v1²/2g = h;
v1 = [root](2gh);
or, if a coefficient is introduced to allow for friction,
v1 = c_v [root](2gh);
where c_v is about 0.97 if the mouthpiece is smooth and well formed.
Q = [Omega] v1 = c_v [Omega] [root](2gh).
[Illustration: FIG. 60.]
Hence the discharge depends on the area of the stream at EF, and not
at all on that at CD, and the latter may be made as small as we please
without affecting the amount of water discharged.
There is, however, a limit to this. As the velocity at CD is greater
than at EF the pressure is less, and therefore less than atmospheric
pressure, if the discharge is into the air. If CD is so contracted
that p = 0, the continuity of flow is impossible. In fact the stream
disengages itself from the mouthpiece for some value of p greater than
0 (fig. 61).
[Illustration: FIG. 61.]
From the equations,
p/G = p_a/G = (v² - v1²)/2g.