A First Course in Dimensional Analysis: Simplifying Complex Phenomena Using Physical Insight

by Juan G Santiago

An introduction to dimensional analysis, a method of scientific analysis used to investigate and simplify complex physical phenomena, demonstrated through a series of engaging examples. This book offers an introduction to dimensional analysis, a powerful method of scientific analysis used to investigate and simplify complex physical phenomena. The method enables bold approximations and the generation of testable hypotheses. The book explains these analyses through a series of entertaining applications; students will learn to analyze, for example, the limits of world-record weight lifters, the distance an electric submarine can travel, how an upside-down pendulum is similar to a running velociraptor, and the number of Olympic rowers required to double boat speed. The book introduces the approach through easy-to-follow, step-by-step methods that show how to identify the essential variables describing a complex problem; explore the dimensions of the problem and recast it to reduce complexity; leverage physical insights and experimental observations to further reduce complexity; form testable scientific hypotheses; combine experiments and analysis to solve a problem; and collapse and present experimental measurements in a compact form. Each chapter ends with a summary and problems for students to solve. Taken together, the analyses and examples demonstrate the value of dimensional analysis and provide guidance on how to combine and enhance dimensional analysis with physical insights. The book can be used by undergraduate students in physics, engineering, chemistry, biology, sports science, and astronomy.

184 pages, Paperback

Published October 22, 2019

Reviews

[George Mann · Rating 4 out of 5]

Not a bad treatment of the topic. As a physics major I relied on dimensional analysis more as a way to double check calculations (if the units didn't come out correct, I probably made an algebra/calculus mistake). But this book opened my eyes to the other possibilities for this approach. In particular, learning how to build scale models that correctly take into account forces at the large scale was illuminating.

I thought the math was approachable and on point, though I fear the prerequisites to understand this text may be a little high. It's probably worth a disclaimer on the front "assumes you know calculus: definite and indefinite integrals and derivatives, plus some ODE and PDE helps!"

Surprisingly this book was an impulse purchase from the wizards at Facebook who show me eerily relevant ads. I thought "oh! that looks interesting" and snapped it up.

My guess is there are two general classes of readers for this book. The first are engineers in industry who are looking to learn techniques they can apply on the job to save money and time. The second are students or general math/physics interest folks who just want to learn more about this field of analysis.

Hope you enjoy the book too!