Which statement best describes open-channel flow and its dependence on channel roughness?

• A. Open-channel flow is independent of roughness.
• B. Open-channel flow depends only on water temperature.
• C. Manning's equation relates discharge to channel roughness and geometry.
• D. Open-channel flow only depends on channel slope.

Answer: (C)

Open-channel flow is governed by friction between the moving water and the channel boundaries. The roughness of the channel controls that friction: a rougher surface increases resistance, which lowers velocity and, for a given cross section and slope, reduces the discharge. Manning’s equation formalizes this relationship by linking discharge to the roughness coefficient, the cross-sectional area, the hydraulic radius (which depends on the wetted perimeter and area), and the channel slope. The familiar form, Q = (1/n) A R^(2/3) S^(1/2), shows plainly that roughness (n) and geometry (A and R) are central to determining how much water flows for a given slope. Temperature does not directly factor into this relationship, and describing flow as independent of roughness would ignore the essential role of channel friction.