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Flow resistance equations for gravel-and boulder-bed streams.

Ferguson, R. I. (2007) 'Flow resistance equations for gravel-and boulder-bed streams.', Water resources research., 43 (5). W05427.


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.

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Publisher statement:Ferguson, R. I, (2007), 'Flow resistance equations for gravel-and boulder-bed streams', Water resources research, 43, 5, W05427, 10.1029/2006WR005422 (DOI). To view the published open abstract, go to and enter the DOI.
Date accepted:No date available
Date deposited:24 March 2010
Date of first online publication:May 2007
Date first made open access:No date available

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