##
FLOW AROUND A CYLINDER

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.