Bed roughness and rainfall impact affect hydraulic friction in overland flow. The relationship between friction, velocity, discharge, and channel slope was examined for the case of shallow, spatially varied flow on rough surfaces. Rainfall was simulated on artificially roughened surfaces in a laboratory. Measured flow velocities were compared to theoretical velocities computed from a dynamic equation for spatially varied flow and from the Darcy-Weisbach uniform flow equation. The measurements showed that the constant that relates the Darcy-Weisbach friction coefficient to Reynolds number can become larger than the theoretical value for smooth laminar flow. An analysis of the dynamic equation showed that frictional forces were much larger than forces resulting from changes in hydrostatic pressure and momentum. Water-surface profiles based on the Darcy-Weisbach friction equation nearly matched those from the dynamic equation for spatially varied flow. A regression was developed from the Darcy-Weisbach equation. The regression accurately predicted flow velocity when absolute roughness, rainfall rate, channel discharge, slope, slope length, and viscosity were known.
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