How to Calculate Flow Over a Weir

Water flows over a broad-based weir at a different rate than over a V-notch weir.
Water flows over a broad-based weir at a different rate than over a V-notch weir. (Image: Jupiterimages/ Images)

A weir is a device that measures the flow of water from streams, basins or open channels. This device is commonly used for outflows from wastewater treatment facilities. There are several types of weirs, including Cipoletti (trapezoidal), broad-crested and V-notch. The calculation of flow over a weir can be simple if you have a means of measuring the water in front of the weir, the appropriate formula and a scientific calculator. It is important to note that the formulas for flow calculation differ for the different types of weirs..

Things You'll Need

  • Measuring stick or rod, with measurements in feet
  • Scientific calculator or computer
  • Safety glasses and gloves if you are measuring flows that are not water

Measure the head, or the height of the water above the weir bottom, at an upstream distance that is at least four times the depth of the water in the weir. The measurement should be taken in feet. This value will be the value for "h" in the final equation.

Measure, in feet, the length of the weir crest immediately above the weir. This value will be that for the symbol "L" in the final equation. This measurement is not needed for V-notch weirs.

Calculate the weir flow in cubic feet per second. The complete equation for calculating the flow of water over broad-crested and Cipoletti weirs is Q = k L h^3/2, where h is raised to the power of 3/2 and the value of k is 1.705 or 3.367, respectively. The value of h^3/2 means that the value of h is first cubed, and then the square root is taken. This calculation can be done easily on a scientific calculator. Alternatively, you can visit a website that has a Cipoletti weir calculator to complete the calculation. Some websites have the capability to convert the flow into metric units, if needed.

For V-notch weirs, the formula varies depending on the angle of the V-notch. The formula for weirs having V-notch angles of 90, 60 and 45 degrees is Q = k * h^2.5, where the value of k is 2.5, 1.443 or 1.035, respectively. For a V-notch weir having an angle of 30 degrees, the formula is Q = 0.685 h^2.45. There are also online sources for doing this calculation.

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