Bed roughness and rainfall impact affect hydraulic friction in overlan
d flow. The relationship between friction, velocity, discharge, and ch
annel slope was examined for the case of shallow, spatially varied flo
w on rough surfaces. Rainfall was simulated on artificially roughened
surfaces in a laboratory. Measured flow velocities were compared to th
eoretical velocities computed from a dynamic equation for spatially va
ried flow and from the Darcy-Weisbach uniform flow equation. The measu
rements showed that the constant that relates the Darcy-Weisbach frict
ion coefficient to Reynolds number can become larger than the theoreti
cal 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 profi
les 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, chann
el discharge, slope, slope length, and viscosity were known.