Order of induced velocities due to vorticity

[vktsn0303]

I'm working to determine the induced velocity on a particle due to every other particle in the fluid domain. In the fluid domain I am dealing with there are at least a million particles. But my question here concerns only two particles. What will be the order of induced velocity if the vorticity of particles is given a value, say, (1/4*pi)*(exp(-r²/sig²)), where 'sig' represents the particle radius and r is the distance between particles in 3D?

vktsn0303