Skip to main content
SpringerLink
Log in

Dimensional Analysis

  • Chapter
  • First Online:
Similarity and Modeling in Science and Engineering

Abstract

Dimensional analysis is supported by two fundamental theorems. The first theorem expresses the dimensional independence of the selected set of fundamental units of measurement. The fundamental set of measuring units comprises the fundamental land complementary units of this set.

“If an equation is dimensionally homogeneous, it can be reduced to relationship among a complete set of dimensionless products.”

Edgar Buckingham (8.7.1867–29.4.1940).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • BAKER, J. E., WESTINE P. S., DODGE F. T.: Similarity methods in engineer-ing dynamics. Elsevier, Amsterdam, 1991, 384 p.

    Google Scholar 

  • BARENBLATT G. I.: Dimensional analysis. Gordon and Breach Science Publisher. New York, 1987, 135 p.

    Google Scholar 

  • BARENBLATT G. I.: Scaling, self similarity, and intermediate asymptotics, Cambridge University Press, 2000, 412 p.

    Google Scholar 

  • BARENBLATT G. I.: Scaling. Cambridge University Press, 2001, 214 p.

    Google Scholar 

  • BATZIAS F. A., NIKOLOU N. P., KAKOS A. S.: Computer aided dimensional analysis for knowledge in chemical engineering processes. In: Proc. Internat. Conference of Computational Methods in Science and Engineering (IICCMSE 2003), Sept. 12–16, 2003, Kastora, Greece, 2003. pp. 74–82.

    Google Scholar 

  • BIRKHOFF G.: Hydrodynamics. A study in logic, fact and similitude. Princeton University Press, Princeton, 151 p.

    Google Scholar 

  • BIRKHOFF G.: Similarity in two-phase fluid flows. In: Group theoretical methods in mechanics. In: Proc. of the point IUTAM/AMU symposium. USSR Academy of Science. Siberian Branch. Novosibirsk, 1978, pp. 58–79.

    Google Scholar 

  • BRIDGMAN, P. W.: Dimensional analysis. New York, AMS Press, 1978, 120 p.

    Google Scholar 

  • BRÜCKNER S. The dimensional analysis for Matlab. In: Proc. 5th International Workshop on Similarity Methods, 4–5. Nov. 2002, Stuttgart University, 2002.

    Google Scholar 

  • BRÜCKNER S., RUDOLPH S.: Hierarchical modeling using dimensional analysis. In: 3rd International Workshop on similarity methods, 13–14 Nov. 2000, Universität Stuttgart, 16 p.

    Google Scholar 

  • BUCKINGHAM E.: On physically similar systems: Illustrations of the use of dimensional analysis. Physical Review, 4 (1914), pp. 345–376.

    Google Scholar 

  • BUCKINGHAM E.: The principle of similitude. Nature, 96 (1915), p. 396–397.

    Google Scholar 

  • BUTTERFIELD R.: Dimensional analysis for geotechnical engineers. Geotechnique, 49 (1999), No. 3, pp. 357–366.

    Google Scholar 

  • CALCHEMY Software Inc.: Automatic units conversion by dimensional Analysis http://calchemy.com/uclive.htm> [cit. 2008–05–23].

  • CARMONA R., TEHRANCHI M. R.: Interest rate models: An infinite dimensional stochastic analysis perspective. Springer 2006, 235 p.

    Google Scholar 

  • CRAIG E.: Dimensional analysis in applied psychological research. Journal of Psychology, 55 (1963), p. 223.

    Google Scholar 

  • CRAIG GLORIA P.: Clinical calculation using dimensional analysis: Instructors manual. Lippincott Williams and Wilkins, 1996.

    Google Scholar 

  • CRAIG GLORIA P.: Clinical calculations made easy: Solving problems using dimensional analysis. Lippincott Williams and Wilkins, 2004.

    Google Scholar 

  • CIZIKOV J. M.: Theorie and modeling of metall cutting processes.(in Russ.) Metallurgia, Moscow, 1970, 296 p.

    Google Scholar 

  • CMELIK R. F., GEHANI N. H. Dimensional analysis with C++. IEEE Software. 1988, Vol. XX, pp. 21–27.

    Google Scholar 

  • DE JONG F. J.: Dimensional analysis for economists. North Holland Publishing Co., Amsterdam, 1967, 220 p.

    Google Scholar 

  • DJAKONOV G. K.: Questions of theory similarity of physico–chemical processes, Moscou, Izdat. AN SSSR, 1956, 206 p.

    Google Scholar 

  • DOUGLAS J. F.: An introduction to dimensional analysis for engineers. Pitman and sons, London, 1969, 137 p.

    Google Scholar 

  • DUNCAN W. J.: Physical similarity and dimensional analysis: An elementary treatise. Edward Arnold, London, 1953, 154 p.

    Google Scholar 

  • EIGENSON L. S.: Modeling (in Russ) Sovetskaia nauka, Moscow, 1952, 372 p.

    Google Scholar 

  • RENAULT-PELTERIE R.: Analyse dimensionnelle et metrologie. F.Rouge,Lausanne, 1950, 112 p.

    Google Scholar 

  • FLEMING R. (ed.): Scale-up in practice. Reinhold Publ., New York, 1958, 134 p.

    Google Scholar 

  • FOCKEN C. M.: Dimensional methods and their applications. Edward Arnold, London, 1953, 224 p.

    Google Scholar 

  • GLOCKNER P. G., SIHGH M. C. (ed.): Symmetry, similarity and group theoretic methods in mechanics. Calgary. The University of Calgary, 1974, 640 p.

    Google Scholar 

  • GÖRTLER H.: Dimensionsanalyse: Teorie der Physikalischen Dimensionen mit Anwendungen. Berlin-Heidelberg, Springer, 1975, 247 p.

    Google Scholar 

  • GUKHMAN A. A.: Introduction to the theory of similarity. Academic Press, 1965.

    Google Scholar 

  • HACKESCHMIDT, M.: Strömungstechnik. Ähnlichkeit-Analogie-Model. Wissenschaftliche Grundlagen des Experimentierens. Leipzig, VEB Deutcher Verlag für Grundstoffindustrie, 1972, 425 p.

    Google Scholar 

  • HANSEN A. G.: Similarity analysis of boundary value problems in engineering. Prentice-Hall, New Jersey, 114 p.

    Google Scholar 

  • HART G. W.: Multidimensional analysis: Algebra and systems for science and engineering. Springer 1995.

    Google Scholar 

  • HAYNES R.: Introduction of dimensional analysis for geographers. Essay 33, In: Concepts and techniques in modern geography. Norwich (UK), Geo Abstracts, 1982.

    Google Scholar 

  • HILFINGER P. N.: An data package for dimensional analysis. ACM Transactions on programming languages and systems. 1988, Vol. 10, No. 2, pp. 189–203.

    Google Scholar 

  • HORNUNG H. G.: Dimensional analysis: Examples of the use of symmetry. Dover Publications. 2006, 80 p.

    Google Scholar 

  • HUNTLEY H. E.:Dimensional analysis. New York, Dover Publications, 1967, 158 p.

    Google Scholar 

  • HUNTLEY H. E.: The divine proportion – A sudy in mathematical beauty. Dover Pub lications Inc., New York, 1970.

    Google Scholar 

  • ISAACSON E., ISAACSON M.: Dimensional methods in engineering and physics. Edward Arnold, London, 1975, 220 p.

    Google Scholar 

  • JACOBY W. G.: Data theory and dimensional analysis. Quantitative applications in the social sciences. Sage University Paper No.78, 1991, 96 p.

    Google Scholar 

  • JUPP E. W.: An introduction to dimensional method. Cleaver-Hume Press, London, 1962, 89 p.

    Google Scholar 

  • KASPRZAK W., LYSIK B., RYBACZUK M.: Dimensional analysis in the identification of mathematical models. World Scientific Pub., 1990.

    Google Scholar 

  • KATTANEK S., GRÖBER R., BODE C.: Ähnlichkeitstheorie. VEB Deutsches Verlag fűr Grundstoffindustrie, 1967, 173 p.

    Google Scholar 

  • KIRPICHEV M. V.: Theory of similarity and heat modeling. (in Russ.), Nauka, Moscow, 1987, 167 p.

    Google Scholar 

  • KLINE S. L.: Similitude and approximation theory. McGraw-Hill, New York, 1965, 228 p.

    Google Scholar 

  • KREITH F.: Fluid Mechanics.(3th chap.:Simulitude-dimensional analysis and date correlation., 14.chap.: Micro/Nanotribology). CRC Press 1999, 224 p.

    Google Scholar 

  • KOŽEŠNIK J.: Theorie of similarity and modeling. (in Czech), Academia, Prague, 1983, 264 p.

    Google Scholar 

  • KREITH F.: Fluid Mechanics. Chapter 3.: Similitude-dimensional analysis and date correlation. Chapter 14.: Micro/Nanotribology. CRC Press 1999, 224 p.

    Google Scholar 

  • KUNEŠ J., TRKOVSKÝ V.: Physical similarity of thermal processes in machine systems. Strojnický časopis 47 (1996), No.4, pp. 254–262.

    Google Scholar 

  • KURTH R.: Dimensional analysis and group theory in astrophysics. Pergamon Press, Oxford 1972, 230 p.

    Google Scholar 

  • KUTATELADZE S.S.: Similarity analyse in thermo-physics. (in Russ), Nauka-Sibirskoe otdelenije. Novosibirsk, 1982, 280 p.

    Google Scholar 

  • KUTATELADZE S. S: Similarity analysis and physical models. (in Russ), Nauka-Sibirskoe otdelenije. Novosibirsk, 1986, 296 p.

    Google Scholar 

  • LANGHAAR H.L.: Dimensional analysis and theory of models. Wiley, New York, 1951, 166 p.

    Google Scholar 

  • LEHMAN P.J.: Dimensional analysis in applied psychological research. J. Psychology 55 (1963), pp. 223–226.

    Google Scholar 

  • MASSEY B. S.: Units, dimensional analysis and physical similarity. London, Van Nostrand Reinhold, 1971, 140 s.

    Google Scholar 

  • MURPHY G.: Similitude in engineering. Ronald Press, New York, 1950, 302 p.

    Google Scholar 

  • NOVIKOV I. I., BORIŠANSKIJ V. M.: Theorie of similarity in thermodynamics and heat transfer. Atomizdat, Moscow, 1979, 184 p.

    Google Scholar 

  • PALACIOS J.: Dimensional analysis. MacMillian, London, 1964, 236 p. PANKHURST R. C.: Dimensional analysis and scale factors. Chapman and Hall, London, 1964, 151 s.

    Google Scholar 

  • PAWLOWSKI J.: Ähnlichkeitstheorie in der physikalisch-technischen Forschung. Grundlagen und Anwendung. Springer, Berlin, 1971, 172 p.

    Google Scholar 

  • PETTY G. W.: Automated computation and consistency checking of physical dimensions and units in scientific programs. Software – Practice and Experience. 2001, Vol. 31, pp. 1067–1076.

    Google Scholar 

  • REZNIAKOV A. B.: Similarity methods. (in Russ), Akademia nauk Kaz. SSR, Alma Ata, 1959, 152 p.

    Google Scholar 

  • SEDOV L. I.: Similarity and dimensional methods in mechanics. Academic Press, New York, 1959, 479 p.

    Google Scholar 

  • SENA L. A.: Units of physical quantities and their dimensions. Mir Publishers, Moscow, 1972.

    Google Scholar 

  • SHIVE J. N., WEBER R. L.: Similarities in physics. Adam Hilger, Bristol, 1982, 275 p.

    Google Scholar 

  • SCHEPARTZ B.: Dimensional analysis in the biomedical science. Thomas, 1980, 172 p.

    Google Scholar 

  • SHIRER D.L., SQUARE W.: A computer program for dimensional analysis. American Journal of Physics. 1972, Vol. 40, No. 3, pp. 489–490.

    Google Scholar 

  • SCHURING D. J.: Scale models in engineering. Pergamon Press,New York, 1977, 299 p.

    Google Scholar 

  • SKOGLUND V. J.: Similitude. Theory and applications. International Textbook, Scranton (PA), 1967, 320 p.

    Google Scholar 

  • SLOAN A. D., HAPP W. W.: Computer programm for dimensional analysis. NASA TND 5165, 1969, 29 p.

    Google Scholar 

  • SMIRNOV V. S.: Similarity method in the theorie of rolling process.(in Russ.) Nauka, Leningrad, 1971, 179 p.

    Google Scholar 

  • SONIN A.A.: The physical basis of dimensional analysis. Massachusetts Institute of Technology, Cambridge, MA, 2001, 56 p.

    Google Scholar 

  • STAICU C. I.: Restricted and general dimensional analysis: Treatment of experimental data. Abacus Press, Tunbridge Wells, Kent, UK, 1982, 304 p.

    Google Scholar 

  • SZÜCS E.: Similitude and modelling. Elsevier, Amsterdam, 1980, 335 p.

    Google Scholar 

  • SZIRTES T.: Applied dimensional analysis and modeling. McGraw Hill, New York, 1997, 790 p.

    Google Scholar 

  • TAYLOR E. S.: Dimensional analysis for engineers. Clarendon Press, Oxford, 1974, 162 p.

    Google Scholar 

  • THOMAS P.H.: Dimensional analysis: A magic art in fire research? Lund University, Rap. 3094, 46 p.

    Google Scholar 

  • TRAUSTEL S.: Modellgesetze der Vergasung und Verhüttung. Akademie Verlag Berlin, 1949, 89 p.

    Google Scholar 

  • UMRIGAR Z. D.: Fully static dimensional analysis with C++. ACM SIGPLAN Notices. 1994, Vol. 29, No. 9, pp. 135–139.

    Google Scholar 

  • VENIKOV V. A.: Theory of similarity and simulation. MacDonald, Technical and Scientific, London, 1969.

    Google Scholar 

  • ZIEREP J.: Ähnlichkeitsgesetze und Modellregeln der Strömungslehre. G.Braun Verlag, Karlsruhe, 1972, 139 p.

    Google Scholar 

  • ZLOKARNIK M.: Scale-up. Modellübertragung in der Verfahrenstechnik. Wiley-VCH, Weinheim, 2000, 226 p.

    Google Scholar 

  • ZLOKARNIK M.: Dimensional analysis and scale- up in chemical engineering. Springer, 1991.

    Google Scholar 

  • WIKIPEDIA.: http://en.wikipedia.org/wiki/Dimensional analysis

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Applied Sciences, University of West Bohemia, Prague, Czech Republic

    Josef Kuneš

Authors
  1. Josef Kuneš
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Josef Kuneš .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Cambridge International Science Publishing

About this chapter

Cite this chapter

Kuneš, J. (2012). Dimensional Analysis. In: Similarity and Modeling in Science and Engineering. Cambridge International Science Publishing Ltd. https://doi.org/10.1007/978-1-907343-78-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-907343-78-0_3

  • Published:

  • Publisher Name: Cambridge International Science Publishing Ltd

  • Print ISBN: 978-1-907343-77-3

  • Online ISBN: 978-1-907343-78-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Societies and partnerships

Search

Navigation