Trapezoidal Channel / Swale Capacity (Manning)
Flow in a TRAPEZOIDAL channel - the shape every real swale, roadside ditch, and lined channel takes.
Example
You enter
- Bottom width b (ft, 0 = V-ditch) 10
- Side slope z (z horizontal : 1 vertical) 2
- Flow depth y (ft) 3
- Manning roughness n 0.03
- Channel slope S (ft/ft) 0.001
You get
- Area (ft²) 48
- Wetted perim (ft) 23.4164
- Hyd radius (ft) 2.04984
- Velocity (fps) 2.52762
- Discharge Q 121.326
- Top width (ft) 22
- Hyd depth (ft) 2.18182
- Froude 0.301682
Details, formula, and sources
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.
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.
The Manning relation and trapezoidal section geometry are public engineering formulas; typical n values are published in every state drainage manual.
Estimate. AHJ and licensed professional govern.
Field names used by the API: bottom_width_ft, side_slope_z, depth_ft, n, s_slope, area_sf, wetted_perim_ft, hyd_radius_ft, velocity_fps, flow_cfs, top_width_ft, hyd_depth_ft, froude
- Uniform flow prismatic channel at normal depth; no backwater, no freeboard allowanceManning uniform-flow assumption
- Froude length scale hydraulic depth D = A/T, the correct scale for a non-rectangular sectionopen-channel hydraulics (Chow)
- Roughness entered n is a user input (about 0.013 concrete, 0.030 grassed earth, 0.035 natural); no table shippeduser input