Trapezoidal Channel Flow Calculator
Compute the flow in a trapezoidal open channel with Manning's equation. Enter the bottom width, flow depth, side slope, roughness and bed slope, and the tool returns the discharge, velocity, flow area and water-surface top width.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the channel bottom width b and the flow depth y in metres.
- Enter the side slope z as horizontal:vertical (e.g. 1.5 for 1.5H:1V; use 0 for a rectangular channel), Manning's n and the bed slope S in m/m.
- Read the flow rate (m³/s and L/s), velocity, flow area and top width, with the working shown in the steps.
How it works
A trapezoidal section has area A = (b + z·y)·y and wetted perimeter P = b + 2y·√(1+z²), giving hydraulic radius R = A/P. These go into Manning's equation Q = (1/n)·A·R^(2/3)·S^(1/2). The mean velocity is Q/A and the water-surface top width is T = b + 2z·y.
Worked example
Worked example. A channel with b = 2 m, y = 1 m, z = 1.5, n = 0.025 and S = 0.001: A = (2 + 1.5)·1 = 3.5 m², P = 2 + 2·√3.25 = 5.606 m, R = 0.6243 m, so Q = (1/0.025)·3.5·0.6243^(2/3)·√0.001 = 3.234 m³/s at 0.924 m/s.
Common mistakes
- Reading the side slope the wrong way round — z is horizontal run per unit vertical rise (H:V), so a flatter bank has a larger z.
- Using the top width instead of the bottom width for b.
- Picking too smooth an n for a vegetated or stony channel, which overstates the capacity.
Frequently asked questions
What if my channel is rectangular?
Set the side slope z to 0. The area becomes b·y and the wetted perimeter b + 2y, matching a rectangular channel exactly.
Is this normal-depth (uniform) flow?
Yes. It assumes steady, uniform flow at the entered depth in a straight prismatic channel. Bends, backwater, supercritical transitions and overbank flow require a fuller hydraulic analysis.
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Tip: Enter any known values to calculate the remaining results.
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