## Sources and Sinks

Letbe a model flow velocity function (so thatfor every simple closed contourinwhose inside also lies in) with domainand letbe a punctured open disc inwith centreThen

is a source of strengthiffor every simple closed contoursurrounding

is a sink of strengthiffor every simple closed contoursurrounding

In each case the contour is traversed in the positive counterclockwise sense.

Example: Find the strength of the source at the pointfor the complex velocity function

The source strength iswhere C is the unit circle soandThe integral becomes

by Cauchy's Residue Theorem.

Example: Show that there is no source or sink at the pointfor the complex velocity function

The source strength iswhere C is the circle centre the origin, radius 1 over 2 soand

The functionis analytic insidesoby Cauchy's Theorem. The integral becomes

hence there is no source of sink at the origin.