12.3.3. Non-dimensionalization and Order of Magnitude Analysis

Try these first

1. 1.

   What is non-dimensionalization?

   Hint

   Think about simplifying equations for comparison.

2. 2.

   Define Reynolds Number.

   Hint

   It determines flow characteristics.

3. 3.

   What does the Reynolds number indicate?

   • Flow turbulence level
   • Viscosity
   • Pressure

   Hint

   Remember, it compares inertial and viscous forces.

4. 4.

   True or False: Non-dimensionalization always results in the same type of equation regardless of system size.

   • True
   • False

   Hint

   Think about the importance of dimensionless forms.

5. 5.

   Given a scenario where a fluid flows over a flat plate with a known viscosity and velocity, calculate the Reynolds number and predict whether the flow is laminar or turbulent. Use a flaw assumption of a plate length.

   Hint

   Use typical values for density and viscosity if not provided.

6. 6.

   Analyze a flow situation applying non-dimensionalization to the Navier-Stokes equations. Identify terms to retain and eliminate based on their order of magnitude.

   Hint

   Consider simplifying terms as much as possible, focus on key driving forces in flow.