Open Channel Flow Calculator — Manning's Equation
Apply Manning's equation to a rectangular open channel: enter the channel width, flow depth, bed slope and roughness coefficient to get discharge (Q), mean velocity, hydraulic radius and the Froude number that classifies flow as subcritical or supercritical.
Channel lining / type
m
m
Volumetric flow rate — Manning equation, SI units, rectangular channel
- 1
Cross-section area
3 × 1 = 3 - 2
Wetted perimeter
3 + 2 × 1 = 5 - 3
Hydraulic radius
3 ÷ 5 = 0.6A larger hydraulic radius means less boundary friction per unit of flow area. - 4
Discharge Q
(1 ÷ 0.013) × 3 × 0.6^(2/3) × √0.001 = 5.191
How does this calculator work?
Manning's equation Q = (1/n) × A × R^(2/3) × S^(1/2) gives discharge in a rectangular open channel from width, depth, slope and roughness. The hydraulic radius R = A/P captures friction efficiency. The Froude number Fr = V/√(gy) classifies flow as subcritical (Fr < 1) or supercritical (Fr > 1). All values in SI units.
Formula
How this is calculated
Manning's equation is the most widely used empirical formula for steady, uniform flow in open channels (rivers, canals, drainage ditches). For a rectangular cross-section with bottom width b and flow depth y the cross-sectional area is A = b × y, the wetted perimeter is P = b + 2y, and the hydraulic radius R = A/P. Discharge Q is then (1/n) × A × R^(2/3) × S^(1/2), where S is the channel slope (dimensionless, e.g., 0.001 = 1 m drop per 1 km) and n is the roughness coefficient, which captures the retarding effect of the channel boundary.
The Froude number Fr = V / √(g·y) classifies the flow: Fr < 1 is subcritical (tranquil), Fr = 1 is critical (maximum discharge for the given specific energy), and Fr > 1 is supercritical (rapid). Subcritical flow is typical in rivers and irrigation canals; supercritical flow occurs on steep chutes and spillways. The Q-versus-depth chart shows how discharge grows non-linearly with increasing depth for the same channel geometry and slope.
This calculator uses the SI form of the equation (coefficient = 1.0). The US customary version uses 1.486 instead. Uniform flow is assumed — the water-surface slope equals the bed slope and depth is constant along the reach. Transitions, bends, backwater effects and sediment transport are not modelled.
Frequently asked questions
Manning's n is an empirical measure of channel resistance due to boundary texture and shape. Smooth concrete gives n ≈ 0.010–0.013; clean natural gravel channels n ≈ 0.025–0.035; heavily vegetated or irregular channels n ≈ 0.050–0.100. Standard tables (e.g., Chow 1959) list values by material — this calculator includes common presets.
The hydraulic radius R = A/P is the cross-sectional area divided by the wetted perimeter (the length of channel boundary in contact with water). A larger R means relatively less friction per unit area — wide, shallow channels have a smaller R and therefore lower flow for the same depth than deeper, narrower channels of identical cross-sectional area.
Fr < 1 (subcritical): flow is slow and depth-controlled; disturbances propagate both upstream and downstream. Fr = 1 (critical): theoretical maximum discharge for the energy available. Fr > 1 (supercritical): flow is fast and slope-controlled; disturbances travel only downstream and a hydraulic jump can occur where the flow transitions back to subcritical.
Also known as
TG we-Calculate Editorial Team. (2026). Open Channel Flow Calculator — Manning's Equation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/open-channel-flow-calculator
TG we-Calculate Editorial Team. "Open Channel Flow Calculator — Manning's Equation." TG we-Calculate. 2026. https://we-calculate.com/calculator/open-channel-flow-calculator.
TG we-Calculate Editorial Team, "Open Channel Flow Calculator — Manning's Equation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/open-channel-flow-calculator
@misc{wecalculate_open_channel_flow_calculator, title = {Open Channel Flow Calculator — Manning's Equation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/open-channel-flow-calculator}}, year = {2026}, note = {TG we-Calculate} }
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