Flow resistance equations for gravel‐ and boulder‐bed streams

Abstract

Alternative general forms are considered for equations to predict mean velocity over the full range of relative submergence experienced in gravel‐ and boulder‐bed streams. A partial unification is suggested for some previous semiempirical models and physical concepts. Two new equations are proposed: a nondimensional hydraulic geometry equation with different parameters for deep and shallow flows, and a variable‐power resistance equation that is asymptotic to roughness‐layer formulations for shallow flows and to the Manning‐Strickler approximation of the logarithmic friction law for deep flows. Predictions by existing and new equations using D 84 as roughness scale are compared to a compilation of measured velocities in natural streams at relative submergences from 0.1 to over 30. The variable‐power equation performs as well as the best existing approach, which is a logarithmic law with roughness multiplier. For predicting how a known or assumed discharge is partitioned between depth and velocity, a nondimensional hydraulic geometry approach outperforms equations using relative submergence. Factor‐of‐two prediction errors occur with all approaches because of sensitivity to operational definitions of depth, velocity, and slope, the inadequacy of using a single grain‐size length scale, and the complexity of flow physics in steep shallow streams.