10.2.1. Introduction to Velocity Potentials

Try these first

1. 1.

   What is a velocity potential?

   Hint

   Think about the relationship between potential and velocity.

2. 2.

   What is the condition required for a flow to be irrotational?

   Hint

   Recall how we defined vorticity.

3. 3.

   What is the primary function of velocity potentials in fluid mechanics?

   • To represent pressure fields
   • To represent velocity fields
   • To represent temperature fields

   Hint

   Think about how you can derive velocities from scalar functions.

4. 4.

   True or False: Vorticity must be negligible for velocity potentials to be applied?

   • True
   • False

   Hint

   Recall the condition we discussed regarding vorticity.

5. 5.

   Demonstrate how to derive one velocity component from a given velocity potential. Use φ(x, y) = x² + y² as your potential function.

   Hint

   Make sure to apply the partial derivative correctly.

6. 6.

   Assume a fluid field where it shows evident vorticity; explain why velocity potentials cannot be employed effectively here.

   Hint

   Consider how vorticity is indicative of turbulence.