Potential flow in 2d)

In fluid dynamics, potential flow in two dimensions is simple to analyse using complex numbers.

The basic idea is to define a holomorphic function . If we write

then the Cauchy-Riemann equations show that

(it is conventional to regard all symbols as real numbers; and to write

and ).

The velocity field , specified by

then satisfies the requirements for potential flow:

and

Lines of constant are known as streamlines and lines of constant are known as equipotential lines (see equipotential surface). The two sets of curves intersect at right angles, for

Thus the flow flows along the lines of constant .

It is interesting to note that is also satisfied, this relation being eqivalent to (the automatic condition gives ).

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