Velocity potential

if u and w can be expressed as the partial derivatives of a function ,

i.e. :   ( = velocity potential)

Then the irrotationality condition is satisfied automatically, since:

In order for the continuity equation to be satisfied we must have:

Once the velocity potential is determined, the whole velocity field is known:

Definition of (also gradient of )

So: The goal is to find the velocity potential, , which satisfies Laplace equation.