Abstract
In this introductory chapter some basic ideas of the dimensional analysis are outlined using a number of the instructive examples. They illustrate the applications of the \( \rm Pi \)-theorem in the field of hydrodynamics and heat and mass transfer.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A demonstration of this statement can be found in Sedov (1993).
- 2.
This idea was expressed first by D. Bernoulli in 1727 who wrote that pressure of perfect gas is related to molecule velocities squared.
- 3.
It is emphasized that in the problem on flow in the boundary layer over a semi-infinite plate, a given characteristic scale \( L \) is absent. According to the self-similar Blasius solution of this problem, the dimensionless coordinate \( \overline y = y/{(\nu x/{u_{\infty }})^{{1/2}}} \) with \( {(\nu x/{u_{\infty }})^{{1/2}}} \) playing the role of the length scale (Sedov 1993).
- 4.
Dimensionless groups can be also found directly by transformation of the functional equations of a specific problem using the \( \rm Pi \)-theorem (see Sect. 2.5). A detailed list of dimensionless groups related to flows of incompressible and compressible fluids in adiabatic and diabatic conditions, flows of non-Newtonian fluids and reactive mixtures can be found in Handbook of Chemistry and Physics, 68th Edition, 1987–1988, CBC Inc. Boca Roton, Florida, and in Chart of Dimensionless Numbers, OMEGA Technology Company. See also Lykov and Mikhailov (1963) and Kutateladze (1986).
- 5.
With an equal number of data points for each one of the four governing parameters.
- 6.
References
Barenblatt GI (1987) Dimensional analysis. Gordon and Breach Science Publication, New York
Barenblatt GI (1996) Similarity, self-similarity, and intermediate asymptotics. Cambridge University Press, Cambridge
Blackman DR (1969) SI units in engineering. Macmillan, Melbourne
Bridgman PW (1922) Dimension analysis. Yale University Press, New Haven
Buckingham E (1914) On physically similar system: illustrations of the use of dimensional equations. Phys Rev 4:345–376
Chart of Dimensionless Numbers (1991) OMEGA Technology Company.
Douglas JF (1969) An introduction to dimensional analysis for engineers. Isaac Pitman and Sons, London
Hinze JO (1975) Turbulence, 2nd edn. McGraw-Hill, New York
Huntley HE (1967) Dimensional analysis. Dover Publications, New York
Ipsen DC (1960) Units, dimensions, and dimensionless numbers. McGraw-Hill, New York
Jones JB, Hawkis GA (1986) Engineering thermodynamics. An introductory textbook. John Wiley & Sons, New York
Kestin J (v.1, 1966; v.2, 1968) A course in thermodynamics. Blaisdell Publishing Company, New York
Kutateladze SS (1986) Similarity analysis and physical models. Nauka, Novosibirsk (in Russian)
Landau LD, Lifshitz EM (1987) Fluid mechanics, 2nd edn. Pergamon, Oxford
Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hill, Englewood Cliffs
Loitsyanskii LG (1966) Mechanics of liquid and gases. Pergamon, Oxford
Lykov AM, Mikhailov Yu A (1963) Theory of heat and mass transfer. Gosenergoizdat Moscow-Leningrad (English translation 1965. Published by the Israel Program for Scientific Translation. Jerusalem)
Madrid CN, Alhama F (2005) Discriminated dimensional analysis of the energy equation: application to laminar forced convection along a flat plate. Int J Thermal Sci 44:331–341
Ramaswamy GS, Rao VVL (1971) SI units. A source book. McGraw-Hill, Bombay
Reynolds O (1886) On the theory of lubrication. Philos Trans R Soc 177:157–233
Sedov LI (1993) Similarity and dimensional methods in mechanics, 10th edn. CRC Press, Boca Raton
Spurk JH (1992) Dimensionsanalyse in der Stromungslehre. Springer-Verland in Berlin, New York
Weast RC Handbook of chemistry and physics, 68th edition. 1987–1988. CRC, Boca Raton, FL.
Williams W (1892) On the relation of the dimensions of physical quantities to directions in space. Philos Mag 34:234–271
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Yarin, L.P. (2012). Basics of the Dimensional Analysis. In: The Pi-Theorem. Experimental Fluid Mechanics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19565-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-19565-5_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19564-8
Online ISBN: 978-3-642-19565-5
eBook Packages: EngineeringEngineering (R0)