Rectangular Weir Discharge Calculator
Enter the discharge coefficient C, crest width L and head H to compute flow over a rectangular weir from Q=C·L·H^(3/2) (m³/s), used for irrigation and open-channel flow measurement.
Input Data
Results
At a glance:A measuring weir is a plate with a notch set across a channel so water accumulates then drops freely over the opening; because the geometry is fixed, discharge relates deterministically to the head H above the crest, so measuring H gives the flow — ideal for simple field metering. A rectangular notch makes a rectangular weir; with a thin, sharp-edged crest it is a rectangular sharp-crested weir, whose discharge is best estimated by the Francis formula Q=C·L·H^(3/2). Q is discharge (m³/s). C is the discharge coefficient (~1.84 in SI for a sharp-crested rectangular weir). L is the crest width (m). H is the head (m) — the vertical drop from crest to the calm upstream surface, measured at least ~4H upstream. The key feature is the 3/2 exponent: Q scales with H^1.5, so a small rise in H increases flow faster — double H and Q rises to 2^1.5≈2.83×. Example: C=1.84, L=2 m, H=0.3 m → Q=1.84×2×0.3^1.5≈0.605 m³/s (about 2178 m³/h); at H=0.4 m, Q≈0.931 m³/s, showing the sensitivity. Uses: irrigation metering, small-stream and drainage gauging, and laboratory flow measurement. Notes: use C≈1.84 only for an SI sharp-crested rectangular weir; C shifts with H/weir-height, thickness and approach velocity; measure H in calm water away from the drawdown; for side contractions apply the Francis end-contraction correction L−0.1nH; keep free outflow (downstream below the crest); use metric units.
Formula
Francis formula: Q = C·L·H^(3/2).
C≈1.84 (SI sharp-crested rectangular); L crest width; H head.
Discharge ∝ H^1.5: a small head rise raises flow faster.
$$Q = C\,L\,H^{3/2}$$How to Use
- Enter the discharge coefficient C (1.84 for SI rectangular sharp-crested).
- Enter the crest width L and the measured head H (m).
- The tool computes the discharge Q (m³/s) from the Francis formula.
Case Studies
Irrigation channel metering
Rectangular sharp-crested weir, C=1.84, L=2 m, H=0.3 m.
Q = 1.84×2×0.3^1.5 ≈ 0.605 m³/s.
≈2178 m³/h — used to allocate irrigation water to fields.
Head sensitivity
At H=0.4 m the same weir gives Q≈0.931 m³/s.
The 3/2 exponent makes flow rise faster than head.
Accurate H reading is critical for flow accuracy.
FAQ
What is the Francis formula?
Q=C·L·H^(3/2) for a rectangular weir, with C≈1.84 (SI sharp-crested), L the crest width (m) and H the head above the crest (m). It converts a simple head reading into discharge.
Why the 3/2 power?
Discharge grows with the 1.5 power of head, so doubling H raises Q by about 2.83×. That sensitivity is why careful head measurement is essential.
What is the discharge coefficient C?
It lumps gravity, crest shape and flow contraction; ~1.84 for an SI sharp-crested rectangular weir. It shifts slightly with H/weir-height and approach velocity, so precision work uses a rating curve.
Where is the head measured?
Upstream at least ~4H from the crest, where the surface is calm and flat. Too close and the surface has already dropped, underestimating H and Q.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.