Weir Head from a Target Flow
The inverse of the weir-flow tile: the head over a sharp-crested weir needed to pass a target flow. V-notch H = (Q/C)^(1/2.48); suppressed rectangular H = (Q/(C L))^(2/3); the contracted weir's L - 0.2 H is solved by fixed-point iteration. A 90-degree V-notch passing 0.446 cfs needs 0.50 ft of head. Sizes a weir box or sets a staff-gauge mark for a design flow. Head below ~0.2 ft is a low-accuracy reading; free, non-submerged, ventilated flow required. The operator of record governs.
Formula and source
90-degree V-notch: H = (Q/C)^(1/2.48), C=2.49. Suppressed rectangular: H = (Q/(C L))^(2/3), C=3.33. Contracted rectangular: L-0.2H solved by fixed-point from the suppressed seed. 1 cfs = 448.831 GPM.
Per the USBR Water Measurement Manual (public domain) - the V-notch and Francis rectangular-weir equations solved for the head, the inverse of the weir-flow tile, by name.
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