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Problem 9.46
[3]
Given:
Pattern of flat plates
Find:
Drag on separate and composite plates
Solution:
Basic equations:
c
f
τ
w
1
2
ρ
⋅
U
2
⋅
=
c
f
0.730
Re
x
=
For separate plates
L
7.5 cm
⋅
=
W
7.5 cm
⋅
=
U1
m
s
⋅
=
From Table A.8 at 20
o
C
ν
1.01
10
6
−
×
m
2
s
⋅
=
ρ
998
kg
m
3
⋅
=
First determine the nature of the boundary layer
Re
L
UL
⋅
ν
=
Re
L
7.43
10
4
×
=
so definitely laminar
The drag (one side) is
F
D
A
τ
w
⌠
⎮
⎮
⌡
d
=
F
D
0
L
x
τ
w
W
⋅
⌠
⎮
⌡
d
=
We also have
τ
w
c
f
1
2
⋅
ρ
⋅
U
2
⋅
=
1
2
ρ
⋅
U
2
⋅
0.730
Re
x
⋅
=
Hence
F
D
1
2
ρ
⋅
U
2
⋅
W
⋅
0
L
x
0.730
Ux
⋅
ν
⌠
⎮
⎮
⎮
⌡
d
⋅
=
0.730
2
ρ
⋅
U
3
2
⋅
W
⋅
ν
⋅
0
L
x
x
1
2
−
⌠
⎮
⎮
⌡
d
⋅
=
The integral is
0
L
x
x
1
2
−
⌠
⎮
⎮
⌡
d2
L
1
2
⋅
=
so
F
D
0.730
ρ
⋅
W
⋅
ν
L
⋅
U
3
⋅
⋅
=
F
D
0.0150N
=
This is the drag on one plate.
The total drag is then
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This note was uploaded on 08/25/2011 for the course AME 331 taught by Professor Zohar during the Fall '08 term at University of Arizona Tucson.
 Fall '08
 ZOHAR

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