Rectangular Open-Channel Flow

Estimate uniform unpressurized flow capacity at a specified rectangular channel water depth.

How this calculation works

Manning's equation estimates uniform open-channel flow at an entered water depth. Supply the rectangular channel's internal width, water depth, SI Manning roughness and energy slope in m/m. Depth is the flowing water depth, not the wall height. Width times depth gives flow area; dividing it by the wetted perimeter gives hydraulic radius. The SI Manning relation then yields mean velocity, and velocity times area gives discharge. The Froude number compares velocity with the shallow-water wave-speed scale at that depth. The model assumes a long, prismatic channel with steady uniform flow and energy slope equal to bed slope. It does not solve for normal depth or account for freeboard, backwater, hydraulic jumps, culvert controls or sediment, so the result does not certify flood capacity.

Inputs and units

Channel internal width (m)
Water depth (not wall height) (m)
Manning roughness n (SI) (s/m^(1/3))
Energy/bed slope (m/m)

Method and formula

A = by; wetted perimeter = b + 2y; R = A/(b + 2y); V = R^(2/3) sqrt(S)/n (SI); Q = AV; Fr = V/sqrt(gy), g = 9.80665 m/s².

Worked example

Example inputs

Channel internal width: 2 m
Water depth (not wall height): 1 m
Manning roughness n (SI): 0.02 s/m^(1/3)
Energy/bed slope: 0.001 m/m

Calculation steps

Calculate flow area: A = 2 × 1 = 2 m².
Calculate wetted perimeter and hydraulic radius: P = 2 + 2 × 1 = 4 m; R = 2/4 = 0.5 m.
Apply the SI Manning equation: V = 0.5^(2/3) × sqrt(0.001)/0.02 = 0.996055 m/s.
Calculate discharge at the entered depth: Q = 2 × 0.9960550474 = 1.992110 m³/s.
Calculate Froude number: Fr = 0.9960550474/sqrt(9.80665 × 1) = 0.318070, dimensionless.

Example results

Flow area: 2 m²
Hydraulic radius: 0.5 m
Mean velocity: 0.9960550474 m/s
Discharge at entered depth: 1.992110095 m³/s
Froude number: 0.3180702152 1

Assumptions

Long prismatic rectangular open channel, steady uniform water flow
Energy slope equals bed slope; roughness is user-supplied

Limitations

Not pipe sizing; no freeboard, backwater, hydraulic jumps, culvert control or sediment transport
Normal depth is an input; this does not solve for it or certify flood capacity

Sources

NOAA / National Weather Service: Open-Channel Flow: Manning uniform-flow relationship and assumptions; implemented with SI coefficient one
USACE: Resistance to Flow: Manning uniform open-channel resistance relationship
USGS: Mean Velocity and Longitudinal Dispersion: Definitions: Froude number and hydraulic radius