1.6. Velocity potential and stream function

Try these first

1. 1.

   Define velocity potential.

   Hint

   Think about potential energy in a fluid context.

2. 2.

   What does a stream function represent?

   Hint

   Consider how fluid motion can be illustrated.

3. 3.

   What is velocity potential primarily associated with?

   • Fluid pressure
   • Irrotational flow
   • Viscous flow

   Hint

   Remember the flow conditions where it applies.

4. 4.

   True or False: Stream functions can only be used in three-dimensional flows.

   • True
   • False

   Hint

   Think about the dimensional restrictions of flow representation.

5. 5.

   For a given flow field, derive expressions for the velocity potential and stream function based on specified boundary conditions.

   Hint

   Start with Laplace's equation for irrotational flows.

6. 6.

   Analyze the effect of changing boundary conditions on the existence of unique solutions in a fluid problem.

   Hint

   Consider cases with multiple or no solutions based on how conditions are changed.