9.5.2. Velocity Gradients and Rotations

Try these first

1. 1.

   What is a velocity gradient?

   Hint

   Think about how speed varies in different layers of fluid.

2. 2.

   What does angular velocity measure?

   Hint

   Consider it like spinning around an axis.

3. 3.

   What does a velocity gradient indicate?

   • Change in velocity over time
   • Change in velocity over distance
   • Constant velocity

   Hint

   Focus on the relationship between velocity and distance.

4. 4.

   True or False: Vorticity measures the local rotation of fluid.

   • True
   • False

   Hint

   Consider the movement of fluid particles.

5. 5.

   A fluid element is flowing through a pipe with a diameter change from 2 m to 1 m. Calculate the linear and shear strains experienced by the element.

   Hint

   Use the principles of conservation of volume and understand flow behavior.

6. 6.

   Given a vorticity of 0.5 s^-1 how would you find the angular velocity associated with this vorticity?

   Hint

   Remember the relation between vorticity and angular movement.