§ 46. Partially Submerged Rectangular Orifices and Notches.—When the tail water is above the lower but below the upper edge of the orifice, the flow in the two parts of the orifice, into which it is divided by the surface of the tail water, takes place under different conditions. A filament M1m1 (fig. 49) in the upper part of the orifice issues with a head h′ which may have any value between h1 and h. But a filament M2m2 issuing in the lower part of the orifice has a velocity due to h″ − h″′, or h, simply. In the upper part of the orifice the head is variable, in the lower constant. If Q1, Q2 are the discharges from the upper and lower parts of the orifice, b the width of the orifice, then
Q1 = 2⁄3 cb √2g { h3/2 − h13/2 }
Q2 = cb (h2 − h) √2gh.
(3)
In the case of a rectangular notch or weir, h1 = 0. Inserting this value, and adding the two portions of the discharge together, we get for a drowned weir
Q = cb √2gh (h2 − h/3),
(4)
where h is the difference of level of the head and tail water, and h2 is the head from the free surface above the weir to the weir crest (fig. 50).
From some experiments by Messrs A. Fteley and F.P. Stearns (Trans. Am. Soc. C.E., 1883, p. 102) some values of the coefficient c can be reduced
| h3/h2 | c | h3/h2 | c |
| 0.1 | 0.629 | 0.7 | 0.578 |
| 0.2 | 0.614 | 0.8 | 0.583 |
| 0.3 | 0.600 | 0.9 | 0.596 |
| 0.4 | 0.590 | 0.95 | 0.607 |
| 0.5 | 0.582 | 1.00 | 0.628 |
| 0.6 | 0.578 |