The Flow Mapping Theorem
The Flow Mapping Theorem makes the flow of a fluid around an object easier to find. Ifis an obstacle andis a conformal mapping fromontowhere then it is possible to use the solutionof the Obstacle problem forto solve the obstacle problem for
Letbe an obstacle and letbe a one to one conformal mapping fromontowheresuch that
The velocity functionis the unique solution to the obstacle problem forwith complex potential function
Example: Letbe the intervalwith circulationFind the complex velocity function and the conjugate velocity function.
By the Flow Mapping Theorem the the required complex potential function iswithand
The velocity function is