1.13. Dimensional Homogeneity

Try these first

1. 1.

   What is dimensional homogeneity?

   Hint

   Consider the necessary equality of dimensions.

2. 2.

   Define the Buckingham Pi Theorem.

   Hint

   Think about reducing complexity in equations.

3. 3.

   What does dimensional homogeneity ensure in an equation?

   • That all terms have different dimensions
   • That all terms have the same dimensions
   • No dimensions are used at all

   Hint

   Think about how dimensions relate to each other.

4. 4.

   True or False: The Buckingham Pi theorem reduces the number of variables to a relationship among dimensionless products.

   • True
   • False

   Hint

   Recall how variables change in every experiment.

5. 5.

   Given a fluid flow problem with variables of density, velocity, pipe diameter, and viscosity, identify how many dimensionless groups can be formed using the Buckingham Pi theorem.

   Hint

   Remember to count all relevant variables.

6. 6.

   Explain the consequences of neglecting dimensional homogeneity in an engineering calculation.

   Hint

   Think about the role of dimensions in engineering.