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Problem 5.44
[Difficulty: 2]
Given:
The 2dimensional, incompressible velocity field provided above
Find:
(a) dimensions of the constant A
(b) simplest xcomponent of the velocity
(c) acceleration of a particle at (1,2)
Solution:
We will check the dimensions against the function definition, check the flow field against the continuity equation,
and then apply the definition of acceleration.
0
t
w
z
v
y
u
x
Governing
Equations:
(Continuity equation)
t
V
z
V
w
y
V
v
x
V
u
Dt
V
D
a
p
(Particle acceleration)
Assumptions:
(1) Incompressible flow (
ρ
is constant)
(2) Twodimensional flow (velocity is not a function of z)
(3) Steady flow (velocity is not a function of t)
L
L
t
L
xy
v
A
1
1
Lt
A
1
Since
vA
x
y
it follows that
A
v
xy
and the dimensions of A are given by:
0
y
v
x
u
x
u
Ax
y
v
Based on the assumptions above, the continuity equation reduces to:
Therefore:
Integrating with respect to x will yield the xcomponent of velocity:
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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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