How to Use Broad-Crested Weir Calculator
The Broad-Crested Weir Calculator converts your field measurements into a reliable discharge estimate in seconds. Enter the three key parameters, choose your preferred units, and read the result.
- Select Calculation Mode — Choose Theoretical to use the ideal critical-flow coefficient (Cd = 0.5774), or choose Corrected to enter your own discharge coefficient for a more realistic estimate.
- Choose Length Unit — Select metres (m), centimetres (cm), or feet (ft). The Broad-Crested Weir Calculator converts all inputs to SI before computing.
- Enter Crest Width (L) — Measure the effective length of the weir crest perpendicular to the flow direction.
- Enter Upstream Head (H) — Measure the water depth above the weir crest at a point at least twice the maximum head upstream of the weir face (to avoid drawdown effects).
- Enter Discharge Coefficient (Cd) — Visible only in Corrected mode. Typical values range from 0.84 to 0.90 for well-maintained broad-crested weirs.
- Choose Flow Unit — Select m³/s, L/s, ft³/s, or m³/h for the output.
- Read the Result — The Broad-Crested Weir Calculator shows the computed flow rate and the formula substitution so you can verify every number.
Formula & Theory - Broad-Crested Weir Calculator
The Broad-Crested Weir Calculator uses the standard broad-crested weir discharge equation derived from critical-flow theory:
Q = Cd × L × √g × H^(3/2)| Symbol | Meaning |
|---|---|
| Q | Discharge (m³/s) |
| Cd | Discharge coefficient (dimensionless) |
| L | Effective crest length (m) |
| g | Gravitational acceleration (9.81 m/s²) |
| H | Upstream head above crest (m) |
Critical-Flow Derivation
At the crest of a broad-crested weir the flow passes through critical depth yc. Applying specific energy principles:
yc = (2/3) H
Vc = √(g × yc) = √(2/3 × g × H)
Q = L × yc × Vc = L × (2/3 H) × √(2/3 g H)
= (2/3)^(3/2) × L × √g × H^(3/2)
≈ 0.5774 × L × √g × H^(3/2)The empirical discharge coefficient Cd adjusts this ideal value for energy losses, approach velocity, and weir geometry:
Cd_typical ≈ 0.848 (sharp upstream edge, level crest)Assumptions and Limits
- Free-flow (non-submerged): Tailwater must be below the critical depth at the weir crest. If the downstream channel is high enough to flood the crest, a submergence correction factor is required.
- Stable approach: The upstream channel should be straight and uniform for at least 10× the maximum head length.
- Head measurement location: Measure H at least 2H upstream of the weir face to avoid velocity-head effects near the drawdown zone.
- Approach velocity: The standard formula ignores approach velocity. For high-velocity channels, add the velocity head to H.
The Broad-Crested Weir Calculator is suited for preliminary design, field flow measurement, irrigation channel sizing, and hydraulic education. For final engineering design, consult local hydraulic standards and laboratory-calibrated coefficients.
Use Cases for Broad-Crested Weir Calculator
The Broad-Crested Weir Calculator is indispensable across a range of water-management and engineering contexts:
- Irrigation channel design — Size diversion weirs and distribution gates to deliver the required flow to field blocks.
- River gauging — Use a temporary or permanent broad-crested structure to convert a simple head measurement into a discharge reading during field surveys.
- Stormwater management — Estimate peak overflow rates over broad-crested drop structures in detention basins and retention ponds.
- Drainage engineering — Size overflow spillways and emergency bypasses to safely pass design-storm flows without structure damage.
- Hydraulics education — Demonstrate critical-flow theory and the relationship between head, crest width, and discharge in laboratory or classroom settings.
- Environmental flow assessment — Determine minimum ecological flows passing over weirs in regulated rivers.
The Broad-Crested Weir Calculator supports multiple unit systems, making it equally useful for engineers working in SI, metric, or imperial units.