10.2. Vorticity and Rotationality

Try these first

1. 1.

   Define vorticity in your own words.

   Hint

   Think about how fluid rotates.

2. 2.

   What characterizes a boundary layer?

   Hint

   Consider the effects of viscosity.

3. 3.

   Vorticity is defined as:

   • The divergence of the velocity field.
   • The curl of the velocity field.
   • The speed of the fluid.

   Hint

   Think about the calculation used.

4. 4.

   True or False: Irrotational flow has vorticity.

   • True
   • False

   Hint

   Recall the definitions we've discussed.

5. 5.

   Given the velocity field v = (3y)i + (3x)j, determine if the flow is steady and irrotational, and compute vorticity.

   Hint

   Check the conditions for steady state and use curl to calculate.

6. 6.

   Calculate the vorticity components at the point (0, -1, 1) for u = y^2, v = -xy, and w = 0.

   Hint

   Remember the connections between velocity components!