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Thin vortex filament with constant circulation; find velocity components

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data

    In a xyz cartesian coordinate system, a thin vortex filament with constant circulation Gamma, forms a square (in the xy plane), with each side of the square having length L. You are told that an infinitesimal segment del (vector) of this filament induces an infinitesimal velocity dv (vector) at a point P on the xy plane, according to the given formula.

    dv = Gamma/(4*pi)*(del x r)/(r^3)

    where x is the cross product, r is the vector from the infinitesimal filament segment to point P. Calculate the velocity components at the center of the square.


    2. Relevant equations
    dv = Gamma/(4*pi)*(del x r)/(r^3)



    3. The attempt at a solution

    v = Gamma/(4*pi)*integral(sin(theta)/r^3)dl

    From here, I have no idea how to solve.

    Any help would be much appreciated. Thank you for your time.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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