5.4. Stream Functions Basics

Try these first

1. 1.

   Define a stream function.

   Hint

   Think about the relationship between flow paths and fluid particles.

2. 2.

   What do streamlines represent?

   Hint

   Focus on how fluid particles move through the flow.

3. 3.

   What does a stream function represent?

   • A set of equations
   • A flow pattern
   • A velocity vector

   Hint

   Think about how they simplify the analysis of fluid motion.

4. 4.

   True or False: Streamlines can cross each other.

   • True
   • False

   Hint

   Recall what streamlines indicate about fluid paths.

5. 5.

   For a stream function ψ = 3xy - y^2, find the velocity components u and v. Determine if this satisfies the continuity equation for incompressible flow.

   Hint

   Be careful to calculate the partial derivatives accurately.

6. 6.

   Explain how you would visualize the airflow around a cylindrical object using stream functions. What would you expect to see?

   Hint

   Think about the physical behavior of liquids around solid objects.