Flow resistance in open channels with fixed movable bed

In spite of an increasingly large body of research by many investigators, accurate quantitative prediction of open channel flow resistance remains a challenge. In general, the relations between the elements influencing resistance (turbulence, boundary roughness, and channel shape features, such as discrete obstacles, bars, channel curvature, recirculation areas, secondary circulation, etc.) and mean flow variables are complex and poorly understood. This has resulted in numerous approaches to compute friction using many and diverse variables and equally diverse prescriptions for their use. In this paper, a new resistance law for surface (grain) resistance, the resistance due to the flow viscous effects on the channel boundary roughness elements, is presented for the cases of flow in the transition (5 < Re* <70) and fully rough (Re* ≥ 70) turbulent flow regimes, where Re* is the Reynolds number based on shear velocity and sediment particle mean diameter. It is shown that the new law is sensitive to bed movement without requiring previous knowledge of sediment transport conditions. Comparisons between computation and measurements, as well as comparisons with other well-known existing roughness predictors, are presented to demonstrate its accuracy and range of application. It is shown that the method accurately predicts total friction losses in channels and natural rivers with plane beds, regardless of sediment transport conditions. This work is useful to hydraulic engineers involved with the derivation of depth-discharge relations in open channel flow and with the estimation of sediment transport rates for the case of bedload transport.