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Problem 4.61
[Difficulty: 3]
Given:
Data on flow through a bend
Find:
Find net momentum flux
Solution:
0
=
⋅
∫
CS
A
d
V
r
r
ρ
Basic equations
Momentum fluxes:
mf
x
=m
f
y
=
Assumptions:
1) Steady flow
2) Incompressible flow
Evaluating mass flux at 1, 2 and 3
0
h
1
y
V
1
y
()w
⋅
⌠
⎮
⌡
d
−
V
2
w
⋅
h
2
⋅
+
V
3
w
⋅
h
3
⋅
+
0
=
or
V
3
h
3
⋅
0
h
1
y
V
1
y
()
⌠
⎮
⌡
dV
2
h
2
⋅
−
=
0
h
1
y
V
1max
y
h
1
⋅
⌠
⎮
⎮
⌡
2
h
2
⋅
−
=
V
1max
h
1
h
1
2
2
⋅
V
2
h
2
⋅
−
=
Hence
V
1max
2
h
1
V
3
h
3
⋅
V
2
h
2
⋅
+
⋅
=
Using given data
V
1max
3.8
m
s
=
For the x momentum, evaluating at 1, 2 and 3
mf
x
0
h
1
y
V
1
y
ρ
⋅
V
1
y
⋅
w
⋅
⌠
⎮
⌡
d
−
V
3
cos
θ
⋅
ρ
⋅
V
3
⋅
h
3
⋅
w
⋅
+
=
mf
x
0
h
1
y
V
1max
y
h
1
⋅
⎛
⎜
⎝
⎞
⎠
2
ρ
⋅
w
⋅
⌠
⎮
⎮
⎮
⌡
d
−
V
3
2
ρ
⋅
h
3
⋅
cos
θ
⋅
w
⋅
+
=
V
1max
2
h
1
2
−
h
1
3
3
⋅
ρ
⋅
w
⋅
V
3
2
ρ
⋅
h
3
⋅
w
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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, Flux

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