Weir Head from a Target Flow
The head over a sharp-crested weir needed to pass a target flow.
Example
You enter
- Weir type vnotch90
- Target flow Q (cfs) 0.446
You get
- Required head over crest 0.5 ft
Checked against published worked examples from: USBR.
Details, formula, and sources
ScopeV-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 or table90-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.
Source and editionPer 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.
Free accessFree at usbr.gov/tsc/techreferences/mands/wmm; the user confirms the calibrated weir coefficient.
What governsEstimate. AHJ and licensed professional govern.
API field namesweir_type, target_flow_cfs, head_ft
- Weir condition sharp-crested, ventilated, free-flow; fully contracted, or suppressed for the suppressed optionUSBR Water Measurement Manual
- Contracted solve the contracted weir's L - 0.2 H is solved by fixed-point iteration seeded from the suppressed formscope of this tile