Broad Crested Weir Calculator

A broad-crested weir is a flat-topped obstruction across an open channel over which fluid flows. The calculation relies on critical flow principles where the streamlines are parallel over the crest. First, the discharge coefficient is derived using gravity and the dimensional constant: coefficient = g^(0.5) * (2/3)^(1.5). Next, the total volume flow rate (discharge) is computed using the formula: discharge = coefficient * length * height^(1.5), where length is the crest width and height represents the upstream head above the weir crest.

Let us compute the water discharge over a broad-crested weir with a crest length of 5 meters and an upstream head (height) of 0.75 meters. We assume standard acceleration due to gravity (g) as 9.81 m/s^2. Step 1: Calculate the discharge coefficient using g = 9.81. The square root of 9.81 is approximately 3.132, and (2/3)^(1.5) is about 0.5443. Multiplying these gives a coefficient of approximately 1.705. Step 2: Calculate height to the power of 1.5. 0.75^(1.5) equals approximately 0.6495. Step 3: Multiply the coefficient, length, and height factor together: 1.705 * 5 * 0.6495 = 5.543 cubic meters per second (m^3/s). Thus, the total flow rate is approximately 5.54 m^3/s.

Ensure that your upstream head measurement is taken far enough upstream to avoid the surface drawdown curve directly above the weir crest. Always verify that your channel approach velocity is low enough to treat the approach kinetic energy as negligible, or use total head instead of static height for high-precision engineering applications. Keep units consistent—typically using SI units (meters and seconds)—to prevent scaling errors in your discharge calculations.