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

that is represented here in terms of stream and isopotential lines.

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

Recalling the fact that, by definition, a stream line cannot be crossed by the fluid, this complex potential well represent the irrotational flow around a cylinder of radius R created 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 then called stagnation points.