Q/Q1 = 2/π ∫π0 sin2 φ √ {1 − ε cos φ} dφ.
For
h1 = ∞, ε = 0 and Q/Q1 = 1;
and for
h1 = 0, ε = 1 and Q/Q1 = 0.96.
So that in this case also the difference between the simple formula (5) and the formula above, in which the variation of head at different parts of the orifice is taken into account, is very small.
Notches and Weirs
§ 41. Notches, Weirs and Byewashes.—A notch is an orifice extending up to the free surface level in the reservoir from which the discharge takes place. A weir is a structure over which the water flows, the discharge being in the same conditions as for a notch. The formula of discharge for an orifice of this kind is ordinarily deduced by putting H1 = 0 in the formula for the corresponding orifice, obtained as in the preceding section. Thus for a rectangular notch, put H1 = 0 in (8). Then
Q = 2⁄3 cB √(2g) H3/2,
(11)