A broad-crested weir is a flat-topped barrier across a channel. Water flowing over it reaches critical depth on the crest, so the flow depends only on the upstream head – making it a simple, robust flow meter for irrigation and rivers.
How to use the Broad-Crested Weir Calculator
- Upstream head H
- Weir width L
- Discharge coefficient C_d
- Gravitational acceleration g
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the head above the crest, the weir width and the discharge coefficient (about 0.85–1.0).
Inputs explained
| Field | What to enter |
|---|---|
| Upstream head H | Units: m, cm, mm, km, in, ft … |
| Weir width L | Units: m, cm, mm, km, in, ft … |
| Discharge coefficient C_d | A number |
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
What each result means
- Discharge Q = [Discharge coefficient C_d]×(2÷3)^1.5×sqrt([Gravitational acceleration g])×[Weir width L]×[Upstream head H]^1.5
- Critical depth on the crest = 2×[Upstream head H]÷3
- Velocity on the crest = sqrt([Gravitational acceleration g]×2×[Upstream head H]÷3)
Example values
How the main result changes when Upstream head H changes and everything else stays at the example values above:
| Upstream head H (m) | Discharge Q (L/s) |
|---|---|
| 0.15 | 198.0571 |
| 0.225 | 363.8541 |
| 0.3 | 560.19 |
| 0.375 | 782.8893 |
| 0.45 | 1,029.1347 |
| 0.6 | 1,584.4565 |
Formula
Q = C_d·(2/3)^{3/2}·√g·L·H^{3/2} ≈ 1.705·C_d·L·H^{3/2} (SI), y_c = 2H/3
Worked example
Inputs — Upstream head H: 0.3 m; Weir width L: 2 m; Discharge coefficient C_d: 1; Gravitational acceleration g: 9.80665 m/s².
Results — Discharge Q = 560.18997 L/s; Critical depth on the crest = 0.2 m; Velocity on the crest = 1.4005 m/s.
Key terms
- Head
- Height of the water surface above the crest.
Frequently asked questions
What makes a weir "broad-crested"?
The crest is long enough in the flow direction for parallel flow to form.
Why does critical depth occur?
The crest acts as a control where flow passes from sub- to supercritical.
What is 1.705?
(2/3)^{3/2}·√g in SI units.
How accurate is it?
Within a few percent with a calibrated coefficient.