1. Dimensional Analysis – An Engineering Design Tool 1 Introduce dimensional analysis and demonstrate its use for obtaining constitutive equations for design Discuss non-ideality impact on design A Tidbit for CENG 201a: Introduction to Chemical and Environmental Engineering Learning Goal

2. Engineering versus Science 2 What is the difference between Engineering and science? (Class forms groups, discuss the question and each group report out to the class)

3. http://www.wordle.net/ Word Cloud “Science”

4. http://www.wordle.net/ Word Cloud for “Engineering”

5. My Answer 5 Science makes it known; engineering makes it useful. What that means: Engineers have to design under uncertainty; use correlations and constitutive relations not based on fundamental laws. Engineers rarely operate within the ideal model (chemists use the ideal gas law; chemical engineers use the compressibility relationship).

6. 6 dimensionless temperature dimensionless pressure dimensionless volume (assuming molar volume) Example: Ideal Gas Law: PV = nRT A not so ideal gas law that has engineering use:

7. 7 Dimensionless V plotted against dimensionless P at various dimensionless T

8. 8 Dimensional analysis of a pendulum: Using dimensional analysis to develop a constitutive equation Why are there no units on amplitude?

9. 9 Dimensional analysis of a pendulum Why are there no units on amplitude?

10. 10 Dimensional analysis of the pendulum Terms on the right must have the same dimensions as t p, time. Thus, no term can include mass because it only appears in one parameter describing the pendulum. Thus, We arrange the remaining parameters to obtain function which has dimensions of time: so we deduceor

11. 11 A constitutive equation is arrived at by experimental measurements The experimental observation is a linear relationship between t p and the square root of (l/g). We evaluate the value of f(  ) from the slope of the straight line to find:

12. 12 A constitutive equation is arrived at by experimental measurements The experimental observation is a linear relationship between t p and the square root of ((l/g). We evaluate the value of f(  ) from the slope of the straight line to find:

13. Pendulum non-idealities 13 No friction No air resistance Massless rod connecting pivot and massive bob http://en.wikipedia.org/wiki/Pendulum

14. Activity: test the effect of pendulum rod with mass 14 Design an experiment to measure the effect rod mass on pendulum period Interpret change in period in terms of pendulum variables Compare and discuss data