Manning Open Channel Flow Calculator
Work out the flow rate, velocity and hydraulic radius of a rectangular open channel — a drain, swale, lined canal or box culvert running part-full — with Manning's equation. Enter the bottom width, flow depth, roughness coefficient and bed slope, and the tool returns the discharge in both m³/s and L/s plus the mean velocity.
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 Manning's roughness n for the lining (0.013 for concrete, ~0.022 for earth).
- Enter the bed slope S as a fall per metre (0.001 = 1 in 1000) and read off the flow rate, velocity and hydraulic radius.
How it works
For a rectangular section the flow area is A = b·y and the wetted perimeter is P = b + 2y, so the hydraulic radius is R = A/P. Manning's equation then gives Q = (1/n)·A·R^(2/3)·S^(1/2), the steady uniform (normal-depth) discharge. The mean velocity is simply v = Q/A. Everything is in SI units — metres, m³/s and m/s.
Worked example
Worked example. A 1 m-wide concrete channel (n = 0.013) flows 0.5 m deep on a slope of 0.001. A = 1 × 0.5 = 0.5 m², P = 1 + 2×0.5 = 2 m, so R = 0.25 m. Q = (1/0.013) × 0.5 × 0.25^(2/3) × 0.001^0.5 = 0.483 m³/s (482.7 L/s), and the velocity is 0.483 / 0.5 = 0.965 m/s.
Common mistakes
- Entering the slope as a percentage or as '1 in 500' instead of a decimal fraction (0.002) — the square-root of slope has a big effect on the answer.
- Using the top width or the full channel height instead of the actual flow depth y and bottom width b of the wetted rectangle.
- Picking too low a roughness n; a smooth-concrete value applied to a weathered or debris-lined channel will overstate the capacity.
Frequently asked questions
Does this handle trapezoidal or circular channels?
No — this tool is for a rectangular section (A = b·y, P = b + 2y). Trapezoidal channels add side-slope terms and part-full pipes use a circular-segment geometry, so they need their own calculators.
What is uniform (normal-depth) flow?
Manning's equation assumes steady flow at a constant depth down a prismatic channel, where the friction slope equals the bed slope. Near transitions, drops, weirs or backwater the depth varies and a gradually-varied-flow analysis is needed instead.
Related tools
- Pipe Flow Calculator
- Culvert Flow Rough Calculator
- Stormwater Runoff Calculator
- V-Notch Weir Flow Calculator
- Trapezoidal Channel Flow Calculator
- Broad-Crested Weir Flow Calculator
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