2.4. Rate of Rotation

Try these first

1. 1.

   Define rotational flow in your own words.

   Hint

   Think about fluid particles moving in circles.

2. 2.

   What is irrotational flow?

   Hint

   It means no local rotation at all.

3. 3.

   In rotational flow, at least one angular velocity component is non-zero.

   • True
   • False

   Hint

   Think of the definition of rotation.

4. 4.

   Vorticity is defined as twice the angular velocity.

   • True
   • False

   Hint

   Remember the formula involving angular velocities.

5. 5.

   Given a velocity field defined by u = 2xy, v = x^2 - 2y, calculate the vorticity and interpret its physical meaning.

   Hint

   Differentiate u and v!

6. 6.

   Consider a flow with angular velocities ω_x = 0.3, ω_y = 0.2, and ω_z = 0.1. Determine if this flow is rotational or irrotational and justify your answer.

   Hint

   Refer back to the definitions discussed.