A frictional-kinetic model for the flow of granular materials through a wedge-shaped hopper

A quasi-one-dimensional model is used to examine the steady flow of granular materials through a wedge-shaped hopper with smooth, steep walls. Hybrid frictional-kinetic equations are used in an attempt to overcome some of the dificulties faced by earlier works, which were based on frictional equations. Owing to computational difficulties, two different solution procedures are used: (i) in the upper region, where frictional effects dominate, and (ii) the lower region which includes the exit slot and a part of the particle jet below the hopper, where kinetic and frictional effects are expected to be comparable. The equations are integrated numerically in (i). In (ii), they are linearized, and a semi-analytical solution is constructed. In contrast to the works of Kaza & Jackson (1982a) and Prakash & Rao (1991), the density varies smoothly across the exit slot. The density profile is qualitatively similar to the data of Fickie, Mehrabi & Jackson (1989). However, the range of density variation is much smaller than that observed. Owing to the approximations used, and perhaps also to the form of the kinetic constitutive equations, kinetic effects are dominated by frictional effects, except close to the downstream boundary