(a) Average rate of rotation of two line segments at +/ 45 degrees
(b) Show that this is the same as in the example
Problem 5.84
[Difficulty: 3]
Given:
Viscometric flow of Example 5.7, V = U(y/h)i, where U = 4 mm/s and h = 4 mm
Find:
Solution:
We will apply the definition of rotation to the given velocity field.
V
2
1
Governing
Equation:
(Definition of rotation)
Assumptions:
(1) Steady flow
(2) Incompressible flow
Considering the lines shown:
u
c
u
a
y
u
l sin
θ
1
ω
ac
u
c
u
a
sin
θ
1
l
since the component
normal to l is
u sin
θ
1
ω
ac
y
u
l sin
θ
1
sin
θ
1
l
y
u
sin
θ
1
2
U
h
sin
θ
1
2
Now consider this sketch:
u
b
u
d
y
u
l sin
θ
2
ω
bd
u
d
u
b
sin
θ
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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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