The hydraulic resistance of sand streambeds under steady flow conditions

Abstract

Laboratory and river data has been analyzed in terms of applied power principles to determine the relationships between absolute roughness and bed deformation under steady state sediment transport conditions. It has been found that the full spectrum of bed conditions can be represented by simple relationships within a single system. As the bed forms grow, the unit stream power being applied along the bed decreases. The process of deformation continues until equilibrium is reached. Dynamic equilibrium is reached with the average rate of deposition of particles equal to the rate of re-suspension. By expressing the applied power in terms of the size of the boundary eddies i.e. the bed form sizes and comparing this with the power required to suspend the sediment particles, the link is obtained between absolute roughness and particle characteristics. Transition from lower regime conditions to upper regime conditions is initiated when the applied (laminar) power along the bed becomes greater than that which is required to maintain turbulent flow. Flow along the bed becomes fully turbulent, the (large) bed forms are rapidly broken down and fully turbulent conditions prevail until the applied turbulent power again becomes greater than that which is required for a laminar boundary layer. From this point onwards upper regime bed forms develop and equilibrium is again reached when the eddies that fit in with the bed forms grow large enough for the rate of entrainment of particles to be equal to the rate of deposition. A single diagram has been developed for determining flow resistance under all flow conditions as well as for identifying bedform types.