3.4. Navier–Stokes equations

Try these first

1. 1.

   Define viscous fluid in your own words.

   Hint

   Think about how honey flows compared to water.

2. 2.

   What does the Stokes Hypothesis entail?

   Hint

   Consider fluid compressibility and stress.

3. 3.

   What do Navier-Stokes equations primarily describe?

   • Forces acting on solids
   • Motion of viscous fluids
   • Air pressure systems

   Hint

   Think about fluid types in motion.

4. 4.

   True or False: The divergence of velocity must be zero for incompressible flow.

   • True
   • False

   Hint

   How does fluid density affect flow equations?

5. 5.

   Consider a cylindrical pipe with a viscous liquid flowing through it. Using the Navier-Stokes equations, derive how pressure changes along the length of the pipe.

   Hint

   Start by defining your variables and using the conservation of momentum.

6. 6.

   Prove how the Stokes Hypothesis can be employed to simplify the Navier-Stokes equations for an incompressible fluid.

   Hint

   Think about the properties of fluid and how they relate to stress and volume.