5.2. Introduction

Try these first

1. 1.

   What is a stream function?

   Hint

   Think about how we combine two velocity components.

2. 2.

   Name an application of stream functions in fluid dynamics.

   Hint

   Consider areas where complex flow needs to be simulated.

3. 3.

   What is a stream function?

   • A way to measure fluid density
   • A mathematical function to describe fluid flow
   • A physical representation of fluid motion

   Hint

   Focus on definitions discussed in class.

4. 4.

   The divergence of the velocity field must equal what for steady fluid flows?

   • True
   • False

   Hint

   Recall the mass conservation equation from our discussions.

5. 5.

   Develop a numerical simulation using a stream function to depict the flow around a cylinder. Consider the parameters such as fluid density and velocity.

   Hint

   Start with a basic cylindrical flow and apply the principles we've learned.

6. 6.

   Analyze a real-world application where stream functions are used in engineering, such as in the design of aircraft or underwater vehicles. Discuss how they optimize performance.

   Hint

   Research examples of aircraft or submarines that utilize computational fluid dynamics.