Friction Factors for Flow in Sand-Bed Channels

A new predictor is developed for friction factors of flows in sand-bed channels. A dimensional analysis is pursued to obtain the form of the quantities entering the relation between the geometry of the bed features, the flow properties, and the equivalent shear stress due to the form-drag of the ripples, dunes, etc. Theoretical considerations of the bed stability lead to expressions for the length and height of the bed features in terms of the properties of the bed sediment and flow. These are introduced into the expression yielded by the dimensional analysis, and the resulting frictional relation is quantified with field and laboratory data. The graphical relation of Lovera and Kennedy is used to obtain the flat-bed friction factor. The predictor is evaluated using field data not included in preparation of the graphical relation between the bed-form friction factor, Froude number, and relative roughness. The depth-discharge relations predicted are found to be in good agreement with the measured data.