Biomedical Engineering Reference
In-Depth Information
Example 12.1
Find the wall stress at the bottom of a large silo, 4.0 m in diameter and 20 m in
height, that uses a flat bottom for its discharge. Compare the stress when the silo
is filled with wood chips (bulk density 300 kg/m
3
) with that when it is filled with
water.
Given that the wall-to-wood chip friction coefficient, k
f
, is 0.37, assume the
Janssen coefficient, K, to be 0.4.
Solution
We use
Eq. (12.8)
to calculate the vertical pressure, P
0
, in the silo. Data given
are as follows:
b
is 300 kg/m
3
.
The bulk density of the wood chips,
ρ
The wall
solid friction coefficient, k
f
, is 0.37.
The diameter, D, is 4.0 m.
The height, H,is20m.
The Janssen coefficient, K, is 0.4.
0
@
0
@
1
A
1
A
5
ρ
Dg
4k
f
K
4Hk
f
K
D
P
0
1
exp
2
2
2
4
0
@
1
A
3
5
5
300
4
9
:
81
4
20
0
:
37
0
:
4
3
3
3
3
3
5
1
2
exp
2
18
;
854 Pa
4
0
:
37
0
:
4
4
3
3
Since the lateral pressure, P
w
, is proportional to the vertical pressure, P
v
,
P
w
7542 Pa
For water, the vertical pressure is the weight of the liquid column:
P
0
KP
0
0
:
4
18
;
854
5
5
3
5
gH
Because the lateral and vertical pressures are the same (i.e., K
5
ρ
5
1.0), we can
write:
200 Pa
The lateral pressure for water is therefore (196,200/7542) or 26 times greater
than that for wood chips.
P
w
P
0
1000
9
:
81
20
196
;
5
5
3
3
5
12.3.2.7 Chute Design
In a silo, the solids are withdrawn through chutes at the bottom. Previous
discussions examined solids flow through the silo. Now, we will look at the
flow out of the silo through the chute, which connects the silo to the feeder.
A proper chute design ensures uninterrupted flow from storage to feeder.
Improper design results in nonuniform flow.
Figure 12.9
illustrates the prob-
lem, showing partial solids flow with a uniform-area chute and full solids
flow with a properly designed chute. As the solids accumulate on the belt,
their uniform flow through the hopper prevents them from accumulating at
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