Analytical approach of funnel flow discharge

Abstract

Design engineers often encounter problems because of the special mechanical behavior of granular materials. Such a typical problem is predicting discharge rate of silos and hoppers. This important design parameter must be known during the development of material transport devices attached to the container, but the calculation of this parameter may be challenging because well-known theories of hydrodynamics are not applicable. Several models are formed to evaluate discharge rate of silos, although most of them based on experimental observations are unable to explain physics of particle outflow. Oldal’s theory accounts for granular discharge of funnel flow, cylindrical silos with formation, and collapse of unstable arches above the orifice. It is applied to rectangular hoppers in this paper to generalize and prove this theory. An extended equation is derived by applying the original hypothesis that is validated using laboratory experiments and numerical simulations.