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Broad-Crested Weir Discharge Calculator

Calculates volumetric discharge flow rate, critical depth on the crest, and approach head for broad-crested weirs used in open channel flow metering.

Transverse width of the weir crest across channel.

Energy head measured upstream of the weir relative to the crest elevation.

Height of the weir crest above the upstream channel bed.

Calibration discharge coefficient (typically 0.93 to 0.98 for rounded-nose broad-crested weirs).

Calculated Result
3.51 m³/s

Broad-Crested Weir Flow Rate (Q)

Volumetric Discharge (L/s)

3513 L/s

Critical Depth on Crest (yc)

0.533 m

Discharge Factor (2/3)^1.5·√g

1.705

Total Upstream Stage

2.00 m

Calculation Breakdown

  1. Broad-Crested Critical Depthyc = (2/3) · H = (2/3) · 0.8 = 0.533 m
  2. Weir Discharge EquationQ = Cd · (2/3)^(3/2) · √g · b · H^(3/2) = 0.96 · 1.705 · 3 · (0.8)^1.5 = 3.51 m³/s

What Is the Broad-Crested Weir Discharge Calculator?

A broad-crested weir is an obstruction with a sufficiently long horizontal crest such that streamlines become parallel and flow passes through critical depth.

The crest length in the flow direction must typically satisfy 0.08 < H/L < 0.50 to qualify as broad-crested.

How Does the Broad-Crested Weir Discharge Calculator Work?

Because critical flow occurs over the crest, the discharge is strictly a function of upstream head H raised to the 3/2 power.

Tailwater submergence does not affect the flow rate until downstream water levels rise above roughly 70–80% of upstream head.

Broad-Crested Weir Discharge Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Q=Cd(23)3/2g⋅b⋅H3/2≈1.705⋅Cd⋅b⋅H3/2,yc=23HQ = C_d \left(\frac{2}{3}\right)^{3/2} \sqrt{g} \cdot b \cdot H^{3/2} \approx 1.705 \cdot C_d \cdot b \cdot H^{3/2}, \quad y_c = \frac{2}{3} H

Critical flow discharge relationship across broad-crested weir crests.

How to Use the Broad-Crested Weir Discharge Calculator

  1. Input crest width, head over crest, weir height, and discharge coefficient Cd.
  2. Review flow rate in m³/s and L/s, and critical depth on the crest.

Step-by-Step Example Calculation

Irrigation Canal Metering Weir

Input Values:

weirCrestWidthMeters:2.5
upstreamHeadAboveCrestM:0.6
weirCrestHeightMeters:1
dischargeCoefficientCd:0.95
Worked Steps: Computes discharge flow rate Q ~ 1.88 m³/s.

Understanding Your Result

Directly converts water stage measurements from ultrasonic or staff gauges into volumetric flow rate.

Factors That Affect the Result

  • Rounding the upstream edge of the crest prevents flow separation and increases Cd closer to 0.98.

When Should You Use This Calculator?

  • Canal discharge monitoring, dam intake structures, and hydrological gauging stations.

Assumptions & Limitations

  • Assumes free-discharge conditions without modular drowning or significant aeration cavitation.

Frequently Asked Questions

What is the difference between sharp-crested and broad-crested weirs?+
Sharp-crested weirs have a thin blade where water springs clear (nappe flow), while broad-crested weirs support parallel critical flow directly on the crest.
What is the modular limit of a broad-crested weir?+
The ratio of downstream head to upstream head (typically ~0.75) above which tailwater submergence begins to retard discharge.

Calculation Accuracy & Reference Note

Standard ISO 3846 and USBR Water Measurement Manual standard.

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