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Problem 4.134
[Difficulty: 3]
CS
(moves to
left at speed
V
c
)
y
x
c
d
R
x
V
j
+ V
c
V
j
+ V
c
t
R
Given:
Water jet striking moving cone
Find:
Thickness of jet sheet; Force needed to move cone
Solution:
Basic equations: Mass conservation; Momentum flux in x direction
Assumptions:
1) Steady flow
2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow 5) Jet relative velocity is
constant
Then
ρ
−
V
1
⋅
A
1
⋅
ρ
V
2
⋅
A
2
⋅
+
0
=
ρ
−
V
j
V
c
+
()
⋅
π
D
j
2
⋅
4
⋅
ρ
V
j
V
c
+
⋅
2
⋅
π
⋅
R
⋅
t
⋅
+
0
=
(Refer to sketch)
Hence
t
D
j
2
8R
⋅
=
t
1
8
4in
⋅
2
×
1
9in
⋅
×
=
t
0.222 in
⋅
=
Using relative velocities, x momentum is
R
x
u
1
ρ
−
V
1
⋅
A
1
⋅
⋅
u
2
ρ
V
2
⋅
A
2
⋅
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 Fall '07
 Lear
 Fluid Mechanics, Flux

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