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Manning's Equation — Open-Channel Discharge

Related: Topic 6: Open-Channel Flow — normal depth, critical depth, and exam traps
Related: Formula quick-reference index

Solve for discharge in a prismatic channel under uniform flow. Pick a cross-section, enter the geometry, roughness, and slope — the calculator returns area, wetted perimeter, hydraulic radius, velocity, and discharge.

V = (k/n) · R^2/3 · S^1/2 Q = AV

k	1.0 for SI (m/s), 1.486 for US units (ft/s)
R = A/P	hydraulic radius = area / wetted perimeter
n	Manning's roughness (concrete ≈ 0.013, earth ≈ 0.022)
S	longitudinal bed slope (m/m or ft/ft)

Unit system Channel shape Bottom width b (m) Flow depth y (m) Side slope z (H:V) Diameter D (m) Manning's n Bed slope S

For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook.