v²/2g = h2 - h3 = h, (3)
where h is the difference of level of the head and tail water, and may
be termed the _effective head_ producing flow.
[Illustration: 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 = [root][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