11,217 20.215 2.99967 3.514 3.4891 3.5016 3.4917 Crawley Pipe. Crawley to Edinburgh. Experiment by Mr. James Leslie Soft. 29 15 in.=1.25 44,400 226. 3.4634 1 3.833 3.8268 Colington Pipe. From Clubbie Dean Reservoir to Castle Hill. By Mr. Leslie, Do. From Torduff Cistern to Castle Hill. do. do. Do. From Clubbie Dean Reservoir to Torduff Cistern. do. Soft. Soft- Soft. 8 8 16 in.=1.333 1.333 1.333 29,580 25,765 3,815 420. 230. 184. 6.8158 5.2521 14.5030 •6.7199 5.291 12.498 6.59805 5.2307 12.062 Main from Belvidere Road to Brixton. By Mr. Jair Do. do. do. Do. do. do. Do. do. do. Do. do. do. Do. from Ditton to Brixton. es Simpson do. do. do. do. do. Hard. Hard. Hard. Hard. Hard. Hard. 19 in.=1.58333 1.58333 1.58333 1.58333 1.58333 30 in.=2.5 22,440 22,440 22,440 22,440 22,440 54,120 41.0 43.5 34.0 27.5 24.0 25.0 2.73411 2.80183 2.5225 2.2601 2.0569 1.7690 1 2.5367 2.6173 2.2971 2.0514 1.9070 1.5502 2.5775 2.6549 2.3472 2.11095 1.9720 1.6296 Note.-The Crawley Pipe is of three sizes, viz.: 20, 18, and 15 inches diameter. It has been calculated above as if of 15 inches diameter throughout. A closer calculation would give a greater difference between the actual delivery and the results from the formulas. Formulas used in Table M. Hawkesley's. v=48.0125 /- J vL+54d See Civil Eng. and Architects' Journal, Vol. X VIII., p. 99, line 28. (D.) Prony's (2). v= v L See Prony's Recherches Physico-Mathimatiques sur la theorie des Eauo) Courantes, § 210. (£'.) Eytelwein's. v=47.8731 /--- v L+54d See Memoires de VAcademic des Sciences de Berlin, 1814 et 1815, p. 165. . D'\ I <D '•- / h 0.00003767485T ( .) u uissonb . \ V o,OOO417568k+L0.015536]+ [ 0.000417568^4-[0.015536] J [0.015536] See D'Aubuissori1 s Hydraulics, (Bennett's translation,) p. 206, top. Where v=Velocity, in feet per second. h=the Head, in feet. d=Diameter of pipe, in feet. L=Length of pipe, in feet. 15 formulas, but simply as an expression from the results of the particular experiments made this season, by which I prefer to be ruled in our own case. Mr. James Leslie, Civil Engineer, in his paper on the flow of water through pipes, read before the London Institution of Civil Engineers, and in part printed for their use, mentions several experiments made by him on the rates of delivery of the Edinburgh mains. In the same pamphlet, Mr. James Simpson, the President of the Institution, gives the result of some experiments made by himself on the water deliveries of pipe lines of different diameters. Some of these are presented in Table M, for the purpose of comparison. In these experiments the deliveries given, generally agree very tolerably with the established formulas given in our Table. The delivery of the Edinburgh pipe is an exception. I am not able to give sufficient reasons why these experi- ments of Mr. Simpson and others should correspond quite nearly with the formulas, from which our experiments differ so importantly. The good condition of the pipes as respects corrosion, sedi- ment and collections of air, would probably in a great measure explain the difference. The pipes experimented on by Mr. Simpson carry the hard waters of the London Basin, which do not produce tubercular corrosion; they were probably clean pipes of their original capacity: the New York pipes carry soft water, and show al- ready considerable tubercular incrustation. The old Crawley pipe of Edinburgh is effected in the same way, as are also the Jersey City mains. I had honed to have been able to use the modified formula 16 proposed by Mr. Leslie, and found to agree so well with the experiments detailed by him, but it does not correspond suffi- ciently nearly with the results of our experiments on the Croton and Jersey City pipes, made under the ordinary every-day con- ditions of their water deliveries. Respectfully submitted, JAMES P. KIRKWOOD. 17 NOTE 1. Conditions of an Experiment made by George S. Greene, Esq., Civil Engineer, to ascertain the rate of flow of the water passing through the two 36 inch mains situated between the Receiving Reservoir of the Croton Works, and what is called the Distribut- ing Reservoir at Forty-second Street, New York City. The length of each main is 11,217 feet. There are three horizontal curves on each main of 90° each; each curve is about 90 feet radius. The grade of the avenue on which the pipes are laid undu- lates considerably, but there exists no abrupt vertical curvature. The Receiving Reservoir is divided into two divisions by an earthen embankment. The southern division was the one used in this experiment, and when the Receiving Reservoir is mentioned here it is to be understood as the southern division of that Reservoir simply. The Distributing Reservoir is also divided into two apart- ments, but they were used as one in this experiment. During this experiment the "Receiving Reservoir''was re- ceiving no water from the Croton Conduit, the sluice gates having been all shut down some hours before the commence- ment, nor from any other source: and no water passed out of it except through the two 36 inch mains which are laid in the Fifth Avenue; the stop-cocks of the other mains communicating with it were shut down. All connections with the two 36 inch mains were shut down, and the mains themselves were open only for delivery of water into the Distributing Reservoir. The Distributing Reservoir received no water except from these two 36 inch mains. From the southern side of this Reservoir, two similar 36 inch mains were open delivering water into the city. These were the only mains open to the passage of water out of the Distributing Reservoir. The water in this Reservoir rises every night from three to five feet, and falls proportionately every day, the consumption 18 of water by the city being less during the night than the Res- ervoir's receipt of water from above; and more during the day. The experiment was made on Saturday the 10th cf July, be- tween the hours of 10 A. M. and 6 P. M. During the eight hours above mentioned, the Receiving Res- ervoir fell 2.16 feet, and delivered into the Distributing Res- ervoir (=21.204 cubic feet per pipe, per second) 1,221,328 cub. ft. During the same time the water fell in the Distributing Reservoir (which is small com- pared with the other Reservoir) 3.448 feet. The two city pipes on the south side were therefore drawing off more from the Forty- second Street Reservoir than it was receiving by the two pipes delivering into it from the upper Reservoir. The delivery into the city in excess of the amount received here was, by calcula- tion, 72,875 " Total delivery from the Distributing Reser- voir into the city during the eight hours aforesaid by the two 36 inch effluent pipes 1.294,203 " Delivery into the city by one of these pipes in the same time 647,101.5 " Delivery in twelve hours of the day (6 A. M. to 6 P. M.) at same rate 970,652 " Delivery during the twelve hours of night, from 6 P. M. to 6 A. M., taken at one fourth of that for the twelve day hours. 242,663 " 1,213,315 " Equal to, in New York gallons 9,479,023 The second 36 inch effluent main, the same. . 9,479,023 19 Besides the two 36 inch mains delivering water into the city from the Distributing Res- ervoir, there are two 30 inch mains which deliver into* ;the city directly from the " Re- ceiving Reservoir." I will suppose these 30 inch mains, (act- ing under the same head here as the 36 inch mains,) to deliver in such proportion to their diameters as the formula prescribes, or as -/d6. This gives for one 30 inch main a delivery of 6,009,113 And for the other the same 6,009,113 Total estimated consumption of New York City per twenty-four hours30,976,272 galls. Equal to 24,781,019 imperial gallons, equal to 3,964,963 cubic feet. The only point in these calculations which is assumed and not well ascertained from experiment, is the consumption of water during the twelve night hours, viz.: from 6 P. M. to 6 A. M. I have judged this to amount to one quarter of the day con- sumption. But Mr. Greene believes that it amounts to at least one third. On account of the inconvenience which the lowering of the Reservoir a few feet produces to the consumers in the high parts of the city, we refrained from continuing the experiment through the whole twenty-four hours. The two pipes (36 inch) laid over the Harlem High Bridge, when empty of water in October last, were examined inside and found to be very considerably encrusted with tubercles. These tubercles were generally conical in shape, and varied from one quarter to live eighths of an inch in height. The pipes experimented on between the two Reservoirs have not been examined, that I am aware of, with this view since they were laid; but as they have been in use as long as these pipes over the High Bridge, and the water passes through them at a less velocity, they are probably corroded in the same way. 20 NOTE 2. Report by C. W. Boynton, Assistant Engineer, of an experiment upon the cast iron main leading from the Receiving Reservoir to the Distributing Reservoir of the Jersey City Water Works. The object of this experiment was to ascertain the amount of water flowing in a given time from one of these Reservoirs to the other, and consequently the discharging capacity of the connecting main. It will be necessary to give a general description of the rela- tive situations of the Reservoirs and of the pipe line. The Receiving Reservoir, situated on the elevated land east of the Passaic River, near Belleville, was the basin in which the quantity of water passing through the pipe was measured. The dimensions of this Reservoir were obtained by a survey of its flowage line at an elevation of 157* feet above high water in the Passaic River. The slopes of the Reservoir are covered with brick laid in cement, and their inclination is 1| to 1. Through the kindness of Mr. G. H. Bailey, Chief Engineer of the Jersey City Water Works, we have the following informa- tion in regard to the connecting main. The main is enlarged by a mouth piece, at the Receiving Res- ervoir, to a form very nearly that of the contracted fluid vein, so that there is no obstruction to the free discharge of the water there. The entire length of the main is 29,715 feet, of which all but 128 feet, where the pipe is turned downwards as an inverted syphon beneath the draw at the Hackensack River, is 20 inches in diameter; the remainder having a diameter of 24 inches. * This is upon the supposition that the 130 feet mark on the guage rod at the Pipe Tower of the Distributing Reservoir, the point to which I referred my levels, is accurately 130 feet above high water in the Passaic. 21 In this main there are the following curves: IN THE PORTION OF 20 INCHES DIAMETER. Radius of Curve. Amount of Deflection. Feet. 3 90° 20 96° 25 38° 30z 60 70° 180 42° 200 79° 950 32° Unknown ) but over J " 22° 30' IN THE PORTION OF 24 INCHES DIAMETER UNDER THE DRAW AT THE HACKENSACK RIVER. Radius of Curve. Amount of Deflection. Feet. 4.9 90° 4.9 90° 4.9 90° 4.9 90° 22 The Distributing Reservoir is situated upon Bergen Hill, in Hudson City. The ends of the connecting main in both Reservoirs were covered with water, and therefore the difference of level be- tween the surface of the water in the two Reservoirs at any time, gave the head under which the discharge was then taking place. The difference in elevation of two fixed points, one at each Reservoir, was carefully determined by levelling between them, and the surface of the water was, at its various elevations, re- ferred to these points. At the Receiving Reservoir, a portion of the well of the gate house was separated by a temporary partition from the re- mainder. This partition extended below the water surface sufficiently far to prevent the disturbance of the latter, in the separated portion, by currents of water entering the main, and still per- mitted free communication from below with the main part of the well, so that the water would maintain the same level inside the partition as in the Reservoir itself. Within the part of the well thus separated the elevation of the water surface was determined, during the experiment, by means of a float and attached guage staff. The height of the water surface was also noted outside of the gate house by measurement with a levelling rod, (when darkness did not prevent,) and the records were found to agree very nearly with the first measurement. The mean of both observations was the one used in arriving at the result. At the Distributing Reservoir observations were taken from the guage rod on the pipe tower. 23 The following are the recorded observations at the two Reservoirs: At the Receiving Reservoir. At the Distributing Reservoir. Time of Observation. Elevation of Water Surface. Time of (Ibservation. Elevation of W ater Surface. Sept. 25th, 1858. Feet. Sept. 25th, 1858. Feet. 6h 33|m, A.M. 155.029 6h 00m, A.M. 124.5 *7h 16m. " 154.989 *llh 33|m. " 154.669 i 12h 16m, P.M. 154.482 12h 00m, M. 124.48 5h 16m. " 153.992 6h 00m, P.M. 124.48 9h 16m, " 153.614 Sept. 26th. Sept. 26th. 6h 00m, A.M. 124.54 12h 16m, P.M. 152.166 12h 00m, M. 124.56 6h 16m, " 151.604 6h 00m. P.M. 124.604 Sept. 27 th. Sept. 27 th. 7h 29m, A.M. 150.356 6h 00m, A.M. 124.71 The annexed Table 1 gives a statement of the information obtained by the experiment. Column (1) contains the recorded elevations of the water surface at the Receiving Reservoir. Column (2) is obtained by calculation from the dimensions of the Reservoir. Column (3) gives the difference between the elevations in column (1). * These observations, taken so near the time of the preceding and following ones, are not used in calculating the result. 24 Column (4) contains the quantities discharged from the Res- ervoir, as calculated from columns (2) and (3). Column (5) gives the difference in the recorded times of ob- servation. Columns (6), (7) and (8) need no explanation. Column (9) is obtained by subtracting from the elevation of the water surface in the Receiving Reservoir, the elevation of the surface of the water in the Distributing Reservoir at the same time, as deduced from the observations made at the latter, which, it will be seen, were not simultaneous with those at the Receiving Reservoir. Column (10) is obtained from column (9) by the formula r - - *7 2 h= A 2 Where Hj=the head at the commencement of the discharge. H2= " " end of the discharge. h =mean head under which the discharge occurs. and A. =the distance of the centre of gravity of the water prismoid above the middle point of its altitude. Some discrepancies will be observed in the results of the Table; these were doubtless caused by small errors in the deter- mination of the elevations of the water surface. Such could hardly be avoided without more accurate means of measurement than were at our disposal. It remains to compare our results with those obtained from the various formulas in ordinary use for determining the dis- charge of water through pipes. The following have been considered the most reliable. As expressed by their authors, the units employed are various, but for convenience in comparison and calculation, I have re- duced all to their equivalent expressions in English feet.* (./?.) Hawkesley's. j See Civil Eng. and Architect's Journal, Vol. XVIII., p. 99, line 28. * In these reductions I have taken The French metre=3.28089 English feet. " Prussian Foot= 1.02972 " TABLE I. Tabular Statement of the Results of Experiments on the Jersey City Water Works. 1 2 3 4 5 6 1 8 9 10 Successive Elevations of the Water Surfaces. Area included within the flowage line at these Ele- vations. Fall of the Surface. Quantity dis- charged from Reservoir. Time, in Seconds. Discharge, in Cubic Feet per Second. Area of Discharge, in Square Feet. Mean velocity, in feet per Second. Heads. Mean Heads under which Discharge occurs. FEET. 155.029 154.482 153.992 153.614 152.166 151.604 150.356 SQAURE FEET. 122869.79 121773.32 120797.65 120047.92 117191.86 116091.81 113664.18 FEET. 0.547 0.490 0.378 1.448 0.562 1.248 CUBIC FEET. 66910.00 59430.00 45520.00 171762.00 65553.00 143369.00 20550 18000 14400 54000 21600 47580 3.25595 • 3.3017 3.1611 3.1808 3.0348 3.01322 2.18167 H It U It 1.4924 1.51337 1.44893 1.45795 1.39107 1.381155 30.529 30.002 29.512 29.119 27.606 27.000 25.646 30.262 29.758 29.317 28.365 27.302 26.325 Mean of above Experiments on the Jersey City Water Works. Total Quan- tity discharged from the Reservoir. Total Time of Discharge, in Seconds. Discharge, in Cubic Feet per Second. Area of Discharge, in Square Feet. Mean velocity, in feet per Second. Mean Head under which Discharge . occurs. CUBIC FEET. 552544.00 176130 3.13714 2.18167 1.43795 28.1285 25 (B.) Blackwell's. v=47.913 I- vL This formula takes into account the curves of the pipe. See Hughes on Water Works. Formula (?>?>), p. 336. (C.) Prony's (1). v= +0.00665)-0.0816. See Prony's Recherches Physico- sur la des Eaux Courantes, § 184. (D.) Prony's (2). ¥=^(2494.69^+0.02375)-0.15412. See Prony's Recherches Physico-Mathimatiques sur la thtorie des Eaux Courantes, § 210. (F.) Eytel wein's. v=47.8731 /- V L+54d See Memoires de I'Academic des Sciences de Berlin, 1814 et 1815, p. 165. (F.) D'Aubuisson's (1). v_ / h I 0.00003767485y P V 0.000417568^+[0.015536]+ [ 6.000417568^+[0.015536] 0.00003767485r [0.015536] See D'Aubuisson's Hydraulics, (Bennett's translation,) p. 206, top. (G.) D'Aubuisson's (2). v=^(2394.82^+0.00814)-0.090224. See Neville's Hyd. Formula! (109), p. 118. Simplification by omit- ting the constant [0.015536], and reducing. (H.) Weisbach's. T, r 0 01 71 559 7 h-0.015538v* =0.015538-n- 0.01439+ d I v v J See Julius Weisbach's Ingenieur und Maschinen Mechanik. Vol. I., p. 748. In all the above v=Velocity, in feet per second. h=thc Head, in feet. d=Diameter of pipe, in feet. L=Length of pipe, in feet. 26 None of these formulas except Blackwell's [B], which takes into account the curves, make any allowance for changes of direction or capacity of the pipe. In the Jersey City main there are no abrupt bends, and for the determination of the loss of head by the curves, I have em- ployed the formula of Julius Weisbach. h.=^-ux [o.131 + See Weisbach's Ingenieur und JWaschinen Mechanik. Vol. L, p. 770. When he=Head lost by the resistance of the curves, in feet. 4 = the deflection of the pipe from its right line di- rection, in degrees. r=the radius of the interior of the pipe, in feet. R=the radius of curvature of the axis of the pipe, in feet. v=the Velocity of the water passing through the pipe, in feet per second. g=32.18=acceleration due to gravity. By means of this formula the values of the total loss of head from curves in the pipe has been calculated for as great a range of velocities as will result in the use of the formulas above em- ployed for their calculation. These are inserted in the following Table. Table 2. Values of the Velocity. 1.7 1.8 1.9 2.0 2.1 Total loss of head from resistance of curves. 0.0218 0.0244 0.0272 0.0302 0.0333 The enlargement of the pipe in passing the draw at the Hackensa'ck River, and its subsequent contraction, are made by means of reducers, five feet long, and therefore the change in velocity is so gradual that we may consider the loss of head from this cause inappreciable. 27 We have, however, a gain of head, equal to the difference between the head lost by the friction of the water in passing through 128 feet of 20 inch, and the same length of 24 inch pipe. This difference I have calculated, by Weisbach's formula | H], for various velocities of the water in the 20 inch pipe, and the values thereof are appended in the following Table. Table 3. Velocity of the water in the 20 inch pipe. . v=1.7 v=l .8 v=1.9 v=2.0 v = 2.1 Gain of head of 128 ft. of 24 inch pipe over the same length of 20 inch pipe 0.0532 0.0589 0.0648 0.0710 0.0774 Since the loss of head by the influence of the curves, and its gain by the enlargement of the main, depend for their value upon the velocity of the water in the pipe, it is necessary in employing any of the above formulas for finding the velocity, to first calculate the latter approximately, by the formula which we intend using, neglecting in this calculation the influence upon the head of the curves and enlargements. The velocity being in this manner determined, Tables (2) and (3) give the correction to be applied to the head; that ob- tained from (2) being a subtractive, and that from (3) an addi- tive correction. From this corrected head a closer approximation to the velocity is obtained by the formula. The value of the velocity thus resulting, gives us more nearly the value of the resistances of curves and enlargements, and thus a still more accurate value of the corrected head, from which, by again applying the formula, a value of the velocity is 28 obtained sufficiently accurate for comparison with the results of the experiment. These values of the velocity have been calculated by all the formulas above given, and the results, together with those de- rived by actual experiment, are inserted in the accompanying tabular statement marked K. Tabular Comparison of the New York and Jersey City Experi ments. K. _ - - - ------ ■ z_l. : - - - - - --------- EET PER SECO: VD. - EXPERIMENTS: Where, and by whom, made. Mean Heads under which the discharge occurred. VALUES OF THE VELOCITY, IN F - - Diameter of the Pipe, in feet. Length of Pipe, in feet. As deduced from the discharge. By Hawkesley's formula. MJ By Blackwell's formula. MJ By Prony's formula (1). MJ By Prony's formula (2). mj By Eytelwein's formula. MJ By D'Aubuisson's formula (1). MJ By D'Aubuisson's formula (2). MJ By Weisbach's formula. MJ On the 20 inch Main between the Reservoirs ' / 1.6667 29,715 30.262 1.4924 1.97399 1.97624 1.9206 1.91068 1.97063 1.927302 1.92923 2.03255 of the Jersey City Water Works. ' 1.6667 29,715 29.758 1.51337 1.9575 1.9597 1.9039 1.89338 1.95416 1.9105 1.9123 2.01294 By G. H. Bailey and C. W. Boynton. > 1.6667 29.715 29.317 1.44893 1.94293 1.94514 1.8891 E87838 1.93963 1.8957 1.8976 1.99688 128 feet of this Main is 24 inches diameter. 1.6667 29,715 28.365 1.45795 1.91112 1.9133 1.8570 1.8453 1.90789 1.8632 1.8650 1.95938 Allowance is made in the calculation for this / 1.6667 29,715 27.302 1.39107 1.8750 1.877115 1.8204 1.8077 1.87180 1.8263 1.8282 1.91797 enlargement, and the curves in the pipe. 1.6667 29,715 26.325 1.381155 1.84115 1.84323 1.7861 1.7726 1.83801 1.7918 1.7936 1.87943 Jersey City Water Works. Mean result. I 1.6667 1 29,715 28.1285 1.43795 1.90031 1.9053 1.8489 1.837 1.8999 1.855 1.857 1.9502 - -■ - - ' 1 - ... .. . portnulas used in Table K. (./?.) Hawkesley's. v=48.0125 /--- vL+54d See Civil Eng. and Architects1 Journal, Vol. XVIII., p. 99, line 28. (B.) Blackwell's. v=47.913 /- This formula takes into account the CU1 veh the pipe. \ L See Hughes on Water Works. Formula ('i$),p. 336. t€.) Prony's (1). v= See Prony's Recherches Physico-Mathimatiques sur la theorie des Eaux CouraneS' § (D.) Prony's (2). v= See Prony's Recherches Physico- sur la theorie des Eaux Couran eS' § (E.Y Eytelwein's. v=47.8731 I_ v J VL+54d See Memoires de I1 Academic des Sciences de Berlin, 1814 et 1815, p. 165. _ _____--3767485t_ '8 0.00003767485t (F.) DAubuissons (1). --[0.015536] j 0.000417568L+[0.015536] See D'Aubuisson's Hydraulics, (Bennett's translation,) p. 206, top. (G.) D'Aubuisson's (2). v=^(2394.82^+0.00814)-0.090224. See Seville's Hyd. Formula (1W>). p. 118. Simplification of [F], by omitting the cons^ [0.01553(>], and reducing. vs T; f 0 01 71 S'iQ 1 (H.) Weisbach's. h-0.015538va =0.015538-0.01439+ --/A- I d L v • v J See Julius Weisbach's Ingenieur und Maschinen Mechanik. Vol. I.,p. 748. Where v=Velocity, in feet per second. h=the Head, in feet. d=Diameter of pipe, in feet. L=Length of pipe, in feet. Comparison of Calculations from Established Formulas, with the Results of Various Experiments on Pipes. M. EXPERIMENTS: WHERE, AND BY MADE. Character of the Water. Age of the Pipe laid, in years. Diameter of Pipe, in feet. Length of Pipe, in feet. Head of Water, in feet. VELOCITIES, IN FEET PER SECOND. As taken from the Experiments. By Prony's formula (2). (D.) By D'Aubuisson's formula (1.) (F.) By Hawkesley's formula. By Eytelwein's formula. Ck; *■ Jersey City Water Works. Main from the Belleville Reservoir to the Hudson City Reservoir. By G. H. Bailey and C. W. Boynton. Of this Main 128 ft. is 24 inches diameter. Correction for this enlargement, as a]s0 for the curves, is made Soft. Soft. 4 20 in.=1.6667 1.6667 29,715 29,715 30.262 29.758 1.4924 1.51337 1.91068 1.89338 1.927302 1.9105 1.97399 1.9575 1.97063 1.95416 Jersey City Water Works. Mean result Soft. 4 1.6667 29,715 28.1285 • 1.43795 1.837 1.855 1.90031 1.8999 Croton Aqueduct. Main from the Receiving Reserve to the Distributing Res- ervoir. By G. S. Greene. There arc in this Maitl three right angled curves of 90 ft. radius, for which allowance is made in the ;alculations ... Soft. 16 36 in.=3.0 11,217 20.215 2.99967 3.514 3.4891 3.5016 3.4917 - -- Crawley Pipe. Crawley to Edinburgh. Experimen- by Mr. James Leslie Soft. 29 15 in. = 1.25 44,400 226. 3.4634 3.833 3.8268 Online-ton Pine. From Clubbie Dean Reservoir to Jastle Hill. By Mr. Leslie. Do. From Torduff Cistern to Castle Fin. do. do. Do. From Clubbie Dean Reservoir to torduff Cistern. do. Soft. Soft. Soft. 8 8 16 in.=1.333 1.333 1.333 29,580 25,765 3,815 420. 230. 184. 6.8158 5.2521 14.5030 *6.7199 5.291 1 2.498 6.59805 5.2307 12.062 -- - - Main from Belvidere Road to Brixton. By Mr. Jaiies Simpson Do. do. do. do. Do. do. do. do. Do. do. do. do. Do. do- do. do. Do. from Ditton to Brixton. do. Hard. Hard. Hard. Hard. Hard. Hard. 19 in. = 1.58333 1.58333 1.58333 1.58333 1.58333 1 30 in.=2.5 22,440 22,440 22,440 22,440 22,440 54,120 41.0 43.5 34.0 27.5 24.0 25.0 2.73411 2.80183 2.5225 2.2601 2.0569 1.7690 2.5367 2.6173 2.2971 2.0514 1.9070 1.5502 2.5775 2.6549 2.3472 2.11095 1.9720 1.6296 ■ Note.-The Crawley Pipe is of three sizes, viz; 20, 18, and 15 inches diameter. It has been calculated above as if of 15 inches diameter throughout. A closer calculation would give a greater difference between the actual delivery and the results from the formulas. iFormulas used in Table M. I I i (I Hawkesleys. k J \'L+a4d See Civil Eng. and. Architects' Journal, Vol. XVIII., p. 99, line 28. (D.) Prony's (2). v= V See Prony's Recherches Physico-Math&natiques sur la theorie des Eaux Courantes, § 210. (£.) Eytelwein's. v=47.8731 See Memoires de I'Academic des Sciences de Berlin, 1814 et 1815, p. 165. - - - ----- F To T . ,Q m I h , 0.00003767485r (F.) D Aubuissons (1). v_J____0 00 3417568k+[0.015536] J 0.000417568^+[0.015536] d See D'Aubuisson's Hydraulics, (Bennett's translation,) p. 2S)Q,top. Where v=Velocity, in feet per second h=the Head, in feet. d=Diameter of pipe, in feet. L=Length of pipe, in feet. 29 NOTE 3. Extract from Proceedings of Institution of Civil Engineers, Lon- don, February, 1855. " Mr. Murray had prepared the following table, showing the delivery of water, by pipes of small and of large dimensions, through moderate and more extended lengths and under vari- ous pressures, and he contended, that far from throwing dis- credit upon the researches of the experimenters, whose works he had mentioned, the accuracy of the formulas had been satis- factorily confirmed by practice. DISCHARGE THROUGH PIPES, CALCULATED BY SEVERAL FORMULA. Diameter of Pipe. Length. Head or Pressure. Discharge per Minute. Calculated Discharge per Minute. INCHES. FEET. FEET. CUB. FEET. CUB. FEET. 2 3,300 12.75 1.617 1.507 Du Buat. .... .... .... 1.609 Prony. .... 1.509 Eytelwein. .... . . . 1.59 Poncelet. 14,930 51.00 11.333 11.252 Du Buat. • • • • 11.491 Prony. .... 10.784 Eytelwein. .... 11.281 Poncelet. 12.789 3,837 12.90 155 158 Du Buat. . • • • 155 Prony. .... 145 Eytelwein. 141 Poncelet. 12.789 14,963 21.582 111 99 Du Buat. .... 102 Prony. «... .... 99 Eytelwein. .... 98 Poncelet. 19.184 5,052 4.929 217 223 Du Buat. .... .... .... 230 Prony. .... 215 Eytelwein. .... .... 226 Poncelet. 30 5,280 9.00 880 926 Du Buat. • • • • 932 Prony. • • • • .... 865 Eytelwein. .... .... .... 910 Poncelet. 30 In explanation of the Table it was stated, on the authority of Dr. Robinson, (vide Robinson's ' Mechanical Philosophy,' vol. ii, p. 441) that water was brought into the town of Dun- bar, in East Lothian, from a spring, through pipes, the first length of which was 1,100 yards, of 2 inches diameter, with a declivity of 12 feet 9 inches. The actual quantity discharged was 1.617 cubic foot per minute. The mean calculated quantity was 1.5539 cubic foot per minute. Again it was shown by Mr. Jardine, (vide Brewster's Ency- clopaedia; Art. ' Hydrodynamics,' p. 526) that the main pipe of the Edinburgh Water Works, extending from the fountain head, at Comiston, to the reservoir at the Castle Hill, Edin- burgh, was of lead throughout, 14,950 feet in length, 4| inches in diameter, and the head was 51 feet above the point of deliv- ery. The maximum discharge during five consecutive years, was 11.333 cubic feet per minute. The mean calculated quantity was 11.202 cubic feet per minute. The next three results were taken from Bossut's 'Treatise on Hydrodynamics' brought into English measures, and they were stated to be his own experiments, combined with those of Couplet. The pipes were of iron with several horizontal and vertical bends, which were taken into account in the lengths mentioned:- The first yielded The second " Cubic Feet per Minute. 155 Ill Meau calcu- lated quantity. 150 cub. ft. per min. 90.5 " The third " 217 223.5 " The last statement of the table was obtained from the late Mr. Chapman, C. E., of Newcastle; but whether it was de- rived from actual measurement, or was simply the result of his experience, was uncertain. From a pipe of 30 inches diameter, with a fall of 9 feet per mile, the actual quantity discharged was 880 cubic feet per minute. The mean calculated quantity was 908 cubic feet per minute. The following were the formula? employed in the calculations of the table:- 31 Du Buat's Formula reduced to English Measure 307(-/R-0.1) _ V=-' L _o.3(VR-O.l) VS-L(VS+1.6) K 7 V=velocity in inches per second. R=hydraulic mean depth=| diameter. *S=slope or difference of level. L=hyperbolic logarithm, and found by multiplying the com- mon logarithm by 2.3026. In the following formulae English feet were employed :- V being the velocity per second. I) " diameter H " head of pressure, L " the length of the pipe. Prony's simple Formula. V=48.449 V L Eytelwein's Formula, as given by Tredgold (vide Tredgold's 'Tracts on Hydraulics,' p. 215.) V=45.5 /_LLJjL VL+47D Poncelet's formula. V = 47.95 /-JILL V L+54D * The explanation of the value of S here given, is, as will be evident by an ex- amination of the formula, erroneous. ,, Length of the pipe. Really S-. '-J'- Head of pressure. 32 NOTE 4. The following (furnished me by J. C. Brevoort, Esq.) is the formula proposed by M. Mary, of the French Academy of Sciences, for determining the flow of water in pipes: v=C V L Where v = Velocity, in feet per second. h = the Head, in feet. d = Diameter of the pipe, in feet. L = Length of the pipe, in feet. C = a Constant which varies with the velocity, and the values of which are obtained from the fol- lowing Table. Values of V. 0.164 0.328 0.656 0.984 1.312 1.640 3.281 6.562 Infinity. Values of C. 34.723 39.722 43.417 44.975 45.753 46.297 47.420 47.945 48.470 In the use of this formula, the value of v is obtained by ap- proximation. A mean value of C being first assumed, the value of v is approximately calculated, which gives us more accurately the value of C; thence results a value of v more nearly correct than the preceding. By two or three applications of the formula, in this manner, the value of v is deduced with sufficient accuracy. s Reference Thirtt' st\r inrh F'i/ie-, xhrtvn tfiics ' Thirty u > r " Trvtnfg . , , „ Trvelvt , , » Sir , Connections r , DIAGRAM shew the jiositwn of CERTAIN WATER PIPE MAINS in the City of NEVV TURK October 1858 . DIAGRAM sh entity the relative jiositwns of the RESERVOIRS *no CONNECTING MAIN JERSEY CEO WATERWORKS. October 1858. Twenty inchPijte , shewn thus Twenty Jour in. du. " "