An approximate theory for pressures and arching in hoppers

Abstract A simple theory is developed which yields the approximate stresses within a granular material or powder flowing in hopper systems and gives the critical factors which ensure continued gravity flow. The stress fields during mass flow have been derived by consideration of the forces acting on elemental slices which are simultaneously yielding within themselves and along the hopper walls. Like Jenike, who has given an exact stress solution for hopper outlets only, when considering arching it is assumed that the powder strength is a function only of the local stresses that prevailed during the preceeding flow. Allowance has now been made, however, for the effect of the limited vertical shear stress that can be developed near a steep smooth wall on potential arch span. Consequently, the ideal hopper, designed from the material strength—stress characteristics is likely to have steep smooth walls which get steeper towards the outlet.