Rheologica Acta

, Volume 4, Issue 3, pp 218–225

# A theoretical equation for the flow of granular solids from a hopper

• I. R. McDougall
• A. C. Evans
Originals

## Summary

Failure in shear is responsible for the inception of flow in granular solids but once the particles cease to be in contact with each other the concept of shear has little validity and there is more resemblance to the flow of a fluid. Applied to the flow of cohesion-free material from a horizontal aperture at the base of a hopper, these ideas are shown to lead to a relatively simple means of calculating a pseudo-pressure at the base of the hopper, which can be substituted into a pressure-drop relationship of theBernouilli type to give a theoretical equation for the flow rate from the aperture.

The derivation depends essentially on the treatment of the moving solids as a fluid, and on the existence of an “active” condition in the material at the moment when movement commences. Both of these concepts are examined in detail. The theoretical flow equation is shown to fit in well with published correlations.

## Keywords

Polymer Flow Equation Theoretical Equation Granular Solid Theoretical Flow
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Nomenclature

A

area of hopper or cylinder base

A0

area of orifice

Dc

diameter of hopper or cylinder

D0

diameter of orifice

F

frictional work term

G

solids mass flow rate

g

gravitational acceleration

k

a constant

L

lateral force

n

an exponent

P

fluid pressure

R

normal force

t, t′

tangent of angle

U

perimeter of hopper or cylinder

v

linear velocity

W

weight of solids

x

potential energy term

z

height of solids fill in container

δ

infinitesimal thickness

θ

angle of maximum shear stress

μ

coefficient of internal friction of solids = tangent of drained angle of repose

μ′

coefficient of friction between solids and bunker wall

ϱ

fluid density

ϱB

bulk density of solids

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