Differential equation for the flow rate of discharging silos based on energy balance

Abstract

Since the early work of Hagen in 1852 and Beverloo et al. in 1961, the flow rate of granular material discharging through a circular orifice from a silo has been described by means of dimensional analysis and experimental fits, and explained through the "free fall arch" model. Here, in contrast with the traditional approach, we derive a differential equation based on the energy balance of the system. This equation is consistent with the well known Beverloo rule thanks to a compensation of energy terms. Moreover, this new equation can be used to explore new conditions for silo discharges. In particular, we show how the effect of friction on the flow rate can be predicted. The theory is validated using discrete element method simulations.

arXiv comment11 pages, 8 figures

References in corpus (8)

• Rheophysics of dense granular materials : Discrete simulation of plane shear flows
• The granular silo as a continuum plastic flow: the hour-glass vs the clepsydra
• Pressure and Motion of Dry Sand -- Translation of Hagen's Paper from 1852
• Rheology of sediment transported by a laminar flow
• Granular discharge rate for submerged hoppers
• Forced flow of granular media: Breakdown of the Beverloo scaling
• Velocity profiles in forced silo discharges
• A differential equation for the flow rate during silo discharge: Beyond the Beverloo rule

Cited by in corpus (6)

• Flow in an hourglass: particle friction and stiffness matter
• Silo discharge of mixtures of soft and rigid grains
• External pressure dependence of Granular Orifice Flow: transition to Beverloo flow
• Collisional regime during the discharge of a 2D silo
• Flow rate from a vertical silo with a tilted orifice
• Average outpouring velocity and flow rate of grains discharged from a tilted quasi-2D silo