Problem 4.77
[Difficulty: 2]
R
x
y
x
CS
c
d
Given:
Water flow through elbow
Find:
Force to hold elbow
Solution:
Basic equation: Momentum flux in x direction for the elbow
Assumptions:
1) Steady flow
2) Incompressible flow 3) Uniform flow
Hence
R
x
p
1g
A
1
⋅
+
p
2g
A
2
⋅
+
V
1
ρ
−
V
1
⋅
A
1
⋅
()
⋅
V
2
ρ
V
2
⋅
A
2
⋅
⋅
−
=
R
x
p
1g
−
A
1
⋅
p
2g
A
2
⋅
−
ρ
V
1
2
A
1
⋅
V
2
2
A
2
⋅
+
⎛
⎝
⎞
⎠
⋅
−
=
From continuity
V
2
A
2
⋅
V
1
A
1
⋅
=
so
V
2
V
1
A
1
A
2
⋅
=
V
1
D
1
D
2
⎛
⎜
⎝
⎞
⎠
2
⋅
=
V
2
0.8
m
s
⋅
0.2
0.04
⎛
⎝
⎞
⎠
2
⋅
=
V
2
20
m
s
⋅
=
Hence
R
x
350
−
10
3
×
N
m
2
⋅
π
0.2 m
⋅
2
⋅
4
×
75
10
3
×
N
m
2
⋅
π
0.04 m
⋅
2
⋅
4
×
−
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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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