Steady Gravity Flow of Frictional-Cohesive Solids in Converging Channels

Frictional-cohesive solids such as soil, ores, chemicals, sugar, flour are regarded as plastic and represented by the Jenike-Shield yield function [1] during steady flow. The stress-strain rate relations are based on isotropy, continuity, and a one-to-one dependence of density on the major pressure. In plane strain and in axial symmetry the stress field requires the solution of a system of two hyperbolic partial differential equations. The velocity field can then be computed by solving another system of two linear homogeneous partial differential equations of the hyperbolic type. In straight conical channels, a particular stress field called the “radial stress field” assumes a special importance because evidence has been presented elsewhere that all general fields tend to approach the radial stress fields in the vicinity of the vertex. Examples of numerical solutions of radial stress fields are given.