complex potential

Taken together with the velocity potential, the stream function may be used to derive a complex potential.

Velocity potential, stream function and complex potential.

In this regard, u+iv would be the complex potential, where u is the potential function and v is the stream function.

If a circular cylinder is placed into that flow, the complex potential for the new flow is given by:

In most cases, the stream function is the imaginary part of the complex potential, while the potential function is the real part.

This complex potential was discussed as early as the nineteenth century, by the French mathematician Paul Émile Appell.

Both Airy's stress function and Muskhelishvili's complex potentials as well as the constitutive equations governing the elasto-plastic behaviour of flawed bodies will be examined.