9.5. Rate of Rotations and Angular Velocity

Try these first

1. 1.

   What is angular velocity?

   Hint

   Consider how it relates to spinning objects.

2. 2.

   Define vorticity.

   Hint

   Think about how we describe rotation mathematically.

3. 3.

   What is the primary measure of local rotation in a fluid particle?

   • Velocity
   • Acceleration
   • Vorticity

   Hint

   Think about a fluid's tendency to spin.

4. 4.

   Angular velocity is defined as what?

   Hint

   Related to how fast something spins.

5. 5.

   A fluid element experiences an angular rotation of 5 rad/s around the z-axis. If the velocity gradient in the x-direction is 3 s^-1, what is the resultant angular velocity?

   Hint

   Utilize the formula for angular velocity based on velocity gradients.

6. 6.

   Examine a cylindrical pipe flowing fluid from a smaller to a larger diameter. Describe the strains experienced by the fluid elements.

   Hint

   Visualize how fluid must adapt to changing diameters.