Daily supply of water to each person in the following cities: New York, 52 gallons. Boston, 97. Philadelphia, 36. Baltimore, 25. St. Louis, 40. Cincinnati, 30. Chicago, 43. Buffalo, 48. Albany, 69. Jersey City, 59. Detroit, 31. Washington, 19. London, 30. Reservoirs. The following is a list of some of the principal reservoirs with their contents in cubic feet and days' supply: Rivington Pike, near Liverpool, 504,960,000 cubic feet, holds 150 days' supply. Bolton, 21 millions cubic feet = 146 days' supply. Bateman's Compensation, near Manchester, has 155 million cubic feet. 74 days' supply. Preston, 4 reservoirs, 26,720,000 cubic feet — 180 days' supply. Croton, New York, 2 divisions, 24 millions cubic feet. Chicago, Illinois, the water will be, in 1867, taken from a point two miles from the shore of Lake Michigan, in a five-foot tunnel, thirty-two feet under the bottom of the Lake, thus giving an exhaustless supply of pure water. The water now supplied is taken from a point forty-five feet from the shore, and half a mile north of where the Chicago River enters Lake Michigan, consequently the supply is a mixture of sewage, animal matter and decomposed fish, with myriads of small fish as unwelcome visitors. CONDUITS OR SUPPLY MAINS. 310B*. Best forms for open conduits, are semi-circle, half a square, or a rectangle whose width — twice the depth, half a hexagon, and parabolic when intended for sewering. (See sec. 133.) Covered conduits ought not to be less than 3 feet wide and 34 high, so as to allow a workman to make any repairs. A conduit 4 feet square with a fall of 2 feet per mile, will discharge 660,000 imperial gallons in one hour. The conduit may be a combination of masonry on the elevated grounds, and iron pipes in the valleys; the pipes to be used as syphons. The ancients carried their aqueducts over valleys, on arches, and sometimes on tiers of arches. They sometimes had one part covered and others open. Open ones are objectionable, owing to frost, evaporation and surface drainage. DISCHARGE THROUGH PIPES AND ORIFICES. 810c*. Pipes under pressure. Pipes of potter's clay, can bear but a light pressure, and therefore are not adapted for conveying water. Wooden Pipes, bear great pressure, but being liable to decay, are not to be recommended. Cast Iron Pipes, should have a thickness as follows: t 0.03289 + 0.015 D. Here d diameter, and t thickness of the metal. D'Aubisson's Hydraulics. t=0.0238, d + 0.33. According to Weisbach. Claudel gives the following, which agrees well with Beardmore's table of weight and strength of pipes. t 0.00025 h d for French metres. 0.00008 h d for English feet. Here t― thickness, h = total height due to the velocity, and d diameter. Lead Pipes, will not bear but about one-ninth the pressure of cast iron, and are so dangerous to health, as to render them unfit to be used for drawing off rain water, or that which is deficient in mineral matter. The pressure on the pipe at any given point, is equal to the weight of a column of water whose height is equal to that of the effective height, which is the height, h diminished by the height due to the velocity in the pipe. Pressure h―015,536 v2. Here v is the theoretical velocity. Torricillis' Fundamental Formula, is V = √2 g h for theoretical velocity. v=my/2gh for practical or effective velocity. The value of 2g is taken at 64.403 as a mean from which it varies with the latitude and altitude. The value of g can be found for latitude L, and altitude A, assuming the earth's radius R. 82.17 (1.0029 Cos. 2 L) × (1 2 L) × (1 − 24) The value of m, the coefficient of efflux is due to the vena contracta. Its value has been sought for by eminent philosophers with the following result: As the prism of water approaches an outlet, it forms a contracted vein, (vena contracta) making the diameter of the prism discharge less than that of the orifice, and the quantity discharged consequently less by a multiplier or coefficient, m. The value of m is variable according to the orifice and head, or charge on its centre. Vena Contracta. The annexed figure shows the proportions of the contracted vein for circular orifices, as found by Michellotti's latest experiments. AB is the entrance, and a b the corresponding diameter at outlet; that is the theoretical orifice, A B, is reduced to the practical or actual one, a b. When A B = 1, then C D = 0.50, and a 6 — 0.787; therefore the area of the orifice at the side AB=1X.785 and that at ab .7872×0.7854; that is the theoretical is to the actual as 1 is to 0.619 ... m = 0.619. The values of m have been given by the following: Dr. Bryan Robinson, Ireland, in 1739, gives m — 0.774. NOTE. It is supposed that Dr. Robinson used thick plates, chamfered or rounded on the inside, thereby making it approach the vena contracta, and consequently increasing the value of m or coefficient of discharge. Kejecting Robinson and Marriot's, we have a mean value of m = 0.622, which is frequently used by Engineers. Taking a mean of Bossuet, Michellotti, Eytelwein and Xavier, we find the value of m 0.617, which appears to have been that used by Neville in the following formulas, where A sectional area of orifice, r radius, Q discharge in cubic feet per second, h=heighth of water on the centre of the orifice, and m = 0.617 coefficient of discharge. Hence it appears, that when h=r, the top of the orifice comes to the surface, and that when h becomes greater or equal to 3 r, that the general equation Q = 8.03 m √ H × A, requires no modification. 1 r 1 1 32 h2 1024* h 1 Adjutages, with cylindrical tubes, whose lengths = 24 times their diameters, give m = 0.815. Michellotti, with tubes an inch to 3 inches diameter and head over centre of 3 to 20 feet, found m = 0.813. The same result has been found by Bidone, Eytelwein and D'Aubisson. Weisbach, from his experiments, gives m = 0.815. Hence it appears that cylindrical tubes will give 1.325 times as much as orifices of the same diameter in a thin plate. = 1.00. For tubes in the form of the contracted vein, m — For conical tubes converging on the exterior, making a converging < of 183°, m = 0.95. For conical diverging the narrow end toward the reservoir and making the diverging <= 5° 6′, m = 1.46, and the inner diameter to the outer as 1 is to 1.27. NOTE. The adjutage or tube, must exceed half the diameter (that length being due to the contracted vein) so as to exceed the quantity discharged through a thin plate. Circular Orifices. Q=3.908 d3 √/h. Cylindrical adjutage as above. Q— 5.168 d2 √ĥ. Tube in the form of vena contracta. Q: = 5.678d2 √/h. In a compound tube, (see fig., sec. 310c*) the part A a b B is in the form of the contracted vein, and a b E F a truncated cone in which D G 9 times a b and EF 1.8 times a b. This will make the discharge 2.4 times greater than that through the simple orifice. (See Byrne's Modern Calculator, p. 821.) Orifices Accompanied by Cylindrical Adjutages. When the length of the adjutage is not more than the diameter of the orifice, then m = 0.62. Length 2 to 3 times the diameter, m = 0.82. 36 times m= 68. 310D*. Orifices Accompanied with Conical Converging Adjutages. When the adjutage converges towards the extremity, we find the area of the orifice at the extremity of the adjutage the height h of the water in the reservoir above the same orifice. Then multiply the theoretical discharge by the following tabular coefficients or values of m : The above is Castel's table derived from experiments made with conical adjutages or tubes, whose length was 2.6 times the diameter at the extremity or outlet. In the annexed figure A C D B represents Castel's tube where m n is 2.6 times C D and angle A O B = < of convergence. NOTE. It appears that when the angle at O is 13 degrees the coefficient of discharge will bejthe greatest. The discharge may be increased by making m n equal to C D, A B 1.2 times C D, and rounding or chamfering the sides at A and B. In the next two tables, we have reduced Blackwell's coefficient from minutes to seconds, and call C m. Q = 8.03 m A √h or Q CA√b, where C is the value of 8.03 m in the last column. h is always taken back from the overfall at a point where the water appears to be still. Experiments 1 to 12, by Blackwell, on the Kennet and Avon Canal. Experiment 13, by Blackwell and Simpson, at Chew Magna, England. |