11.1.7. Third Example

Try these first

1. 1.

   Define irrotational flow.

   Hint

   Think about the relationship between rotation and flow.

2. 2.

   What does the continuity equation represent?

   Hint

   Consider conservation principles.

3. 3.

   Which of the following describes an irrotational flow?

   • A flow with constant velocity
   • A flow with zero vorticity
   • A turbulent flow

   Hint

   Think about the concept of rotation in a fluid.

4. 4.

   True or False: A flow's vorticity can be non-zero in an irrotational flow.

   • True
   • False

   Hint

   Reflect on the definition of irrotational flow.

5. 5.

   Given the velocity field u = y^2, v = -2xy, prove whether it is irrotational or not.

   Hint

   Recollect the formula for vorticity.

6. 6.

   Consider φ(x,y) = 3x^2 + 4y. Is this potential function consistent with an incompressible flow?

   Hint

   Use the Laplace condition in the analysis.