4.1.4. Taylor Series Applications

Try these first

1. 1.

   Define mass conservation.

   Hint

   Think about the law of conservation in physics.

2. 2.

   What is a control volume?

   Hint

   Consider the volume through which fluid flows.

3. 3.

   What does the mass conservation equation express?

   • Rate of mass inflow
   • Rate of mass outflow
   • Rate of change of mass storage

   Hint

   Think about how mass interacts in a closed system.

4. 4.

   True or False: In incompressible flow, changes in density can occur.

   • True
   • False

   Hint

   Consider what incompressible means.

5. 5.

   A control volume of fluid experiences inflow at a rate of 5 kg/s and outflow at 3 kg/s. If the initial mass in the control volume is 10 kg, what is the new mass after 5 seconds?

   Hint

   Identify inflow and outflow rates correctly before calculating.

6. 6.

   Explain how changes in pressure affect compressible fluid flow and derive a modified mass conservation equation considering variable density.

   Hint

   Recall how the ideal gas law connects pressure and density.