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Fluid Mechanics

Manning Open-Channel Flow Calculator

Open-channel flow has a free surface and is driven by gravity along the channel slope, not by a pressure gradient like full-pipe flow. The Manning equation is the standard empirical relationship for estimating the normal (uniform) flow a channel carries from its geometry, slope, and surface roughness. This calculator treats a simple rectangular channel: it builds the flow area, wetted perimeter, and hydraulic radius from the bottom width and flow depth, then applies the SI Manning equation to return the flow rate and the mean velocity. It is a preliminary normal-flow estimate for a single prismatic rectangular section — useful for sizing launders, drains, and channels at a concept level, but not a substitute for a proper hydraulic study with survey data, downstream control, and freeboard.

TypeInteractive engineering calculator

Calculator

Velocity:
Result
Flow area (A)0.5 m²
Wetted perimeter (P)2 m
Hydraulic radius (R)0.25 m
Flow rate (Q)0.482673 m³/s
Flow rate (Q)1737.62 m³/h
Velocity (v)0.965347 m/s
Simple rectangular normal-flow estimate only — not for culvert design, flood studies, gradually varied flow, backwater, hydraulic jumps, or sediment transport. Add freeboard above the computed depth and verify with survey, roughness basis, and downstream control before design.

Formulas

Flow area
A = b × y
Wetted perimeter
P = b + 2y
Hydraulic radius
R = A / P
Manning equation (SI)
Q = (1/n) × A × R^(2/3) × S^(1/2)
Velocity
v = Q / A

Diagram

Manning: Q = (1/n)·A·R^(2/3)·S^(1/2)free surfaceybQ = (1/n)·A·R^(2/3)·S^(1/2), R = A/P

Worked example

A rectangular channel 1.0 m wide carries water 0.5 m deep on a slope of 0.001 m/m with Manning n = 0.013. Find the flow rate and velocity.

  1. 01A = 1.0 × 0.5 = 0.50 m²; P = 1.0 + 2 × 0.5 = 2.00 m; R = 0.50 / 2.00 = 0.25 m
  2. 02Q = (1/0.013) × 0.50 × 0.25^(2/3) × 0.001^(1/2)
  3. 03Q = 76.9 × 0.50 × 0.397 × 0.0316 = 0.483 m³/s ≈ 1,738 m³/h
  4. 04v = 0.483 / 0.50 = 0.965 m/s
Result

Flow rate ≈ 0.483 m³/s (≈ 1,738 m³/h) at a mean velocity ≈ 0.965 m/s.

FAQ

Why is open-channel flow different from pipe flow?
Open-channel flow has a free surface at atmospheric pressure and is driven by the channel slope under gravity, so capacity depends on the water depth. Full-pipe flow is driven by a pressure gradient. Because of this, a pipe pressure-drop calculator should not be used on a channel, launder, or partially full drain.
What Manning n should I use?
n reflects the channel surface roughness: smooth finished concrete is low (≈0.011–0.013), rougher concrete or masonry higher, and natural earth or vegetated channels much higher. The flow scales with 1/n, so the roughness basis strongly affects the result — choose n from the actual surface and condition.
Does this handle non-rectangular channels?
No. This tool assumes a rectangular section, so the area is b×y and the wetted perimeter is b+2y. Trapezoidal, circular, or natural sections have different geometry and are not covered here.
Is this the normal depth or the actual depth?
The calculator returns the flow that a given depth carries under the normal (uniform) flow assumption. Real channels can run at a different depth because of downstream controls, transitions, or unsteady flow. Use it as a preliminary estimate, and add freeboard above the computed depth in any real design.

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