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Scaling Analysis A Valuable Technique In Engineering Teaching And Practice

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2001 Annual Conference


Albuquerque, New Mexico

Publication Date

June 24, 2001

Start Date

June 24, 2001

End Date

June 27, 2001



Page Count


Page Numbers

6.868.1 - 6.868.12

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Paper Authors

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Vadim Guliants

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Eugene Kopaygorodsky

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William Krantz

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Session 3513

Scaling Analysis – A Valuable Technique In Engineering Teaching And Practice

Eugene M. Kopaygorodsky, William B. Krantz, Vadim V. Guliants University of Cincinnati


This paper describes a scaling technique that can be used as a teaching tool in engineering courses that involve the development of mathematical models for physical processes. This scaling technique provides a systematic means for achieving the minimum parametric representation of a physical problem. Moreover, since it involves order-of-one scaling, it permits assessing the relative importance of the various terms that appear in a mathematical model. As such, scaling analysis is of considerable value in engineering practice as well. The scaling analysis method is illustrated via an example problem involving Pressure-Swing Adsorption (PSA) for producing oxygen-enriched air. Its utility is demonstrated by showing that it can provide quantitative criteria for invoking simplifying assumptions that oftentimes are made without rigorous justification. Moreover, this example illustrates how scaling analysis can be used to assess the performance of novel process innovations, in this case Ultra-Rapid PSA that is being proposed for providing a portable device for supplying oxygen to patients suffering from Chronic Obstructive Pulmonary Disease (COPD).

I. Introduction

Scaling analysis is a useful technique that involves a systematic method for recasting the describing equations for a physical process in dimensionless form. The end result of a proper scaling analysis is a set of dimensionless equations that describes a physical process in terms of the minimum number of dimensionless parameters. Moreover, a proper scaling analysis insures that the dependent and independent variables and their derivatives are scaled to be of order one. When the describing equations are scaled in this manner, the magnitude of the dimensionless groups that multiply certain terms permits assessing simplifying assumptions that can be invoked in solving the physical problem.

Scaling analysis is particularly useful as a teaching tool since it permits quantifying concepts that are sometimes presented in an intuitive way. For example, the concept of a hydrodynamic boundary layer is often justified using nonquantitative “hand-waving” arguments. It also useful as a teaching tool that provides a systematic method for making simplifying assumptions in the description of a physical problem that oftentimes are made without justification. A knowledge of

Proceedings of the 2001 American Society for Engineering Education Annual Conference & Exposition Copyright © 2001, American Society for Engineering Education

Guliants, V., & Kopaygorodsky, E., & Krantz, W. (2001, June), Scaling Analysis A Valuable Technique In Engineering Teaching And Practice Paper presented at 2001 Annual Conference, Albuquerque, New Mexico.

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