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Dimensional Analysis – An Engineering Design Tool

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

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Dimensional Analysis – An Engineering Design Tool

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

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

  3. Word Cloud “Science”

  4. Word Cloud for “Engineering”

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

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

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

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

  10. Dimensional analysis of the pendulum Terms on the right must have the same dimensions as tp, 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 deduce or

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

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

  13. Pendulum non-idealities • 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 • 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

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