The superposition of a doublet and a uniform flow gives the complex potential


that is represented here in terms of streamlines and equipotential lines.

Note that one of the streamlines is closed and surrounds the origin at a constant distance equal to


Recalling the fact that, by definition, a streamline cannot be crossed by the fluid, this complex potential represents the irrotational flow around a cylinder of radius R approached by a uniform flow with velocity U.

Moving away from the body, the effect of the doublet decreases so that far from the cylinder we find, as expected, the undisturbed uniform flow.

In the two intersections of the x-axis with the cylinder, the velocity is found to be zero. These two points are thus called stagnation points.