The theory of complex variable comes in naturally in the study of fluid phenomena.Let us define, w = φ + iψ with φ velocity potential and ψ stream function of a two dimensional fluid flow. w is called the complex potential function.Then w turns out to be analytic because the Cauchy-Riemann conditions, ∂φ/∂x =∂ψ/∂y ; ∂φ/∂y = −∂ψ/∂x are exactly the natural flow conditions that have to be satisfied. Suppose, velocity potential for a two dimensional fluid flow is given by the function φ(x, y) = y/x2+ y2− 2xy.Find out the stream function. Also find the complex potential function for the fluid flow.

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