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Let's take circulation strength of each vortex τ and distance between them is r. I feel the answer should be 2τ/πr but my friend is arguing its τ/2πr.

So my thought process goes like, if you have a single filament of strength τ then integrating the biot savart law with distance at r/2 we get the velocity due to one vortex to be τ/πr. So as we have two vortices I added the two velocities as both of the vortices would push it the total velocity would be 2τ/πr

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    $\begingroup$ So how did you both derive your answers? Diagrams and analysis need to be shown. $\endgroup$
    – Solar Mike
    Aug 10 '21 at 5:40
  • $\begingroup$ So my way of thinking was that if you have a single filament of strength τ then integrating the biot savart law with distance at r/2 we get the velocity due to one vortex to be τ/πr. So as we have two vortices I added the two velocities as both of the vortices would push it the total velocity would be 2τ/πr $\endgroup$ Aug 10 '21 at 8:03
  • $\begingroup$ Inprove your questuon - don’t add detail in comments. $\endgroup$
    – Solar Mike
    Aug 10 '21 at 8:14
  • $\begingroup$ Cool thanks, Actually I'm new here so it'd take some time and help from people like you to adapt 😄 $\endgroup$ Aug 10 '21 at 11:38
  • $\begingroup$ So, it may help you to avoid downvotes and close votes if you start here: engineering.stackexchange.com/tour $\endgroup$
    – Solar Mike
    Aug 10 '21 at 11:41

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