Publication details for Professor Rob FergusonFerguson, R.I. (2007). Flow resistance equations for gravel-and boulder-bed streams. Water Resources Research 43(5): W05427.
- Publication type: Journal Article
- ISSN/ISBN: 0043-1397, 1944-7973
- DOI: 10.1029/2006WR005422
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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.