3.1.11. Mass Conservation Equations Derived

Try these first

1. 1.

   What is a control volume?

   Hint

   Think about what you would measure within a specified area.

2. 2.

   What does the Reynolds Transport Theorem relate?

   Hint

   Consider mass and its movement.

3. 3.

   What does the Reynolds Transport Theorem connect?

   • Change of momentum
   • Change of mass
   • Change of temperature

   Hint

   Consider what quantity is conserved in fluid mechanics.

4. 4.

   True or False: The divergence of a velocity field being negative indicates a source.

   • True
   • False

   Hint

   Think about flow directions and sources versus sinks.

5. 5.

   A pipe system experiences a mass inflow of 2 kg/s and outflow of 1.5 kg/s. Calculate the change in mass within a control volume over a time of 5 seconds.

   Hint

   Use the relationship of inflow and outflow in your calculation.

6. 6.

   Derive the continuity equation using the divergence theorem for an incompressible fluid.

   Hint

   Relate the divergence of velocity to mass conservation.