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How to Calculate Water Flow Over a Rectangular Weir

Hydrologists and engineers often install weirs in streams or channels where they need to measure the water flow. The weir provides a constant width over which the water flows, rather than the varying width of a stream, making flow volume calculations simpler. To calculate flow over a weir, you need to know the width of the weir and the head on the weir;

"head" means the depth from the top of the weir to the water's surface. Rectangular weirs may be sharp crested or broad crested; water spills over a narrow edge on a sharp-crested weir but flows over a wide surface on a broad-crested weir.

Instructions

- 1
  Select a weir coefficient for your calculation. In general, use 3.33 for a sharp-crested rectangular weir or 3.087 for a broad-crested rectangular weir. Be aware, however, that individual weirs are calibrated to determine their weir coefficients; if you know the coefficient specific to your weir, use that instead of the general coefficient. The weir coefficient has units of feet to the power of 0.5 divided by seconds: ft^0.5/s.
- 2
  Multiply the weir coefficient by the width of the weir. If a sharp-crested weir is 10 feet wide, for example, calculate (10 ft)*(3.33 ft^0.5/s) to get 33.3 ft^1.5/s.
- 3
  Raise the weir head to the power of 1.5. Use a measured head depth, or plug in various depths to find the flow volume under various stream conditions. For a weir head of 1.5 feet, for example, (1.5 ft)^1.5 equals 1.84 ft^1.5.
- 4
  Multiply the head raised to 1.5 by the product of the weir coefficient and width to get the flow over the weir. For example, (33.3 ft^1.5/s)*(1.84 ft^1.5) equals 61.3 cubic feet per second, usually abbreviated cfs.

Nature