Environmental Engineering Reference
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Fig. 2 Some flow regimes, during operation, in an L-valve. These regimes depend on the intensity
of aeration
2 Gravity Flow: A Simple Model
As can be seen in Fig. 1 a the L-valve has itself an angle. If, it as was noticed by
Knowlton and Hirsan ( 1978 ) and Woodcock and Mason ( 1987 ), that a gravity granu-
lar flow there occurs. It is illustrated in Fig. 3 where three snapshots permit conclude
that a granular column (picture on the left-hand side) cannot be maintained when the
angle of the valve is smaller than
ʸ r . In this case D
=
1
.
90 cm
,
w
=
1
.
25 cm and,
65 =
33 =
consequently,
57 rad.
We have estimated, from data of the snapshots in Fig. 3 , that the granular column
is reduced at a rate
ʱ =
56
.
0
.
98 rad and
ʸ r
=
0
.
ʽ =
0
.
47 cm
/
s; See Fig. 4 .
ʱ ʸ r a gravity flow does not occurs and the granular column
must be maintained. See Fig. 4 .
In recent works on the estimation of the mass flow rate from circular holes in face
walls of bins with thick walls we have shown (Medina et al. 2013 , 2014 ) that the
intensity of the flow must be proportional to
Conversely, if
ʸ r ).
As both problems are very
Fig. 3 Snapshots of an
L-valve with
ʱ =
0
.
98 rad
and
57 rad. This
valve does not maintain the
granular column
ʸ
=
0
.
r
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