The relationship between the transport of bed load, the formation of dunes, and the hydraulic resistance of alluvial streams is evaluated. The total resistance is caused partly by friction and partly by expansion losses, which may be estimated by Carnot’s formula. Only the frictional part of the total energy is effective in the transport of bed load. The number of dimensionless parameters necessary to characterize a given flow regime is examined and it is argued that, for a given slope and bed material, a definite relationship must exist between the water depth and the bed load parameters. Furthermore, two different rivers with the same slope are similar (with regard to hydraulic roughness) when the Froude number F and bed load parameter θ, are common. It is postulated that two rivers with F and θ’ common are similar even when their slopes differ, but in that case corresponding to the law of models with distorted vertical scale. This leads to a simple relation from which prediction of the stage-discharge relationship is possible.