Flows from Bins: New Results - Selected Topics of Computational and Experimental Fluid Mechanics - page 161

from orifices on side walls has been largely neglected and, to our knowledge, only a
few works have been published (Bagrintsev and Koshkovskii 1977 ; Davies and Foye
1991 ; Davies and Desai 2008 ; Franklin and Johanson 1950; Sheldon and Durian
2010 ; Medina et al. 2013 , 2014 ), perhaps due to the asymmetric flow profile which
occurs close to the vertical wall. Despite it, the practical use of lateral outlets is also
very frequent, for instance, in household silos.
In their seminal papers on the flow of granular solids through circular orifices at
the bottom of silos, (Hagen 1852 , see Fig. 7 ) and more than a century later, Beverloo
et al. ( 1961 ) reported that the most suitable correlation to predict the mass flow
rates, m 0 , from bottom exits in open-top bins, silos and hoppers is the so called
Hagen-Beverloo correlation, which has the form

m 0 = g 1 / 2

5 / 2

c ˁ ( D − kd ) , (1)

where c is the dimensionless discharge coefficient, is the bulk density of the granular

material, g is the acceleration of gravity, k is a dimensionless constant with typical
values k

ˁ

2 (Brown and Richards 1970 ; Beverloo et al. 1961 ; Wieghart 1975)
and d is the mean grain diameter.
Equation ( 1 ) expresses that the mass flow rate, when grains are big, is reduced due
to the effect of excluded volume. Conversely, when D

∼ 1 −

d the term ( D − kd ) ₒ D

and thus the mass flow rate increases and does not involves the grain diameter.
On the other hand, despite the enormous utility of the granular flow on the side
walls only a few studies have been conducted to test the validity of the Hagen-
Beverloo correlation in such a configuration (Bagrintsev and Koshkovskii 1977 ;
Davies and Foye 1991 ; Davies and Desai 2008 ; Franklin and Johanson 1950; Sheldon
and Durian 2010 ).
Recently, in a couple of works (Medina et al. 2013 , 2014 ), we derived a formula
for themass flow rate through orifices on sidewalls, m , that embraces the dependence
on the orifice diameter D and the wall thickness w for granular solids in the limit

Fig. 7 G.H.L. Hagen ( http://en.wikipedia.org/wiki/Gotthilf_Hagen )