text: Given an incompressible two-dimensional flow which is also irrotational we have:
  Which is in cylindrical coordinates 
  We look for a solution with separated variables:
  which gives
  Given the left part depends only on r and the right parts depends only on , the two parts must be equal to a constant independent from r and . The constant shall be positive.
  Therefore,
  The solution to the second equation is a linear combination of  and 
  In order to have a single-valued velocity (and also a single-valued stream function) m shall be a positive integer.
  therefore the most generic solution is given by
  The potential is instead given by