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The resistance to uniform flow in straight gravel-bed rivers is basically dependent on the flow geometry, the cross-sectional variation in roughness heights, and the roughness height of the graded gravel bed sediment. The effect of these factors on the resistance to flow is evaluated and a general approach for the estimation of the Darcy-Weisbach friction factor is presented. Independent field data indicates that the method can be successfully applied to predict the resistance to uniform flow in gravel-bed rivers.
Richard D. Hey (1979) studied this question.