Environmental Engineering Reference
In-Depth Information
6 Conclusions
In this work we have studied experimentally the problem of the mass flow rate of
granular material through circular orifices on vertical side walls of bins as a small
step toward understanding grains flowability. We have shown that friction (the angle
of repose) plays an essential role in all these cases through the existence of a limit
of flowability. In a first case, we have studied, simultaneously, the dependence of
m
on the diameter of the orifice, the grain's diameter and the wall thickness by using,
well characterized, round grains of mustard and tapioca. Experiments show that the
excluded volume effect occurs for big grains through the term
2
. Thus
the estimation of the mass flow rate for holes on side walls satisfies, very accurately,
the formula
m
=
5
/
(
D
−
kd
g
)
g
1
/
2
5
/
2
c
ˁ
(
D
−
kd
)
[
arctan
(
D
/
w
)
−
ʸ
r
]
, where in our experiments
the dimensionless discharge coefficient has the value
c
0.1, when the cgs units
are used. Thus, we believe that Eq. (
4
) is a general formula valid in a wide range of
practical configurations.
In a second case we have studied experimentally the problem of the mass flow
rate of granular material through circular orifices in tilted bins. Our new correla-
tion Eq. (
7
) takes into account the wall thickness which other models consider as
obvious (Franklin and Johanson
1955
; Sheldon and Durian
2010
;Liu
2014
). Con-
sequently, we have proposed a new correlation that predicts the value for which the
flow is arrested
∼
ʲ
∗
=−
(ʱ
−
ʸ
r
)
, and it reduces to Eq. (
9
) when
ʲ
=
0. Moreover,
the current model is correct up to a value close to
2. The theory fits pretty well
the experimental data for a wide range of cases. Finally, we hope the new predic-
tions of our modified Janssen model of pressures and traction can be experimentally
corroborated soon.
ˀ/
Acknowledgments
Authors wish to thank the support by Facultad de Ciencias UNAM and by SIP
IPN through the project 20141404.
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