Based on Kelvin's theorem, large parts of common flow fields are irrotational. In those parts, it is possible to replace the three velocity components by a single scalar ``velocity potential''.
For irrotational flows
This will be outside the boundary layers and wakes. Function is called the velocity potential. The flow is called potential flow or irrotational.Two-dimensional potential flow:
Exercise:
For ideal stagnation point flow (u,v)= a(x,-y),
- Does the velocity potential exist?
- If so, what is ?