5.4.2.2. Cylindrical Coordinate Systems

Try these first

1. 1.

   What does a stream function represent in fluid mechanics?

   Hint

   Think about how we visualize flow.

2. 2.

   State the difference between compressible and incompressible flow.

   Hint

   Consider how gases and liquids behave.

3. 3.

   What does a stream function help visualize?

   • Pressure variation
   • Fluid velocity
   • Flow streamlines

   Hint

   Focus on the representation of fluid paths.

4. 4.

   True or False: The velocity field can be derived from stream functions.

   • True
   • False

   Hint

   Recall the differentiation process.

5. 5.

   Given the stream function ψ = r²sin(θ), find the velocity components and demonstrate how the flow behaves in a radial direction.

   Hint

   Utilize polar derivatives to solve.

6. 6.

   Analyze a cylindrical tank where the velocity of fluid outflow varies with height. Using stream functions, determine how this affects the preservation of mass.

   Hint

   Remember that mass in equals mass out for steady flow.