Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-28T22:08:38.767Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  31 March 2017

Don S. Lemons
Affiliation:
Bethel College, Kansas
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Galilei, Galileo, Two New Sciences, translated by Crew, Henry and de Salvio, Alfonso, (Chicago, IL: Encyclopedia Britannica Inc., 1952), p. 187.Google Scholar
Huntley, H. E., Dimensional Analysis (Mineola, NY: Dover, 1967), p. 33.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), 345376.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), 345376.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. 282283.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
Barenblatt, G. I., Scaling, Self-Similarity, and Intermediate Dynamics (Cambridge, UK: Cambridge University Press, 1996), pp. 18 ff.Google Scholar
Helmholtz, Hermann, On the Sensations of Tone 6th Edition (Gloucester, MA: Peter Smith, 1948), pp. 4344.Google Scholar
Bridgman, Percy, Dimensional Analysis (New Haven, CT: Yale University Press, 1922), p. 107.Google Scholar
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), 175186.Google Scholar
Lindberg, David C., The Beginnings of Western Science (Chicago, IL: University of Chicago Press, 1992), p. 305.CrossRefGoogle Scholar
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.Google Scholar
Godwin, R. P., The Hydraulic Jump (‘Shocks’ and Viscous Flow in the Kitchen Sink), American Journal of Physics 61 (9), (1993) 829832.Google Scholar
Nansen, Fridtjof, Farthest North (Edinburgh, UK: Birlinn, 2002), p. 186.Google Scholar
Vuik, C., Some Historical Notes on the Stefan Problem, Nieuw Archief voor Wiskunde, 4e serie 11 (2), (1993) 157–167.Google Scholar
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. 911.Google Scholar
Taylor, Lloyd W., Physics: The Pioneer Science (Mineola, NY: Dover, 1941), pp. 592593.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. 286292.Google Scholar
Schiff, L., Quantum Mechanics 3rd Edition (New York, NY: McGraw Hill, 1968) pp. 397 ff.Google Scholar
Planck, Max, Theory of Heat Radiation (Mineola, NY: Dover, 2011), pp. 205206. Number 164.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Don S. Lemons, Bethel College, Kansas
  • Book: A Student's Guide to Dimensional Analysis
  • Online publication: 31 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316676165.010
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Don S. Lemons, Bethel College, Kansas
  • Book: A Student's Guide to Dimensional Analysis
  • Online publication: 31 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316676165.010
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Don S. Lemons, Bethel College, Kansas
  • Book: A Student's Guide to Dimensional Analysis
  • Online publication: 31 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316676165.010
Available formats
×