Flow resistance equations for gravel-and boulder-bed streams

Ferguson, R.I.

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.

Citation

Ferguson, R. (2007). Flow resistance equations for gravel-and boulder-bed streams. Water Resources Research, 43(5), Article W05427. https://doi.org/10.1029/2006wr005422

• Journal Article Type: Article
• Publication Date: May 22, 2007
• Deposit Date: Oct 6, 2008
• Publicly Available Date: Mar 24, 2010
• Journal: Water Resources Research
• Print ISSN: 0043-1397
• Electronic ISSN: 1944-7973
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 43
• Issue: 5
• Article Number: W05427
• DOI: https://doi.org/10.1029/2006wr005422