Open Channel Geometry — Reference
Section properties for Manning's and critical-flow analysis. A = flow area, P = wetted perimeter, R = A/P = hydraulic radius, T = top width, D = A/T = hydraulic depth. Side slope z is horizontal:vertical (z H : 1 V), depth y, bottom width b.
Section Property Formulas
| Shape | Area A | Wetted perim. P | Hyd. radius R | Top width T |
|---|---|---|---|---|
| Rectangular | b·y | b + 2y | by/(b+2y) | b |
| Trapezoidal | (b + zy)y | b + 2y√(1+z²) | A/P | b + 2zy |
| Triangular | z·y² | 2y√(1+z²) | zy / 2√(1+z²) | 2zy |
| Circular* | (D&sub0;²/8)(θ − sinθ) | D&sub0;θ/2 | (D&sub0;/4)(1 − sinθ/θ) | D&sub0; sin(θ/2) |
*Circular (partly full), diameter D&sub0;, flow depth y: θ = 2·arccos(1 − 2y/D&sub0;) radians. Full pipe: A = πD&sub0;²/4, R = D&sub0;/4.
Manning's Equation
V = Q/A = (k/n) R2/3 S1/2. S is the channel (friction) slope; n is Manning's roughness. Normal depth is found by solving Manning's for the y that passes the design Q — iterative for all shapes except the simplest.
Best Hydraulic Section (Max Q for Given Area)
| Shape | Optimum condition | R at optimum |
|---|---|---|
| Rectangular | b = 2y (width = twice depth) | y/2 |
| Trapezoidal | Half-hexagon: z = 1/√3 (60° sides) | y/2 |
| Triangular | z = 1 (90° vee, sides at 45°) | y/(2√2) |
| Semicircle | Overall most efficient open shape | y/2 |
Sources: Chow, V.T. (1959), Open-Channel Hydraulics, Table 2-1. Sturm, T.W., Open Channel Hydraulics. Standard prismatic-channel geometry.
Related cheat sheets and tools
Feed these section properties into the Manning's tool with an n value, check the flow regime with the Froude / hydraulic-jump card, and protect the channel with riprap sizing. For modeling a channel network within a full watershed, see HydroComplete.