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Problem 4.58
[Difficulty: 3]
Given:
Data on flow through a control surface
Find:
Net rate of momentum flux
Solution:
∫
⋅
CS
dA
V
V
r
r
ρ
Basic equation: We need to evaluate
Assumptions:
1) Uniform flow at each section
From Problem 4.24
V
1
10
ft
s
⋅
=
A
1
0.5 ft
2
⋅
=
V
2
20
ft
s
⋅
=
A
2
0.1 ft
2
⋅
=
A
3
0.6 ft
2
⋅
=
V
3
5
ft
s
⋅
=
It is an outlet
()
(
)
() ()
[]
j
A
V
A
V
i
A
V
A
V
A
V
j
V
i
V
A
V
j
V
A
V
i
V
A
V
j
V
i
V
A
V
j
V
A
V
i
V
A
V
V
A
V
V
A
V
V
dA
V
V
CS
ˆ
60
cos
ˆ
60
sin
ˆ
60
cos
ˆ
60
sin
ˆ
ˆ
ˆ
60
cos
ˆ
60
sin
ˆ
ˆ
3
2
3
2
2
2
3
2
3
1
2
1
3
3
3
3
2
2
2
1
1
1
3
3
3
3
2
2
2
1
1
1
3
3
3
2
2
2
1
1
1
−
+
+
−
=
−
+
+
−
=
⋅
−
+
⋅
+
⋅
=
⋅
+
⋅
+
⋅
=
⋅
∫
r
r
r
r
r
r
r
r
r
r
r
r
r
r
r
r
r
Then for the control surface
=
+
−
60
sin
3
2
3
1
2
1
A
V
A
V
Hence the x component is
65
lbm
ft
3
⋅
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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, Flux

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