How to use the weir and orifice flow calculator
- Choose the device: a rectangular weir, a V-notch weir or a round orifice.
- Choose meters or feet.
- Enter the discharge coefficient Cd. The page starts with 0.62 as an example. Use the value for your device and finish.
- Enter the crest length (rectangular), the notch angle (V-notch) or the diameter (orifice), then the head. Read the flow rate.
Formula
Rectangular weir: Q = (2/3) Cd sqrt(2 g) L H^1.5
V-notch weir: Q = (8/15) Cd sqrt(2 g) tan(theta / 2) H^2.5
Orifice: Q = Cd A sqrt(2 g H), with A = pi D^2 / 4
g = 9.80665 m/s2, or 32.174049 ft/s2 in feet
Head H is the height of the water surface above the weir crest, or above the center of the orifice, measured upstream where the water is still.
A rectangular weir, a V-notch and an orifice
A rectangular weir 1 m long with Cd 0.62 and a head of 0.2 m passes (2/3) x 0.62 x sqrt(2 x 9.80665) x 1 x 0.2^1.5 = 0.16373 m3/s, which is 163.73 liters per second.
A 90 degree V-notch with Cd 0.58 and a head of 0.15 m passes 0.011938 m3/s. A round orifice 50 mm across with Cd 0.61 under 2 m of head passes 0.0075015 m3/s at a jet speed of 6.2634 m/s. A weir 3 ft long with a head of 0.5 ft in US units passes 3.5168 cubic feet per second.
Measuring flow with a weir
A weir turns a hard measurement, the flow, into an easy one, the height of the water above a fixed crest. Install the weir with a sharp upstream edge and air under the falling water, measure the head a few times the head's depth upstream, and read the flow from the formula. A V-notch is more accurate than a rectangular weir at small flows, because its opening shrinks with the head.
To convert a flow into other units or a volume over time, use the flow rate calculator. To find how long a tank takes to drain through an outlet, use the tank drain time calculator.
Choosing a coefficient
The coefficient Cd gathers the effects of contraction of the flow, friction and the shape of the edge. Values near 0.6 are common for sharp-edged openings, and they vary with the head and the shape. The values on the page are examples. Use a coefficient from a standard or from a calibration of your own device.
The formulas hold for free discharge, where the water downstream does not rise to the crest or the orifice. If the downstream water backs up, the flow is lower and needs a correction for submergence, which this page does not include. For a pipe that runs full, see the Hazen-Williams pressure drop calculator.
Assumptions and limits
- Discharge is free, with air under the nappe of a weir, and the approach flow is smooth.
- The weir is sharp-crested, and a rectangular weir spans the whole channel with no end contractions.
- Cd is a value you supply. The numbers on the page are examples.
- Head is measured upstream of the drawdown near the crest.
Frequently asked questions
How do I calculate flow over a weir?
Measure the head above the crest and use Q = (2/3) Cd sqrt(2 g) L H^1.5 for a rectangular weir, or the V-notch formula for a triangular opening.
What is a discharge coefficient?
It is a number below 1 that accounts for contraction of the jet and friction. It adjusts the ideal flow to the real flow.
Which is better, a V-notch or a rectangular weir?
A V-notch measures small flows more accurately, and a rectangular weir carries larger flows with a smaller head.
Can I use feet?
Yes. Choose feet and the page uses g = 32.174 ft/s2, with the flow in cubic feet per second.