2.3. Deriving Reynolds Transport Theorem

Try these first

1. 1.

   What is an extensive property?

   Hint

   Think of properties that change with mass.

2. 2.

   Give an example of an intensive property.

   Hint

   Consider properties that remain constant irrespective of mass.

3. 3.

   What defines an extensive property in fluid mechanics?

   • It does not change with mass
   • It depends on the amount of fluid
   • It is always constant

   Hint

   Think about properties that change when more fluid is added.

4. 4.

   The Reynolds Transport Theorem is crucial for analyzing which of the following?

   • True
   • False

   Hint

   Recall its significance in various fluid dynamics scenarios.

5. 5.

   A control volume is defined within a pipe. The fluid density is 1000 kg/m^3. If the pipe has two inlets and one outlet, with inlets having cross-sectional areas of 0.02 m^2 and 0.01 m^2 respectively, calculate the total inflow rate if the velocities are 2 m/s and 3 m/s. What is the total outflow rate if the outlet area is 0.03 m^2 with a velocity of 2 m/s?

   Hint

   Apply the equation for flow rate which is mass flow rate = density × area × velocity.

6. 6.

   Derive the complete expression for an extensive property transported across a surface with changing velocity and density. Discuss implications.

   Hint

   Focus on integration of the flux over your defined surfaces.