13.3.2. Non-Dimensional Analysis

Try these first

1. 1.

   Define dimensional homogeneity in your own words.

   Hint

   Focus on the importance of units being consistent.

2. 2.

   What is Buckingham's Pi Theorem used for?

   Hint

   Think about the number of variables and dimensions.

3. 3.

   What does dimensional homogeneity ensure in an equation?

   • Different dimensions can coexist
   • All terms have the same dimensions
   • Dimensions do not matter

   Hint

   Think about how you check units across an equation.

4. 4.

   True or False: The Reynolds number is a fundamental dimension.

   • True
   • False

   Hint

   Recall the definitions of dimensions vs groups.

5. 5.

   A new fluid is introduced for an experiment involving drag on a sphere. The density of the fluid is 1200 kg/m³, and the dynamic viscosity is 0.0012 Pa.s. Calculate the dimensionless Reynolds number if the diameter is 0.1 m and the flow velocity is 3 m/s.

   Hint

   Recall the formula for Reynolds number and substitute the values properly.

6. 6.

   Using Buckingham's Pi Theorem, if you have 6 variables in a fluid dynamics problem with 3 essential dimensions, how many independent dimensionless groups can you find? Explain your reasoning.

   Hint

   Remember n is the count of variables, k is the number of dimensions.