Open channel flow is water moving under the influence of gravity with a free surface exposed to the atmosphere. Ditches, storm drains flowing partially full, irrigation canals, and natural streams are all open channel flow. The primary design tool is Manning's equation, which relates flow velocity to channel slope, cross-sectional shape, and surface roughness. It has been the standard for open channel design since the 1890s and remains the foundation of stormwater, irrigation, and wastewater conveyance design.
This guide covers the Manning's equation terms, how roughness coefficients vary with channel material and condition, the hydraulic geometry of common channel shapes, and the Froude number check that distinguishes between tranquil and rapid flow regimes.
Manning's Equation
In US customary units: V = (1.486/n) × R^(2/3) × S^(1/2), where V is velocity in ft/s, n is Manning's roughness coefficient, R is the hydraulic radius in feet (cross-sectional flow area divided by wetted perimeter), and S is the channel bed slope in ft/ft. Flow rate Q = V × A, where A is the cross-sectional flow area.
The key insight is that velocity depends on the 2/3 power of hydraulic radius and the 1/2 power of slope. Doubling the slope only increases velocity by 41 % (square root of 2). But making the channel wider and shallower to increase the hydraulic radius has a stronger effect. A trapezoidal channel is hydraulically more efficient than a rectangular one for the same cross-sectional area because it minimizes the wetted perimeter per unit area, maximizing the hydraulic radius.
Open Channel Flow Calculator
Calculate open channel flow using Manning's equation for rectangular, trapezoidal, and circular channels.
Manning's n Roughness Coefficients
The roughness coefficient n captures the resistance of the channel surface and any obstructions to flow. Smooth concrete channels use n = 0.013. Corrugated metal pipe uses n = 0.024. Earth channels in good condition use n = 0.025. Earth channels with weeds and stones use n = 0.035. Natural streams with heavy brush use n = 0.070 or higher. The roughness coefficient has a large impact: changing n from 0.013 to 0.025 nearly doubles the friction and halves the velocity for the same slope and geometry.
For design purposes, use published n values from references like Chow's Open Channel Hydraulics or the FHWA Hydraulic Design Series. When in doubt, use a higher (rougher) n value. This is conservative because it predicts lower velocity and higher flow depths, resulting in a larger channel design. For channels that will have vegetation, design for the vegetated condition (higher n) to ensure adequate capacity during peak events.
Channel Cross-Section Shapes
Rectangular channels are the simplest to analyze but least efficient hydraulically (high wetted perimeter for a given area). They are common for concrete-lined channels and box culverts. Trapezoidal channels (flat bottom with sloped sides) are the most common for earthen ditches and canals. Side slopes of 2:1 or 3:1 (horizontal:vertical) are typical for earth channels to prevent bank erosion.
Circular channels (pipes flowing partially full) require iterative solutions because the flow area and wetted perimeter change nonlinearly with depth. A circular pipe flowing at about 93 % full actually carries more flow than when completely full, because the reduction in friction from the smaller wetted perimeter at 93 % depth more than compensates for the slightly smaller area. Triangular (V-shaped) channels are used for small roadside ditches and handle low flows well but become very wide at high flows.
Open Channel Flow Calculator
Calculate open channel flow using Manning's equation for rectangular, trapezoidal, and circular channels.
Froude Number and Flow Regime
The Froude number (Fr) determines whether the flow is subcritical (tranquil, Fr < 1) or supercritical (rapid, Fr > 1). Fr = V / sqrt(g × D_h), where V is flow velocity, g is gravitational acceleration (32.2 ft/s²), and D_h is the hydraulic depth (flow area divided by top width). At Fr = 1, the flow is critical and is at the boundary between the two regimes.
Most engineered channels are designed for subcritical flow (Fr < 0.8 is a common target) because subcritical flow is stable and predictable. Supercritical flow is fast, shallow, and unstable. Small disturbances create standing waves and hydraulic jumps. If your channel design calculates to supercritical flow, evaluate whether that is acceptable or if you need to reduce the slope, increase roughness (such as rip-rap lining), or use energy dissipation structures at transitions. Steep channels and smooth linings tend to produce supercritical flow.