Open channel flow

Open channel flow occurs whenever a liquid moves with a free surface at atmospheric pressure. Rivers, drainage ditches, irrigation canals, spillways, and sewers flowing partly full are all open channel systems. The key difference from pipe flow is the driving force: closed conduits flow under a pressure gradient, while open channels flow under gravity acting along the channel slope, and the depth of flow becomes an unknown that adjusts with the discharge.

Two geometric quantities appear throughout the analysis. The hydraulic radius R is the flow area divided by the wetted perimeter, and the channel slope S is the drop in elevation per unit length. Uniform flow is most often computed with Manning's equation, V = (k/n) R^(2/3) S^(1/2), where n is the Manning roughness coefficient for the channel lining and k is a unit constant. Multiplying velocity by flow area gives discharge, Q = VA. For a given discharge, the depth that minimizes specific energy is the critical depth, and the cross-section that maximizes hydraulic radius for a given area is the most hydraulically efficient section.

Flow is classified by the Froude number, Fr = V / √(gD), which compares inertial to gravitational forces using hydraulic depth D. Subcritical flow (Fr < 1) is deep and slow, and disturbances can travel upstream, so control is exerted from downstream. Supercritical flow (Fr > 1) is shallow and fast, and control comes from upstream. Critical flow occurs at Fr = 1. A transition from supercritical to subcritical flow produces a hydraulic jump, an abrupt rise in depth that dissipates energy — a behavior engineers use deliberately in stilling basins below spillways.

Open channel flow is a named topic in the water resources and environmental engineering section of the FE Civil exam, and it builds directly on the fluid mechanics material covering mass and energy conservation. Expect calculation problems using Manning's equation, hydraulic radius, and the Froude number, all supported by the FE Reference Handbook.