How this calculator works
Manning flow combines wetted area, hydraulic radius and energy slope. Under steady uniform flow, energy slope equals bed slope. Custom trapezoids and triangles allow different bank slopes. Efficient rectangular geometry has width twice depth; the fully optimized trapezoid uses side slopes 1/sqrt(3) and bottom width 2y/sqrt(3); the efficient triangle has 1:1 banks. A semicircle is evaluated filled to its rim. The freeboard allowance is supplied by you and added to water depth, rather than being presented as a universal design rule.
Formula
R = A/P; v = R^(2/3) sqrt(S)/n; Q = Av; mass flow = rho Q. Trapezoid A = y[b + (z1+z2)y/2], P = b + y(sqrt(1+z1^2)+sqrt(1+z2^2)).
Worked example
A 2 m wide rectangle at depth 1 m has A = 2 m2, P = 4 m and R = 0.5 m. With n = 0.01 and S = 0.01, velocity is 6.299605249 m/s and discharge is 12.59921050 m3/s.
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Frequently asked questions
Does this model backwater?
No. Uniform-flow Manning calculations do not determine water-surface profiles near controls, bends or transitions.
Why are custom dimensions still visible in efficient mode?
Those fields apply only to custom design. Efficient mode derives the proportions from water depth; the displayed results show the dimensions actually used.
Is the freeboard sufficient for design?
It is only your entered allowance. Waves, debris, uncertainty and local requirements need a separate design assessment.