Now an orifice producing a rectangular jet must itself be very approximately rectangular. Let B be the breadth, H1, H2, the depths to the upper and lower edges of the orifice. Put
b (h23/2 − h13/2) / B (H23/2 − H13/2) = c.
(7)
Then the discharge, in terms of the dimensions of the orifice, instead of those of the jet, is
Q = 2⁄3 cB √2g (H23/2 − H13/2),
(8)
the formula commonly given for the discharge of rectangular orifices. The coefficient c is not, however, simply the coefficient of contraction, the value of which is
b (h2 − h1) / B (H2 − H1),
and not that given in (7). It cannot be assumed, therefore, that c in equation (8) is constant, and in fact it is found to vary for different values of B/H2 and B/H1, and must be ascertained experimentally.
Relation between the Expressions (5) and (8).—For a rectangular orifice the area of the orifice is ω = B(H2 − H1), and the depth measured to its centre is 1⁄2 (H2 + H1). Putting these values in (5),