Problem 4.38

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Problem 4.38 [Difficulty: 2]
Given: Data on flow at inlet and outlet of a reducing elbow
Find: Find the maximum velcoity at section 1
Solution:
0=⋅∫
CS
AdV
rrρBasic equation
Assumptions: 1) Steady flow 2) Incompressible flow
Evaluating at 1, 2 and 3
0
h1
yV1 y( ) w⋅
⌠⎮⌡ d− V2 w⋅ h2⋅+ V3 w⋅ h3⋅+ 0=
or
V1max
h1 0
h1
yy
⌠⎮⌡ d⋅
V1max
h1
h1
2
2
⋅= V2 h2⋅ V3 h3⋅+=
Hence V1max
2
h1
V3 h3⋅ V2 h2⋅+( )⋅=
V1max
2
0.5 m⋅ 5
m
s
⋅ 0.15× m⋅ 1 m
s
⋅ 0.2× m⋅+⎛⎜⎝
⎞
⎠⋅= V1max 3.80
m
s
=