Open Channel Flow Calculator (Manning Equation)

Estimate velocity V and discharge Q in an open channel with the Manning equation (uniform-flow approximation). You can also solve for water depth y or slope S from a target flow rate.

Educational use only: do not use this output for detailed design, safety judgments, or legal compliance checks.

S is the energy gradient. For learning, this tool approximates riverbed slope ≈ S.

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Example preset

Choose a preset to fill the form and refresh results instantly.

Inputs

Forward (calculate V,Q)

Results

Flow rate Q [m³/s]
Flow velocity V [m/s]
Hydraulic radius R [m]
Froude number Fr [-]
Cross-sectional area A [m²]
Wetted perimeter P [m]
Hydraulic radius R [m]
Hydraulic depth Dm=A/T [m]
Froude number Fr [-]
Flow regime
Estimated water depth y [m]
Iteration details

Cross-sectional view (outline)

Displays the cross-sectional shape according to the input value.

Graph

Display a graph with valid input.

Calculation formula and procedure

R = A / P V = (1/n) × R^(2/3) × S^(1/2) Q = A × V

Flow area A, wetted perimeter P, and top width T are calculated for rectangular, trapezoidal, and partially full circular sections. Depth is solved with bracketed bisection; slope is solved analytically.

At the full-depth boundary y=D, Q and V can be evaluated from Manning's equation, but hydraulic depth and a free-surface Froude number are not defined.

FAQ

What does the Froude number Fr indicate?

Fr compares inertial and gravitational effects. Fr<1 is subcritical flow, Fr≈1 is critical flow, and Fr>1 is supercritical flow.

What does slope S mean?

S is the energy gradient in Manning's equation. For this educational estimate, the channel-bed slope is used as an approximation when uniform flow is assumed.

Which Manning roughness coefficient n should I use?

Choose n from a source appropriate to the channel material, vegetation, irregularity, alignment, and maintenance condition. The presets are reference examples, not design values.

Can I use the circular-section result for a pressurized pipe?

No. This calculator models open-channel flow with a free surface. It does not model a pressurized full pipe.

Why can a partially full circular section have two depths for one discharge?

Circular-section Manning discharge reaches a maximum before the section is completely full and then decreases slightly toward y=D. Between the full-depth discharge and the maximum discharge, one target Q has a shallow and a deeper mathematical depth. The calculator selects the shallow depth and also reports the deeper alternative.

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