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Problem 4.130
[Difficulty: 3]
Given:
Data on jet boat
Find:
Formula for boat speed; flow rate; value of k; new speed and flow rate
Solution:
CV in boat
coordinates
Basic equation:
Momentum
Given data
D7
5
m
m
⋅
=
V
j
15
m
s
⋅
=
V1
0
m
s
⋅
=
ρ
1000
kg
m
3
⋅
=
Applying the horizontal component of momentum
F
drag
V
ρ
−
Q
⋅
()
⋅
V
j
ρ
Q
⋅
⋅
+
=
or, with
F
drag
kV
2
⋅
=
2
⋅
ρ
Q
⋅
V
j
⋅
ρ
Q
⋅
V
⋅
−
=
2
⋅
ρ
Q
⋅
V
⋅
+
ρ
Q
⋅
V
j
⋅
−
0
=
Solving for
V
V
ρ
Q
⋅
2k
⋅
−
ρ
Q
⋅
⋅
⎛
⎝
⎞
⎠
2
ρ
Q
⋅
V
j
⋅
k
+
+
=
(1)
For the flow rate
QV
j
π
4
⋅
D
2
⋅
=
Q
0.0663
m
3
s
=
To find k from Eq 1, let
α
ρ
Q
⋅
⋅
=
then
V
α
−
α
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.
 Fall '07
 Lear
 Fluid Mechanics

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