| Description |
This paper is an extract from a Ph.D. thesis written by Johanson in the Department of Mechanical Engineering, College of Engineering, University of Utah; it follows earlier publications by Jenike [e.g. 1,5]. The purpose of the work has been to develop a mathematical theory of flow of bulk solids. The term 'bulk solids' encompasses both frictiona (granular) and cohesive materials, and specifically describes such solids as ore, coal, concentrates, chemicals, flour, sugar. While there exist papers describing the behavior of these solids in bins and hoppers, the authors believe that this is the first time that stress and velocity fields have been computed mathematically for steady flow in converging channels under the action of gravitational forces. The method used in this paper is based on the concepts of soil mechanics and plasticity adapted by Jenike and Shield [3] to permit the steady flow of frictional solids. In Chapter I the applicable features of the theory of steady state flow are stated. The solution of the general problem of stress and velocity fields for plane strain and axial symmetry requires the solution of two systems, each comprising two hyperbolic differential equations In Chapter II the differential equations are transformed into difference equations in preparation for the numerical work which follows in Chapter IV. Types of possible boundary conditions are considered and the difference equations are adapted to those types. Useful combinations of boundary conditions are then described. A particular solution, called the radial stress field, is described in Chapter III. This solution applies to converging channels with straight walls and has been treated at length in reference 5. In this paper experimental observations are given to substantiate the existence of such fields. Certain cases of more general boundary conditions are computed and observed in Chapter IV. They substantiate the existence of radial stress fields and verify experimentally the physical assumptions made in the derivation of the theory. |
