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# Topic: Buckingham Pi theorem

###### In the News (Fri 24 May 19)

 Buckingham's pi-theorem   (Site not responding. Last check: 2007-10-11) Buckingham, E. On physically similar systems; illustrations of the use of dimensional equations. Curtis, W.D., Logan, J.D., Parker, W.A. Dimensional analysis and the pi theorem. Edgar Buckingham (1867–1940) was educated at Harvard and Leipzig, and worked at the (US) National Bureau of Standards (now the National Institute of Standards and Technology, or NIST) 1905--1937. www.math.ntnu.no /~hanche/notes/buckingham   (432 words)

 Buckingham Pi theorem The Buckingham π theorem is a key theorem in dimensional analysis. This theorem describes how every physically meaningful equation involving n variables can be equivalently rewritten as an equation of n-m dimensionless parameters, where m is the number of fundamental units used. Proofs of the π theorem often begin by considering the space of fundamental and derived physical units as a vector space, with the fundamental units as basis vectors, and with multiplication of physical units as the "vector addition" operation, and raising to powers as the "scalar multiplication" operation. ebroadcast.com.au /lookup/encyclopedia/bu/Buckingham_Pi_theorem.html   (409 words)

 Application of Buckingham Pi theorem to dam breach model The theorem, its usage and its limitations are reviewed in the context of water flow through a trapezoidal notch in a trapezoidal reservoir embankment (dam breach model). The Buckingham Pi theorem may sometimes be misused as a general solution method for complex engineering problems. The resulting dimensionless physical law must be checked by experiment, or whatever, in an effort to determine the validity of the original assumptions." Nor is it necessarily valid to take any particular pi-variable and construct a physical law by setting that variable equal to the general formula for pi-variables in a given problem. www.aquarien.com /noabpt/noabpta1.html   (1406 words)

 Buckingham π theorem - Wikipedia, the free encyclopedia Most importantly, the Buckingham π theorem provides a method for computing sets of dimensionless parameters from the given variables, even if the form of the equation is still unknown. Buckingham, E. On physically similar systems; illustrations of the use of dimensional equations". Buckingham, E. "Model experiments and the forms of empirical equations". en.wikipedia.org /wiki/Buckingham_Pi_theorem   (1010 words)

 Buckingham Pi Theorem Text - Physics Forums Library Mathworld defines the Buckingham Pi Theorem like this: physical laws are independent of the form of the units; therefore, acceptable laws of physics are homogeneous in all dimensions. I like your nice application of the buck pi theorem very much, but technically it seems you are not restating the theorem, but assuming the theorem, and then applying it. The point of the theorem is that the equation is homogeneous in the first place. www.physicsforums.com /archive/index.php/t-34909.html   (852 words)

 Chapter 7   (Site not responding. Last check: 2007-10-11) Select a number of repeating variables, where the number required is equal to the number of reference dimensions (usually the same as the number of basic dimensions). Form a pi term by multiplying one of the nonrepeating variables by the product of repeating variables each raised to an exponent that will make the combination dimensionless. Similarity between a model and a prototype is achieved by equating pi terms. www.eng.iastate.edu /me333c/chapter_7.htm   (196 words)

 Pi Pi Pi (upper case Π, lower case π) is the 16th letter of the Greek alphabet. In Greek, the letter is pronounced /piː/ (as in pee); in English, though, it is pronounced /paɪː/ (as the word pie). Dimensionless parameters constructed using the Buckingham Pi theorem of dimensional analysis. www.mlahanas.de /Greeks/LX/Pi.html   (208 words)

 2001_August_a4   (Site not responding. Last check: 2007-10-11) This article presents a motivation for trying dimensional analysis, describes the use of the Buckingham Pi Theorem for performing the analysis, and suggests some non-dimensional coordinates that may be useful. The Buckingham Pi Theorem states that a list of parameters used to describe a problem can be reduced in number by combining the variables using an algorithm that is based upon the dimensions of the variables. As is often the case, the complete statement of the theorem is more appropriate for individuals who are already comfortable with dimensional analysis than for people who are new to the topic. www.electronics-cooling.com /html/2001_august_a4.html   (1887 words)

 The world's top dimensional analysis websites Furthermore, the arguments to exponential, trigonometric and logarithmic functions must be dimensionless numbers, which is often achieved by multiplying a certain physical quantity by a suitable constant of the inverse dimension. This theorem describes how every physically meaningful equation involving n variables can be equivalently rewritten as an equation of n-m dimensionless parameters, where m is the number of fundamental units used. There are many ways of combining the five arguments of to form dimensionless groups, but the Buckingham Pi theorem states that there will be two such groups. www.websbiggest.com /wiki-article-tab.cfm/dimensional_analysis?   (1253 words)

 Application of Buckingham Pi theorem   (Site not responding. Last check: 2007-10-11) The theorem we have stated is a very general one, but by no means limited to Fluid Mechanics. It is used in diversified fields such as Botany and Social Sciences and books and volumes have been written on this topic. What we will consider is a procedure to use the theorem and arrive at non-dimensional numbers for a given flow. www.aeromech.usyd.edu.au /aero/fprops/dimension/node9.html   (336 words)

 Wikinfo | Dimensional analysis The Buckingham π-theorem forms the basis of the central tool of dimensional analysis. This theorem describes how every physically meaningful equation involving n variables can be equivalently rewritten as an equation of n-m dimensionless parameters, where m is the number of fundamental dimensions used. There are many ways of combining the five arguments of f to form dimensionless groups, but the Buckingham Pi theorem states that there will be two such groups. www.wikinfo.org /wiki.php?title=Dimensional_analysis   (1493 words)

 Life Lexicon (G) It is based on an important p44 oscillator discovered by Dave Buckingham in early 1992, shown here in an improved form found in January 2005 by Jason Summers using a new p4 sparker by Nicolay Beluchenko. It is generally assumed that the gliders should be arranged so that they could come from infinity - that is, gliders should not have had to pass through one another to achieve the initial arrangement. Glider syntheses for all still lifes and known oscillators with at most 14 cells were found by Dave Buckingham. www.argentum.freeserve.co.uk /lex_g.htm   (1696 words)

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