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This chapter describes the use of complex analysis to facilitate calculations in twodimensional, incompressible, irrotational
fluid dynamics. Incidentally, incompressible, irrotational flow is usually referred to as potential flow, because the
associated velocity field can be represented in terms of a velocity potential that satisfies Laplace's equation. (See Section 4.15.)
In the following, all flow patterns are assumed to be such that the
coordinate is ignorable. In other words,
the fluid velocity is everywhere parallel to the

plane, and
. It follows that all line
sources and vortex filaments run parallel to the
axis. Moreover, all solid surfaces are of infinite extent in the
direction, and
have uniform crosssections. Hence, it is only necessary to specify the locations of line sources, vortex filaments, and
solid surfaces in the

plane. More information on the use of complex analysis in twodimensional fluid
mechanics can be found in Batchelor 2000, MilneThomson 1958, MilneThomson 2011, and Lamb 1993.
Richard Fitzpatrick
20160331