10.3. Velocity Potentials and Pressure Gradients

Try these first

1. 1.

   Define velocity potential.

   Hint

   Consider the relationship between velocity and a scalar function.

2. 2.

   What does it mean for flow to be irrotational?

   Hint

   Think about flow behavior and vorticity.

3. 3.

   What is a velocity potential?

   • A measure of fluid pressure
   • A scalar function giving the velocity field
   • A type of fluid behaviour

   Hint

   Think about how potential translates into flow.

4. 4.

   True or False: Irrotational flow can be analyzed using velocity potentials.

   • True
   • False

   Hint

   Recall the definition of irrotational flow.

5. 5.

   A pipe of varying diameter carries water. Calculate the velocity change at two sections and find the relation to pressure gradients.

   Hint

   Remember the continuity principle about flow rate.

6. 6.

   Demonstrate how velocity potentials can be utilized to simplify a complex fluid flow problem involving multiple forces.

   Hint

   Consider derivatives and how they relate back to the original fluid properties.