Broad-Crested Weir Flow Calculator
Compute the volumetric flow rate (discharge) over a broad-crested weir given the upstream head, crest length and discharge coefficient. The calculator also derives the critical depth and velocity at the crest and plots the Q–H relationship.
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Volumetric discharge over the broad-crested weir
- 1
Weir coefficient C = (2÷3) × √(2g÷3)
(2 ÷ 3) × √(2 × 9.807 ÷ 3) = 1.7046This constant ≈ 1.705 m½/s comes from critical-flow theory applied at the weir crest. - 2
Head term H^(3/2)
0.5^(3/2) = 0.3536 - 3
Flow rate Q
0.848 × 1.7046 × 3 × 0.3536 = 1.5332
How does this calculator work?
A broad-crested weir discharges Q = Cd × 1.705 × L × H^(3/2) in SI units (m³/s), where Cd ≈ 0.848 for a standard weir, L is crest length in metres, and H is upstream head in metres. Critical depth at the crest is (2/3)H and Froude number equals 1. Formula assumes free-flow (non-submerged) conditions.
Formula
How this is calculated
A broad-crested weir is a hydraulic structure with a flat horizontal crest long enough in the flow direction for critical flow conditions to develop at the crest — typically the crest length exceeds about three times the upstream head. At critical flow, the Froude number equals 1.0, and the depth at the crest is the critical depth hc = (2/3) × H, where H is the upstream head above the crest. Applying energy principles and critical-flow theory gives the discharge formula Q = (2/3) × Cd × L × √(2g/3) × H^(3/2), which in SI units simplifies to Q ≈ Cd × 1.705 × L × H^(3/2).
The discharge coefficient Cd accounts for friction losses, boundary-layer effects, and deviations from ideal conditions. For a well-designed, sharp-entrance broad-crested weir in good condition, Cd ≈ 0.848 (as tabulated in BS EN ISO 4374 and BS 3680 Part 4C). It decreases for rounded or poorly-formed crests, very low heads (where surface tension matters), or conditions where the downstream tailwater causes submergence. Submergence (where the downstream depth approaches or exceeds the critical depth) invalidates this formula — it requires a submerged-weir correction that is beyond the scope of this calculator.
The velocity of approach from the upstream channel is assumed negligible relative to the head H. For wide channels with modest flow this is a good approximation. Where approach velocity is significant, replace H with the total head H + V²/(2g), where V is the mean approach velocity.
Frequently asked questions
A sharp-crested (thin-plate) weir has a crest so thin that the nappe springs clear and the head-discharge relationship is given by the Francis formula (Q ∝ H^(3/2) with Cd ≈ 0.61). A broad-crested weir has a horizontal crest long enough for critical depth to form on it; the coefficient Cd is higher (≈0.848) and the flow is less sensitive to downstream conditions — making it a better flow-measurement structure in field settings.
No — this formula applies only to free-flow (modular) conditions where the downstream tailwater is below about 75–80% of the critical depth on the crest. If the weir is submerged, the discharge is reduced and you need a submergence correction factor. Check submergence by comparing the downstream depth to the upstream head.
For a standard broad-crested weir in good condition with a sharp upstream corner, Cd ≈ 0.848 (ISO 4374). Rounded upstream edges raise it slightly; roughness, algae growth, or geometric irregularities lower it. For critical applications, calibrate Cd from field measurements comparing discharge to measured head.
Also known as
TG we-Calculate Editorial Team. (2026). Broad-Crested Weir Flow Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/broad-crested-weir-calculator
TG we-Calculate Editorial Team. "Broad-Crested Weir Flow Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/broad-crested-weir-calculator.
TG we-Calculate Editorial Team, "Broad-Crested Weir Flow Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/broad-crested-weir-calculator
@misc{wecalculate_broad_crested_weir_calculator, title = {Broad-Crested Weir Flow Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/broad-crested-weir-calculator}}, year = {2026}, note = {TG we-Calculate} }
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