Wikipedia:Articles for deletion/Non-dimensionalization and Scaling of Navier-Stokes Equation


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was   keep. -Scottywong | gossip _ 21:39, 27 September 2012 (UTC)

Non-dimensionalization and Scaling of Navier-Stokes Equation

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This is not a notable encyclopaedic topic in itself, in my opinion. A web-search gives not many results on the topic as such. While nondimensionalization and scaling are important, the nondimensionalization to be used critically depends on the flow problem at hand. There are a plethora of nondimensionalizations of the N-S equations possible, e.g. with possible different scalings in different directions, leading to different types of modelling for different problems (e.g. boundary layer theory). I believe the strategies to do so are typical subjects of coursebooks, but not of Wikipedia. Crowsnest (talk) 12:50, 11 September 2012 (UTC)


 * Agreed. No expert on NS-eqns yet but I know non-dimensionalization and scaling, all the article talks about is the procedure and how to do it for the NS-eqns (obviously). Someone may want to merge this into the main article in a few years time, creating work for those that would merge. REDUNDANT is relevant. Perhaps the main intension is to summarize all the different conventions? Maschen (talk) 13:49, 11 September 2012 (UTC)
 * Should add the obvious - for now there are no sources, when there should be: Identifying reliable sources. Not a problem in principle for now, since sources may be found later, but if not then no sources are a reason to delete. Maschen (talk) 13:56, 11 September 2012 (UTC)


 * Keep. It's no wonder Crowsnest didn't get any hits searching on the exact string "nondimensionalization of the navier-stokes equations". But something a little more flexible like scaling laws fluid mechanics give lots of hits. Also, any fluid mechanics text will devote a lot of space to the concept; I'll add an example in the references. As for there being a plethora of nondimensionalizations of the N-S equations, I see that as an argument for discussing them in one place. There can be a discussion of the different nondimensional numbers and their significance. Some of the material in Dynamic similitude could be added to this page. RockMagnetist (talk) 17:01, 11 September 2012 (UTC)


 * It strikes me that the items you mention broaden the subject as compared to the article title (i.e. about the N-S equations): your search string is about "fluid mechanics", the addition to the article's references section is the book "Physical fluid dynamics", while the WP article Dynamic similitude is not about equations but about experiments.
 * You remark that many fluid mechanics texts "... devote a lot of space to the concept ...", which is exactly the point why I have problems with the subject of this article. The concepts, theory and techniques as used in non-dimensionalization, scaling, similitude are of general applicability in physics, and there are not different ones for the N-S equations. The application of these concepts and techniques to various physics problems requires skill and experience. Wikipedia is an encyclopedia, so teaching the skills how to apply these concepts, theories and techniques to various topics is outside its scope, see WP:HOWTO.
 * There are so many different problems in fluid mechanics, with each asking for a different non-dimensionalizations and scalings – even for the same problem in different regions of the flows, e.g. around a wing: boundary layers, outer flows, shocks, wakes, turbulence, aeroelasticity, etc. Who is going to decide what to incorporate: text books and journal papers have a limitless variety on examples with different scalings (justifiable for the fluid flow problem they study). To me it seems much better to add the appropriate scalings and non-dimensionalizations to each article in which they apply (and wikilink to the general articles on non-dimensionalization, similitude (model), scaling law, invariant (physics), dimensional analysis, scale analysis (mathematics), etc).
 * Further note that the N-S equations themselves may be regarded as the product of scaling and similitude arguments, through the notions of continuum mechanics and a Newtonian fluid assumption for the relationship between the fluid stresses and deformation, see Navier-Stokes equations. -- Crowsnest (talk) 13:29, 12 September 2012 (UTC)
 * You make a convincing case that a good article on this subject will be hard to write. However, that is not a criterion for deletion. The article clearly passes the notability test: a chapter on scaling in fluid mechanics is, of course, entirely devoted to scaling of the N-S equations. It wouldn't be hard to find many more sources. If you don't like the search terms I chose, how about scaling navier stokes equation? I don't see any other reason for deletion that could apply. RockMagnetist (talk) 16:47, 13 September 2012 (UTC)


 * I do not agree with you that the article passes the notability test. To my opinion, it does not pass the last bullet ("Presumed") of WP:GNG: "... Editors may reach a consensus that although a topic meets this criterion, it is not appropriate for a stand-alone article. For example, such an article may violate what Wikipedia is not, perhaps the most likely violation being Wikipedia is not an indiscriminate collection of information. ...". I believe the article will inevitably (if expanded from its present rudimentary form) become a textbook/howto instead of an encyclopaedic article. -- Crowsnest (talk) 12:17, 27 September 2012 (UTC)


 * Note: This debate has been included in the list of Science-related deletion discussions.  —Tom Morris (talk) 17:12, 11 September 2012 (UTC)


 * Merge (if reliable sources can be added) into Navier–Stokes equations which is only 58 KB wikitext at present. Anyone with an interest deep enough to actually solve the equations should be made familiar with the modern way of doing so. I believe this is the current best practice, but I'm not expert enough to say with any certainty, so let's see some sources. &mdash; Cup co  02:37, 17 September 2012 (UTC)
 * Actually, 58 kB is pretty large. According to a rule of thumb, it falls under "May need to be divided (likelihood goes up with size)." However, I notice that there is nothing on scaling in Navier–Stokes equations. Something should be added on the subject as it is an important aspect of solving them. RockMagnetist (talk) 16:01, 17 September 2012 (UTC)
 * That was total bytes, not readable prose size which is typically half around there. &mdash; Cup co  18:19, 17 September 2012 (UTC)
 * Good point. The readable prose size is 28 kB. Still, the most relevant reason for a merger is that the page is short and unlikely to be expanded within a reasonable time. As Crowsnest has pointed out above, if anything there is too much material for a single article. RockMagnetist (talk) 18:28, 17 September 2012 (UTC)


 * Relisted to generate a more thorough discussion so a clearer consensus may be reached.


 * Please add new comments below this notice. Thanks, Deryck C. 14:41, 19 September 2012 (UTC)


 * Keep - specialized but highly useful for the Project's core readership - college students - who are unlikely to be able to calculate dimensions on their own. Bearian (talk) 21:18, 20 September 2012 (UTC)
 * To me, that seems to be more in line with the aims of Wikiversity than of Wikipedia, see WP:NOTTEXTBOOK. -- Crowsnest (talk) 21:50, 20 September 2012 (UTC)
 * We wouldn't think of excluding how to calculate the standard deviation. This article is even less of a how-to because, well, it requires specialized numerical methods software. It's more encyclopedic because of its difficulty and the fact that we can only hope to show an overview. &mdash; Cup co  21:57, 20 September 2012 (UTC)
 * Calculating the standard deviation is a method, as are non-dimensionalization and scaling. But applying it to the Navier-Stokes equations, for a certain flow problem, is a skill. It is like there is an article on weeding, an article on flower garden, and then creating an article on weeding of flower gardens. -- Crowsnest (talk) 09:51, 21 September 2012 (UTC)

Yes - non-dimensionalization and scaling are general procedures, and need skill and practice, which is out of the scope of WP, as Crowsnest says above. Same for dimensional analysis of physical quantities. This article seems to be trying to "teach" these for the NS eqns.

On the other hand there are specialized articles like Navier–Stokes existence and smoothness and Derivation of the Navier–Stokes equations, but these are sufficiently notable on their own and relieve the main article's size and audience, and are much less on "teaching" and more on describing topics, IMO. Maschen (talk) 10:42, 21 September 2012 (UTC)


 * Note: sources with inline citations have been added. I still say merge, but now my second choice is to keep. &mdash; Cup co  06:19, 24 September 2012 (UTC)


 * Btw I didn't get round to it earlier, but I strongly oppose merging. The main article (NS eqns) would become far too big and unreadable. I only suggested that if people wanted to merge, it would create extra work, and didn't think at the time that this article alone would plenty of material (as RockMagnetist and Crowsnest say). Maschen (talk) 06:54, 24 September 2012 (UTC)


 * Comment - someone has been adding quite a lot of content to this page. RockMagnetist (talk) 16:56, 25 September 2012 (UTC)


 * It's the IP 14.139.34.2, most of the additions are just references and the other cylindrical coord components of the NS eqn. Maschen (talk) 18:23, 25 September 2012 (UTC)


 * Indeed a lot of content has been added, and a lot of effort is made by the two main authors. But all is on one type of non-dimensionalization (with only the Reynolds number being the non-dimensional quantity of importance, and only one characteristic length scale) in different coordinate systems.
 * In my opinion, the present status of the article gives an highly unbalanced view on the subject suggested by the article's name. As can be seen in the List of dimensionless quantities there are many named dimensionless quantities associated with fluid flow, and even many more unnamed ones can be found in the literature. E.g. the books referenced – by you and me – in the "Further reading" section contain a lot of examples of different types of non-dimensionalizations for different flow problems (not to forget those on many different flows in scientific journal papers on fluid dynamics, turbulence and heat transfer). -- Crowsnest (talk) 21:18, 25 September 2012 (UTC)


 * Keep -Though a lot of content is available on Navier Stokes Equation but the importance of this page is that it talks about how to deal with the non-dimensionalization. Converting the same equation into non-dimensionalised form and then highlighting the importance of the same has been dealt in a crisp and clear manner which is helpful for students to understand. — Preceding unsigned comment added by Biwas Mrinmoy (talk • contribs) 10:20, 26 September 2012 (UTC)

Keep An article in Wikipedia keeps changing as other users keeps updating the article. An article in itself is not complete unless various experts in the field keep updating. This article would be useful for students and faculty as ready reference and can be added various dimensions to it be updating it further. Such information may be available in text books etc. but it will be more useful if it is available online on Wikipedia as it more accessible — Preceding unsigned comment added by Om.prakashh.singh (talk • contribs) 10:43, 26 September 2012 (UTC)


 * Keep - This topic contains a lot of information that can be updated and can become a big article so it is not recommended to merge with another article. Here this article has given brief introduction to the topic and described about the importance of it. The general result of the equations upon non-dimensionalizing are explained. It can further be updated by considering various conditions in a real situation and accordingly the modified equations can be added. — Preceding unsigned comment added by Teja.v36 (talk • contribs) 11:32, 26 September 2012 (UTC)


 * Comment: To my opinion, this is just as undesirable as Non-dimensionalization and scaling of Newton's second law (note that the Navier-Stokes equations are just the application of Newton's second law to a Newtonian fluid in continuum mechanics). As long as you do not know the case on/for which the non-dimensionalization and scaling is to be applied, it is meaningless. The questions one has when making/using some model to a certain problem are: which simplifications are allowable, which approximations still lead to results of a desired accuracy? Are gravity, electromagnetic forces, quantum or relativistic effects important? Can I use the continuum hypothesis, or can a body be considered rigid, or even as a point mass? Are relativistic gravity effects important, or can I use Newton's law of gravity? Those questions are associated with different meaningful (skillful) non-dimensionalizations of each problem. Where it is crucial that the important (and problem-specific) characteristic values of the key problem parameters/fields are quantified. So the vast diversity of different (types of) problems leads to a sheer countless number of different meaningful non-dimensionalizations (and associated simplified model equations or scale models), which cannot be covered in such an article. It will result in a textbook or HowTo, which are the aim of projects like Wikiversity but not of Wikipedia. -- Crowsnest (talk) 13:07, 26 September 2012 (UTC)


 * Fortunately, the sources listed in this article are not stymied by the diversity of possible non-dimensionalizations. They discuss some of the general considerations, cover some of the most commonly used parameters (such as the Reynolds number), and then mention relevant parameters for various phenomena such as convection. The article would summarize such information, so it wouldn't be textbook or howto. This could be a useful main article for Category:Dimensionless numbers of fluid mechanics. RockMagnetist (talk) 01:22, 27 September 2012 (UTC)
 * Yes, but why should the article be based on just these sources? You added Tritton, and I added some additional examples of books associated with the subject. If you look at e.g. the contents of: you see a book "... stymied by the diversity of possible non-dimensionalizations", as you put it. Each topic – c.q. fluid-dynamics equation – he treats is the result of some (set of) non-dimensional quantities being very large or small. And the author says on page xvii: "... I have been highly selective in my choice of topics and in many cases the choice of subjects is based on my own interest and judgment". Perhaps this makes the problem I have with the subject of the article more clear (a sheer endless expandable textbook/howto).
 * P.S. The given example of a non-dimensionalization in the article (in its present status) is already in Reynolds number. -- Crowsnest (talk) 11:17, 27 September 2012 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.