Talk:Dimensional analysis

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Cherif F. Matta, Lou Massa, Anna V. Gubskaya, and Eva Knoll (2011). "Can One Take the Logarithm or the Sine of a Dimensioned Quantity or a Unit? Dimensional Analysis Involving Transcendental Functions". Journal of Chemical Education. Retrieved 23 May 2016. An example of a flawed argument that nevertheless reaches the correct conclusion is Wikipedia's entry, as of September 2010, and which dismisses the insertion of a dimensioned quantity into the argument of a transcendental function on the basis of the Taylor expansion of these functions (20). The Wikipedia article argues that the Taylor expansion of transcendental functions leads to terms of different dimensions that cannot be added or subtracted (rule 1), and hence, the argument cannot be dimensioned.{{cite news}}: CS1 maint: multiple names: authors list (link)

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The Factor-Label Method

I think there is too much emphasis in the article on this relatively routine topic. It would be of great interest to show that the method of algebraic substitution (e.g. 1 yd <= 3 ft) yields equivalent results to the factor-label method. The more important principle is that quantities and units are subject to the rules of algebra, including substitution and cancellation, i.e. quantity calculus. Quantity calculus needs to be mentioned as a pre-requisite topic and referenced near the top of this article, and not just mentioned as a related area at the bottom.

In order to explain this adequately, likely the topic of quantity equations must be introduced, and perhaps contrasted with value equations.

It is an interesting fact that Bridgman works primarily with value equations in his seminal reference, yet reaches all the important results just the same. But Bridgman is not mentioned (although he is listed as a reference). Also Bridgman's theorem should be introduced and discussed somewhere - it is the only important theorem of dimensional analysis, besides Buckingham's pi theorem. In his book he proves his theorem first, then uses that result to prove the pi theorem.Antiskid56 (talk) 03:09, 23 July 2020 (UTC)[reply]

What you say makes sense. The sections on the factor-label method could be trimmed down to a fraction of its current content. At present, it reads a bit like an example sheet for a junior school class. —Quondum 13:02, 23 July 2020 (UTC)[reply]

Even the top-level paragraph introducing this article is somewhat misleading, in my opinion. The essence of dimensional analysis is not really tracking the units and dimensions of quantities in a calculation. This is much too narrow in scope. It has more to do with considering how a calculation must change if the base units were to change in size. This is the essence of the subject as originally considered by Fourier in his analysis of heat equations. Bridgman says (paraphrasing here) that dimensional analysis has something of the character of an analysis of an analysis. This is the correct view - it is a meta-analysis of the original analysis, asking what must change if the sizes of the base units were to change. And this meta-analysis leads to conclusions about the forms the equations are allowed to take. Simply tracking and converting dimensions and units does not really capture the essence of the subject at all.Antiskid56 (talk) 15:10, 27 July 2020 (UTC)[reply]

Agreed. If you (or others) are feeling energetic, a complete rewrite would not be a bad idea. —Quondum 16:24, 27 July 2020 (UTC)[reply]

This article, I think, mixes 'unit conversion' with what I would call dimensional analysis; specifically resolving a physical situation to M L T N etc. I think it needs splitting into two - I'm not Wikipedia savvy enough to do it - but it is a poor article at prrsent — Preceding unsigned comment added by 2A00:23C4:1594:E600:D52:B352:BBAD:C28 (talk) 16:03, 29 January 2021 (UTC)[reply]

I went ahead and moved the offending section into Conversion of units. fgnievinski (talk) 00:33, 29 August 2022 (UTC)[reply]

Dimensional analysis use in healthcare

I am faily new to the idea of dimensional analysis. I will soon be teaching a class for nursing students using diemsional analysis to calculate medication dosages. I guess I thought there might be more information regarding the use of diensional analysis in healthcare. I am so new to this process that I really dont even know what to ask. I was looking for help but did not find it in this article. MbrsnLyf (talk) 20:38, 5 March 2023 (UTC)[reply]

What you're looking for can be found in the Conversion of units page-I'll go make sure that's been properly linked/referenced in the article. Quantivariate (talk) 16:54, 29 May 2023 (UTC)[reply]

Extensive quantities

It is mentioned above that dimensional analysis is a meta-analysis of the relations between quantities, and how they should be related if we change the units we use to measure them. But for me, this puts the cart before the horse. Before we get to the mathematics, we need some empirical, scientific idea to justify our analysis. A formula might be right in situation A, and if it is, then it should be right for any consistent system of units. But why should that rightness tell me anything about situation B? Why should a theory of arbitrary human unit choices lead to a theory that can deduce the speed of a ship from it's scale model? Certainly, two coordinate systems that can be used to describe a game of chess can also be used to describe a game of checkers, but we don't expect to be able to deduce winning strategies of one based on the other just by a coordinate transformation. I subscribe to the school of Sonin (2001) and Tolman (1917) that the root of dimensional analysis needs to be with the observation that some physical quantities behave additively -- the whole is the sum of the parts. So, if we break a fly brick in two, the weight of the original brick is equal to the sum of the weights of the two pieces. I believe this was part of Tolman's motivation for defining the concepts of extensive and intensive quantities which are core to thermodynamic theory -- once we have empirically identified extensive quantities, we have a first-principles justification for rescalings like ship-speed extrapolation. Uscitizenjason (talk) 18:40, 11 September 2023 (UTC)[reply]

A better example needed?

The article text states:

"Even when two physical quantities have identical dimensions, it may nevertheless be meaningless to compare or add them. For example, although torque and energy share the dimension T−2L2M, they are fundamentally different physical quantities."

In light of the Work-Kinetic Theory for Rotation:

W_torque = ΔKE_rotation

where:

W=∫ I_rot dω / dt⋅dθ

Work and energy have the same dimensionality ( [M1 L2 T−2] ) as do torque and energy (ie: the amount of energy applied in the form of torque does work to increase rotational kinetic energy), so mightn't Wikipedia need a better example of two quantities with the same dimensions but which are fundamentally not comparable?

~~ 76.30.103.137 (talk) 00:06, 20 January 2024 (UTC)[reply]