Theory of Sand Filtration

A set of nonlinear partial differential equations with dimensionless variables, for filtration of dilute unisized suspension in water through homogeneous sand beds under constant rates of vertically downward flow, is presented. The equations describe the space-time variation of suspension concentration and specific deposit in a filter medium. An expression for dimensionless filter coefficient relating all physical variables of filtration is obtained by dimensional analysis. Solutions of the equations were obtained with the aid of a digital computer using the finite difference method. The analytically determined suspension concentrations at different time intervals and depths of bed agreed adequately with the experimental values. An equation relating head loss per unit depth and specific deposit within the filter bed is derived and the validity of the proposed equation is verified with the experimental head loss data.