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Topic: Dimensional analysis

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Buckingham Pi theorem

Dimensionless number

Similitude (model)

Fundamental unit

Natural units

Dimension

Planck units

Power number

List of mathematical theorems

Reynolds number

Drag equation

Gauss Jordan elimination

Maxwells equations

Nusselt number

Boussinesq approximation

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	Dimensional analysis - Wikipedia, the free encyclopedia
		Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities.
		In the most primitive form, dimensional analysis may be used to check the plausibility of physical equations: the two sides of any equation must be commensurable or have the same dimensions, i.e., the equation must be dimensionally homogeneous.
		Dimensional analysis is also used to derive relationships between the physical quantities that are involved in a particular phenomenon that one wishes to understand and characterize.
	en.wikipedia.org /wiki/Dimensional_analysis (3450 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Dimensional analysis is a mathematical tool often applied in physics, chemistry, and engineering to simplify a problem by reducing the number of variables to the smallest number of "essential" parameters.
		In the most primitive form, dimensional analysis is used to check the correctness of algebraic derivations: in every physically meaningful expression, only quantities of the same dimension can be added or subtracted.
		A typical application of dimensional analysis occurs in fluid dynamics.
	www.wikiwhat.com /encyclopedia/d/di/dimensional_analysis.html (767 words)

	Dimensional Analysis
		Dimensional Analysis relies on the fundamental principle that any equation or relation between variables must be dimensionally consistent; that is to say that each term in the relationship must have the same dimensions.
		The requirement of dimensional consistency places a number of constraints on the form of the functional relation between variables in a problem and forms the basis of the technique of dimensionless analysis which enables the variables in a problem to be expressed in dimensional groups.
		Dimensional analysis, however, will give no information about the form of the functions, nor will it provide a means of evaluating numerical proportionality constants.
	www.see.ed.ac.uk /~johnc/teaching/advfluidmechanics5/2003-04/fluids18/dimensional.html (956 words)

	How to scale up scientifically: the author reviews dimensional analysis as a straight-forward approach to scale ... (Site not responding. Last check: 2007-11-06)
		Dimensional analysis is a method for producing dimensionless numbers and deriving functional relationships among them that completely characterize the process.
		Dimensional analytical procedure was first systematically applied to fluid flow 90 years ago by Lord Rayleigh (1), on the basis of the principle of similitude referred to by Newton in one of his early works.
		Dimensional analysis can be simplified by arranging all relevant variables from the relevance list into a matrix, with a subsequent transformation yielding the required dimensionless numbers.
	www.highbeam.com /doc.aspx?DOCID=1G1:130969605&ctrlInfo=Round20%3AMode20e%3ADocG%3AResult&ao= (2399 words)

	Dimensional analysis
		Dimensional analysis thus makes a very very complex problem (trying to determine the behaviour of a function of five variables---essentially impossible in practice) a very much simpler one: the determination of a function of one variable, the Reynolds number.
		where is some constant (physical analysis shows that is one, to within an order of magnitude).
		To empirically determine the Reynolds number dependence, instead of experimenting on huge bodies with fast flowing fluids (such as real-size airplanes in wind-tunnels), one may just as well experiment on small models with slow flowing, more viscous fluids, because these two systems are similar.
	www.xasa.com /wiki/en/wikipedia/d/di/dimensional_analysis.html (1140 words)

	College Chemistry: Dimensional Analysis
		The guiding principle of dimensional analysis is that you can multiply anything by “1” without changing the meaning.
		Another concept necessary to understanding dimensional analysis is that units that are on the top and bottom of an expression cancel out.
		Dimensional analysis is a technique for converting units based upon equalities.
	www.chemistry24.com /college_chemistry/dimensional-analysis.html (345 words)

	Dimensional Analysis
		Dimensional analysis provides a strategy for choosing relevant data and how it should be presented.
		In dimensional analysis we are only concerned with the nature of the dimension i.e.
		The result of performing dimensional analysis on a physical problem is a single equation.
	www.efm.leeds.ac.uk /CIVE/CIVE1400/Section5/dimensional_analysis.htm (1254 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-06)
		Date: 11/28/2001 at 12:00:37 From: Doctor Greenie Subject: Re: Dimensional Analysis Hi, Danielle - Dimensional analysis is a tool that can be used to determine how to manipulate formulas by analyzing the dimensions in the formulas.
		Another elementary application of dimensional analysis is in converting units of measure.
		Finally, here is a link to a page in the Dr. Math archives where dimensional analysis is used to solve a "fun" problem: Dimensional Analysis http://mathforum.com/library/drmath/view/56728.html I hope this helps.
	mathforum.org /library/drmath/view/55396.html (510 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-06)
		I'm glad to see that dimensional analysis is being taught somewhere - it seems to be a topic that is unfortunately missing from the curriculum in many schools.
		Let's work this problem first without using dimensional analysis, so we will be able to confirm later that our solution to the problem using dimensional analysis is correct.
		Thanks again for a problem that can be used nicely to demonstrate the use of dimensional analysis.
	www.mathforum.org /library/drmath/view/56728.html (495 words)

	Dimensional Analysis - Part 3
		By defining the electric field as volts per meter, we also fix the dimensional equivalent of "volt" in fundamental units as shown in Eq.
		From these relationships, we surmise that the dielectric constant multiplied by the electric field is equal to the source of the electric field, as shown in eq.
		As we have seen, dimensional analysis is a tool of astounding power.
	www.geocities.com /electrogravitics/da3.html (955 words)

	Prediction of 28 Days Compressive Strength 53-Grade Cements using Dimensional Analysis (Site not responding. Last check: 2007-11-06)
		To overcome this difficulty, a dimensional analysis method for predicting the 28-day compressive strength of 53-grade cements is presented in this paper.
		A unique trial-and-error procedure is presented that generates the universal dimensional analysis formulation, wherein one of the experimental data sets, called the control point, generates the dimensional analysis equation, whereas the other data set, the check point, is used to validate the already formed dimensional analysis equation.
		The results of dimensional analysis are then compared with the available experimental results.
	www.pubs.asce.org /WWWdisplay.cgi?0530472 (175 words)

	WebQuest - Dimensional Analysis: Everyday Applications (Site not responding. Last check: 2007-11-06)
		According to Texas A and M University, "Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value."
		Dimensional analysis is simply converting numbers of one type of unit to another type of unit through polynomial multiplication and simplification.
		This is just one of the many questions dimensional analysis can answer for us.
	education.ed.pacificu.edu /sweb/537fri/dimensional (212 words)

	Dimensional Analysis Techniques (Site not responding. Last check: 2007-11-06)
		Dimensional analysis, in which you substitute for each variable in a formula its unit of measurement, is a valuable tool that allows you to check whether the powers, products, and quotients are correct in a formula.
		To check a formula for dimensional consistency, merely substitute in the appropriate metric unit for each variable and simply each term.
		We can use dimensional analysis to determine which version of the formula is correct.
	online.cctt.org /physicslab/content/Phy1HON/lessonnotes/dimensionalanalysis/lessondimensionalanalysis.asp (198 words)

	Talk:Dimensional analysis : Dimensional analysis/comments
		In the most primitive form, dimensional analysis is used to check the correctness of algebraic derivations: in every physically meaningful equation, the dimensions of the two sides must be identical.
		Furthermore, the arguments to exponential, trigonometric and logarithmic functions must be dimensionless numbers, which is typically achieved by multiplying a certain physical quantity by a suitable constant of the inverse dimension.
		I admit that I don't know how to use dimensional analysis to solve PDE's (do you have any references?), but this paragraph was really just the beginning, showing the most primitive "dimensional analysis" as taught in college chemistry classes: make sure that the dimensions are right.
	www.fastload.org /di/Dimensional_analysis___comments.html (824 words)

	Dimensional analysis -- CFD-Wiki, the ultimate free CFD reference
		Every relation between n physical variables can be written in a an equivalent nondimensional form, and the number of the dimensionless variables of this new relation is always smaller than the original one.
		The good thing about dimensional analysis is that it shows us that we don't need to try out every possible combination of parameters.
		Dimensional anlysis tells us how to build a model so that we can convert the data from the experiment with the model to the actual prototype.
	www.cfd-online.com /Wiki/Dimensional_analysis (893 words)

	Medication Math for the Nursing Student
		Dimensional analysis (also known as the factor-label method) is by far the most useful math trick you'll ever learn.
		When doing dimensional analysis it is essential that all the units given should be used and accounted for.
		This may be a case of a book being the worst textbook on dimensional analysis available--with the exception of all the others.
	www.alysion.org /dimensional/analysis.htm (14977 words)

	Dimensional Analysis, Inc. - Provider of Dimensional Inspection Services and Quality Assurance Support
		Dimensional Analysis, Inc. is a provider of Dimensional Inspection Services and Quality Control Support, located in the Chicago Metropolitan area, and is committed to the accurate and reliable dimensional measurement of manufactured components and tooling.
		Dimensional Analysis will always give you accurate, dependable data that will result in the least amount of production downtime.
		Realizing the need for an independent Quality Assurance Service, Dimensional Analysis, Inc. was founded in 1996 to provide the Manufacturing and Quality Assurance industry with reliable, accurate and unbiased third party dimensional inspection of manufactured components.
	www.dimensionalanalysisinc.com (290 words)

	Dimensional Analysis Toolbox
		Weitere Informationen zur "Dimensional Analysis Toolbox for Matlab" können Sie unter
		The Dimensional Analysis Toolbox for Matlab is an engineering tool for experimental as well as theoretical work.
		Dimensional Analysis is a well-known engineering technique giving scaling parameters for a problem.
	sbrs.ccdastro.de /prod01.htm (327 words)

	Dimensional Analysis - Inspection Services (Site not responding. Last check: 2007-11-06)
		Dimensional Analysis can calibrate your custom made fixture to assure perfect results every time.
		At Dimensional Analysis, you don't get voice mail, you talk to a person in our office that can answer your questions immediately.
		Dimensional Analysis, Inc. will continue to provide the latest technology, while continually making organizational improvements that provide enhanced communication, responsiveness and service to our customers.
	www.dimensionalanalysisinc.com /services.html (162 words)

	Nanotech Math - Dimensional Analysis (Site not responding. Last check: 2007-11-06)
		A one dimensional objects lives in a line, two dimensional objects live in a plane, and a three dimensional object lives in space.
		As an example of a two dimensional object, consider a monolayer of surfactant molecules floating on the surface of water, i.e.
		However, in the case of an LB film the pressure value represented by "P" is a two dimensional analogue to 3-D pressure known as "lateral pressure".
	www.nanoword.net /library/weekly/000315a.php (393 words)

	Dimensional Analysis...Measuroo.com
		Dimensional analysis is a mathematical tool often applied in physics, chemistry, and engineering to understand physical situations that are so complicated that it is difficult or impossible to derive the underlying differential equations.
		It should be noted that very different physical quantities may have the same dimensions: work and torque, for example, both have the same dimensions, M L2T-2,.
		Dimensional analysis thus makes a very complex problem (trying to determine the behaviour of a function of five variables) a much simpler one: the determination of the drag as a function of only one variable, the Reynolds number.
	www.measuroo.com /dimensionalanalysis.html (904 words)

	Dimensional Analysis
		First used by J. Fourier in 1822, dimensional analysis is a simple and powerful technique for learning about the dependence of a phenomenon on the dimensions and properties of the system that exhibits the phenomenon.
		You are all familiar with the phenomenon of water waves on the surface of the ocean.
		We cannot use dimensional reasoning to determine the proportionality factor, but experience suggests that such factors are usually within a factor of 10 of unity.
	www.physics.hmc.edu /analysis/dimensions.php (421 words)

	Nanotech Math - Dimensional Analysis
		Nanotubes and DNA behave like a one dimensional solid when one considers their electronic properties.
		They are one dimensional because electrons (or positive holes) traveling through them can only follow one path, thus they are analogous to a one way street.
		Strange as it may sound, quantum dots are an example of a zero dimensional solid.
	www.nanoword.net /library/weekly/000315b.php (270 words)

	Math Skills - Dimensional Analysis
		Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value.
		The only danger is that you may end up thinking that chemistry is simply a math problem - which it definitely is not.
		We also can use dimensional analysis for solving problems.
	www.chem.tamu.edu /class/fyp/mathrev/mr-da.html (306 words)

	91.06.03: Scaling the Natural World Using Dimensional Analysis
		This rate and dimensional analysis method has slowly moved into textbooks and has completely replaced the method of ratio-and-proportions taught exclusively in junior and senior high school mathematics textbooks.
		Dimensional analysis is a simple, problem-solving, error-reducing procedure which seems to require less conceptual reasoning power to understand than does the ratio.
		Three research studies on proportional calculations with emphasis on the rate concept, dimensional analysis, and hands-on manipulative experiments were field tested in the ninth and tenth grades.
	www.yale.edu /ynhti/curriculum/units/1991/6/91.06.03.x.html (4986 words)

	Dimensional Analysis (Site not responding. Last check: 2007-11-06)
		Dimensional Analysis is a technique used in the physical sciences and engineering to reduce physical properties such as acceleration, viscosity, energy, and others to their fundamental dimensions of length (L), mass (M), and time (T).
		Acceleration, for example, is expressed as L/T in dimensional analysis because it is a distance (L, length) per unit of time (T) squared; whether the actual units of length are expressed in the English or metric system is immaterial.
		Dimensional Analysis in Data Modelling, in C R Smith et al (eds), Maximum Entropy and Bayesian Methods, Seattle 1991, Kluwer Academic Publishers (1992), pp 121-126.
	www.mcs.vuw.ac.nz /~vignaux/diman.html (253 words)

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