310E*. OVERFALL WEIRS, COEFFICIENT OF DISCHARGE. BLACKWELL'S SECOND EXPERIMENTS. Overfall of cast iron, 2 inches thick, 10 ft. long, square top. Canal.had wing walls, making an angle of 45 degrees. From the above we have a mean value of m= = 0.723. The reservoir used on the Avon and Kennet canal, in England, contained 106,200 square feet, and was not kept at the same level, but the quantity discharged for the experiment was not more than 444 cubic feet, which would reduce the head but .05 inch. In the Chew Magna we have an area of 5717 square feet kept constantly full by a pipe 2 inches in diameter from a head of 19 feet. The inlet of the pipe to the overfall being 100 feet, consequently the water approaches the fall with a certain degree of velocity, which partially accounts for the difference in value of m, in experiments 13 and 5. Poncelet and Lebros' experiments on notches, 8 inches long, open at top: From these small notches we have a mean value of m = .603. Du Buat's experiments on notches 18.4 long, give a mean coefficient .632. Smeaton and Brindley, for notches 6 inches wide and 1 to 6 high, give .637. Rennie, for small rectangular orifices, gives as follows: Head 1 to 4 feet, orifice 1 inch square, mean value of m = .613. 2 inches long and † high, m = .613. 2 inches long and § deep, m = .632. The following table is from Poncelet and Lebros' experiments on covered orifices in thin plates. Width of the orifice .20 metre (about 8 inches) length, and h = height of the orifice. 1: Here the water takes the form of the hydraulic cure, nearly that of a parabolic, and its sectional area The co-efficient increases as 23 14. the orifice approaches the sides or bottom. Let C coëft. of perfect contraction, and C' :- coëft. of partial contraction, then C' C+, o qn.-Neville. The presence of a coursoir, mill-race, or channel, has no sensible effect on the discharge, when the head on its centre is not below .50 to .60 metres, for orifice of .20 to 15 metres high, .30 to 40 for 10 metres high, and .20 for .05 metres high. The charge on the centre is seldom below the above. --Morin's Aide Memoire, p. 27. 310f. Example 10: From Neville's Hydraulics, p. 7. What is the discharge in cubic feet per minute from an orifice 2 ft. 6 in. long, and 7 in. deep; the upper edge being 3 in. under the surface of apparent still water in the reservoir. area, S of orifice 1.458 square feet. 6.5 in. 0.541666 ft. surface of the water in the 165 metres. lh = 2.5 ft. x 7" H-half of 7" +3 reservoir above the centre of the orifice. The square root of 0.541666 0.736. Head on centre of orifice - 6.5 in. VI Ratio of length of orifice to its height 4. Then opposite, 165 metres, and under / 4/, find m 0.616 Q = 8.03 × 0.616 x 1.458 × 0.736 Q = 481.8 × 0.616 × 1.458 × 0.736 Neville makes == 0.628, and Q M. Boileau, in his Traite de la 1854,) recommends Poncelet and Lebros' value of m in the general formula. cubic ft. per second. cubic ft. per minute. Mesure des eaux courantes, (Paris, mAN 2 g h or Q = }} Complete contraction is when the orifice is removed 1.5 in. to twice its lesser diameter of the fluid vein. The French make .625 for sluices near the bottom, discharges either above or under the water. D Castel has found that 3 sluices in a gate did not vary the value of m. 310g. Let Rhyd, mean depth; V = surface velocity, by Sec. 312; diam.; 1 radius of circular orifices; 2 === mean, and w bottom velocities; Q- discharge in cubic feet per second; T ( time in seconds; A area of section of conduit; I the head; per unit height divided by the horizontal distance between the reservoir and out-let. ! Q Q 0.835 V for large channels, by Ximes, Funk, and Bruning. surface, W bottom velocities. 0.80 V, and W = .60 V, by Conference on Drainage and Irrigation at Paris in 1849 and 1850. 8.025 m AN h is the general formula where A sectional area. RI 0.00002427 V + 0.000111416 V2 all in feet, Eytelwein; from which IO he gives V WR in which formulas he puts R f=twice the fall in feet per mile, and I inclination, the length. ΙΟ II 310 gives V VR is used by Beardmore and many Engineers. For clear, straight rivers, with average velocities of 1.5, Neville 92.3 R 1, and for large velocities V = 93.3 √ R 1. ◊ He says that co-effts. decrease rapidly when velocities are below 1.5 ft. per second. In his second edition of his valuable treatise on hydraulics, he states that the best formula proved by experiments for discharges over weirs is. 310h. AI. Boileau, in his Traites de la Mesure des eaux courantes, p. 345: For discharge through orifices, sectional area of reservoir at still water, h diff. of level between the summit of the section O and that of the section (remous d'aval) where the ripple begins. In his tables he makes the value of m, coüift. of contraction for short remous, or eddy, when the orifice is 310:1. Let Q 2 = 8.025 my h Q 4.879 A 0.622, 0.600 when it attains the summit, and 0.68S surrounded by the remous. the quantity in feet per second. effective discharge in cubic ft. per second, # = variable. orifice surrounded on all sides, Q = 5.048 A √horifice surrounded on three sides, Q = 4.253 A √h orifice coincides with sides and bottom, - 0.608 0.629 112 0.684 as last sluice makes angle 60° against stream, m = 0.740 as last but. sluice makes the angle 45′′, sluice vertical, orifice near the bottom, 11 0.800 m = 0.625 0.530 0.750 2 sluices, or orifices, within 10 ft. of each other, m Q = 6.019 A √h the flood gates make 160° with the current, and m == that there are 3 sluices guarded to conduct the water into the buckets of a water wheel sum of the areas. Tv = 5.35 m √ h - mean vel, for regular orifices, open at top, and is the time required to empty a given vessel when there is no efflux, and is double the time required to empty the same when the vessel or reservoir is kept full. 5.35 (+0.0349410 w 2). Here the water comes to the reservoir with a given velocity, w. time to bring both to the same level in can:1 locks. 3101. For D'Arcy's Formula, see p. 264. He has given for 1⁄2 inch, pipes m = 65.5 and 7 == 65.5 Nr s 3101. Neville's general formula for pipes and rivers: v = 140 (ri)1⁄2 – (r i)1⁄2 here r = hyd, mean depth, and i inclination. Frances, in Lowell, Mass., has found for over falls, m =.623. (See his valuable experiments made in Lowell. Thompson, of Belfast College, Ireland, has found from actual experiments that for triangular notches, m == 0.618, and Q = 0.317 / 5-3 — cubic feet per minute, and / heal in inches. M. Girard says it is indispensible to introduce 1.7 as a co-ëfficient, due aquatic plants and irregularities in the bottom and sides of rivers. Then the hydraulic mean depth (see Sec. 77,) is found by multiplying the wetted peremeter by 1.7 and dividing the product into the sectional area. A velocity of 22 feet per second in sewers prevents deposits.--London Saverage. 310. Spouting Fluids. -Let T tom, * = bot top of edge of vessel, and B orifice in the side, and BS horizontal distance of the point where the water is thrown. (See fig. 60.) BS 2 √ TO. OB = 2 O E, by putting OE for the ordinate through O, making a semi-circle described on F B. 310K. On the application of water as a motive power: Q = cubic ft. per minute, h height of reservoir above where the water falls on the theoretical horse-power. wheel, P Available horse-power 12 cubic ft., falling 1 ft. per second, and is generally found to 66 to 73 per cent. of the power of water expended. Assume the theoretical horse-power as 1, the effective power will be as follows: P = .00123 Q for over-shot wheels, and Q = 777 P_divided by h P .00113 Qh for high-breast wheels, and Q P = .00101 Q ʼn for low-breast wheels, and Q P = .00066 Qh for under-shot wheels, and Q 882 P divided by h 962 P divided by h 1511 P = .00113 Q h for Poncelet's undershot wheels, and Q divided by h For under-shot wheels, velocity due to the head × 0.57 will be equal to the velocity of the periphery, and for Poncelet's, 0.57 will be the multiplier. |