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  1. Home
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  3. A Student's Guide to Dimensional Analysis
  • Cited by 9
Publisher:
Cambridge University Press
Online publication date:
March 2017
Print publication year:
2017
Online ISBN:
9781316676165
DOI:
https://doi.org/10.1017/9781316676165
Series:
Student's Guides
Subjects:
Physics and Astronomy, Engineering, Mathematical Methods, General and Classical Physics, Engineering: General Interest, Engineering Mathematics and Programming
Information

Book description

This introduction to dimensional analysis covers the methods, history and formalisation of the field, and provides physics and engineering applications. Covering topics from mechanics, hydro- and electrodynamics to thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis. Introducing basic physics and fluid engineering topics through the mathematical methods of dimensional analysis, this book is perfect for students in physics, engineering and mathematics. Explaining potentially unfamiliar concepts such as viscosity and diffusivity, the text includes worked examples and end-of-chapter problems with answers provided in an accompanying appendix, which help make it ideal for self-study. Long-standing methodological problems arising in popular presentations of dimensional analysis are also identified and solved, making the book a useful text for advanced students and professionals.

Reviews

'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. … 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.'

Virginia Greco Source: CERN Courier

'Dimensional, or unit, analysis is a useful tool for finding relations between variables that describe a physical system. Although it has applications across all fields of physics, it is not a regular part of a typical undergraduate physics curriculum. … Don Lemons addresses that gap. … His latest book is written in a casual style, as if he were talking to his students and giving them step-by-step guidance. Lemons shares his personal experience applying dimensional analysis to problems. For instance, he discusses the hydraulic jump, a phenomenon one can see in a kitchen sink. … Such anecdotes make dimensional analysis more accessible and less intimidating. … Lemons’s book is a well-written entry-level text that will be of value to curious undergraduates in physics and engineering.'

Hong Lin Source: Physics Today

'The approach taken to the subject is example based: each chapter contains several examples which are dealt with in detail and end with exercise problems. Many of the exercise problems are interesting and are sure to pique the interest of the reader … A good handle on dimensional analysis is probably the most important skill that a modeller should have and this book is an ideal introductory text on the topic. The manner in which the book is written and the material is presented makes it ideal for students who wish to study the material on their own; it is also very useful for instructors involved in teaching courses on modelling. The production quality of the book is very high. The book will be very useful for students, early stage researchers and instructors in physics, mathematics and engineering and I have no hesitations in recommending it.'

M. P. Gururajan Source: Contemporary Physics

'A short introduction that can stimulate students’ interest, broaden their analytical toolbox, and enhance their understanding of the subject.'

Misha Prepelitsa Source: SIAM Review

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Contents

Contents
References

References

1.Galilei, Galileo, Two New Sciences, translated by Crew, Henry and de Salvio, Alfonso, (Chicago, IL: Encyclopedia Britannica Inc., 1952), p. 187.
2.Huntley, H. E., Dimensional Analysis (Mineola, NY: Dover, 1967), p. 33.
3.Fourier, Joseph, The Analytical Theory of Heat, translated by Freeman, Alexander (Mineola, NY: Dover, 1878), Book II, Section IX, Articles 157–162. Fourier closes his discussion of dimensional analysis with the comment that, “On applying the preceding rule to the different equations and their transformations, it will be found that they are homogeneous with respect to each kind of unit, and that the dimension of every angular or exponential quantity is nothing. If this were not the case some error must have been committed in the analysis … .”
4.Rayleigh, Lord (Strutt, John William), The Principle of Similitude. Nature, March 18, (1915).
5.Buckingham, Edgar, On Physically Similar Systems; Ilustrations of the Use of Dimensional Equations. Physical Review, Vol. IV, no. 4, (1915), 345–376.
6.Langhaar, H. L. emphasizes this aspect of the theorem. See his Dimensional Analysis and Theory of Models (Hoboken, NJ: Wiley, 1951), p. 18.
7.Buckingham, Edgar, On Physically Similar Systems; Ilustrations of the Use of Dimensional Equations. Physical Review, Vol. IV, no. 4, (1915), 345–376.
8.This definition reformulates an equivalent one found in Van Driest, E. R., On Dimensional Analysis and the Presentation of Data in Fluid Flow Problems. J. Applied Mechanics, Vol. 13, no. 1, (1946) A–34. See also H. L. Langhaar, Dimensional Analysis and Theory of Models (Hoboken, NJ: Wiley, 1951), p. 29.
9.The number of effective dimensions is also the “rank of the dimensional matrix” – a mathematical concept exploited in fluid mechanics engineering texts. See, for instance, Fox, R. W., McDonald, A. T., and Pritchard, P. J., Fluid Mechanics (Hoboken, NJ: Wiley, 2004), pp. 282–283.
10.The concept, although not the name, of imposed dimension originates with Bridgman, Percy’s highly recommended text Dimensional Analysis (New Haven, CT: Yale University Press, 1922). See, in particular, pp. 9–11, 63–66, 67–69, and 77–78. Others, including H. E. Huntley, Dimensional Analysis, (Mineola, NY: Dover, 1967), use the concept of imposed dimensions.
11.Barenblatt, G. I., Scaling, Self-Similarity, and Intermediate Dynamics (Cambridge, UK: Cambridge University Press, 1996), pp. 18 ff.
12.Helmholtz, Hermann, On the Sensations of Tone 6th Edition (Gloucester, MA: Peter Smith, 1948), pp. 43–44.
13.Bridgman, Percy, Dimensional Analysis (New Haven, CT: Yale University Press, 1922), p. 107.
14.Taylor, G., The Formation of a Blast Wave by a Very Intense Explosion. II. The Atomic Explosion of 1945. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 201, No. 1065, (Mar. 22, 1950), 175–186.
15.Lindberg, David C., The Beginnings of Western Science (Chicago, IL: University of Chicago Press, 1992), p. 305.
16.See Aristotle, , The Basic Works of Aristotle editor McKeon, Richard, (New York, NY: Random House, 1966) Physics, Book IV, chapter 8, p. 216a, lines 14–17. See also David C. Lindberg, The Beginnings of Western Science (Chicago, IL: University of Chicago Press, 1992), pp. 59–60.
17.Godwin, R. P., The Hydraulic Jump (‘Shocks’ and Viscous Flow in the Kitchen Sink), American Journal of Physics 61 (9), (1993) 829–832.
18.Nansen, Fridtjof, Farthest North (Edinburgh, UK: Birlinn, 2002), p. 186.
19.Vuik, C., Some Historical Notes on the Stefan Problem, Nieuw Archief voor Wiskunde, 4e serie 11 (2), (1993) 157–167.
20.Bridgman, Percy, Dimensional Analysis (New Haven, CT: Yale University Press, 1922), problem 19, p. 108.
21.Traditionally the “Boussinesq problem.” See Bridgman, Percy, Dimensional Analysis (New Haven, CT: Yale University Press, 1922), pp. 9–11.
22.Taylor, Lloyd W., Physics: The Pioneer Science (Mineola, NY: Dover, 1941), pp. 592–593.
23.Dunmore, John, Pacific Explorers: The Life of John Francois de La Perouse 1741–1788 (Palmerston North, NZ: The Dunmore Press Limited, 1985), pp. 286–292.
24.Schiff, L., Quantum Mechanics 3rd Edition (New York, NY: McGraw Hill, 1968) pp. 397 ff.
25.Planck, Max, Theory of Heat Radiation (Mineola, NY: Dover, 2011), pp. 205–206. Number 164.

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