Environmental Engineering Reference
In-Depth Information
Fig. 11
Plot of the experimental mass flow rates through holes on side walls,
m
, as a function
of
ˁ
g
1
/
2
5
/
2
(
D
−
kd
)
[
ʱ
−
ʸ
r
]
.
The linear fit given by Eq. (
4
)yields
c
=
0
.
13 for mustard and (a)
c
=
.
0
15 for tapioca (b). Error bars are of 4%
m
0
. This procedure allows us to find that
m
0
∼
ˁ
g
1
/
2
5
/
2
for both types of
(
D
−
kd
)
grains. Moreover, we have found that
k
1 for tapioca.
Plots of the mass flow rates measured for holes on the side walls,
m
, as a function
=
1
.
5 for mustard and
k
=
g
1
/
2
5
/
2
of
show that the experimental data for both
granular materials were well fitted by straight lines (see Fig.
11
). So, the best relation
that fits the experimental data has the form
ˁ
(
D
−
kd
)
,
[
arctan
(
D
/
w
)
−
ʸ
r
]
m
=
g
1
/
2
5
/
2
ˁ
(
−
)
[
(
/
)
−
ʸ
r
]
,
c
D
kd
arctan
D
w
(4)
where the dimensionless discharge coefficient
c
has the value
c
=
0
.
13 for mustard
and
c
15 for tapioca.
From these results, we can establish that Eq. (
4
) is a generalized Hagen-Beverloo
law for the mass flow rate of holes on the side walls. Incidentally, by employing the
several values of
D
used in the experiments with mustard and tapioca and using their
respective angles of repose, we have verified that relation (
4
) predicts very accurately
the thicknesses of the walls for which the outflow will be arrested.
=
0
.
4 Tilted Bins
4.1 The Problem
Here we report a series of experiments of the discharge for tilted bins. Bins with
orifices in a side face of a rectangular acrylic-box were gradually inclined from the
horizontal position up to the position where the granular flow is arrested in order to
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