3.1.5. Partial Differential Equations

Try these first

1. 1.

   What is a control volume?

   Hint

   Think of it as a specific area in fluid dynamics.

2. 2.

   What does the principle of mass conservation state?

   Hint

   Focus on the idea of mass balance.

3. 3.

   What principle does the mass conservation equation represent?

   • Mass can be created
   • Mass is constant
   • Mass is variable

   Hint

   Think about how mass behaves in fluid dynamics.

4. 4.

   The divergence of velocity vectors indicates the presence of what?

   • True
   • False

   Hint

   Recall the physical interpretations of divergence.

5. 5.

   Consider a cylindrical tank filled with water. If the inflow rate is 10 L/min and the outflow rate is 8 L/min, what is the net change in mass within the tank over 10 minutes?

   Hint

   Calculate the difference between inflow and outflow rates first.

6. 6.

   Using the notion of mass conservation, explain how would you approach deriving the equations governing the flow of air through a variable density medium?

   Hint

   Consider how density affects total mass in your control volume.