AAE 334, Fall 2011, Homework 9 SOLUTIONS
Due Wednesday, September 21 at the beginning of class.
1.
Solve for the induced velocity at points (x, y) in the flow below by adding up two semiinfinite vortices of
equal strength,
.
Hint: no integration needed, just apply the simple result from Monday’s lecture twice.
2.
Can you also solve this problem by subtracting the velocity field induced by a finitelength vortex from the
velocity field of an infinite vortex?
Show.
Same hint as in #1.
See the red shading above.
This shows the right end of the triangle joining
P
to both ends of
the left semiinfinite vortex line.
Use the simple formula from Monday’s lecture,
B
A
y
z
y
x
w
cos
cos
4
0
,
,
.
Call the velocity induced by the left vortex
Left
w
.
Then,
as
0
A
and
1
cos
A
for the red triangle, and substituting for
B
cos
,
2
2
3
3
1
4
0
,
,
y
x
x
x
x
y
z
y
x
w
Left
.
Similarly for the green region on the right,
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 Fall '09
 COLLICOTT
 Fluid Dynamics, infinite vortex

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