It does not dependent on the path has a velocity potential it is related with the product of the velocity vector, and the length along the path between the two distinct point A and B. This is what I understand, so can I say that we will come to this that the necessary condition now for the velocity potential phi to exists it that the flow has to be irrotational. Unless flow irrotational only for a irrotational flow we can have del square phi is 0 and basically the velocity potential phi exit in this case.