Environmental Engineering Reference
In-Depth Information
Fig. 4 Plot of height as a
time function. We assumed
that the initial level of the
column is at z
0cm.From
these data we estimate that
the granular column it is
reduced at a mean velocity
ʽ =
=
0
.
47 cm
/
s
similar, we use the same criterion to estimate the mass flow rate in the L-valve, so
the mass flow rate m LV
in an L-valve with gravity flow, must be
am sp arctan D
ʸ r
m LV =
am sp ʸ r ) =
,
(1)
w
where a is the discharge coefficient, m sp is the mass flow rate from a standpipe, only
due to the gravity action, which obeys the relation
m sp =
1
/
2 D 5 / 2
c
ˁ b g
.
(2)
In Eq. ( 2 ), c is other discharge parameter (related only to the standpipe),
ˁ
b is
the bulk density and
ʸ r is the angle of repose of the granular material. The relation
( 2 ) was regarded as valid by Kesava and Nott ( 2008 ) to estimate the flow rate from
vertical, circular pipes and it is known as the Hagen's law (Medina et al. 2013 ).
In the next section we performed experiments to show that Eqs. ( 1 ) and ( 2 )are
correct.
3 Experiments
Initially, we did experiments to measure m sp , the mass flow rate from vertical pipes,
in order to check if Eq. ( 2 ) is valid. We performed experiments by using beach
sand (composed of irregular grains of mean diameter d
=
0
.
03 cm, bulk density
cm 3 and angle of repose
33 ±
5 =
ˁ b
008 rad
(other properties of this material were reported elsewhere: Medina et al. 2014 ).
=
1
.
5
±
0
.
01 g
/
ʸ
r
=
0
.
0
.
57
±
0
.
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