The Flow Mapping Theorem
The Flow Mapping Theorem makes the flow of a fluid around an object easier to find. If
is an obstacle and
is a conformal mapping from
onto
where
then it is possible to use the solution
of the Obstacle problem for
to solve the obstacle problem for
Theorem
Letbe an obstacle and letbe a one to one conformal mapping fromontowhere
such that
for
The velocity function
is the unique solution to the obstacle problem forwith complex potential function
Example: Letbe the interval
with circulation
Find the complex velocity function and the conjugate velocity function.
By the Flow Mapping Theorem the the required complex potential function is
with
and
We have
The velocity function is
Hence
