# Professor Megan McClean

BIOMEDICAL ENGINEERING 330: ENGINEERING PRINCIPLES OF MOLECULES, CELLS, AND TISSUES)

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.