5.4.2.1. Compressible Stream Functions

Try these first

1. 1.

   Define a stream function in the context of fluid mechanics.

   Hint

   Think about how streamlines help in understanding fluid motion.

2. 2.

   What is the primary benefit of using compressible stream functions?

   Hint

   Consider how simplification can help in calculations.

3. 3.

   What does a stream function help to visualize?

   • Only velocity
   • Flow patterns
   • Pressure gradients

   Hint

   Think about its role in representing fluid motion.

4. 4.

   True or False: Compressible flow ignores changes in fluid density.

   • True
   • False

   Hint

   Reflect on the definition of compressible flow.

5. 5.

   Given a stream function, derive the expressions for velocity components u and v and prove if the flow is steady or unsteady.

   Hint

   Focus on differentiating correctly and applying the definitions of velocity components.

6. 6.

   Consider a scenario where you have a compressible flow. How would you modify the stream function to account for density variations?

   Hint

   Reflect on the main differences between compressible and incompressible formulations.