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Problem *4.124
[Difficulty: 5]
Given:
Plates coming together
Find:
Expression for velcoity field; exit velocity; plot
Solution:
Apply continuity using deformable CV as shown
Basic equation:
= 0
Assumptions: Incompressible, uniform flow
Given data:
V
0
0.01
m
s
⋅
=
h
0
2mm
⋅
=
R
100 mm
⋅
=
Continuity becomes
or
t
π
r
2
⋅
h
⋅
()
∂
∂
V2
⋅
π
⋅
r
⋅
h
⋅
+
0
=
π
r
2
⋅
dh
dt
⋅
⋅
π
⋅
r
⋅
h
⋅
+
π
r
2
⋅
V
0
⋅
⋅
π
⋅
r
⋅
h
⋅
+
=
0
=
Hence
Vr
V
0
r
2h
⋅
⋅
=
If V
0
is constant
hh
0
V
0
t
⋅
−
=
so
Vrt
,
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 Fall '07
 Lear
 Fluid Mechanics

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