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THE COMPLEX POTENTIAL
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Consider a steady incompressible, inviscid, irrotational two-dimensional flow. The velocity potential and the stream function are related by the following equations (Eq. (2.81)):
and both satisfy Laplace’s equation. Note that Eq. (6.12) yields the Cauchy Riemann conditions for Ф and Ф to be the real and imaginary parts of an analytic function F of a complex variable. We define the complex potential as
F = Ф + і V
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and note that its derivative
is the complex conjugate of the velocity and is called the complex velocity. Any analytic function of a complex variable can represent the complex potential of some flow.
