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Broad-Crested Weir Flow Calculator

Estimate the discharge over a broad-crested rectangular weir from the crest width, the head of water above the crest and a discharge coefficient. Broad-crested weirs are common flow-measurement and level-control structures in stormwater channels, spillways, irrigation systems and treatment plants.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the crest width b in metres — the width of the weir measured across the channel.
  2. Enter the head H in metres — the height of the upstream water surface above the top of the crest, measured back from the drawdown.
  3. Enter the discharge coefficient Cd (about 0.85 for a rounded upstream edge) and read the flow Q in m³/s and L/s plus the unit discharge q per metre of crest width.

How it works

For a broad crest the water passes through critical depth on the sill, which fixes the discharge from the head alone: Q = Cd · (2/3) · √(2g/3) · b · H^(3/2). The constant (2/3)·√(2g/3) equals about 1.7049 with g = 9.81 m/s², so the working form is Q ≈ 1.705 · Cd · b · H^1.5. The unit discharge q = Q ÷ b is the flow carried per metre of crest width. The 3/2 power means discharge rises steeply with head, so accurate head measurement matters most.

Worked example

Worked example. A 2 m wide broad-crested weir carries a head of 0.30 m with Cd = 0.85. The coefficient is (2/3)·√(2·9.81/3) = 1.7049, so Q = 0.85 × 1.7049 × 2 × 0.30^1.5 = 0.476 m³/s, i.e. 476.2 L/s, with a unit discharge of 0.238 m²/s.

Common mistakes

  • Measuring the head at the crest itself — H must be the upstream head, taken back from the drawdown where the surface is still level.
  • Using the broad-crested formula outside its valid H/L range: at low H/L the weir behaves as sharp-crested and at high H/L it becomes short/round-crested, each with a different coefficient.
  • Ignoring downstream submergence — the equation assumes free discharge; a drowned (submerged) weir passes less flow than the formula predicts.

Frequently asked questions

What is a good discharge coefficient to use?

Around 0.85 is typical for a broad-crested weir with a rounded upstream edge. A sharp upstream corner separates the flow and lowers the effective coefficient, so use a value from the relevant standard or a calibrated rating for precise metering.

How is a broad-crested weir different from a sharp-crested one?

A broad-crested weir has a horizontal crest long enough for the flow to run parallel and pass through critical depth on the crest, so its coefficient sits near 0.85. A sharp-crested (thin-plate) weir sheds a springing nappe and uses a different equation and coefficient. The right choice depends on the ratio of head to crest length, H/L.

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