2.6. Practice Problem: Components of Rotation

Try these first

1. 1.

   Define irrotational flow.

   Hint

   Think about what happens when fluids do not rotate.

2. 2.

   What is vorticity?

   Hint

   Consider its relationship to fluid rotation.

3. 3.

   What does a non-zero angular velocity indicate?

   • The fluid is irrotational
   • The fluid experiences rotation
   • The fluid is incompressible

   Hint

   Consider the definitions of rotational and irrotational flows.

4. 4.

   True or False: Irrotational flow has non-zero vorticity.

   • True
   • False

   Hint

   Recall what defines irrotational flow.

5. 5.

   Given u = z + x² and v = -2y, derive the components of rotation about all axes.

   Hint

   Make sure to apply the definitions accurately.

6. 6.

   If a flow field is defined by u = 3x - 5y, v = 8y + z, determine under which conditions it is irrotational.

   Hint

   Check the relationship between derivatives and irrotational flow.