4.1.8. Case Studies and Problems

Try these first

1. 1.

   Define the continuity equation.

   Hint

   Think about mass flow.

2. 2.

   What is divergence in fluid mechanics?

   Hint

   Consider vector fields.

3. 3.

   What does the continuity equation express?

   • Mass conservation
   • Energy conservation
   • Momentum conservation

   Hint

   Think about the principle of mass flow.

4. 4.

   True or False: Incompressible flow assumes density varies with pressure.

   • True
   • False

   Hint

   Reflect on the definitions of incompressible flow.

5. 5.

   Consider a cylindrical tank with a piston compressing air. If the piston moves at a speed of 0.1 m/s, calculate how the density changes with time if initially, the density is known.

   Hint

   Account for changes in the volume and apply the continuity equation.

6. 6.

   Given a two-dimensional flow field represented as v(x,y) = (x, y^2), determine if the flow is incompressible or not.

   Hint

   Remember to differentiate with respect to each variable and sum them.