Compute weir flow from head and geometry. Includes rectangular, V-notch, trapezoidal, and broad crests options. Adjust coefficients, contractions, and save clean output files fast.
Energy head (optional): Ht = H + Va²/(2g)
| Weir model | Discharge equation | Notes |
|---|---|---|
| Rectangular sharp-crested | Q = (2/3)·Cd·b_eff·√(2g)·Ht^(3/2) | b_eff ≈ b − 0.1·n·Ht (end contractions) |
| Triangular V-notch | Q = (8/15)·Cd·√(2g)·tan(θ/2)·Ht^(5/2) | θ in degrees |
| Trapezoidal (z:1 sides) | Q = √(2g)·Cd·[(2/3)·b·Ht^(3/2) + (8/15)·(1/z)·Ht^(5/2)] | z = horizontal per 1 vertical |
| Broad-crested | Q = Cd·b·(2/3)^(3/2)·√g·Ht^(3/2) | Critical-control idealization |
Cd estimation (optional): Rehbock relation Cd = 0.611 + 0.08·(Ht/W) (often referenced for limited Ht/W ranges).
| Case | Type | H | b | θ | Cd | Q (approx.) |
|---|---|---|---|---|---|---|
| A | Rectangular sharp-crested | 0.20 m | 0.50 m | — | 0.62 | ~0.16 m³/s |
| B | V-notch | 0.18 m | — | 60° | 0.62 | ~0.05 m³/s |
| C | Broad-crested | 0.25 m | 1.00 m | — | 1.00 | ~0.21 m³/s |
Sharp‑crested weirs convert upstream head into a predictable discharge, making them practical for canals, test rigs, and small intakes. With careful installation, they provide repeatable estimates without moving parts.
Measure head H above the crest at a calm upstream point, away from drawdown near the plate. Many operators place the gauge several head depths upstream so the water surface is nearly level. If approach velocity is noticeable, the energy head may be higher than H and should be corrected.
Rectangular and trapezoidal weirs use crest length b, while V‑notch weirs use notch angle θ. Trapezoidal sides are entered as z:1 (horizontal:vertical). Keep dimensions consistent with the selected unit system, and confirm the plate is sharp‑crested (not broad‑crested).
This calculator applies standard sharp‑crested relations: rectangular flow scales with Ht3/2, V‑notch flow scales with Ht5/2, and trapezoidal flow combines both components. The √(2g) term provides the gravity scaling, and intermediate terms are displayed for checking.
The discharge coefficient Cd captures contraction and losses at the crest. In many clean conditions, Cd is often around 0.58–0.62 for sharp‑crested rectangular weirs and similar for V‑notch plates. Field Cd can drop when edges are rounded, the crest is not level, or approach flow is disturbed by bends, gates, or debris. Use calibration data when available.
If the weir is not suppressed by channel walls, end contractions reduce the effective crest length. The calculator lets you enter the number of end contractions and adjusts b to an effective width. For suppressed installations, set contractions to zero and prevent side leakage.
When upstream velocity head matters, use Ht = H + Va²/(2g). Va is based on approach area, so realistic approach width and depth improve the correction. The effect is usually small at low flows and larger in shallow, fast approaches.
Ventilate the nappe, keep the crest sharp, and avoid submergence unless you apply a separate correction. Take repeated readings at steady conditions and average them when the surface is wavy. Report weir type, dimensions, Cd source, head location, and whether Ht correction was used. CSV and PDF exports help document runs consistently.
Stay within the manufacturer or design head range, and keep the nappe ventilated. Very low heads can be sensitive to reading errors, while very high heads may cause submergence or approach effects that reduce accuracy.
Use site calibration if possible. Otherwise start with typical sharp‑crested values near 0.60, then adjust based on installation quality, crest sharpness, and approach conditions. Document the chosen Cd in your report.
Apply it when upstream velocity is not negligible compared with head, such as shallow or fast approach channels. Enter approach width and depth so the calculator can estimate Va and compute Ht = H + Va²/(2g).
End contractions occur when the nappe contracts at free ends of a rectangular crest. They reduce effective width and therefore discharge. If the weir is flush with channel walls (suppressed), set end contractions to zero.
V‑notch discharge varies with head to the 5/2 power, so small changes in head produce measurable changes in flow. That sensitivity improves resolution for low discharges compared with a wide rectangular crest.
It reports free‑flow discharge using sharp‑crested relations. If downstream water level submerges the nappe, measured discharge can be lower than free flow. Use a dedicated submergence correction method or avoid submerged operation.
Include weir type, units, head H, any velocity‑head correction inputs, Cd value and source, geometric dimensions, and the computed discharge. The CSV and PDF exports help keep these items together for records.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.