2.9. Relationship Between Potential and Stream Functions

Try these first

1. 1.

   Define the stream function in fluid mechanics.

   Hint

   Think about what properties are preserved along streamlines.

2. 2.

   What does the potential function represent?

   Hint

   Consider how potential is related to energy and flow.

3. 3.

   What is the main character of a stream function?

   • Flows through solids
   • Constant along streamlines
   • Dependent on pressure

   Hint

   Think about what it means for flow continuity.

4. 4.

   True or False: The potential function can describe the velocity of fluid particles in irrotational flow.

   • True
   • False

   Hint

   Recall what the potential function quantifies.

5. 5.

   Given a stream function and its equations, derive the potential function and confirm its characteristics under specified conditions.

   Hint

   Examine the characteristics of Laplace and work through to confirm irrotational flow.

6. 6.

   Consider a case with known velocity fields. Determine if the flow is irrotational based on the calculated vorticity components.

   Hint

   Match derived vorticity against established definitions.