Abstract
Edgar Buckingham was born on July 8, 1867 in Philadelphia, Pennsylvania, USA and died on April 25, 1940 in Washington, DC. He had his studies in Harvard, USA, at the University of Strasbourg, France and the University of Leipzig, Germany, where he received his PhD in 1893. From 1902 to 1906 he worked as a soil physicist at the US Bureau of Soils and afterwards accepted (1907) a post at the National Bureau of Standards, where he remained until his retirement in 1937. He performed a lot of work in the discipline of soil physics and published the results in some widely acknowledged papers, [1, 2]. In 1914 he presented the paper [3], in which he summed up the theory of the \(\varPi \) theorem with its fundamental significance for the analysis of dimensions, see also [4].
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Notes
- 1.
Görtler in [6] questioned that the \(\varPi \) theorem was formulated first by E. Buckingham. He gives in this book a historical survey about the origination of the \(\varPi \) theorem.
- 2.
The number of physical variables n should be restricted to the most important ones.
- 3.
\(p=0\) would be optimal, because no dimensionless number exists and the physical problem can be directly solved up to a constant by the \(\varPi \) theorem.
- 4.
The three basic dimensions are extended by the temperature T.
- 5.
Other authors notice that some coefficients have to be guessed.
- 6.
There are two definitions of the Froude number: \(Fr = v^2/gh\) and \(Fr' = v/\sqrt{gh}\) depending on the application case, see Sect. 6.2.
- 7.
Of course we did it in view of the result we know.
- 8.
This definition is true, if the coefficient of thermal expansion \(\beta \) is chosen to be \(\beta = 1/T_\infty \), which is a good approximation for the perfect gas case, see Sect. 6.4.
- 9.
For ship design and ship flow often the square root of the Froude number is used, \(Fr' = \sqrt{Fr} = v_\infty /\sqrt{g \, L}\), see Sect. 6.2.
References
Buckingham, E.: Contributions to our knowledge of soils. Bulletin 25, USDA Bureau of Soils, Washington (1904)
Buckingham, E.: Studies on the movement of soil moisture. Bulletin 38, USDA Bureau of Soils, Washington (1907)
Buckingham, E.: On Physically Similar Systems: Illustration of the Use of Dimensional Equations. Phys. Rev. 4, 345–376 (1914)
Buckingham, E.: The principle of similitude. Nature 36, 396–397 (1915)
Zierep, J.: Ähnlichkeitsgesetze und Modellregeln der Strömungsmechanik. G. Braun Verlag, Karlsruhe (1972)
Görtler, H.: Dimensionsanalyse, Theorie der physikalischen Dimensionen und Anwendungen. Springer, Berlin (1975)
Krause, E.: Strömungslehre, Gasdynamik und aerodynamisches Laboratorium. Teubner Verlag, Stuttgart (2003)
Hirschel, E.H.: Basics of Aerothermodynamics, 2nd edn. Springer, Berlin (2015)
Schlichting, H., Gersten, K.: Boundary Layer Theory, 8th edn. Springer, Berlin (2000)
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Weiland, C. (2020). Dimensional Analysis—Buckingham’s \(\varPi \) Theorem. In: Mechanics of Flow Similarities. Springer, Cham. https://doi.org/10.1007/978-3-030-42930-0_2
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DOI: https://doi.org/10.1007/978-3-030-42930-0_2
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