Blasius

The Blasius theorem gives a convenient formula for the force on a two-dimensional body in an incompressible potential flow field.

The direct way to find the force on the body is to integrate the pressure forces over the surface:

(We ignore viscous stresses, if any.)

We can combine the force components in a complex conjugate force:

since

Assuming steady flow, the Bernoulli law gives:

Now since is contant (the body is a streamline). So we get the Blasius formula:

In order to use this, we need to know how to do integrals of complex functions around closed contours.