Modified Manning formula for flow in alluvial channels with sand-beds

A new velocity formula, in the form of a modified Manning equation, is proposed for flow prediction in alluvial channels. The study shows that the flow resistance complies with a single law in the lower flow regimes for I < theta/theta(cr) < 250, where theta is the Shields parameter and theta(cr) is its critical value. When 7.5 < theta/theta(cr) < 250, the upper and lower regimes follow different resistance laws. A new criterion to demarcate the upper and lower regimes is proposed. The method is direct and involves input parameters that are readily available, in practice. The main advantage of this method is that we need not know the velocity or flow depth a priori once the flow discharge is, known. The new velocity formula is used in conjunction with these resistance laws and it incorporates directly the bed geometry on flow resistance. The validity of the formula is tested with 4824 sets of flume and field data covering the entire flow regimes. The computed and measured velocities are in good agreement where the mean normalized error and standard deviation for the predicted velocities are 10.6% and 9.6%, respectively.