6.5.1. Internal Resistance Force

Try these first

1. 1.

   What is the internal resistance force?

   Hint

   Think about forces acting internally within a fluid.

2. 2.

   What do we use Cauchy's equations for?

   Hint

   Consider the equations as foundational for other fluid mechanics equations.

3. 3.

   What do Cauchy's equations describe in fluid mechanics?

   • Relationship between pressure and velocity
   • Relationship between stress and motion
   • Relationship between temperature and pressure

   Hint

   Think about the flows and how they experience forces.

4. 4.

   True or False: The internal resistance force is only relevant in solids.

   • True
   • False

   Hint

   Consider fluid flow dynamics.

5. 5.

   A water pipe has a diameter reduction that causes internal pressure to change. Analyze the stress tensor at two points before and after the reduction and how it impacts the fluid flow.

   Hint

   Consider both shear and normal stress components in the calculations.

6. 6.

   Using Cauchy's equations, derive a specific case for a viscous fluid passing through a narrow channel and discuss the implications for flow rate.

   Hint

   Review how viscosity factors into Cauchy’s equations under flow conditions.