Open Channel Flow Calculator

Open channel flow refers to the flow of a liquid, typically water, in a conduit or channel where the liquid surface is exposed to the atmosphere. Unlike pipe flow, which is driven by pressure, open channel flow is driven primarily by gravity. Examples include rivers, streams, irrigation canals, and drainage ditches.

Manning's equation is an empirical formula used to calculate the average velocity of flow in an open channel: V = (1/n) × R^(2/3) × S^(1/2), where V is velocity, n is Manning's roughness coefficient, R is the hydraulic radius, and S is the channel slope. Discharge Q is then calculated as Q = V × A, where A is the cross-sectional flow area.

Manning's n quantifies the resistance of the channel boundary to flow. Lower values indicate smoother surfaces (e.g. smooth concrete ≈ 0.011–0.013), while higher values indicate rougher surfaces (e.g. natural rivers with vegetation ≈ 0.035–0.05). The rougher the channel, the slower the flow for a given slope and depth.

The hydraulic radius (R) is the ratio of the wetted cross-sectional area (A) to the wetted perimeter (P): R = A/P. It characterizes how efficiently a channel conveys flow. A larger hydraulic radius means more of the cross-section is moving water relative to the friction-producing boundary, resulting in higher velocity and discharge.

The Froude number (Fr) is a dimensionless ratio comparing inertial forces to gravitational forces: Fr = V / √(g × D), where D is the hydraulic depth. If Fr < 1, flow is subcritical (tranquil); Fr = 1 is critical flow; and Fr > 1 is supercritical (rapid). Understanding the flow regime is important for designing stable channels and avoiding erosion.

The most hydraulically efficient cross-section is one that conveys the maximum discharge for a given area and slope. A semicircle is theoretically the most efficient shape, but trapezoidal channels with a specific side slope are the most efficient among practical shapes. A trapezoid is most efficient when its half-top-width equals the sloped side length, approximating a half-hexagon.

Bed shear stress (τ) is the frictional force per unit area exerted by flowing water on the channel bed: τ = γ × R × S, where γ is the unit weight of water (approximately 9810 N/m³), R is the hydraulic radius, and S is the slope. It determines whether the channel boundary material will erode, and is critical for channel lining design.

This calculator supports circular channels running partially full, which is common for culverts and sewer pipes. Enter the pipe diameter and the actual flow depth. The calculator computes the wetted area and perimeter for the partial-circle cross section and applies Manning's equation accordingly. For a full pipe, set flow depth equal to the diameter.