# Broad-Crested Weir Calculator

URL: https://speedycalculator.com/calculators/physics/broad-crested-weir/
Last updated: 2026-10-30

> The broad-crested weir calculator finds the discharge over a broad-crested weir from the upstream head, the weir width and a discharge coefficient, plus the critical depth and velocity on the crest.

## Inputs

- Upstream head H (m, cm, mm, km, in, ft, yd, mi)
- Weir width L (m, cm, mm, km, in, ft, yd, mi)
- Discharge coefficient C_d
- Gravitational acceleration g (m/s², ft/s², g, cm/s²)

## Results

- Discharge Q
- Critical depth on the crest
- Velocity on the crest

## 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
```

## Explanation

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

FieldWhat to enterUpstream head HUnits: m, cm, mm, km, in, ft …Weir width LUnits: m, cm, mm, km, in, ft …Discharge coefficient C_dA numberGravitational acceleration gUnits: 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)0.15198.05710.225363.85410.3560.190.375782.88930.451,029.13470.61,584.4565

## 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.

## FAQ

**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.


## Sources

- [Fluid Mechanics (F. M. White) – reference text](https://www.mheducation.com/highered/product/fluid-mechanics-white-chul/M9781260258318.html)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)