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Problem 5.63
[Difficulty: 3]
We will apply the continuity equation to the control volume shown:
Given:
Flow between parallel disks through porous surface
Find:
a
pz
V
r
r
V
z
V
z
z
V
z
v
0
r
2h
0
v
0
1
z
h
v
0
h
Solution:
a
pz
v
0
2
h
z
h
1
CS
CV
A
d
V
V
d
t
0
Governing
Equations:
(Continuity)
t
V
V
V
Dt
V
D
a
p
(Particle Accleration)
Assumptions:
(1) Steady flow
(2) Incompressible flow
(3) Uniform flow at every section
(4) Velocity in
θ
direction is zero
Based on the above assumptions the continuity equation reduces to:
0
ρ
v
0
π
r
2
ρ
V
r
2
π
r
h
Solving for Vr:
V
r
v
0
r
We apply the differential form of continuity to find
V
z
1
r
r
rV
r
z
V
z
0
1
r
r
r
v
0
h
z
V
z
Therefore:
V
z
z
v
0
h
d
fr
()
v
0
z
h
Now at z = 0:
V
z
v
0
Therefore we can solve for f(r):
v
0
v
0
0
h
v
0
So we find that the zcomponent of velocity is:
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.
 Fall '07
 Lear
 Fluid Mechanics

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