Enter the bottom width of the weir and the height of the upstream water above the weir to calculate the weir flow rate.
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Weir Flow Formula
The following formula is used to calculate a flow rate of a rectangular weir.
Q = 3.247 * L * H^1.48 – [ (.566*L^1.9) / (1+2*L^1.87) ] *H^1.9
- Where Q is the flow rate (ft^3/s)
- L is the bottom width of the weir (ft)
- H is the hight of the water above the weir crest (ft)
Weir Flow Definition
A weir flow is defined as the volumetric flow rate of water out of a rectangular weir with a given width of the weir and the height of the water above the weir.
How to calculate weir flow?
Example Problem #1:
The first step in calculating the volumetric flow of water through a weir is to determine the bottom width of the weir. For this example, the width is measured to be 5 ft.
Next, determine the height of the upstream water above the weir crest. In this case, the height is measured to be 10 ft.
Finally, using the formula above, the weir flow rate is found to be:
Q = 3.2471 * L * H^1.48 – [ (.566*L^1.9) / (1+2*L^1.87) ] *H^1.9
= 3.2471*(5)*(10^1.48) – [ (.566*(5)^1.9) / (1+2*(5)^1.87) * (10^1.9) ]
= 467. 265 ft^3 / s.
Example Problem #2:
In this next example, we will use the same method as Example 1 to calculate the flow rate.
First, we determine the width of the weir. This is measured to be 30 ft.
Next, we determine the height. This is measured to be 20 ft.
Finally, we calculate the flow rate using the same formula:
= 3.2471*(30)*(20^1.48) – [ (.566*(30)^1.9) / (1+2*(30)^1.87) * (20^1.9) ]
= 8113.356 ft^3/s (cfs)