In the case of large orifices such as weirs, the velocity can be directly determined by using a Pitot tube (§ 144).
| Fig. 17. |
The coefficient of discharge, which for practical purposes is the most important of the three coefficients, is best determined by tank measurement of the flow from the given orifice in a suitable time. If Q is the discharge measured in the tank per second, then
c = Q/ω √ (2gh).
Measurements of this kind though simple in principle are not free from some practical difficulties, and require much care. In fig. 18 is shown an arrangement of measuring tank. The orifice is fixed in the wall of the cistern A and discharges either into the waste channel BB, or into the measuring tank. There is a short trough on rollers C which when run under the jet directs the discharge into the tank, and when run back again allows the discharge to drop into the waste channel. D is a stilling screen to prevent agitation of the surface at the measuring point, E, and F is a discharge valve for emptying the measuring tank. The rise of level in the tank, the time of the flow and the head over the orifice at that time must be exactly observed.
| Fig. 18. |
For well made sharp-edged orifices, small relatively to the water surface in the supply reservoir, the coefficients under different conditions of head are pretty exactly known. Suppose the same quantity of water is made to flow in succession through such an orifice and through another orifice of which the coefficient is required, and when the rate of flow is constant the heads over each orifice are noted. Let h1, h2 be the heads, ω1, ω2 the areas of the orifices, c1, c2 the coefficients. Then since the flow through each orifice is the same
Q = c1ω1 √ (2gh1) = c2ω2 √ (2gh2).
c2 = c1 (ω1/ω2) √ (h1/h2).
| Fig. 19. |