Introduction

If the two-dimensional motion of an ideal fluid consists of an outward radial flow from a point and is symmetrical in all directions, then the point is called a simple source. A source at the origin can be considered as a line perpendicular to the z-plane along which fluid is being created. If the rate of emission of volume of fluid per unit length is , then the origin is said to be a source of strength m, the complex potential for the flow is

and the velocity V at the point (x,y) is given by

For fluid flows a sink is a negative source and is a point if inward radial flow at which the fluid is considered to be absorbed or annihilated.

Let an ideal fluid flow in a domain in the z-plane be effected by a source located at the point . Then the flow at the points z, which lie in a small neighborhood of the point , is approximated by that of a source with complex potential

The image of a source under a conformal mapping is a source.

The technique of conformal mapping can be used to determine the fluid flow in a domain D in the z-plane that is produced by sources and sinks. If a conformal mapping w = S(z) can be constructed so that the image of sources, sinks, and boundary curves for the flow in D are mapped onto sources, sinks, and boundary curves in a domain G where the complex potential is known to be , then the complex potential in D is given by .

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(c) John Mathews, 1998, 2006