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HW9solution - AAE 334 Fall 2011 Homework 9 SOLUTIONS Due...

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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 semi-infinite 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 finite-length 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 semi-infinite 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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