where h is the difference of level of the head and tail water, and may be termed the effective head producing flow.
| Fig. 42. |
Case where the Pressures are different on the Free Surface and at the Orifice.—Let the fluid flow from a vessel in which the pressure is p0 into a vessel in which the pressure is p, fig. 42. The pressure p0 will produce the same effect as a layer of fluid of thickness p0/G added to the head water; and the pressure p, will produce the same effect as a layer of thickness p/G added to the tail water. Hence the effective difference of level, or effective head producing flow, will be
h = h0 + p0/G − p/G;
and the velocity of discharge will be
v = √ [ 2g { h0 + (p0 − p) / G } ].
(4)
We may express this result by saying that differences of pressure at the free surface and at the orifice are to be reckoned as part of the effective head.
Hence in all cases thus far treated the velocity of the jet is the velocity due to the effective head, and the discharge, allowing for contraction of the jet, is
Q = cωv = cω √ (2gh),