Problem 4.90
[Difficulty: 2]
R
x
CS
R
y
y
x
Given:
Data on nozzle assembly
Find:
Reaction force
Solution:
Basic equation: Momentum flux in x and y directions
Assumptions:
1) Steady flow
2) Incompressible flow
CV 3) Uniform flow
For x momentum
R
x
V
2
cos
θ
()
⋅
ρ
V
2
⋅
A
2
⋅
⋅
=
ρ
V
2
2
⋅
π
D
2
2
⋅
4
⋅
cos
θ
⋅
=
From continuity
A
1
V
1
⋅
A
2
V
2
⋅
=
V
2
V
1
A
1
A
2
⋅
=
V
1
D
1
D
2
⎛
⎜
⎝
⎞
⎠
2
⋅
=
V
2
2
m
s
⋅
7.5
2.5
⎛
⎝
⎞
⎠
2
×
=
V
2
18
m
s
=
Hence
R
x
1000
kg
m
3
⋅
18
m
s
⋅
⎛
⎝
⎞
⎠
2
×
π
4
×
0.025 m
⋅
2
×
cos 30 deg
⋅
×
Ns
2
⋅
kg m
⋅
×
=
R
x
138 N
⋅
=
For y momentum
R
y
p
1
A
1
⋅
−
W
−
ρ
Vol
⋅
g
⋅
−
V
1
−
ρ
−
V
1
⋅
A
1
⋅
⋅
V
2
sin
θ
⋅
ρ
V
2
⋅
A
2
⋅
⋅
−
=
R
y
p
1
π
D
1
2
⋅
4
⋅
W
+
ρ
Vol
⋅
g
⋅
+
ρπ
⋅
4
V
1
2
D
1
2
⋅
V
2
2
D
2
2
⋅
sin
θ
⋅
−
⎛
⎝
⎞
⎠
⋅
+
=
where
W
4.5 kg
⋅
9.81
×
m
s
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 Fall '07
 Lear
 Fluid Mechanics, Flux

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