# Forced flow of granular media: Breakdown of the Beverloo scaling

## TL;DR

This paper investigates how high-rate work input affects granular flow through orifices, revealing the breakdown of Beverloo scaling and identifying a new universal relation involving dissipated power.

## Contribution

It demonstrates the loss of Beverloo scaling under forced conditions and introduces a universal relation based on dissipated power and flow rate explained by $(I)$ rheology.

## Key findings

- Flow rate increases with applied pressure during discharge.
- Universal relation between dissipated power and flow rate emerges.
- Beverloo scaling breaks down under high work conditions.

## Abstract

The Beverloo scaling for the gravity flow of granular materials through orifices has two distinct universal features. On the one hand, the flow rate is independent of the height of the granular column. On the other hand, less well-known yet more striking, the flow rate is fairly insensitive to the material properties of the grains (density, Young's modulus, friction coefficient, etc.). We show that both universal features are lost if work is done on the system at a high rate. In contrast to viscous fluids, the flow rate increases during discharge if a constant pressure is applied to the free surface of a granular column. Moreover, the flow rate becomes sensitive to the material properties. Nevertheless, a new universal feature emerges: the dissipated power scaled by the mean pressure and the flow rate follows a master curve for forced and unforced conditions and for all material properties studied. We show that this feature can be explained if the granular flow in the silo is assumed to be a quasistatic shear flow under the $\mu(I)$-rheology.