Flow Under Gravity
Open channel flow — in rivers, canals, gutters, and drainage ditches — is driven by gravity rather than pressure. The fluid surface is exposed to the atmosphere, and the component of gravitational force along the channel slope provides the energy to overcome friction. Unlike pipe flow, the cross-section is not fixed but varies with discharge, making open channel hydraulics both more complex and more visually intuitive than pressurized flow.
Manning's Equation
Robert Manning's 1889 empirical formula V = (1/n)R^(2/3)S^(1/2) remains the most widely used equation in open channel design. It relates velocity to three quantities: the roughness coefficient n (representing bed and bank material), the hydraulic radius R (a measure of channel efficiency), and the slope S. For a rectangular channel, R = by/(b + 2y), showing that wider, deeper channels are hydraulically more efficient.
Subcritical vs Supercritical
The Froude number Fr = V/sqrt(gy) divides flow into two regimes. Subcritical flow (Fr < 1) is deep and slow — downstream conditions control the water surface. Supercritical flow (Fr > 1) is shallow and fast — upstream conditions dominate. At Fr = 1 (critical flow), specific energy is minimized. The transition between regimes creates hydraulic jumps (supercritical to subcritical) with vigorous turbulence and energy dissipation used in dam spillway design.
Designing Channels
Engineers select channel shape, dimensions, slope, and lining to carry a design discharge at an acceptable velocity. Too slow and sediment deposits; too fast and the bed erodes. The Manning equation, combined with Froude number checks, guides the design. This simulator shows the velocity profile, discharge, and flow regime for a rectangular channel, helping you see how each parameter affects the overall hydraulic behavior.