Problem 4.157
[Difficulty: 2]
Given:
Mass moving betweem two jets
Find:
Time st slow to 2.5 m/s; plot position; rest position; explain
Solution:
Apply x momentum
Assumptions:
1) All changes wrt CV
2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow 5) Constant jet area
The given data is
ρ
999
kg
m
3
⋅
=
M5
k
g
⋅
=
V2
0
m
s
⋅
=
U
0
10
m
s
⋅
=
U
2.5
m
s
⋅
=
A
100 mm
2
⋅
=
Then
a
rf
−
M
⋅
u
1
ρ
−
VU
−
()
⋅
A
⋅
[]
⋅
u
2
ρ
−
+
⋅
A
⋅
⋅
+
u
3
m
3
⋅
+
=
where
a
rf
dU
dt
=
u
1
−
=
u
2
+
−
=
and
u
3
0
=
Hence
dU
dt
−
M
⋅
ρ
A
⋅
−
2
−
+
2
+
⎣
⎦
⋅
=
4
ρ
⋅
A
⋅
V
⋅
U
⋅
=
Separating and integrating
dU
U
4
ρ
⋅
A
⋅
V
⋅
M
−
dt
⋅
=
or
ln U
( )
ln U
0
−
4
ρ
⋅
A
⋅
V
⋅
M
−
t
⋅
=
UU
0
e
4
ρ
⋅
A
⋅
V
⋅
M
−
t
⋅
⋅
=
(1)
Solving for t
t
M
4
ρ
⋅
V
⋅
A
⋅
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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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