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Problem 4.82
[Difficulty: 2]
R
x
y
x
CS
c
d
Given:
Water flow through orifice plate
Find:
Force to hold plate
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
⋅
ρ
V
2
2
A
2
⋅
V
1
2
A
1
⋅
−
⎛
⎝
⎞
⎠
⋅
+
=
From continuity
QV
1
A
1
⋅
=
V
2
A
2
⋅
=
so
V
1
Q
A
1
=
20
ft
3
s
⋅
4
π
1
3
ft
⋅
⎛
⎝
⎞
⎠
2
⋅
×
=
229
ft
s
⋅
=
and
V
2
V
1
A
1
A
2
⋅
=
V
1
D
d
⎛
⎝
⎞
⎠
2
⋅
=
229
ft
s
⋅
4
1.5
⎛
⎝
⎞
⎠
2
×
=
1628
ft
s
⋅
=
NOTE: problem has an error: Flow rate should be 2 ft
3
/s not 20 ft
3
/s!
We will provide answers to both
Hence
R
x
200
−
lbf
in
2
⋅
π
4in
⋅
2
⋅
4
×
1.94
slug
ft
3
⋅
1628
ft
s
⋅
⎛
⎝
⎞
⎠
2
π
1.5 in
⋅
2
⋅
4
×
229
ft
s
⋅
⎛
⎝
⎞
⎠
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 Fall '07
 Lear
 Fluid Mechanics, Flux

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