About Weir & Notch Flow Calculator
The weir flow calculator computes the discharge over a thin-plate (sharp-crested) weir from the measured head over the crest. Thin-plate weirs are the standard primary devices for measuring flow in open channels and laboratory flumes, and each geometry has a well-established head-discharge relationship.
Choose a rectangular (suppressed) weir, a triangular V-notch, or a Cipolletti trapezoidal weir; enter the crest width or notch angle, the head H, and the discharge coefficient Cd. The tool returns the discharge Q, states the exact equation applied, and plots a rating curve of discharge against head so you can interpret field measurements.
How It Works
- Select the weir type: rectangular, V-notch, or Cipolletti.
- Enter the crest width b (rectangular and Cipolletti) or the included notch angle (V-notch), the head H over the crest, and the discharge coefficient Cd where applicable.
- The calculator applies the appropriate head-discharge equation and reports the discharge together with the effective coefficient and the formula used.
- It plots the rating curve so you can convert any measured head to a discharge.
Worked Example
A suppressed rectangular weir has crest width b = 2 m and a measured head H = 0.3 m, with discharge coefficient Cd = 0.62. The discharge is Q = Cd * (2/3) * sqrt(2g) * b * H^(3/2) = 0.62 * 0.6667 * sqrt(19.62) * 2 * 0.3^(1.5) = 0.602 m^3/s. This is within about half a percent of the engineering shortcut Q = 1.84 * b * H^(1.5) = 0.605 m^3/s. A 90-degree V-notch at the same head with Cd = 0.593 would pass Q = 0.593 * (8/15) * sqrt(2g) * tan(45 deg) * 0.3^(2.5) = 0.069 m^3/s, close to the familiar Q = 1.38 * H^(2.5).
Formulas
- Rectangular (suppressed) weir
Q = Cd * (2/3) * sqrt(2g) * b * H^(3/2)- Rectangular engineering form
Q = 1.84 * b * H^(3/2) (equivalent to Cd ~ 0.62, SI)- Triangular V-notch weir
Q = Cd * (8/15) * sqrt(2g) * tan(theta/2) * H^(5/2)- 90-degree V-notch engineering form
Q = 1.38 * H^(5/2) (Cd ~ 0.593, theta = 90 deg, SI)- Cipolletti (trapezoidal) weir
Q = 1.86 * b * H^(3/2)
Standards & References
- ISO 1438: Thin-plate weirs
- Bos, Discharge Measurement Structures (ILRI)
- USBR Water Measurement Manual
Frequently Asked Questions
When should I use a V-notch instead of a rectangular weir?
A V-notch is more accurate at low flows because its discharge varies with H^(5/2), giving a larger head change per unit flow. Rectangular and Cipolletti weirs suit larger, steadier discharges where the wider crest avoids excessive upstream head.
What discharge coefficient should I use?
For a fully aerated, sharp-crested rectangular weir Cd is about 0.62, and for a 90-degree V-notch about 0.593. Coefficients vary with head, crest height, and approach conditions, so use a value from a calibration or the relevant standard when accuracy matters. The tool lets you enter your own Cd.
Why does the Cipolletti weir use a fixed coefficient?
A Cipolletti weir has trapezoidal 4:1 (H:V) side slopes that compensate for end contractions, so its discharge follows the simple form Q = 1.86 b H^(1.5) without a separate end-contraction correction. The 1.86 constant already embeds the effective coefficient.
What head should I measure?
Measure the head H as the vertical distance from the weir crest (or V-notch vertex) up to the undisturbed upstream water surface, taken far enough upstream (typically 4 to 5 times the maximum head) to avoid the surface drawdown near the weir.