2D Incompressible

Even if a flow is not irrotational, it is still possible to replace the velocity components by a single scalar unknown if the flow is two-dimensional and incompressible:

For two-dimensional incompressible flows:

Function is called the streamfunction. Lines of constant are the streamlines.

Exercise:

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

• Does the streamfunction exist?
• If so, what is ?
• How do the lines of constant look?

You should now be able to do 18.1