Rectangular Weir Flow Rate Calculator

Understanding Rectangular Weir Flow Rate Calculator

A rectangular weir is a standard device for measuring open channel flow. The Francis formula gives the volumetric flow rate over the weir.

How to use this calculator

1. Enter the weir length, head, discharge coefficient, and use consistent units.
2. Make sure the head is measured above the crest and is not too close to zero.
3. Click calculate to get the flow rate over the weir.
4. Check the displayed formula and example to understand how the result was obtained.

The formula explained

The formula computes the volumetric flow rate over a rectangular weir. It combines the weir length, the head above the crest, gravity, and a discharge coefficient to estimate how much water passes per unit time.

• Q = flow rate, usually in ubic meters per second
• \(C_d\) = discharge coefficient, a dimensionless factor that accounts for real-flow effects
• L = length of the weir opening
• g = acceleration due to gravity, about 9.81 m/s^2
• H = head above the weir crest

Step by step method

1. Start with the Francis formula, \(Q = \frac{2}{3} C_d L \sqrt{2g} H^{3/2}\).
2. Substitute the given values for \(C_d\), \(L\), \(g\), and \(H\).
3. Compute \(H^{3/2}\), then multiply by \(\frac{2}{3}\), \(C_d\), \(L\), and \(\sqrt{2g}\).

Worked example

Problem. Find the flow rate over a rectangular weir if \(C_d = 0.62\), \(L = 1.2\,\text{m}\), and \(H = 0.25\,\text{m}\). Use \(g = 9.81\,\text{m/s}^2\).

1. Use \(Q = \frac{2}{3} C_d L \sqrt{2g} H^{3/2}\).
2. Substitute the values: \(Q = \frac{2}{3}(0.62)(1.2)\sqrt{2(9.81)}(0.25)^{3/2}\).
3. This gives \(Q \approx 0.194\,\text{m}^3/\text{s}\).

Tips and common mistakes

• Use the same unit system throughout, especially for \(L\), \(H\), and \(g\).
• If the head measurement is noisy or very small, the flow estimate can change a lot, so measure carefully.

Frequently asked questions