13.1.1. Dimensional Homogeneity

Try these first

1. 1.

   What are the fundamental dimensions used in fluid mechanics?

   Hint

   Think of basic measurements.

2. 2.

   Define dimensional homogeneity.

   Hint

   Consider what happens if units don’t match.

3. 3.

   What does dimensional homogeneity ensure in an equation?

   • All terms have the same dimension
   • All terms are zero
   • All terms equal unity

   Hint

   Think about the relationship of units.

4. 4.

   True or False: The Reynolds number is a dimensionless quantity.

   • True
   • False

   Hint

   Think about its role in fluid dynamics.

5. 5.

   Consider a system with three dependent variables: pressure (p), velocity (V), and dynamic viscosity (μ). Using Buckingham’s Pi theorem, find the number of dimensionless groups.

   Hint

   Count variables and use the theorem.

6. 6.

   If the drag force on a cylinder depends on its diameter, fluid velocity, density, and viscosity, describe how you would form a dimensionless group.

   Hint

   Focus on balancing out units.