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The Question of Units: Bothersome Details or Keys to Understanding?

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2017 ASEE Annual Conference & Exposition


Columbus, Ohio

Publication Date

June 24, 2017

Start Date

June 24, 2017

End Date

June 28, 2017

Conference Session

Learning and Assessment in ME 1

Tagged Division

Mechanical Engineering

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Paper Authors


Mark Schumack University of Detroit Mercy

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Mark Schumack is Professor of Mechanical Engineering at the University of Detroit Mercy, where he teaches courses in heat transfer, thermodynamics, fluid mechanics, and energy systems. His ongoing pedagogical interests include developing ways to teach energy conservation and sustainability principles. His research interests include thermal/fluid modeling using computational techniques, with applications in the automotive, manufacturing, and energy fields. Dr. Schumack earned his BS, MS, and Ph.D. degrees in Mechanical Engineering from the University of Michigan.

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The Question of Units: Bothersome Details or Keys to Understanding?

Students can be inclined to treat units conversions in engineering problems as an ancillary exercise, necessary perhaps for a complete solution but not necessarily important to a good understanding of the material. This paper describes the types and sources of units confusion students can have, explores the ways in which units calculations are abused, analyzes the ways in which student attitudes about units intersect with instructor and industry attitudes, discusses strategies for motivating students to appreciate the importance of units, and makes the case for how the adoption of a universal units approach can remove confusion and establish a solid groundwork for understanding fundamental engineering principles.

The paper begins with a brief review of how units are addressed in teaching the three areas normally associated with mechanical engineering: solid mechanics and machine design, manufacturing processes, and the thermal sciences. This includes a discussion of the wide variety of ways in which textbooks approach units, ranging from avoidance (a purely abstract presentation) to cursory attention (presentations that include numerical examples with spotty consideration of units conversions) to rigorous units accounting methods.

Student confusion about units takes many forms. The paper identifies four of these forms and then describes five sources of confusion, including misleading derivations and inadequate distinctions between relationships based on physical laws and those generated empirically. The paper describes how students can abuse units calculations by using them as a “crutch” in several different ways. Lessons from the dimensional analysis approach normally found in fluid mechanics texts are enumerated.

How students feel about units can be influenced by both classroom experiences and exposure to industrial attitudes during internships. The author explains how differing emphasis among instructors can affect student appreciation for careful units treatment, and how interaction with engineers in industry can both bolster and tarnish student understanding of the importance of units.

Motivation for the careful consideration of units is introduced by highlighting communication issues (along with striking examples of what can go wrong), and explaining how a rigorous cancellation process can help diagnose conceptual errors in the problem solution.

Finally, the author outlines a proposed standard approach for the treatment of units across the mechanical engineering curriculum. This approach involves developing student skills in applying a general physical relationship to a specific situation, performing the mathematical operations necessary to isolate the required result in terms of given information, substituting numerical data along with given units, and completing the analysis by doing conversions and cancellations. The presentation ends by highlighting the importance of critical evaluation of calculated results in developing sound engineering judgment.

Schumack, M. (2017, June), The Question of Units: Bothersome Details or Keys to Understanding? Paper presented at 2017 ASEE Annual Conference & Exposition, Columbus, Ohio. 10.18260/1-2--28996

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