Open Channel Flow Calculator

This calculator relies primarily on Manning's equation, an empirical formula predicting the average velocity of liquid flowing in a conduit where the liquid is not entirely enclosed by surfaces. The fundamental velocity equation is expressed as V = (1 / n) * R^(2/3) * S^(1/2), where V represents the mean velocity, n is Manning's roughness coefficient reflecting channel bed friction, R is the hydraulic radius (cross-sectional area divided by wetted perimeter), and S is the slope of the energy line, approximated here by the channel bed slope. Once velocity is found, the volumetric flow rate (discharge, Q) is calculated using the continuity equation: Q = V * A, where A is the cross-sectional area of the water flow.

Consider a rectangular open concrete channel engineered to drain stormwater runoff. The design parameters include a bottom width of 3 meters, a water flow depth of 1.5 meters, a channel slope of 0.002, and a Manning's roughness coefficient for finished concrete of 0.013. First, we compute the cross-sectional area: A = 3 m * 1.5 m = 4.5 m². Next, we find the wetted perimeter: P = bottom width + (2 * depth) = 3 + (2 * 1.5) = 6 meters. The hydraulic radius is R = A / P = 4.5 / 6 = 0.75 meters. Applying Manning's velocity equation: V = (1 / 0.013) * (0.75)^(2/3) * (0.002)^(0.5) ≈ 76.92 * 0.8255 * 0.0447 ≈ 2.84 meters per second. Finally, the discharge rate is Q = V * A = 2.84 m/s * 4.5 m² = 12.78 cubic meters per second.

Always verify your Manning's roughness coefficient (n), as selecting an incorrect value for natural earthen channels versus smooth concrete can drastically alter velocity outcomes. Ensure accurate measurement of your channel bed slope; even minor fluctuations over long distances significantly impact flow momentum. Finally, always account for freeboard safety margins in your final designs to accommodate unexpected surges or debris blockage.