Sharp-Crested Rectangular Weir Calculator
Discharge over a thin-plate rectangular weir from crest length and upstream head. Used for flow measurement in ditches, lab flumes, and small treatment-plant outflow structures.
Default C = 3.33 in US units (≈ 1.84 in SI) is the Francis coefficient for sharp-crested weirs.
When to use a sharp-crested weir
Sharp-crested weirs are accurate flow measurement devices for steady or slowly-varying flow in small to medium channels — typical applications include irrigation ditch metering, water-treatment plant effluent measurement, laboratory flumes, and stream gauging in ungauged watersheds. Accuracy is ±2–3% with proper installation.
Installation requirements
- Weir plate vertical, at right angles to flow.
- Crest sharp (not rounded). Rounded crest = broad-crested weir; different equation.
- Approach channel straight for at least 4× the channel width upstream.
- Head H measured at a stilling well at least 4H upstream of the weir.
- Free fall on the downstream side; nappe must be ventilated to atmospheric pressure or the weir becomes submerged and inaccurate.
Suppressed vs. contracted
A suppressed weir spans the full channel width — the channel walls suppress the end contractions of the nappe. A contracted weir is shorter than the channel width, allowing end contractions on both sides. The Francis equation reduces the effective length by 0.1H per end contraction (so 0.2H for two-sided contraction).
Range of applicability
The equation is valid for H/P ≤ 0.4, where P is the weir height (crest above channel bottom). For higher H/P, the approach velocity head becomes significant and the basic equation under-predicts discharge by 5–15%. For tall weirs (H/P → 0), accuracy is best.
Reference: USBR (1997). Water Measurement Manual (3rd ed.), Chapter 7. Original: Francis, J.B. (1855). Lowell Hydraulic Experiments. Also Brater & King's Handbook of Hydraulics, Chapter 5.