Lesson: Dimensional Analysis

Overview of this Lesson

DA involves organizing variables into grouping such that the primary dimensions cancel out. These groups are called $\pi \mathrm{-groups}$. We use $\pi \mathrm{-groups}$ to characterize the physical world.

Benefits of this Lesson

  • Learn how to characterize a system by using independent and dependent variables. Learn how to convert these variables into $\pi \mathrm{-groups}$.
  • Learn how to characterize a full-scale system (e.g. a dam, a large turbine, …) by using data obtained from a simple, low-cost experiment, often a scale model.
  • Learn how to use data from an experiment to predict the performance of a system that has not yet been built

Goals (Results we intend to create).

  • Learners know main concepts
    • $\pi \mathrm{-group}$
    • Model and Prototype
    • Similitude (subconcepts include geometric similitude and dynamic similitude)
  • Procedural Knowledge. Learners can
    • Develop a system model
    • Apply the $\pi \mathrm{-Buckingham}$ theorem to identify the number of $\pi \mathrm{-groups}$.
    • Apply the step-by-step method to find $\pi \mathrm{-groups}$.
    • Relate $\pi \mathrm{-groups}$ and variables between models and prototypes
  • Factual Knowledge.
    • Describe meaning of common pi-groups (Table 8.3).
    • Explain how to achieve similitude (2 key ideas).

Resources (sources of knowledge for reaching goals)

  • Chapter 8

Plan (steps to reach the goals)

1. Goal Setting.
Recommend: Write down personal goals for this lesson. Ask yourself, what do I want? What are my motivations for studying engineering? Make your goals specific (i.e. measurable) and challenging. For more information, see "how to write goals."

2. System model & finding pi-groups.
a. Read p. 249 to 256.
b. Explain how to develop a system model. (ideas will be presented in class)
c. Explain pi-Buckingham theorem (in your own words)
d. Explain the step-by-step method (in your own words).
e. Text problems 8.6, 8.15, 8.18.

3. Common pi-groups
a. Read p. 256 to 258.
b. Questions to consider. What are the most common pi-groups? What are the associated physics?

4. Similitude.
a. Skim p. 249 to 273.
b. Get ideas about similitude down (recommend: MREAC on similitude).
c. Text problems 8.42, 8.61, 8.74.

5. Review of this lesson (Reflective Thinking)
b. Quality. How well did you hit the goals? What is your present level of performance? Why?
a. Strengths. During this lesson, what actions best helped you hit meaningful goals? Why were these actions valuable?
c. Improvements. On this lesson, what problems or issues did you encounter? What actions could you take that will allow you to overcome these problems/issues? What actions will you commit to taking?
d. Insights. During this lesson, what did you discover about your own learning process?

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