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.

*This tool is for educational use only. It cannot be used for detailed design, safety judgments, or confirmation of legal compliance.

*S is the energy gradient. This tool uses an approximation of 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 average 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

Cross-sectional type (A, P): Supports rectangular, trapezoidal, and circular (partially filled) sections. Solving for depth (Q→y) uses the bisection method, and solving for slope (Q→S) uses an analytical formula.

FAQ

What does the Froude number Fr indicate?

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

What does S (slope) mean?

S in the Manning equation is the energy gradient. For learning, this tool approximates the slope to be approximately equal to the riverbed slope.

Which roughness coefficient n should I use?

The value changes depending on the waterway material, vegetation, meandering, etc. The preset values ​​are for reference only, and please be sure to check the supporting documents for design purposes.

Can the circular cross section results be used for pressure pipes?

Cannot be used. Here, we assume a partially filled flow in an open channel with a free water surface.

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