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Weir Flow Calculator

Formula

The formula to calculate the flow rate of a rectangular weir is:

$Q = 3.247 \times L \times H^{1.48} - \left( \frac{0.566 \times L^{1.9}}{1 + 2 \times L^{1.87}} \right) \times H^{1.9}$

Where:

$Q$ is the flow rate (ft³/s)
$L$ is the width of the weir (ft)
$H$ is the height of the water above the weir crest (ft)

What is Weir Flow?

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.

Example Calculation 1

Let's assume the following values:

Width of the Weir (L) = 5 ft
Height of Water Above Weir Crest (H) = 2 ft

Using the formula:

$Q = 3.247 \times 5 \times 2^{1.48} - \left( \frac{0.566 \times 5^{1.9}}{1 + 2 \times 5^{1.87}} \right) \times 2^{1.9} \approx 3.247 \times 5 \times 2.7545 - \left( \frac{0.566 \times 16.925}{1 + 2 \times 57.874} \right) \times 3.317 \approx 44.764 - 0.156 \approx 44.206 \text{ ft³/s}$

The Flow Rate is approximately 44.206 ft³/s.

Example Calculation 2

Let's assume the following values:

Width of the Weir (L) = 3 ft
Height of Water Above Weir Crest (H) = 1.5 ft

Using the formula:

$Q = 3.247 \times 3 \times 1.5^{1.48} - \left( \frac{0.566 \times 3^{1.9}}{1 + 2 \times 3^{1.87}} \right) \times 1.5^{1.9} \approx 3.247 \times 3 \times 1.8375 - \left( \frac{0.566 \times 7.69}{1 + 2 \times 15.45} \right) \times 2.129 \approx 17.868 - 0.090 \approx 17.157 \text{ ft³/s}$

The Flow Rate is approximately 17.157 ft³/s.