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Problem 4.133
[Difficulty: 3]
CS
(moves
at speed U)
y
x
c
d
R
x
R
y
Given:
Water jet striking moving vane
Find:
Expressions for force and power; Show that maximum power is when U = V/3
Solution:
Basic equation: Momentum flux for inertial CV
Assumptions:
1) Steady flow
2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow
5) Jet relative velocity is constant
Then
R
x
u
1
ρ
−
V
1
⋅
A
1
⋅
()
⋅
u
2
ρ
V
2
⋅
A
2
⋅
⋅
+
=
VU
−
−
ρ
−
⋅
A
⋅
[]
⋅
−
(
) cos
θ
⋅
ρ
−
⋅
A
⋅
⋅
+
=
R
x
ρ
−
2
A
⋅
cos
θ
() 1
−
⋅
=
This is force on vane; Force exerted by vane is equal and opposite
F
x
ρ
−
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 Fall '07
 Lear
 Fluid Mechanics, Flux

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