Radial shear stresses on the surface of curved channel beds due to secondary flow increase with increasing bed roughness and affect the direction of flow of sediment particle motion over a channel bed. By means of an analysis it was shown that this flow direction approaches the tangential diredtion of the flow with increasing bed roughness while flow over smooth curved channel beds shows a stronger deviation from the tangential direction. Accordingly fluid or sediment particles moving at a curved channel bed and originating from the outer wall region reach the inner wall much faster in a flow over a smooth bed than over a rough bed. This analytical result was confirmed by experiments in circular planform channels with fixed beds of varying roughness and also by alluvial bed experiments in circular channels.