2.10. Practice Problem: Calculating Stream Function and Flow Rate

Try these first

1. 1.

   Define Stream Function.

   Hint

   Think about how it relates to fluid flow.

2. 2.

   Calculate the flow rate between stream functions ψ₁ = 5 and ψ₂ = 10.

   Hint

   Use the difference method for flow rates.

3. 3.

   What is a stream function?

   • A type of fluid
   • A scalar function for streamlines
   • A force acting on fluids

   Hint

   Think about how it's used in fluid dynamics.

4. 4.

   Flow rate is calculated by which method?

   • True
   • False

   Hint

   Recall how we calculate flow rate.

5. 5.

   If φ is defined as φ = x^2 - 3xy + y^2, derive the stream function and then calculate the flow rate between points (2,1) and (2,2).

   Hint

   Start by finding u and v using partial derivatives.

6. 6.

   Given φ = xy^2 - x^2 + 2y, determine how to express ψ and then compute the flow rate between the streamline at points (1,1) and (1,2).

   Hint

   Remember to integrate correctly to get ψ from the velocity potential φ.