Trapezoidal Channel / Swale Capacity (Manning)
The section the rectangular channel tile says is separate: every real swale, roadside ditch, and lined channel is trapezoidal. A = (b + z y) y, P = b + 2y sqrt(1 + z^2), Q = A (1.486/n) R^(2/3) sqrt(S), with the Froude number taken on the hydraulic depth A/T, which is the right length scale for a non-rectangular section. A 10-ft bottom, 2:1 banks, 3 ft deep at n 0.03 on 0.1% carries 121 cfs at 2.53 ft/s. Bottom width 0 is a V-ditch; z = 0 reproduces the rectangle exactly.
Formula and source
A = (b + z y) y; P = b + 2 y sqrt(1 + z^2); R = A/P; V = (1.486/n) R^(2/3) S^(1/2); Q = A V; T = b + 2 z y; D = A/T; Fr = V/sqrt(g D).
Manning uniform flow in a prismatic trapezoidal section, as compiled in Chow's Open-Channel Hydraulics, by name; no roughness table reproduced - n is entered.
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