5.3.2. Understanding Streamlines

Try these first

1. 1.

   What is a streamline?

   Hint

   Think about how the fluid moves.

2. 2.

   Define stream function.

   Hint

   Consider its role in fluid analysis.

3. 3.

   What do streamlines represent in fluid mechanics?

   • Pressure differences
   • Directions of fluid flow
   • Temperature changes

   Hint

   Think about how fluids travel.

4. 4.

   True or False: The volume of fluid passing between two streamlines can be determined by the difference in their stream function values.

   • True
   • False

   Hint

   Recall how stream functions relate to flow.

5. 5.

   For a given flow field, determine the stream function if the velocity components are u = 3y and v = -3x.

   Hint

   Use integration and correlate the equations.

6. 6.

   Explain how the streamline pattern changes when fluid flows from a wider section to a narrower section.

   Hint

   Consider the continuity equation and what it tells us about velocity in varying cross-sections.