# What is the velocity of a fluid particle at the center of a infinitely long counter-rotating vortex pair?

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

• So how did you both derive your answers? Diagrams and analysis need to be shown. Aug 10 '21 at 5:40
• 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 Aug 10 '21 at 8:03