Flow Around a Rankine Half-Body

The Rankine half-body is the curve that satisfies the equation

for .

The parameter describes the width of the half-body. Indeed, as , it is easy to see that , and that total width of the body approaches . Here is a graph of the Rankine half-body.

Note that the Rankine half-body does not pass through the origin; rather its vertex is at the point ; indeed

The vector field that described the flow of a fluid around a Rankine half-body is given by

with the parameters

- which gives the width of the Rankine half-body, and

- which gives the velocity of the fluid far from the body.

Changing the parameters or simply re-scales the resulting vector field.