Applying flow resistance equations to overland flows

Resistance to flow determines routing velocities and must be adequately represented both within stream channels and over hillslopes when making predictions of streamflow and soil erosion. The limiting assumptions inherent in flow resistance equations can be relaxed if the spatial and temporal scale over which they are applied is restricted. This requires a substantial methodological advance in the study of overland flows over natural surfaces. It is suggested that terrestrial laser scanning will allow a greater understanding of overland flow hydraulics and present opportunities to investigate resistance to flow over complex morphologies. The Darcy-Weisbach, Chézy and Manning equations are the most widely used empirical equations for the calculation of flow velocity in runoff and erosion models. These equations rest on analyses originally developed for one-dimensional pipe flows and assume conditions which are not met by overland flows. The following assumptions are brought into question: flow can be described as uniform; flow is parallel to the surface; flow is of a constant width and the boundary to the flow is longitudinally uniform; grain roughness is homogeneous over the wetted perimeter and can be considered as random; form roughness and other sources of flow resistance can be ignored; resistance is independent of flow depth; and resistance can be modelled as a function of the Reynolds number. A greater appreciation of the processes contributing to resistance to overland flows must be developed. This paper also presents a brief history of the development of flow resistance equations.