Trapezoidal Channel Calculator

Flow properties in a prismatic trapezoidal open channel using Manning's equation. Solve for flow rate Q, bed slope S₀, or Manning's n. Includes Froude number, critical depth, specific energy, and slope classification.

Open Channel Flow · Hydraulics

Inputs

Solve for:

Bottom width b (m)

Set b = 0 for a triangular channel

Side slope H:V z (dimensionless)

z = 0 vertical walls · z = 1/√3 ≈ 0.577 most efficient · z = 1.5 common earthen

Flow depth (normal depth) y (m)

Manning's roughness n (dimensionless)

Bed slope S₀ (m/m)

Theory

Trapezoidal geometry:

T = b + 2z·y (top width)

A = (b + z·y)·y (flow area)

P = b + 2y·√(1+z²) (wetted perimeter)

R_h = A / P (hydraulic radius — used in Manning's)

D_h = A / T (hydraulic depth — used in Froude number)

Manning's equation (uniform / normal flow):

V = (1/n) × R_h^2/3 × S₀^1/2

Q = V × A

Manning's equation applies only to uniform (normal) flow — depth, velocity, and cross-section are constant along the channel. The depth entered is therefore the normal depth y_n.

Solve for different unknowns:

Find Q: Q = (A/n) × R_h^2/3 × S₀^1/2

Find S₀: S₀ = (V·n / R_h^2/3)² where V = Q/A

Find n: n = A·R_h^2/3·S₀^1/2 / Q

Slope and Froude classification:

Slope type	Condition	Normal flow
Mild	y_n > y_c, S < S_c	Subcritical (Fr < 1)
Critical	y_n = y_c, S = S_c	Critical (Fr = 1)
Steep	y_n < y_c, S > S_c	Supercritical (Fr > 1)

Most efficient (best hydraulic) trapezoidal section:

z = 1/√3 ≈ 0.577 (60° side slopes)

b = 2y / √3 (half of a regular hexagon)

R_h = y / 2 (maximum discharge per unit area)

This geometry maximises flow for a given cross-sectional area and slope, minimising excavation cost. It is the standard for lined irrigation canals.