What this calculator does
Weirs measure flow with nothing moving but water. This calculator converts a measured head over the crest into a discharge for four standard weir shapes, using the classic coefficients that apply to a sharp, fully ventilated crest.
How to use it
- Choose the weir type: rectangular suppressed, rectangular with two end contractions, a 90° V-notch, or a Cipolletti trapezoidal notch.
- Enter the crest length for the rectangular and Cipolletti types; the V-notch has no crest length.
- Measure the head over the crest in metres, upstream of the nappe.
- Apply corrections where the nappe is submerged or the approach velocity is high.
Governing formula
Q = 1.84·L·H^1.5 (rectangular) ; Q = 1.38·H^2.5 (V-notch) Where:
-
L= Crest length [m] -
H= Head over the crest [m]
Derived Equations:
Q = 1.84(L − 0.2H)H^1.5 Q = 1.86·L·H^1.5 Worked example — 120 mm over a 1.5 m suppressed rectangular weir
The figures below were produced by running this page's own engine with the example inputs (Weir type, Crest length (m), Head over the crest (m)). If the calculator returns something different for the same numbers, that is a bug, not a rounding difference.
| Discharge | 0.11 m³/s |
|---|---|
| Discharge | 114.73 L/s |
| Discharge per metre of crest | 0.08 m²/s |
| Weir type | Rectangular suppressed |
| Assessment | Rectangular suppressed: Q = 0.115 m³/s (114.7 L/s) at 0.12 m head. Apply on a sharp-crested, fully ventilated crest — otherwise multiply by a carry-over/velocity-approach correction. |
- Q = 1.84 × 1.5 × 0.12^1.5 ≈ 0.115 m³/s.
- That is 115 L/s across a 1.5 m crest, or about 0.077 m²/s per metre.
- Check that the tailwater does not submerge the nappe, or apply the submergence correction.
Assumptions & limitations
Engineering calculation. Sharp-crested weir formulae with the standard coefficients. Submergence, velocity of approach and end contractions other than two are not corrected.
- Assumes a sharp crest, a fully ventilated nappe and no submergence; a submerged weir passes noticeably less.
- Coefficients are for SI units and clear water; viscous or very low-head flows need other relationships.
- Tailwater submergence and approach velocity corrections can change the result by 10–20 %.
This tool supports professional engineering work; it does not replace a sealed design. Confirm every result against the applicable standard and a licensed engineer before it is built.
References & standards
- ISO 1438-1 — flow measurement through open channels, weirs.
- USBR Water Measurement Manual — weir discharge relationships.
- Chow, Open-Channel Hydraulics — weir flow.