8.2.2. Simplifications for analytical solutions

Try these first

1. 1.

   What does the term 'incompressible flow' refer to?

   Hint

   Think about fluids that do not experience volume changes.

2. 2.

   Name one assumption made when working with Navier-Stokes equations.

   Hint

   Consider how viscosity behaves in different fluids.

3. 3.

   What is the primary assumption made for incompressible fluids?

   • The density remains constant
   • Viscosity varies with temperature
   • The flow is always turbulent

   Hint

   Think about the conditions when liquid flows.

4. 4.

   True or False: Euler’s equations only apply to scenarios where viscosity is significant.

   • True
   • False

   Hint

   Consider when you can ignore viscous forces.

5. 5.

   Given a fluid flowing through a horizontal pipe with varying diameters, describe how you would apply the Navier-Stokes equations and under which conditions you might simplify them.

   Hint

   Focus on where flow behavior changes significantly.

6. 6.

   Explain the process of deriving Bernoulli's equation from the Navier-Stokes equations using specific assumptions.

   Hint

   Consider what conditions allow for integration along streamlines.