The gravity-driven flux of particles through an aperture

The discharge of granular materials from a silo is a key mechanism in the handling and processing of powders and grains. The mass flux of grains exiting through the aperture is commonly described by the Beverloo's correlation, which seemingly captures the role of the aperture and particle sizes. Despite its ubiquitous usage, systematic experiments verifying this relation have mainly been conducted for a limited range of parameters. Here, we conduct a large number of discharge experiments varying the particle- and the aperture sizes and shapes. The results are rationalized through a Froude number, which compares the observed drainage to jet of grains in free fall. We develop an expression for the flux, linking the particle size and the hydraulic diameter of the aperture. When the opening is much larger than an individual grain, the measured discharge can be predicted without the need for any constants. This framework is extended to the case where inter-particle cohesion is present and verified through experiments with different types of cohesion and various amounts of stickiness.