If a particular fluid motion is irrotational, meaning that
it is then possible to represent the field of flow in terms
of a single scalar function 
as
or, componentwise,
The quantity , referred to as the velocity potential,
is a function of x,y,z,t in the most general case. Unlike the
streamfunction, which is applicable for divergenceless, two-dimensional
flow, the velocity potential may exist even for three-dimensional
flow. However, the necessary condition for the
existence of as defined by Eq. (192) is somewhat more
restrictive since, in effect, Eq. (191) requires that
