2.8. Potential Function

Try these first

1. 1.

   Define the potential function and its role in fluid dynamics.

   Hint

   Think about how it relates to flow velocity.

2. 2.

   What does the Laplace equation represent in fluid dynamics?

   Hint

   Consider the relationship to fluid conservation.

3. 3.

   What represents the potential function?

   • Velocity in compressible flows
   • Velocity in irrotational flows
   • Pressure in fluid flows

   Hint

   Focus on flow conditions.

4. 4.

   True or False: The Laplace equation can be satisfied by any scalar function.

   • True
   • False

   Hint

   Consider conditions for application.

5. 5.

   Consider a potential function Φ(x, y) = 4x^2 + 3y^2 - 5xy. Determine the velocity components and check if this satisfies Laplace's equation.

   Hint

   Differentiate with respect to x and y to find components.

6. 6.

   Given a velocity potential Φ = x^3 - 3xy^2, compute the streamlines and determine the flow rate between two points.

   Hint

   Use the formulas you've learned for u and v to analyze flow between points.