Page images
PDF
EPUB

310E*. OVERFALL WEIRS, COEFFICIENT OF DISCHARGE.

[graphic][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][ocr errors][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][subsumed][subsumed][subsumed][ocr errors][ocr errors][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][subsumed][subsumed][subsumed][ocr errors][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][ocr errors][subsumed][subsumed][subsumed]

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.

[graphic][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

From the above we have a mean value of m= = 0.723.

[ocr errors]

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:

[graphic]
[ocr errors][ocr errors]

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.

[ocr errors]
[ocr errors]
[ocr errors]

2 inches long and † high, m = .613.

[ocr errors]

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:

[merged small][merged small][graphic][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed]

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'

[ocr errors]

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.

[ocr errors]
[ocr errors]

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.

[ocr errors]

6.5 in.

0.541666 ft. surface of the water in the

165 metres.

[ocr errors]

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.

[blocks in formation]

cubic ft. per second.

cubic ft. per minute.
320.4 cubic feet.

Mesure des eaux courantes, (Paris,

mAN 2 g h or Q = }}
m lh x 2 g h

Complete contraction is when the orifice is removed 1.5 in. to twice its lesser diameter of the fluid vein.

[ocr errors]

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.

[ocr errors][merged small][merged small][merged small]

!

Q

Q

[ocr errors][ocr errors][merged small]

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.
quantity in cubic feet;

[blocks in formation]
[blocks in formation]

RI 0.00002427 V + 0.000111416 V2 all in feet, Eytelwein; from which

IO
II

he gives V WR in which formulas he puts R f=twice the fall in feet per mile, and I inclination,

the length.

[blocks in formation]

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.

[blocks in formation]

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.

[merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][ocr errors]

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,

[merged small][merged small][merged small][merged small][ocr errors]

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.

[merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small]

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

[merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small]

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

[merged small][ocr errors][merged small][merged small]

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:

[merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

P = .00123 Q for over-shot wheels, and Q = 777 P_divided by h

P .00113 Qh for high-breast wheels, and Q

[ocr errors]

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
822 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.

« PreviousContinue »