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Unformatted text preview: time leaving that surface. Therefore, the strength of a source equals the total
amount of fluid per unit time emerging out of that source.
Similarly, if the curl fails to vanish at an isolated point, then the fluid has a vortex at that
point. The m oment of the vortex is then the vector whose coordinates are the path
integrals, of circles perpendicular to the axes around that point, if the integrals exists. The
vortex strength is the magnitude of the moment. Physically, it measures the total angular
momentum of a ring of fluid with unit mass per unit length rotating about the axis given
by the moment vector.
In the real world, point sources are just sources of fluid placed somewhere, and sinks are
drains or suctions. We gat vortices by inserting spinning cylinders in the liquid and
waiting until it reaches a steady state.
How does this all effect the complex part of it? Since we are only interested here in fields
that have isolated sinks and vortices, the field is represented everywhere else by a
complex potentia...
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This document was uploaded on 03/20/2014 for the course MATH 144 at Hofstra University.
 Fall '03
 StefanWaner
 Math, Algebra, Geometry, Complex Numbers

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