Both

We will now restrict ourselves to flows that are both irrotational and 2D incompressible. We will call those flows ``ideal''.

In terms of the velocity potential, by the simple existence of , irrotationality is automatic. But incompressibility requires:

Exercise:

Give a few examples of incompressible potential flows.

In terms of , incompressibility is satisfied automatically. But irrotationality,

requires:

Exercise:

For ideal stagnation point flow (u,v)= a(x,-y),

• Is ?
• Is ?

The boundary conditions for and will be different. For flow around steady bodies, the body is a streamline, so that is constant on the body (Dirichlet boundary condition). Also the velocity normal to the body surface will be zero, so that (Neumann boundary condition.)

You should now be able to do 18.8