10.5.4. Smooth Function Requirements

Try these first

1. 1.

   What is a velocity potential function?

   Hint

   Think about how we can simplify vector fields.

2. 2.

   What condition allows the use of velocity potential functions?

   Hint

   Consider what happens to vorticity in irrotational flows.

3. 3.

   What is the formula for velocity potential function in a fluid flow?

   • V = ∇φ
   • V = φ∇
   • V = φ / ∇

   Hint

   Recall how potential functions represent velocity fields.

4. 4.

   True or False: Irrotational flows can have significant vorticity.

   • True
   • False

   Hint

   Remember the definition of irrotational flow.

5. 5.

   Given a fluid moving between two plates with a known velocity profile, derive the pressure distribution along the flow.

   Hint

   Focus on the balance of pressure gradients based on the velocity profile.

6. 6.

   Design a scenario where potential functions fail and explain the outcome.

   Hint

   What happens to fluid motion in turbulence?