About the Broad Crested Weir
A broad-crested weir is a raised, flat-topped obstruction spanning an open channel with a crest long enough (relative to the upstream head) that the flow passing over it reaches critical depth on the crest itself. Because the depth at that critical section is fixed by the flow rate alone, measuring the upstream head above the crest is enough to compute the discharge — no downstream depth reading required. This makes broad-crested weirs a common flow-measurement structure in irrigation channels, spillways, and laboratory flumes.
Understanding the formula
The discharge over a rectangular broad-crested weir is:
Q = (2/3) × Cd × b × √(2g/3) × H1.5
where Q is the discharge (m³/s), Cd is a dimensionless discharge coefficient that accounts for real losses, b is the crest width across the channel (m), g is gravitational acceleration (9.81 m/s²), and H is the upstream head measured above the crest (m). The formula is derived from critical-flow theory: at the control section on the crest, the critical depth is hc = (2/3)H, and the ideal (Cd = 1) discharge is Q = b × √g × hc1.5. Substituting hc gives the equation above, then Cd (typically 0.85–1.00) is applied to match real weirs, which lose some energy to friction along the crest and non-uniform velocity distribution.
The flow-regime check (H/L)
The formula only holds while the crest is genuinely "broad" relative to the head. That is checked with the ratio of upstream head to crest length in the flow direction, H/L. As a widely used rule of thumb, broad-crested behavior is expected roughly in the range 0.08 < H/L < 0.33. Below 0.08 the crest is so long relative to the head that boundary friction along the crest distorts the simple critical-flow assumption; above about 0.33 the crest is too short for critical flow to fully establish, and the structure starts to behave more like a sharp-crested weir. This calculator reports your H/L ratio and flags whether it falls inside that typical window.
Working with units
- All inputs here use SI units: meters for lengths and head, and the result is in cubic meters per second (with a liters-per-second conversion alongside it).
- Keep the head H measured from the still-water surface upstream of the weir down to the crest — not the depth downstream.
- The formula assumes a rectangular channel and crest with negligible approach velocity; very high approach velocities require an additional velocity-head correction not included here.
Knowing the limits
This is the standard "ideal" broad-crested weir equation used for planning and teaching. Real installations should use a laboratory- or field-calibrated Cd whenever precision matters, since edge rounding, crest roughness, and approach conditions all shift the coefficient. Always verify your H/L ratio falls in the valid range before trusting the discharge estimate.