5.3. Applications Problems

Try these first

1. 1.

   Define stream function and its significance in fluid dynamics.

   Hint

   Think about how it reduces complexity in fluid analyses.

2. 2.

   What is the role of mass conservation in fluid dynamics?

   Hint

   Recall that this is a fundamental principle.

3. 3.

   What does a stream function represent?

   • Fluid velocity
   • Flow direction
   • Fluid pressure

   Hint

   Think about the role of streamlines.

4. 4.

   True or False: Mass conservation states that mass can be created in a closed system.

   • True
   • False

   Hint

   Consider the fundamental principles here.

5. 5.

   Consider a fluid flowing around a cylindrical object. Apply the concept of stream functions to analyze the flow behavior and derive the velocity components.

   Hint

   Use the relationships established in class about stream functions.

6. 6.

   A rectangular area experiences airflow that shows varying velocities across different streamlines. How would you apply the mass conservation equations to calculate flow through specific boundaries?

   Hint

   Connect these calculations back to the fundamental continuity equations discussed.