Consider a uniform flow with velocity U in the positive x direction combined with two free vortices...

Question

Consider a uniform flow with velocity U in the positive x direction combined with two free vortices of equal strength located along the y-axis. Let one vortex located at y = a be a clockwise vortex and the other at y = - a be a counterclockwise vortex, where K is a positive constant. It can be shown by plotting streamlines that for Ua/K

Q

David · Accepted Answer

Solution:-
Compute the stream function for uniform flow and the two vortices by using the following 
Reaction: 
1 2
2
1
ln ln
ln
,
Uy k r k r
r
Uy k
r
Drawthetwovortices on x and y plane as shown


  
 
1 2
2 2 2
1
2 2 2
2
1 2
2
1
2 2
1/2
2 2
2 2
2 2
tan ,

Consider a uniform flow with velocity U in the positive x direction combined with two free vortices of equal strength located along the y-axis. Let one vortex located at y = a be a clockwise vortex...

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