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(a) Circulation about a contour bounded by x = 0.4 m, x = 0.6 m,
y = 0, and y = 8 mm.
(b) Result if evaluated
Δ
x = 0.2 m further downstream
Problem 5.71
[Difficulty: 4]
Given:
Sinusoidal approximation to boundarylayer velocity profile:
u
U sin
π
2
y
δ
where
δ
5mm
at
x
0.5 m
Neglect the vertical component of velocity.
U
0.5
m
s
Find:
Solution:
We will apply the definition of circulation to the given velocity field.
s
d
V
Governing
Equation:
(Definition of circulation)
From the definition of circulation we break up the integral:
da
cd
bc
ab
s
d
V
s
d
V
s
d
V
s
d
V
Since the velocity is zero over ab, and since
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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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