A Study on the Two-Dimensional Distribution of Pressure in Powder Filled in a Cylindrical Vessel

Abstract

Hereunder is presented a theory of two-dimensional distribution of the equilibrium pressure in powder filled in a cylindrical vessel. This problem was treated by Janssen and Lvin, respectively. Janssen assumed the vertical stress to be constant over a horizontal plane, while Lvin assumed it to be non-uniform. The latter author applied an ultimate equilibrium condition of stresses to the volume element of ring-shape in the powder mass, and arrived at the curious conclusion that the stress was always zero on the axis of the cylinder.
In this paper, we derive an equation of two-dimensional pressure distribution in powder on a r-h plane in a cylindrical vessel at equilibrium. The equation is solved with a boundary condition that the pressure at the free surface is zero. The solution indicates the existence of two regions, one including the free surface and the other including the axis of the cylinder. In the first region, the pressure increases with the distance from the free surface of the powder system. In the second region, the pressure changes with both the depth and the distance from the axis of the cylinder.