Settlement of Solid Particles in Open-Channel Flow

The boundary condition at the bed is assumed so that the particles coming to the bed are deposited there so that there is no particle entrainment from the bed into the flow. The boundary condition at the free surface is such that there is no net transport of particles across the free surface. The initial condition is assumed as an instantaneous plane source. The problem is formulated in the Eulerian sense and then Aris moment transformations are employed. The following quantities are analytically predicted: (1)The vertical distribution and the fraction of particles retained in suspension; (2)the probability density function of the duration of the retention period of particles in suspension and the mean retention period; and (3)following the hypothesis that the distribution of deposited particles follows an exponential function with increasing time, the mean and the variance of settling length of particles.