Broad Crested Weir Calculator - Q, Velocity, and Modularity

A broad crested weir calculator solves the discharge over a flat-crested, rectangular weir that is wide in the direction of flow, using Q = C L H^(3/2) where C is the effective discharge coefficient, L is the crest length, and H is the head above the crest.

• • Irrigation canal flow measurement: Estimate the flow delivered to a farm turnout from a rectangular flat-crested weir built into a canal.
• • Stormwater and culvert checks: Sanity-check the discharge passing a broad-crested control section in a detention pond or culvert headwall.
• • Lab and classroom hydraulics: Convert a measured head on a flume-mounted broad crested weir into discharge for a fluid mechanics lab.
• • Spillway and low-head dam estimates: Get a quick modular-flow estimate for a small spillway or weir plate that behaves as a broad crested control in its operating range.

Broad crested weirs are flat, horizontal structures that span the full width of a channel. The crest length is large compared with the head, which is what makes the H^(3/2) form work.

Use this broad crested weir calculator when you have measured the upstream head on a rectangular, flat-crested structure and want a discharge value in m^3/s, L/s, cfs, or U.S. gpm.

When you want to keep the upstream energy balance explicit while checking the head on a weir, Bernoulli equation calculator handles the same kind of two-point energy math between any two sections of a streamline.

The calculator evaluates Q = C L H^(3/2) using either an effective C in m^0.5/s or the dimensionless form Q = (2/3) * Cd * L * sqrt(2 g) * H^(3/2), then reports discharge, mean velocity, critical depth, and a modular-range check.

• Q: Volumetric discharge over the weir, in cubic meters per second.
• C: Effective broad crested weir coefficient in m^0.5/s, default 1.45 for a modular rectangular weir.
• L: Crest length in meters, measured perpendicular to the flow direction.
• H: Head over the crest in meters, measured as the upstream water-surface elevation minus the crest elevation.

When the Coefficient Mode is set to Cd, the calculator converts Cd to an effective C using C = (2/3) * Cd * sqrt(2 g) before applying the same Q = C L H^(3/2) form, so both inputs give the same discharge value.

Mean velocity over the crest is reported as v = Q / (L * H), critical depth as yc = (q^2 / g)^(1/3) with q = Q/L, and H/yc sits close to 1.5 in the fully modular range.

According to the USGS TWRI 3-A8 (Discharge measurements at gaging stations), broad-crested weirs are flat-crested structures used as standard discharge control sections, and the modular form Q = C L H^(3/2) with C = 1.45 m^0.5/s applies in the standard H/L range once the nappe passes through critical depth.

According to the NIST SP 811, the standard acceleration of free fall used in the Cd form is g = 9.80665 m/s^2.

Confirming that the nappe stays in the right regime is much easier with Reynolds number calculator in hand so you can see the flow regime that the broad crested coefficient was calibrated for.

Four ideas show up in every practical broad crested weir problem. Understanding them keeps the H^(3/2) formula from being used outside the conditions where it is calibrated.

Once the weir is past the modular range and the approach channel contributes real head loss, friction factor calculator lets you quantify that loss with the same Darcy-Weisbach form used in open channel flow.

Use the calculator in five quick steps. The defaults match the standard modular rectangular weir, so you can usually just enter L and H.

1. 1 Pick the coefficient mode: Choose C for the standard effective coefficient (m^0.5/s) or Cd for a lab-rated dimensionless coefficient.
2. 2 Measure the crest length L: Measure L across the channel at crest elevation. For a rectangular weir in a straight flume, L is just the channel width.
3. 3 Read the head H: Read the upstream water-surface elevation in a stilling well 3 to 4H upstream of the weir, then subtract the crest elevation.
4. 4 Set the coefficient and gravity: Leave C at 1.45 m^0.5/s (and gravity at 9.80665 m/s^2) for a default modular rectangular weir. Change them only for non-standard crest shapes or local g.
5. 5 Add weir height P and tailwater: Enter P to expose the submergence ratio, and yt if you know the downstream level. Leave yt at 0 to skip the submergence check.

For a 1.5 m wide rectangular broad crested weir in an irrigation canal with H = 25 cm and no tailwater, the calculator returns Q ≈ 0.272 m^3/s, v ≈ 0.725 m/s, and H/L = 0.167, all inside the modular range.

If your downstream spec is in gallons per minute or liters per second instead of m^3/s, flow rate converter gives you the unit conversions without leaving the page.

The calculator is built for the kind of decisions that come up in a hydraulic-engineering course, an irrigation audit, or a stormwater review.

• • Multiple discharge units in one place: Q is shown in m^3/s, L/s, cfs, and gpm so you do not have to convert by hand.
• • Modular range check built in: H/L and H/yc are reported alongside the discharge so you see whether the standard C is appropriate or whether the weir is in the sharp-crested or low-head regime.
• • Submergence flag for tailwater effects: Adding P and yt produces a submergence ratio and a regime label, so a downstream pond creeping up the crest is caught before it skews the result.
• • Two coefficient entry modes: Switch between the standard effective C and the dimensionless Cd form without re-deriving the relationship.
• • Mean velocity and critical depth for sanity checks: v = Q / (L*H) and yc = (q^2 / g)^(1/3) are reported so a quick Froude-number style check confirms the flow is in the regime the formula assumes.

The mean velocity over the crest that this calculator reports pairs naturally with velocity calculator when you also need the approach velocity or the downstream channel velocity in the same units.

The H^(3/2) formula is short, but several conditions can move the actual discharge away from the calculator value. Check these before publishing a number.

• • The calculator uses the standard modular rectangular broad crested weir equation; non-rectangular crests (triangular, trapezoidal, ogee) and compound weirs need a different formula.
• • Submerged flow is flagged but not auto-corrected. If yt / (H + P) approaches 0.80, apply a submergence factor or use a drowned-weir rating from a hydraulic reference.
• • The calculator assumes a single, well-defined crest with full width contraction only in the upstream direction. Lateral contraction from piers or abutments is not modeled, so lab or field calibration is recommended for heavily contracted installations.

According to the ISO 18481:2017 (Hydrometry, end depth method at a free overfall), the critical depth at a free overfall is yc = (q^2 / g)^(1/3) with q = Q/L, the same specific-energy minimum that broad-crested weirs rely on for the modular H^(3/2) form.