5.5.1. Conservation of Equations

Try these first

1. 1.

   What is a stream function?

   Hint

   Think about how we manage complex fluid flow equations.

2. 2.

   What does Bernoulli's equation represent?

   Hint

   Consider energy patterns in moving fluids.

3. 3.

   What does a stream function help accomplish in fluid dynamics?

   • A tool for measuring pressure
   • Simplifying flow equations
   • Increasing fluid density

   Hint

   Think about handling complexity in equations!

4. 4.

   True or False: The velocity u from a stream function is found by taking the derivative of the stream function with respect to y.

   • True
   • False

   Hint

   Remember how derivatives relate to changes in functions.

5. 5.

   Given a more complex stream function ψ = x³ - y², find the flow velocities at point (1, 2).

   Hint

   Apply partial derivatives carefully!

6. 6.

   Analyze how velocity patterns change as streamlines converge or diverge around an object.

   Hint

   Visualize how air flows around an airplane wing!