Grain-size distribution in open channel flow by mixing length approach

A mathematical model is developed by theoretical analysis for predicting the grain-size distribution in suspension over sand and sand-gravel beds. By including the viscous shear stress of sediment-fluid mixture and the Reynolds shear stress in terms of mixing length of sediment-mixed fluid, a system of integrodifferential equations of velocity and suspension concentration is developed. The effect of hindered settling is considered in the settling velocity of sediment particle and the effect of particle-particle interaction is taken into account in the reference level. Apart from this, incipient motion probability, pick-up probability and nonceasing probability of a sediment particle are included in the reference concentration. The proposed system of integrodifferential equations is converted into a system of first-order differential equations, and the fourth-order Runge-Kutta method has been adopted for solving the system of equations. The numerical solution of the proposed system reflects the behavior of fluid velocity and grain-size distribution with changing vertical height over a sediment bed comprising nonuniform grain sizes. The computed values of velocity and grain-size distribution are compared with a limited data set due to the unavailability of sufficient data in literature, and good agreement has been observed between them. The proposed model provides least errors in comparison to the other existing models in literature. Copyright (c) 2014 John Wiley & Sons, Ltd.