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Problem 4.145
[Difficulty: 4]
CS
(moves at
speed
instantaneous
speed U)
y
x
c
d
Given:
Water jet striking moving vane/cart assembly
Find:
Angle
θ
at t = 5 s; Plot
θ
(t)
Solution:
Basic equation: Momentum flux in x direction for accelerating CV
Assumptions:
1) No changes in CV
2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow 5) Constant jet relative
velocity
Then
M
−
a
rfx
⋅
u
1
ρ
−
V
1
⋅
A
1
⋅
()
⋅
u
2
ρ
V
2
⋅
A
2
⋅
⋅
+
=
VU
−
−
ρ
−
⋅
A
⋅
[]
⋅
−
(
) cos
θ
⋅
ρ
−
⋅
A
⋅
⋅
+
=
M
−
a
rfx
⋅
ρ
−
2
A
⋅
cos
θ
() 1
−
⋅
=
or
cos
θ
Ma
rfx
⋅
ρ
−
2
⋅
A
⋅
−
=
Since
a
rfx
constant
=
then
Ua
rfx
t
⋅
=
cos
θ
rfx
⋅
ρ
Va
rfx
t
⋅
−
2
⋅
A
⋅
−
=
θ
acos 1
rfx
⋅
ρ
rfx
t
⋅
−
2
⋅
A
⋅
−
⎡
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 Fall '07
 Lear
 Fluid Mechanics, Flux

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