In case the following power-law conformal map is applied, from  to :
then, writing  in polar coordinates as , we have
In the figures to the right examples are given for several values of . The black line is the boundary of the flow, while the darker blue lines are streamlines, and the lighter blue lines are equi-potential lines. Some interesting powers  are:
*: this corresponds with flow around a semi-infinite plate,
*: flow around a right corner,
*: a trivial case of uniform flow,
*: flow through a corner, or near a stagnation point, and
*: flow due to a source doublet
The constant  is a scaling parameter: its absolute value  determines the scale, while its argument  introduces a rotation (if non-zero).