Broad Crested Weir Calculator

Understanding Broad Crested Weir Calculator

A broad-crested weir has a horizontal crest long enough for parallel flow to establish over the crest. Used in irrigation and flood control.

How to use this calculator

1. Enter the discharge coefficient \(C_d\), which accounts for real-world flow effects.
2. Enter the crest length \(L\) in consistent length units.
3. Enter the head over the crest \(H\), measured from the crest to the water surface upstream.
4. Use the calculator to compute the flow rate \(Q\), then check that your units are consistent.

The formula explained

The formula \(Q = C_d L \sqrt{g} H^{3/2}\) computes the discharge over a broad-crested weir. It shows that flow increases with crest length and rises quickly as the head \(H\) gets larger.

• Q = discharge, or flow rate over the weir
• \(C_d\) = discharge coefficient, a factor that adjusts for flow conditions
• L = crest length of the weir
• g = acceleration due to gravity, about \(9.81\,\text{m/s}^2\)
• H = head over the crest, measured in length units

Step by step method

1. Write down the values of \(C_d\), \(L\), \(g\), and \(H\).
2. Compute \(H^{3/2}\), which means \(H \sqrt{H}\).
3. Multiply \(C_d\), \(L\), \(\sqrt{g}\), and \(H^{3/2}\) to get \(Q\).

Worked example

Problem. Find the flow rate over a broad-crested weir with \(C_d = 1.60\), \(L = 2.0\,\text{m}\), and \(H = 0.50\,\text{m}\). Use \(g = 9.81\,\text{m/s}^2\).

1. First compute \(H^{3/2}\). Since \(0.50^{3/2} = 0.50\sqrt{0.50} \approx 0.3536\).
2. Then compute \(\sqrt{g} \approx \sqrt{9.81} \approx 3.13\).
3. Now calculate \(Q = 1.60 \times 2.0 \times 3.13 \times 0.3536 \approx 3.54\).

Tips and common mistakes

• Make sure \(H\) is measured from the crest to the upstream water surface, not from the channel bottom.
• Keep your units consistent, because the formula only gives a meaningful result when length units match.

Frequently asked questions