##
THE VELOCITY POTENTIAL

It is possible to demonstrate that the condition of irrotationality
implies the existence of a *velocity potential* such that

On substituting the definition of potential into the continuity equation
we obtain

The velocity potential must then satisfy the Laplace equation and it
consequently is a harmonic function of space.

Solution of the Laplace equation, with an appropriate set of
boundary conditions, leads then to the determination of the flow field.

Laplace equation has been widely studied in many fields, and shows
some interesting properties. Among the latter, one of the most important
is its linearity. Given two solutions of the Laplace equation, any
linear combination of them (and in particular their sum and difference)
is again a valid solution. The potential of a complex flow can then be
obtained by superimposing potentials of simpler flows.