19.2.1. Linear Momentum Equations

Try these first

1. 1.

   Define a stress tensor in the context of fluid mechanics.

   Hint

   Think of how internal forces are represented.

2. 2.

   What is the difference between normal stress and shear stress?

   Hint

   Consider their orientation with respect to surfaces.

3. 3.

   What is the primary purpose of a stress tensor in fluid mechanics?

   • To measure pressure
   • To describe internal forces
   • To quantify external forces

   Hint

   Think about internal versus external properties.

4. 4.

   True or False: Atmospheric pressure must always be considered in fluid flow analyses.

   • True
   • False

   Hint

   Consider how pressure affects surface balance.

5. 5.

   Consider a cylindrical tank with fluid flowing in and out. Calculate the net momentum flux if inflows are at 5 kg/s with a velocity of 2 m/s and outflows are at 3 kg/s with 1.5 m/s.

   Hint

   Use the momentum equation focusing on net inflow and outflow.

6. 6.

   Using Reynolds Transport Theorem, derive the momentum flux equation for a fixed control volume and discuss any assumptions.

   Hint

   Explore the steady state vs. unsteady relationship in your assumptions.