A theory of the pressure distribution in powder in equilibrium in a cylindrical vessel

A mathematical analysis of the distribution of pressure (vertical stress) in a powder mass filled in a cylindrical vessel is presented, taking into account the variation of pressure with the distance from the axis of the cylinder. The free surface of the powder mass is assumed to be even. It is assumed that vertical stress and horizontal stress are interrelated by Rankine's law. From the equilibrium condition of the powder mass a fundamental equation has been derived to determine the pressure as a function of both the depth and the distance from the axis of the cylinder. A solution satisfying the boundary condition at the free surface has been obtained. It contains a number of indeterminate constants and is reduced to Janssen's formula, provided that the pressure is independent of the distance from the axis of the cylinder. It is shown that our theory agrees fairly well with the experimental data of Yoshioka .