Broad Crested Weir Calculator

This broad crested weir calculator works out the discharge flowing over a broad crested weir from the crest width, the upstream head and the discharge coefficient. A broad crested weir is a raised sill or low dam wide enough along the flow direction that the streamlines run roughly parallel over the crest, forcing the flow through critical depth and giving a stable, predictable relationship between the upstream water level and the flow rate. That is exactly what makes it useful as a flow measuring structure in channels, spillways and irrigation systems. Enter the crest width across the channel, the head measured as the height of the upstream water surface above the crest, and a discharge coefficient of about 0.85 for a well built weir, and the calculator returns the total flow in cubic metres per second and litres per second, the unit discharge per metre of crest width, and the critical depth on the crest, which for a broad crested weir is two thirds of the head. The defaults model a 2 metre wide crest carrying 0.3 metres of head. Raise the head and the flow climbs steeply, because discharge scales with the head to the power of 1.5, so a small rise in level moves a lot more water. Use it to size a measuring weir, rate an existing structure, or check a spillway against a design flood.

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Discharge coefficient (Cd)

Crest width (b)

Upstream head (H)

0.476 m³/s

discharge over the weir

Flow rate476.2 L/s

Unit discharge (per metre)0.238 m³/s

Critical depth on crest0.200 m

Uses the standard broad crested weir equation Q = Cd x 1.705 x b x H^1.5 with g = 9.81 m/s² and lengths in metres. Assumes free (unsubmerged) flow and a head measured clear of the drawdown. Estimate only.

How it works

The theoretical discharge over a broad crested weir combines two constants with the geometry: two thirds raised to the power 1.5, and the square root of gravitational acceleration g. In SI units those multiply to about 1.705, so the flow is the discharge coefficient times 1.705, times the crest width, times the head raised to the power 1.5. The unit discharge is the same expression without the width, giving the flow per metre of crest. Because the flow passes through critical depth on the crest, that critical depth equals two thirds of the upstream head. The power of 1.5 on the head is why discharge is so sensitive to level: doubling the head lifts the flow by a factor of about 2.83.

Worked example

Take a crest 2 metres wide with 0.3 metres of head and a discharge coefficient of 0.85. The head to the power 1.5 is 0.164. The unit discharge is 0.85 times 1.705 times 0.164, about 0.238 cubic metres per second per metre. Multiply by the 2 metre width for a total discharge of 0.476 cubic metres per second, which is 476.2 litres per second. The critical depth on the crest is two thirds of 0.3, which is 0.200 metres.

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Frequently asked questions

What is the broad crested weir discharge formula?

The discharge is Q = Cd times (2/3) raised to the power 1.5, times the square root of g, times the crest width b, times the head H raised to the power 1.5. The two constants combine to about 1.705 in SI units, so Q equals Cd times 1.705 times b times H to the power 1.5, with lengths in metres and Q in cubic metres per second.

What discharge coefficient should I use?

For a well finished broad crested weir the discharge coefficient is typically around 0.85, though it ranges from roughly 0.8 for a rough or short crest up to near 0.9 for a smooth, correctly proportioned crest. The exact value depends on the crest length, the approach conditions and how rounded the upstream edge is.

What is the head on a weir?

The head H is the height of the upstream water surface above the crest of the weir, measured far enough upstream that the surface has not yet started to draw down. It is not the depth of water flowing over the crest itself, which is lower because the flow accelerates and passes through critical depth on the crest.