By Don S Lemons
Cambridge University Press
Dimensional analysis is a mathematical technique that allows one to deduce the relationship between different physical quantities from the dimensions of the variables involved in the system under study. It provides a method to simplify – when possible – the resolution of complex physical problems.
This short book provides an introduction to dimensional analysis, covering its history, methods and formalisation, and shows its application to a number of physics and engineering problems. As the author explains, the foundation principle of dimensional analysis is essentially a more precise version of the well known rule against “adding apples and oranges”; nevertheless, the successful application of this technique requires physical intuition and some experience. Most of the time it does not lead to the solution of the problem, but it can provide important hints about the direction to take, constraints on the relationship between physical variables and constants, or a confirmation of the correctness of calculations.
After a chapter covering the basics of the method and some historical notions about it, the book offers application examples of dimensional analysis in several areas: mechanics, hydrodynamics, thermal physics, electrodynamics and quantum physics. Through the solution of these real problems, the author shows the possibilities and limitations of this technique. In the final chapter, dimensional analysis is used to take a few steps in the direction of uncovering the dimensional structure of the universe.
Aimed primarily at physics and engineering students in their first university courses, it can also be useful to experienced students and professionals. Being concise and providing problems with solutions at the end of each chapter, the book is ideal for self study.
