Book contents
- A Student’s Guide to Dimensional Analysis
- A Student’s Guide to Dimensional Analysis
- Copyright page
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Mechanics
- 3 Hydrodynamics
- 4 Temperature and Heat
- 5 Electrodynamics and Plasma Physics
- 6 Quantum Physics
- 7 Dimensional Cosmology
- Appendix Answers to Problems
- References
- Index
- References
References
Published online by Cambridge University Press: 31 March 2017
Book contents
- A Student’s Guide to Dimensional Analysis
- A Student’s Guide to Dimensional Analysis
- Copyright page
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Mechanics
- 3 Hydrodynamics
- 4 Temperature and Heat
- 5 Electrodynamics and Plasma Physics
- 6 Quantum Physics
- 7 Dimensional Cosmology
- Appendix Answers to Problems
- References
- Index
- References
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- Information
- A Student's Guide to Dimensional Analysis , pp. 98 - 99Publisher: Cambridge University PressPrint publication year: 2017
References
Galilei, Galileo, Two New Sciences, translated by Crew, Henry and de Salvio, Alfonso, (Chicago, IL: Encyclopedia Britannica Inc., 1952), p. 187.Google Scholar
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 … .”Google Scholar
Rayleigh, Lord (Strutt, John William), The Principle of Similitude. Nature, March 18, (1915).CrossRefGoogle Scholar
Buckingham, Edgar, On Physically Similar Systems; Ilustrations of the Use of Dimensional Equations. Physical Review, Vol. IV, no. 4, (1915), 345–376.Google Scholar
Langhaar, H. L. emphasizes this aspect of the theorem. See his Dimensional Analysis and Theory of Models (Hoboken, NJ: Wiley, 1951), p. 18.Google Scholar
Buckingham, Edgar, On Physically Similar Systems; Ilustrations of the Use of Dimensional Equations. Physical Review, Vol. IV, no. 4, (1915), 345–376.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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Bridgman, Percy, Dimensional Analysis (New Haven, CT: Yale University Press, 1922), p. 107.Google Scholar
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Bridgman, Percy, Dimensional Analysis (New Haven, CT: Yale University Press, 1922), problem 19, p. 108.Google Scholar
Traditionally the “Boussinesq problem.” See Bridgman, Percy, Dimensional Analysis (New Haven, CT: Yale University Press, 1922), pp. 9–11.Google Scholar
Taylor, Lloyd W., Physics: The Pioneer Science (Mineola, NY: Dover, 1941), pp. 592–593.Google Scholar
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.Google Scholar
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Planck, Max, Theory of Heat Radiation (Mineola, NY: Dover, 2011), pp. 205–206. Number 164.Google Scholar