13.2. Experimental Design and Dimensional Analysis

Try these first

1. 1.

   What is dimensional homogeneity?

   Hint

   Look at how units must match in equations.

2. 2.

   Name one application of Buckingham's Pi theorem.

   Hint

   Think about simplifying complex experiments.

3. 3.

   What is Buckingham's Pi theorem primarily used for?

   • To prove dimensional homogeneity
   • To determine the number of experiments needed
   • To derive dimensionless groups

   Hint

   Think about simplifying experimental setups.

4. 4.

   True or False: Dimensional analysis is only applicable in fluid mechanics.

   • True
   • False

   Hint

   Consider where else dimensional analysis may be useful.

5. 5.

   Given a fluid flowing past a sphere, derive the expression for the drag force as a function of Reynolds number and other relevant variables.

   Hint

   Begin with Newton's law of viscosity and recall the terms involved.

6. 6.

   Design an experiment to measure the drag force on a cylinder in water. Specify the parameters and how dimensional analysis will assist in minimizing trials.

   Hint

   Think about all physical quantities that influence the outcomes.