Stream Line and Velocity Potential

Define Stream line
A stream line is an imaginary line drawn in a flow field such that a tangent drawn at any point on this line represents the direction of the velocity vector.

In steady flow, a fluid particle will move along a streamline.

Equation of a stream line in a three-dimensional flow is given as
(dx/u) = (dy/v) = (dz/w)

Define Velocity Potential
Velocity Potential is defined as a scalar function of space and time such that its negative derivative with respect to any direction gives the fluid velocity in that direction.

Properties of a velocity potential function
1. If velocity potential exists, the flow should be irrotational
2. If velocity potential satisfies the Laplace equation, it represents the possible steady, incompressible, irrotational flow.