University of Wisconsin–Madison


Professor Megan McClean


1. Learning Outcomes

After completion of this assignment students should have the ability to:

• identify situations that are amenable to analysis using dimensional homogeneity

• clearly explain and summarize, in writing, the concept and importance of dimensional homogeneity

• justify the importance of using dimensional homogeneity in the course and in practical situations (such as analyzing their BME design projects)

2. Assignment Execution

This assignment would be given as an in-class exercise. Students would be allowed to confer in small groups as needed, but each student would be asked to write their own essay. Approximately 15 minutes would be allocated to this assignment. Assignments would be reviewed and graded before the next lecture period, and examples of excellent answers discussed at the beginning of lecture. Common misconceptions present in multiple essays would also be clarified.

3. Student Prompt

You and a classmate are working on a BME design project to build a better extra ventricular drain for patients suffering from traumatic brain injury. You would like to estimate the pressure drop across a particular piece of cylindrical tubing in your device.

Your classmate has already taken BME 330 and comes up with the following formula:

Δ𝑝 = 32𝜇 < 𝑣 > 𝐿 /𝐷

where Δ𝑝 is the pressure drop, 𝜇 is the viscosity of the cerebrospinal fluid, < 𝑣 > is the average velocity of fluid in the tubing, L is the length and D is the inner diameter of the tubing. Even though we haven’t gotten to the fluids section of transport yet, you can quickly tell that this formula isn’t quite correct.

Write a short explanation (<250 words) explaining to your classmate why this equation cannot be correct. Make sure to state and define the key concept that you are using to determine that the original equation is incorrect. Show how you can use this concept to guess at an appropriate correction to the formula. Explain why this concept is crucial to engineers, and more practically, how it might help you to do better on exams.

4. Rubric and Grading Criteria

Grade Criteria (+, , -)

+ Explanations in this category will identify the fact that units on both sides of the equation are not balanced, and therefore the equation is not physically possible. Furthermore, explanations in this category will clearly identify and explain the key concept of dimensional homogeneity (which is being violated by the original equation). Explanations will identify D2 in the denominator as a way to satisfy dimensional homogeneity. A compelling argument for the importance of checking dimensional homogeneity in daily practice as an engineer (and as a BME 330 student) will be made. The explanation will be clearly written containing almost no errors in spelling, punctuation, or grammar.

Explanations in this category will reveal an understanding of the concept of dimensional homogeneity but may be lacking in clarity or fully developed explanation. Explanations that identify the error in the equation, but do not clearly identify and explain the concept of dimensional homogeneity will fall in this category. Explanations that fail to provide a compelling reason for using the concept of dimensional homogeneity will fall in this category. Explanations that correctly identify the key concepts, but are very poorly written will fall in this category.

These explanations will be unsuccessful because the writer fails to identify the key flaw in the original equation, fails to clearly identify and explain dimensional homogeneity, and/or fails to write a coherent, grammatically correct explanation. Answers that are clearly written, but fail to identify the key error and principle of dimensional homogeneity or misrepresent the principles of dimensional homogeneity will fall in this category.