Manning's equation — trapezoidal channel

Uniform steady flow · symmetric trapezoid · SI units

Inputs

Solve for depth Solve for Q

Q — discharge, m³/s

b — bottom width, m

z — side slope, H:V

H — channel height, m

n — Manning's n

S₀ — bed slope, m/m

Sweep range for Q from to

z is horizontal run per unit rise — z = 2 means 2 m out for every 1 m up. Use 0 for vertical walls, or b = 0 for a triangular section. H is the channel itself, invert to top of bank.

Cross-section

Drawn to scale · dashed line is top of bank

Sensitivity sweep

Results

Normal depth — m

Flow area, A: — m²
Wetted perimeter, P: — m
Hydraulic radius, R: — m
Top width, T: — m
Mean velocity, V: — m/s
Froude number, Fr: —
Flow regime: —
Capacity at H: — m³/s
Freeboard: — m

Q = (1/n)·A·R^(2/3)·√S₀ · normal depth by bisection on a strictly increasing Q(y) · prismatic channel, uniform flow · User is responsible for verifying outputs.

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