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Jiří Březina was nominated for deletion. The discussion was closed on 11 December 2019 with a consensus to merge. Its contents were merged into Reynolds number. The original page is now a redirect to this page. For the contribution history and old versions of the redirected article, please see its history; for its talk page, see here. |
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In further reading, the link "Purcell, E. M. "Life at Low Reynolds Number", American Journal of Physics vol 45, pp. 3–11 (1977)" doesn't work. — Preceding unsigned comment added by 150.203.68.87 ( talk) 08:17, 26 September 2019 (UTC)
What on earth does that mean? Elevation? Altitude? I prefer to see the discussion focus on fundamental attributes of the fluid such as pressure, temperature, density or whatever. Saying that the Reynolds numbers are a function of elevation is just wrong. 98.202.242.88 ( talk) —Preceding undated comment added 00:43, 21 January 2010 (UTC).
I think this is a good concept for a section, but it's a mess. First, there's no units on any of the figures - I'd add them, but the whole section needs a work-over....
First, how can a blue whale have a Reynolds number? The Reynolds number is the property of fluid flow: not a baseball, mammal, or boat. Second, none of these figures have references, although I am not disputing their veracity.
This section needs a good table (with citations) that lists typical fluid flows that Wikipedia users could relate to (for understanding of the concept - like the flow in a garden hose, the flow in an HVAC duct, etc), maybe combined with fluid flows that are of more encyclopedic value (like the fluid flow in the brain).
-- Goingstuckey ( talk) 15:43, 18 June 2009 (UTC)
I edited some typical Reynolds numbers, which were already there in the main page. One of them mentioned the fastest fish. The following link [1] is where I extracted 10 ft for the length of a sailfish and 80 mph as a top speed.
In response to the question about how a baseball, etc., can have a Reynolds number, it is not true that the Reynolds numbers is a property only of the flow. It is a property of the combination of the flow and the object. The diameter of a softball is the D in Re. When we talk about the Re of a baseball, it is understood that we mean the Reynolds number associated with the flow around a baseball at a relative airspeed, V, that in embedded in the Re for that flow situation.
Kimaaron ( talk) 15:22, 15 November 2016 (UTC)
Strictly speaking, there is no such thing as an "inertial force." Any object (e.g., a fluid particle) possesses inertia, while it is acted upon by forces. I realize that the definition of a Reynolds number as "a ratio of inertial force to viscous force" is used frequently in both textbooks and peer reviewed literature, but I've always considered it to be sloppy.
Additionally, I would like to point out that neither the quantity μ/L nor the quantity vsρ have units of force, so to list them as forces may be very confusing to the general reader. This will not do for an encyclopedia.
In terms of the equations of motion (e.g., Navier-Stokes equations), if one uses a length scale , a time scale , and a velocity scale , the dimension of the inertial term (i.e., the term which represents the time rate of change of momentum per unit volume) is , while the dimension of the viscous term (i.e., the term represented by the divergence of the viscous stress tensor) is . A Reynolds number is properly the ratio of these terms, . Note that the dimension of the terms in the equations of motion have units of force per unit volume, so that, if multiplied by , they will yield forces. If you must define a Reynolds number as a ratio of forces, then, your "inertial force" should be and your viscous force should be .
-- 71.98.78.28 04:04, 11 June 2007 (UTC)
imo, you guys are way to picky; the use of ratio inertial/viscous force is widely used in many different communities. I think what you are missing is that an article like this has to function on 3 or 4 layers: for the general audience, without say HS algebra, the ratio of force idea is intuitive; for the HS/college algebra set, and then for people ready to deal with angular momentum imo, as a phd who has written several articles here, you are making a common mistake, writing only for thetopmost level. nothing wrong with that, but as wiki is a general encyclopedia, really need a general article you might, as a learning exercise, study the article at britannica.com; not saying it is right, but it is at the right *level* i'm not trying to be rude: i know that it is *really* hard to write down correctly — Preceding unsigned comment added by 50.195.10.169 ( talk) 19:06, 7 October 2013 (UTC)
There seems to be some inconsistency about whether laminar flow ends at 2100 or 2300 in this article, as well as about the upper bound of the unknown regime. The page states that it's 3000, but it should be 4000. From Process Fluid Mechanics by Morton M. Denn, 1980, p 34: "Laminar flow usually ends at Re = 2100; between Re = 2100 and about 4000, the flow seems to pulsate between laminar and turbulent portions. Fully developed turbulence begins at Re of about 4000." My fluid mechanics professor ( http://www.cheme.cornell.edu/cheme/people/profile/index.cfm?netid=laa25) also confirms this version of the flow regime divisions. -- Icefaerie 03:50, 26 February 2007 (UTC)
Definitely a rule of thumb. Laminar flow is definitely expected below a Reynolds number of 2000, but there is a transition zone between 2000 and 4000. In my professional judgment it is safe to treat flows as turbulent at Reynold's numbers greater than 3000 in most cases. One interesting thought to illuminate the uncertainty in where laminar flow ends is that in carefully controlled laboratory settings laminar flow has been achieved at Reynold's numbers as high as 100,000. There is a very interesting article on this in the February 2004 issue of Physics Today. —Preceding unsigned comment added by 68.238.133.228 ( talk) 03:41, 5 January 2009 (UTC)
Back in March 2017, Tvtvashisth edited the Laminar/Turbulent Transition section from 2000 and 4000 to 1000 and 2000. This would be correct if the characteristic dimension of a pipe was the radius, but it isn't, and the article clearly states that it should be diameter. I don't have access to any sources at the moment, but someone should revert that change as soon as possible. 128.187.116.19 ( talk) 17:09, 13 July 2017 (UTC)
In this field dimensionless numbers such as this are known with two letters, no subscript. The page was changed to add a subscript, and I reverted it. - EndingPop 19:02, 15 October 2006 (UTC)
It's a comment to an excellent page named "Reynolds number" ( http://en.wikipedia.org/wiki/Reynolds_number).
Under 'The similarity of flows' subsection, it's stated:
In order for two flows to be similar they must have the same geometry and equal Reynolds numbers. When comparing fluid behaviour at homologous points in a model and a full-scale flow, the following holds:
Re*=Re; p*/(rho* v^2*) = p/(rho v^2) [sorry, I couldn't copy the formula here. p=pressure; rho=density; v=velocity]
The latter equation does not represent the Reynolds number. It is the Euler number Eu=p/(rho v^2), which, along with Re, is one of the major fluid dynamics criteria.
-- 204.174.12.18 23:20, 24 October 2005 (UTC)
I agree. I quote
http://www.engineeringtoolbox.com/euler-number-d_579.html and
Euler number (physics). Also I question the relevence of a section on flow similarity in an article about the Reynolds' number which although yes is a requirement of similar flows is not the end of the story for flow analysis by a long way, a new article about
Similarity of flow or
Flow similarity (etc) should be made about using wind tunnels and aqua tanks in lab experiments to model real flows (eg aerofoil in wind tunnel saving on having to send up a real aircraft). For now I have clarified what is the Re and what is Eu, and made a link to
Euler number (physics).
Fegor
15:06, 17 March 2006 (UTC)
Currently Reynold's number redirects to Reynolds number, whilst Reynolds' number does not exist (note the apostrophes). As a matter of grammer and consistency I think the article should be hosted at Reynolds' number (I do not mean Reynold's number), for precedent look at Bernoulli's principle for when apostrophe should go before the s, and Bayes' theorem or Huygens' principle are examples of when it should go after. Fegor 12:46, 9 March 2006 (UTC)
I have heard that (due to the effects of small Reynolds numbers), that flying for flies and other small insects is much more like swimming than flying. Is this a correct analogy? If true, would it be useful to add as an example?
Rather than putting that it's equal to 2r for circular sections should it be better to put L= 4A/P (A= area, P = perimeter). Would do it myself but I feel I might mess up. Spanish wiki has it this way. -- English - Spanish 14:11, 27 November 2006 (UTC)
"engineers will avoid any pipe configuration that falls within the range of Reynolds numbers from about 2000 to 3000 to ensure that the flow is either laminar or turbulent." What kind of engineers do this and why? Does this apply to pipes in my house? Richard Giuly 12:28, 9 March 2007 (UTC)
I feel that they are often designed well outside of the transition zone because in this region drastic pressure and flow variations can occur making the system difficult to model and design. Most often a civil engineer will design pipelines in cities and homes. —Preceding unsigned comment added by 64.126.190.120 ( talk) 03:49, 5 January 2009 (UTC)
Common values for kinematic viscosity do not belong on this page. That section should be removed. 134.71.155.171 05:42, 30 May 2007 (UTC)
Agreed. I removed the "common values" section. There is already a link to the extensive entry about viscosity. Oanjao 16:10, 31 July 2007 (UTC)
why is mu used as the symbol for the dynamic viscosity? isn't eta the commonly used symbol for this property? —Preceding unsigned comment added by 130.89.137.46 ( talk) 10:51, 13 March 2009 (UTC)
I concur. eta is the symbol used for viscosity in my literature (Biological Physics by Philip Nelson, Physics for scientists and engineers 6th ed. Tipler and Mosca, Physical Biology of the Cell by Rob Phillips et. al as examples), in fact I cannot recall having seen mu used for viscosity before, so I must admit I am a little confused as to why it is used here. Shouldn't convention be followed? Who fixes this? Elvegaro ( talk) 10:23, 8 October 2011 (UTC)
I'm proposing some changes to the definition section, because I think it would be clearer:
Typically it is given as follows:
where is the mean fluid velocity, is the characteristic length, is the (absolute) dynamic fluid viscosity, is the kinematic fluid viscosity, defined as , and is the density of the fluid.
The main changes I made are removing the units, and replacing the HTML entities with TeX markup, so that they appear the same in the equation as in the explanation. I removed the units, because it doesn't seem like they belong there. Why, for example, should velocity care if it's in meters per second or feet per second? Does it change the equation any? If anything, we could list the dimensions, but that is also probably not necessary, or could be covered by linking to the page in question (i.e., velocity becomes velocity, then the reader can look at that page to discover the dimensions of velocity).
I'd also like to point out that quantities used in other formulas such as in lift coefficient don't list the units of each term.
Thoughts? User:!jim talk contribs 18:49, 22 October 2007 (UTC)
The Reynolds number is the ratio of advection of momentum (velocity "diffusion") to the diffusion of angular momentum (vorticity "diffusion"). Most dimensionless numbers in fluid mechanics are defined as the ratio of diffusion constants for different quantities (e.g., heat, mass) to either the "diffusion" constants of momentum (specific momentum = velocity) or angular momentum (specific angular momentum = vorticity). From a dimensional analysis standpoint, diffusion coefficients have units of l2 / t. The "diffusion coefficient" for momentum (i.e., velocity transport) is just ul. The diffusion coefficient for vorticity is just the kinematic viscosity (see the vorticity page). I would suggest that this definition be used since other non-dimensional numbers are defined in terms of a ratio of advection to diffusion of two properties (e.g., see Prandtl Number, ratio of advection to heat diffusion and Schmidt Number, ratio of momentum to mass diffusion). This is the academic standard for defining dimensionless numbers in fluid mechanics. Hope this helps. -- Allen314159 ( talk) 01:09, 12 July 2008 (UTC)
The definition focuses on Reynolds numbers for fluid flows, as does most of the discussion, which is sensible enough. But then the "typical values" section right away mentions Reynolds numbers for solid objects, such as spermatozoa (well, semi-solid) and ocean liners. It would be useful to have a discussion of how the definition (which speaks of fluids flowing) can be extended and applied to solids moving through a fluid; i don't see much in that way. 69.54.65.151 ( talk) 15:59, 25 July 2008 (UTC)
The "typical values" section is only utilizing the length scale of the solid objects and the velocities of fluid flow for the calculation of the Reynolds numbers. The Reynolds numbers calculated for these solid objects describe the fluid flow around them and at their length scales (and not the flow of these solid objects within or with the fluid - that would use of different numbers like the Schmidt Number. I still stand by my academic description above. -- Allen314159 ( talk) 00:08, 1 August 2008 (UTC)
Kimaaron ( talk) 08:07, 15 November 2016 (UTC)
The DEFINITION of Re is rho V L/mu, where L is a characteristic length scale of the flow field. It is typically a characteristic dimension of a solid object or boundary. It might also use a length scale over which the flow itself varies significantly, such as a boundary layer thickness or a shear layer thickness. Once defined in this manner, Re CHARACTERIZES the ratio of the relative contribution of inertial effects and viscous effects. Forces if you like. But the definition is NOT the ratio of inertial to viscous forces. In fact, the inertial forces and viscous forces vary a lot over a flow field, so they are not well defined to start with and they would be very difficult to quantify. Regardless, it is WRONG to state that Re is DEFINED as the ratio of these two quantities. It isn't. It is defined as rho V L/mu. The NASA website referenced in the place where the wrong definition is stated is NOT the authority on definition of Re. For the definition of Re, we need to go back 100 years or so. The only old book I have at hand right now is Abbott and Von Doenhoff (Theory of Wing Sections). It says Re = rho V L/mu I could use that as a reference, but I'd prefer something even older. I'll look around. Once I find it, I plan to edit the main page to make it clear what the definition is and then what this physical interpretation as a ratio of inertial to viscous effects is all about. That does give useful insight into the physical meaning of Re, it just doesn't define it. If someone has a good early reference for the definition of Re, please let me know. Kimaaron ( talk) 06:02, 2 October 2016 (UTC)
I found a paper by Arnold Sommerfeld from 1908 in which he named Reynolds Number for the first time and defined it as we know it today, rho V L/mu. This is the DEFINTION of Re. The business about being a ratio of inertial to viscous forces is an INTERPRETATION of the physical significance of Re. I have edited the main article to use the correct defintion and added a little about Sommerfeld naming Re. Kimaaron ( talk) 08:00, 15 November 2016 (UTC)
I found this comment in the text of the article, but without a response ( Jdpipe ( talk) 05:39, 10 September 2008 (UTC)):
To the best of my knowledge adimensional is not a word. I have never seen it used in any fluid texts. The correct formation is either the compound non-dimensional or the short-form nondimensional. Bradweir ( talk) 21:05, 29 June 2009 (UTC)
There are several errors in the article. People have pointed them out. Why don't they make the changes? Clearly the first line has "Forces" stated when both inertial and viscous "forces" have the wrong units. There are other issues also. Someone needs to fix these. I teach classes that deal somewhat with this area and my students were finding this article more confusion than helpful. —Preceding unsigned comment added by 67.169.201.107 ( talk) 17:07, 11 October 2009 (UTC)
The value "D" in the section regarding the Reynolds number of flow through a pipe is ambiguous. Does that D reference the diameter of the pipe or the length of the pipe. There is no further clarification in the rest of the article. —Preceding unsigned comment added by Adroa ( talk • contribs) 02:02, 14 October 2009 (UTC)
The effect of pipe length is very different from that of the diameter, and for pipes the diameter must be chosen for Re, not the length. Even (above a certain length) the pipe length doesn't matter at the same flow speed. I think that the article does mention that the diameter is chosen; however, it is not made clear why... Harald88 ( talk) 08:44, 26 January 2010 (UTC)
It would be useful if this is elaborated in the definition section: why for example for wings the length can be chosen (if that is indeed correct). Harald88 ( talk) 08:46, 26 January 2010 (UTC)
We need a diagram of, for example, the flow around a sphere at different reynolds, going from laminar to vortex street. I think it really helps cement the concept in intuitively.- Wolfkeeper 13:43, 15 February 2010 (UTC)
If for example the scale model has linear dimensions one quarter of full size, the flow velocity of the model would have to be multiplied by a factor of 4 to obtain similar flow behavior.
This is obviously wrong. A 1/10th scale model of a Piper Cub will not be tested with a wind speed approaching Mach 3. As models scale down, wind speed also scales down (but in a non-linear fashion, I think). It is true however that the Reynold's Number is used to figure out exactly what the speed is. —Preceding unsigned comment added by 131.142.52.246 ( talk) 15:30, 23 March 2010 (UTC)
The section about typical values of Reynolds number must state that those values depend on the geometry of the system/flow. For instance a flow in a pipe stays laminar longer than a flow around a cylinder. Typical values of Reynolds may hint at the fact that transition from laminar -> turbulent hides varied types of flows, in particular attached laminar steady flow -> separated laminar steady -> laminar separated periodic -> transitional periodic -> turbulent (chaotic) This should be explained in the page on flow separation which is quite poor, and could be enhanced by diagram in page 3 of this document: http://www.stanford.edu/class/me469b/handouts/turbulence.pdf — Preceding unsigned comment added by 194.167.134.222 ( talk) 13:16, 1 August 2012 (UTC)
The image in this article says the lower limit is "~49", but Kármán vortex street says it's 90. Which is correct? -- RoySmith (talk) 13:27, 12 August 2012 (UTC)
I want to say in some sort of constructive fashion (seriously) that this is one of the least helpful articles I have ever consulted in Wikipedia. Maybe the problem is with me, but the article did almost exactly nothing to help me find out "What is a Reynolds number?"
Instead of getting an answer to that question, I found out at the very beginning of the article that "Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces." This was encouraging, but it was followed by a sort of disclaimer: "The term inertial forces, which characterize how much a particular fluid resists any change in motion, are not to be confused with inertial forces defined in the classical way."
Because I could not comprehend what the second sentence was telling me not to confuse, the two effectively cancelled out, leaving me with honestly no idea what Reynolds number refers to. Dratman ( talk) 22:54, 24 February 2013 (UTC)
dratman, you are 100% right, this intro is typcial of many technical articles in wiki, the authors have no sense of how to write for a general audience. I think a good intro would be something like: The reynolds numbers describe the behaviour of a fluid (gas or liquid) in terms of how "smooth" the flow is. The fluid flow we are all familiar with - say water coming out of a nozzle - is high Re, and such flow is characterized as unpredictable; a small change in the nozzle causes a big change in teh stream. Fluid flow at low Re is not a common sight; we can say such flow is predictable. In general, low Re occurs at microscopic scales. WE can connect these ideas by thinking of the liquid folding... well, that isn't very good, but it is better then what is there !! — Preceding unsigned comment added by 50.195.10.169 ( talk) 18:48, 7 October 2013 (UTC)
The typesetting of formulæ in this article at present is haphazard, being neither internally consistent, nor consistent with standard recommendations." [1] [2] [3]. —DIV ( 137.111.13.4 ( talk) 07:03, 21 August 2015 (UTC))
Earlier comments have been made about an accessible lead.
I have moved the plunge into maths out of the lead, and given overview of what the RN is used for. Also created definition section with re-ordered and logical narrative. Hopefully this will help the reader to more easily engage. Dougsim ( talk) 15:08, 3 December 2016 (UTC)
The lead says that Gabriel Stokes originated the idea, and gives a larger picture of him than of Reynolds. Could someone please quote the expression in the Stokes paper which is cited which corresponds to the Reynolds number, because I could not find it. Chemical Engineer ( talk) 17:09, 31 December 2016 (UTC)
This article uses the phrase "flow situations" to describe flowing fluid. Would it be appropriate to simply use "fluid flow" instead of "flow situation", as the latter can sound too technical? Somerandomuser ( talk) 18:49, 16 May 2017 (UTC)
Someone has changed v to s in the definition of Re. They argued that V looked too much like nu, so they decided to use s for "speed" instead. This is completely non-standard and it needs to be reverted. We always use v. If they like, they can draw attention to the fact that v looks like nu and caution people to be careful. I tried to revert it, but I think I reverted something else by accident. I don't know enough about editing here to fix this problem with confidence. I'd appreciate it if someone who does know what they are doing could revert the edits please. Thanks, Kimaaron ( talk) 06:57, 28 January 2018 (UTC)
A large portion of explanatory text was removed [2] seemingly arbitrarily from the Derivation section towards the top of the article, as a part of an edit by Attic Salt.
The "derivation" proposed can't go unqualified, for reasons that were given in the removed text, namely:
Thus, simply stating that this is a derivation of -- meaning, rigorous reasoning that demonstrates beyond any doubt the necessity of -- the form of the Reynolds number, is downright nonsense, so please re-instate the comment, either re-formulated, or in its original form.
Apart from this, removing whole paragraphs of text without so much as a word of explanation is unacceptable, so please also give us the reasons for the removal.
In looking at the proposed merger, it does look like some of that article could be salvaged and put here as an example. Most certainly not all of it, but definitely some. However, it seems to me to be just a little too specific, and as written may likely not be of significant help in explaining the concept to the novice reader. The specific type of flow this is describing is granular flow. At the moment, this simply links to granular material, yet nothing about granular flow is described. They are actually two distinct subjects. In my opinion, it would be best to create a separate article about granular flow, and describe the works of people like Ralph Alger Bagnold and Jiří Březina and their contributions to the science (for example, see Bagnold number). Zaereth ( talk) 22:13, 11 December 2019 (UTC)
Section "Derivation 1" has multiple issues and should be removed.
Note that a rigorous and clear derivation is presented under "Derivation 2". — Preceding unsigned comment added by 92.247.118.230 ( talk) 10:42, 28 March 2020 (UTC)
Following international standards (ISO/IEC 80000-11 Quantities and units - Part 11), all so-called characteristic numbers are considered as quantities and shall be written in italic, thus Re. In this standard, it is item 11-4., Reynolds number JOb ( talk) 08:10, 28 April 2022 (UTC)
Hello, the image of the water tap is very misleading I think (please correct me if I am wrong). While it is probably true, that one is turbulent and the other is laminar, the white color of the stream has nothing to do with that. It is air that was mixed in by the mesh at the end of the water tap. I think the image leads one to think turbulent water must look white-ish, even though in reality turbulent flow (for example in a pipe with no air) can look perfectly transparent.
I would recommend removing or replacing that image. Thanks Wikipedia Community 185.65.196.182 ( talk) 07:48, 30 January 2023 (UTC)
I am going to comment here before completely rewriting this section. It is completely incorrect, unsourced, and doesn't even link to potentially helpful pages. I'm baffled how this got added.
One thing written under this heading says "The largest eddies will always be the same size; the smallest eddies are determined by the Reynolds number."— this is patently false and misleading.
In Fluid Mechanics for Chemical Engineers, (by Noel de Nevers, 3rd ed.) it states plainly, "The largest eddies in a confined flow cannot be larger than the dimensions of the confining container. Generally they will be 0.1 to 0.5 times as large as the boundaries of the system or the size of the disturbance causing the turbulence." So obviously, the largest eddies are not always the same size; they scale with the size of the system.
On the other hand, the size of the smallest eddies is related only to the kinematic viscosity and the dissipation rate, not the size of the system— so you could say the small eddies are "always the same size". This size scale is known as the Kolmogorov scale, which already has a Wikipedia page that describes that size quantitatively, so I would link to that.
I guess I'm just looking for permission. I literally made a Wikipedia account to correct this page because it was so terrible. And it's a valuable page... so yeah, I just want someone to tell me I won't be reviled across the internet for destroying someone's inaccurate two paragraphs on this topic. HelpfulWitch ( talk) 20:03, 1 March 2023 (UTC)
Since my edit was reverted with the statement that 'velocity doesn't cause turbulence', even though I provided a citation, I'd like to have some discussion or a counter-citation. googling for 'where is the turbulent section of a pipe' suggests that most people believe the turbulent section is in the center. Also I believe that higher friction (I.e. viscosity) decreases the likelihood of turbulence, doesn't increase it. Yes, the energy to create eddies comes from the interaction of the fluid with the pipe wall but those eddies immediately travel to the center of the pipe because that's where the circular or random motion is easier. Mlwater ( talk) 01:55, 27 April 2023 (UTC)
The "where this will take place" seems very odd to me here. Candles are essentially always burning the same way, only the scale is slightly different. The plume of a candle will generally transition to turbulent, there is nothing to predict here in the sense of "yes/no". So if the "where" is talking about different systems, using this specific example can be very misleading.
We can also understand this as calculating the actual location of the laminar–turbulent transition with Reynolds formula, which would not be correct. Let us look at the diagram from Reynolds's 1883 paper further down in the article. Because unlike with the candle, the Reynolds number does not change once the necked down section is reached. However, the laminar flow is still meta stable for a while before it transitions to turbulent flow. I would argue the same is happening with the candle. While the Reynolds number is not constant due to cooling and mixing with air, it was still only meta stable from the beginning. The transition can also happen all the way down at the flame, making them flicker. There are some articles that talk about this, for example this one. The Reynolds number can not be used to calculate where this transition happens in a meta stable system. The only lenght in the formula is for the characteristic length, for the candle this would be the diameter of the rising column of hot gas.
So there is nothing to predict in the case of a candle. It transitions because it was meta stable to begin with. Am I missing something or is this misleading/wrong? I remove this sentence and change the word "goes" to "transitions". Eheran ( talk) 07:08, 20 December 2023 (UTC)
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Jiří Březina was nominated for deletion. The discussion was closed on 11 December 2019 with a consensus to merge. Its contents were merged into Reynolds number. The original page is now a redirect to this page. For the contribution history and old versions of the redirected article, please see its history; for its talk page, see here. |
It is requested that a physics diagram or diagrams be
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In further reading, the link "Purcell, E. M. "Life at Low Reynolds Number", American Journal of Physics vol 45, pp. 3–11 (1977)" doesn't work. — Preceding unsigned comment added by 150.203.68.87 ( talk) 08:17, 26 September 2019 (UTC)
What on earth does that mean? Elevation? Altitude? I prefer to see the discussion focus on fundamental attributes of the fluid such as pressure, temperature, density or whatever. Saying that the Reynolds numbers are a function of elevation is just wrong. 98.202.242.88 ( talk) —Preceding undated comment added 00:43, 21 January 2010 (UTC).
I think this is a good concept for a section, but it's a mess. First, there's no units on any of the figures - I'd add them, but the whole section needs a work-over....
First, how can a blue whale have a Reynolds number? The Reynolds number is the property of fluid flow: not a baseball, mammal, or boat. Second, none of these figures have references, although I am not disputing their veracity.
This section needs a good table (with citations) that lists typical fluid flows that Wikipedia users could relate to (for understanding of the concept - like the flow in a garden hose, the flow in an HVAC duct, etc), maybe combined with fluid flows that are of more encyclopedic value (like the fluid flow in the brain).
-- Goingstuckey ( talk) 15:43, 18 June 2009 (UTC)
I edited some typical Reynolds numbers, which were already there in the main page. One of them mentioned the fastest fish. The following link [1] is where I extracted 10 ft for the length of a sailfish and 80 mph as a top speed.
In response to the question about how a baseball, etc., can have a Reynolds number, it is not true that the Reynolds numbers is a property only of the flow. It is a property of the combination of the flow and the object. The diameter of a softball is the D in Re. When we talk about the Re of a baseball, it is understood that we mean the Reynolds number associated with the flow around a baseball at a relative airspeed, V, that in embedded in the Re for that flow situation.
Kimaaron ( talk) 15:22, 15 November 2016 (UTC)
Strictly speaking, there is no such thing as an "inertial force." Any object (e.g., a fluid particle) possesses inertia, while it is acted upon by forces. I realize that the definition of a Reynolds number as "a ratio of inertial force to viscous force" is used frequently in both textbooks and peer reviewed literature, but I've always considered it to be sloppy.
Additionally, I would like to point out that neither the quantity μ/L nor the quantity vsρ have units of force, so to list them as forces may be very confusing to the general reader. This will not do for an encyclopedia.
In terms of the equations of motion (e.g., Navier-Stokes equations), if one uses a length scale , a time scale , and a velocity scale , the dimension of the inertial term (i.e., the term which represents the time rate of change of momentum per unit volume) is , while the dimension of the viscous term (i.e., the term represented by the divergence of the viscous stress tensor) is . A Reynolds number is properly the ratio of these terms, . Note that the dimension of the terms in the equations of motion have units of force per unit volume, so that, if multiplied by , they will yield forces. If you must define a Reynolds number as a ratio of forces, then, your "inertial force" should be and your viscous force should be .
-- 71.98.78.28 04:04, 11 June 2007 (UTC)
imo, you guys are way to picky; the use of ratio inertial/viscous force is widely used in many different communities. I think what you are missing is that an article like this has to function on 3 or 4 layers: for the general audience, without say HS algebra, the ratio of force idea is intuitive; for the HS/college algebra set, and then for people ready to deal with angular momentum imo, as a phd who has written several articles here, you are making a common mistake, writing only for thetopmost level. nothing wrong with that, but as wiki is a general encyclopedia, really need a general article you might, as a learning exercise, study the article at britannica.com; not saying it is right, but it is at the right *level* i'm not trying to be rude: i know that it is *really* hard to write down correctly — Preceding unsigned comment added by 50.195.10.169 ( talk) 19:06, 7 October 2013 (UTC)
There seems to be some inconsistency about whether laminar flow ends at 2100 or 2300 in this article, as well as about the upper bound of the unknown regime. The page states that it's 3000, but it should be 4000. From Process Fluid Mechanics by Morton M. Denn, 1980, p 34: "Laminar flow usually ends at Re = 2100; between Re = 2100 and about 4000, the flow seems to pulsate between laminar and turbulent portions. Fully developed turbulence begins at Re of about 4000." My fluid mechanics professor ( http://www.cheme.cornell.edu/cheme/people/profile/index.cfm?netid=laa25) also confirms this version of the flow regime divisions. -- Icefaerie 03:50, 26 February 2007 (UTC)
Definitely a rule of thumb. Laminar flow is definitely expected below a Reynolds number of 2000, but there is a transition zone between 2000 and 4000. In my professional judgment it is safe to treat flows as turbulent at Reynold's numbers greater than 3000 in most cases. One interesting thought to illuminate the uncertainty in where laminar flow ends is that in carefully controlled laboratory settings laminar flow has been achieved at Reynold's numbers as high as 100,000. There is a very interesting article on this in the February 2004 issue of Physics Today. —Preceding unsigned comment added by 68.238.133.228 ( talk) 03:41, 5 January 2009 (UTC)
Back in March 2017, Tvtvashisth edited the Laminar/Turbulent Transition section from 2000 and 4000 to 1000 and 2000. This would be correct if the characteristic dimension of a pipe was the radius, but it isn't, and the article clearly states that it should be diameter. I don't have access to any sources at the moment, but someone should revert that change as soon as possible. 128.187.116.19 ( talk) 17:09, 13 July 2017 (UTC)
In this field dimensionless numbers such as this are known with two letters, no subscript. The page was changed to add a subscript, and I reverted it. - EndingPop 19:02, 15 October 2006 (UTC)
It's a comment to an excellent page named "Reynolds number" ( http://en.wikipedia.org/wiki/Reynolds_number).
Under 'The similarity of flows' subsection, it's stated:
In order for two flows to be similar they must have the same geometry and equal Reynolds numbers. When comparing fluid behaviour at homologous points in a model and a full-scale flow, the following holds:
Re*=Re; p*/(rho* v^2*) = p/(rho v^2) [sorry, I couldn't copy the formula here. p=pressure; rho=density; v=velocity]
The latter equation does not represent the Reynolds number. It is the Euler number Eu=p/(rho v^2), which, along with Re, is one of the major fluid dynamics criteria.
-- 204.174.12.18 23:20, 24 October 2005 (UTC)
I agree. I quote
http://www.engineeringtoolbox.com/euler-number-d_579.html and
Euler number (physics). Also I question the relevence of a section on flow similarity in an article about the Reynolds' number which although yes is a requirement of similar flows is not the end of the story for flow analysis by a long way, a new article about
Similarity of flow or
Flow similarity (etc) should be made about using wind tunnels and aqua tanks in lab experiments to model real flows (eg aerofoil in wind tunnel saving on having to send up a real aircraft). For now I have clarified what is the Re and what is Eu, and made a link to
Euler number (physics).
Fegor
15:06, 17 March 2006 (UTC)
Currently Reynold's number redirects to Reynolds number, whilst Reynolds' number does not exist (note the apostrophes). As a matter of grammer and consistency I think the article should be hosted at Reynolds' number (I do not mean Reynold's number), for precedent look at Bernoulli's principle for when apostrophe should go before the s, and Bayes' theorem or Huygens' principle are examples of when it should go after. Fegor 12:46, 9 March 2006 (UTC)
I have heard that (due to the effects of small Reynolds numbers), that flying for flies and other small insects is much more like swimming than flying. Is this a correct analogy? If true, would it be useful to add as an example?
Rather than putting that it's equal to 2r for circular sections should it be better to put L= 4A/P (A= area, P = perimeter). Would do it myself but I feel I might mess up. Spanish wiki has it this way. -- English - Spanish 14:11, 27 November 2006 (UTC)
"engineers will avoid any pipe configuration that falls within the range of Reynolds numbers from about 2000 to 3000 to ensure that the flow is either laminar or turbulent." What kind of engineers do this and why? Does this apply to pipes in my house? Richard Giuly 12:28, 9 March 2007 (UTC)
I feel that they are often designed well outside of the transition zone because in this region drastic pressure and flow variations can occur making the system difficult to model and design. Most often a civil engineer will design pipelines in cities and homes. —Preceding unsigned comment added by 64.126.190.120 ( talk) 03:49, 5 January 2009 (UTC)
Common values for kinematic viscosity do not belong on this page. That section should be removed. 134.71.155.171 05:42, 30 May 2007 (UTC)
Agreed. I removed the "common values" section. There is already a link to the extensive entry about viscosity. Oanjao 16:10, 31 July 2007 (UTC)
why is mu used as the symbol for the dynamic viscosity? isn't eta the commonly used symbol for this property? —Preceding unsigned comment added by 130.89.137.46 ( talk) 10:51, 13 March 2009 (UTC)
I concur. eta is the symbol used for viscosity in my literature (Biological Physics by Philip Nelson, Physics for scientists and engineers 6th ed. Tipler and Mosca, Physical Biology of the Cell by Rob Phillips et. al as examples), in fact I cannot recall having seen mu used for viscosity before, so I must admit I am a little confused as to why it is used here. Shouldn't convention be followed? Who fixes this? Elvegaro ( talk) 10:23, 8 October 2011 (UTC)
I'm proposing some changes to the definition section, because I think it would be clearer:
Typically it is given as follows:
where is the mean fluid velocity, is the characteristic length, is the (absolute) dynamic fluid viscosity, is the kinematic fluid viscosity, defined as , and is the density of the fluid.
The main changes I made are removing the units, and replacing the HTML entities with TeX markup, so that they appear the same in the equation as in the explanation. I removed the units, because it doesn't seem like they belong there. Why, for example, should velocity care if it's in meters per second or feet per second? Does it change the equation any? If anything, we could list the dimensions, but that is also probably not necessary, or could be covered by linking to the page in question (i.e., velocity becomes velocity, then the reader can look at that page to discover the dimensions of velocity).
I'd also like to point out that quantities used in other formulas such as in lift coefficient don't list the units of each term.
Thoughts? User:!jim talk contribs 18:49, 22 October 2007 (UTC)
The Reynolds number is the ratio of advection of momentum (velocity "diffusion") to the diffusion of angular momentum (vorticity "diffusion"). Most dimensionless numbers in fluid mechanics are defined as the ratio of diffusion constants for different quantities (e.g., heat, mass) to either the "diffusion" constants of momentum (specific momentum = velocity) or angular momentum (specific angular momentum = vorticity). From a dimensional analysis standpoint, diffusion coefficients have units of l2 / t. The "diffusion coefficient" for momentum (i.e., velocity transport) is just ul. The diffusion coefficient for vorticity is just the kinematic viscosity (see the vorticity page). I would suggest that this definition be used since other non-dimensional numbers are defined in terms of a ratio of advection to diffusion of two properties (e.g., see Prandtl Number, ratio of advection to heat diffusion and Schmidt Number, ratio of momentum to mass diffusion). This is the academic standard for defining dimensionless numbers in fluid mechanics. Hope this helps. -- Allen314159 ( talk) 01:09, 12 July 2008 (UTC)
The definition focuses on Reynolds numbers for fluid flows, as does most of the discussion, which is sensible enough. But then the "typical values" section right away mentions Reynolds numbers for solid objects, such as spermatozoa (well, semi-solid) and ocean liners. It would be useful to have a discussion of how the definition (which speaks of fluids flowing) can be extended and applied to solids moving through a fluid; i don't see much in that way. 69.54.65.151 ( talk) 15:59, 25 July 2008 (UTC)
The "typical values" section is only utilizing the length scale of the solid objects and the velocities of fluid flow for the calculation of the Reynolds numbers. The Reynolds numbers calculated for these solid objects describe the fluid flow around them and at their length scales (and not the flow of these solid objects within or with the fluid - that would use of different numbers like the Schmidt Number. I still stand by my academic description above. -- Allen314159 ( talk) 00:08, 1 August 2008 (UTC)
Kimaaron ( talk) 08:07, 15 November 2016 (UTC)
The DEFINITION of Re is rho V L/mu, where L is a characteristic length scale of the flow field. It is typically a characteristic dimension of a solid object or boundary. It might also use a length scale over which the flow itself varies significantly, such as a boundary layer thickness or a shear layer thickness. Once defined in this manner, Re CHARACTERIZES the ratio of the relative contribution of inertial effects and viscous effects. Forces if you like. But the definition is NOT the ratio of inertial to viscous forces. In fact, the inertial forces and viscous forces vary a lot over a flow field, so they are not well defined to start with and they would be very difficult to quantify. Regardless, it is WRONG to state that Re is DEFINED as the ratio of these two quantities. It isn't. It is defined as rho V L/mu. The NASA website referenced in the place where the wrong definition is stated is NOT the authority on definition of Re. For the definition of Re, we need to go back 100 years or so. The only old book I have at hand right now is Abbott and Von Doenhoff (Theory of Wing Sections). It says Re = rho V L/mu I could use that as a reference, but I'd prefer something even older. I'll look around. Once I find it, I plan to edit the main page to make it clear what the definition is and then what this physical interpretation as a ratio of inertial to viscous effects is all about. That does give useful insight into the physical meaning of Re, it just doesn't define it. If someone has a good early reference for the definition of Re, please let me know. Kimaaron ( talk) 06:02, 2 October 2016 (UTC)
I found a paper by Arnold Sommerfeld from 1908 in which he named Reynolds Number for the first time and defined it as we know it today, rho V L/mu. This is the DEFINTION of Re. The business about being a ratio of inertial to viscous forces is an INTERPRETATION of the physical significance of Re. I have edited the main article to use the correct defintion and added a little about Sommerfeld naming Re. Kimaaron ( talk) 08:00, 15 November 2016 (UTC)
I found this comment in the text of the article, but without a response ( Jdpipe ( talk) 05:39, 10 September 2008 (UTC)):
To the best of my knowledge adimensional is not a word. I have never seen it used in any fluid texts. The correct formation is either the compound non-dimensional or the short-form nondimensional. Bradweir ( talk) 21:05, 29 June 2009 (UTC)
There are several errors in the article. People have pointed them out. Why don't they make the changes? Clearly the first line has "Forces" stated when both inertial and viscous "forces" have the wrong units. There are other issues also. Someone needs to fix these. I teach classes that deal somewhat with this area and my students were finding this article more confusion than helpful. —Preceding unsigned comment added by 67.169.201.107 ( talk) 17:07, 11 October 2009 (UTC)
The value "D" in the section regarding the Reynolds number of flow through a pipe is ambiguous. Does that D reference the diameter of the pipe or the length of the pipe. There is no further clarification in the rest of the article. —Preceding unsigned comment added by Adroa ( talk • contribs) 02:02, 14 October 2009 (UTC)
The effect of pipe length is very different from that of the diameter, and for pipes the diameter must be chosen for Re, not the length. Even (above a certain length) the pipe length doesn't matter at the same flow speed. I think that the article does mention that the diameter is chosen; however, it is not made clear why... Harald88 ( talk) 08:44, 26 January 2010 (UTC)
It would be useful if this is elaborated in the definition section: why for example for wings the length can be chosen (if that is indeed correct). Harald88 ( talk) 08:46, 26 January 2010 (UTC)
We need a diagram of, for example, the flow around a sphere at different reynolds, going from laminar to vortex street. I think it really helps cement the concept in intuitively.- Wolfkeeper 13:43, 15 February 2010 (UTC)
If for example the scale model has linear dimensions one quarter of full size, the flow velocity of the model would have to be multiplied by a factor of 4 to obtain similar flow behavior.
This is obviously wrong. A 1/10th scale model of a Piper Cub will not be tested with a wind speed approaching Mach 3. As models scale down, wind speed also scales down (but in a non-linear fashion, I think). It is true however that the Reynold's Number is used to figure out exactly what the speed is. —Preceding unsigned comment added by 131.142.52.246 ( talk) 15:30, 23 March 2010 (UTC)
The section about typical values of Reynolds number must state that those values depend on the geometry of the system/flow. For instance a flow in a pipe stays laminar longer than a flow around a cylinder. Typical values of Reynolds may hint at the fact that transition from laminar -> turbulent hides varied types of flows, in particular attached laminar steady flow -> separated laminar steady -> laminar separated periodic -> transitional periodic -> turbulent (chaotic) This should be explained in the page on flow separation which is quite poor, and could be enhanced by diagram in page 3 of this document: http://www.stanford.edu/class/me469b/handouts/turbulence.pdf — Preceding unsigned comment added by 194.167.134.222 ( talk) 13:16, 1 August 2012 (UTC)
The image in this article says the lower limit is "~49", but Kármán vortex street says it's 90. Which is correct? -- RoySmith (talk) 13:27, 12 August 2012 (UTC)
I want to say in some sort of constructive fashion (seriously) that this is one of the least helpful articles I have ever consulted in Wikipedia. Maybe the problem is with me, but the article did almost exactly nothing to help me find out "What is a Reynolds number?"
Instead of getting an answer to that question, I found out at the very beginning of the article that "Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces." This was encouraging, but it was followed by a sort of disclaimer: "The term inertial forces, which characterize how much a particular fluid resists any change in motion, are not to be confused with inertial forces defined in the classical way."
Because I could not comprehend what the second sentence was telling me not to confuse, the two effectively cancelled out, leaving me with honestly no idea what Reynolds number refers to. Dratman ( talk) 22:54, 24 February 2013 (UTC)
dratman, you are 100% right, this intro is typcial of many technical articles in wiki, the authors have no sense of how to write for a general audience. I think a good intro would be something like: The reynolds numbers describe the behaviour of a fluid (gas or liquid) in terms of how "smooth" the flow is. The fluid flow we are all familiar with - say water coming out of a nozzle - is high Re, and such flow is characterized as unpredictable; a small change in the nozzle causes a big change in teh stream. Fluid flow at low Re is not a common sight; we can say such flow is predictable. In general, low Re occurs at microscopic scales. WE can connect these ideas by thinking of the liquid folding... well, that isn't very good, but it is better then what is there !! — Preceding unsigned comment added by 50.195.10.169 ( talk) 18:48, 7 October 2013 (UTC)
The typesetting of formulæ in this article at present is haphazard, being neither internally consistent, nor consistent with standard recommendations." [1] [2] [3]. —DIV ( 137.111.13.4 ( talk) 07:03, 21 August 2015 (UTC))
Earlier comments have been made about an accessible lead.
I have moved the plunge into maths out of the lead, and given overview of what the RN is used for. Also created definition section with re-ordered and logical narrative. Hopefully this will help the reader to more easily engage. Dougsim ( talk) 15:08, 3 December 2016 (UTC)
The lead says that Gabriel Stokes originated the idea, and gives a larger picture of him than of Reynolds. Could someone please quote the expression in the Stokes paper which is cited which corresponds to the Reynolds number, because I could not find it. Chemical Engineer ( talk) 17:09, 31 December 2016 (UTC)
This article uses the phrase "flow situations" to describe flowing fluid. Would it be appropriate to simply use "fluid flow" instead of "flow situation", as the latter can sound too technical? Somerandomuser ( talk) 18:49, 16 May 2017 (UTC)
Someone has changed v to s in the definition of Re. They argued that V looked too much like nu, so they decided to use s for "speed" instead. This is completely non-standard and it needs to be reverted. We always use v. If they like, they can draw attention to the fact that v looks like nu and caution people to be careful. I tried to revert it, but I think I reverted something else by accident. I don't know enough about editing here to fix this problem with confidence. I'd appreciate it if someone who does know what they are doing could revert the edits please. Thanks, Kimaaron ( talk) 06:57, 28 January 2018 (UTC)
A large portion of explanatory text was removed [2] seemingly arbitrarily from the Derivation section towards the top of the article, as a part of an edit by Attic Salt.
The "derivation" proposed can't go unqualified, for reasons that were given in the removed text, namely:
Thus, simply stating that this is a derivation of -- meaning, rigorous reasoning that demonstrates beyond any doubt the necessity of -- the form of the Reynolds number, is downright nonsense, so please re-instate the comment, either re-formulated, or in its original form.
Apart from this, removing whole paragraphs of text without so much as a word of explanation is unacceptable, so please also give us the reasons for the removal.
In looking at the proposed merger, it does look like some of that article could be salvaged and put here as an example. Most certainly not all of it, but definitely some. However, it seems to me to be just a little too specific, and as written may likely not be of significant help in explaining the concept to the novice reader. The specific type of flow this is describing is granular flow. At the moment, this simply links to granular material, yet nothing about granular flow is described. They are actually two distinct subjects. In my opinion, it would be best to create a separate article about granular flow, and describe the works of people like Ralph Alger Bagnold and Jiří Březina and their contributions to the science (for example, see Bagnold number). Zaereth ( talk) 22:13, 11 December 2019 (UTC)
Section "Derivation 1" has multiple issues and should be removed.
Note that a rigorous and clear derivation is presented under "Derivation 2". — Preceding unsigned comment added by 92.247.118.230 ( talk) 10:42, 28 March 2020 (UTC)
Following international standards (ISO/IEC 80000-11 Quantities and units - Part 11), all so-called characteristic numbers are considered as quantities and shall be written in italic, thus Re. In this standard, it is item 11-4., Reynolds number JOb ( talk) 08:10, 28 April 2022 (UTC)
Hello, the image of the water tap is very misleading I think (please correct me if I am wrong). While it is probably true, that one is turbulent and the other is laminar, the white color of the stream has nothing to do with that. It is air that was mixed in by the mesh at the end of the water tap. I think the image leads one to think turbulent water must look white-ish, even though in reality turbulent flow (for example in a pipe with no air) can look perfectly transparent.
I would recommend removing or replacing that image. Thanks Wikipedia Community 185.65.196.182 ( talk) 07:48, 30 January 2023 (UTC)
I am going to comment here before completely rewriting this section. It is completely incorrect, unsourced, and doesn't even link to potentially helpful pages. I'm baffled how this got added.
One thing written under this heading says "The largest eddies will always be the same size; the smallest eddies are determined by the Reynolds number."— this is patently false and misleading.
In Fluid Mechanics for Chemical Engineers, (by Noel de Nevers, 3rd ed.) it states plainly, "The largest eddies in a confined flow cannot be larger than the dimensions of the confining container. Generally they will be 0.1 to 0.5 times as large as the boundaries of the system or the size of the disturbance causing the turbulence." So obviously, the largest eddies are not always the same size; they scale with the size of the system.
On the other hand, the size of the smallest eddies is related only to the kinematic viscosity and the dissipation rate, not the size of the system— so you could say the small eddies are "always the same size". This size scale is known as the Kolmogorov scale, which already has a Wikipedia page that describes that size quantitatively, so I would link to that.
I guess I'm just looking for permission. I literally made a Wikipedia account to correct this page because it was so terrible. And it's a valuable page... so yeah, I just want someone to tell me I won't be reviled across the internet for destroying someone's inaccurate two paragraphs on this topic. HelpfulWitch ( talk) 20:03, 1 March 2023 (UTC)
Since my edit was reverted with the statement that 'velocity doesn't cause turbulence', even though I provided a citation, I'd like to have some discussion or a counter-citation. googling for 'where is the turbulent section of a pipe' suggests that most people believe the turbulent section is in the center. Also I believe that higher friction (I.e. viscosity) decreases the likelihood of turbulence, doesn't increase it. Yes, the energy to create eddies comes from the interaction of the fluid with the pipe wall but those eddies immediately travel to the center of the pipe because that's where the circular or random motion is easier. Mlwater ( talk) 01:55, 27 April 2023 (UTC)
The "where this will take place" seems very odd to me here. Candles are essentially always burning the same way, only the scale is slightly different. The plume of a candle will generally transition to turbulent, there is nothing to predict here in the sense of "yes/no". So if the "where" is talking about different systems, using this specific example can be very misleading.
We can also understand this as calculating the actual location of the laminar–turbulent transition with Reynolds formula, which would not be correct. Let us look at the diagram from Reynolds's 1883 paper further down in the article. Because unlike with the candle, the Reynolds number does not change once the necked down section is reached. However, the laminar flow is still meta stable for a while before it transitions to turbulent flow. I would argue the same is happening with the candle. While the Reynolds number is not constant due to cooling and mixing with air, it was still only meta stable from the beginning. The transition can also happen all the way down at the flame, making them flicker. There are some articles that talk about this, for example this one. The Reynolds number can not be used to calculate where this transition happens in a meta stable system. The only lenght in the formula is for the characteristic length, for the candle this would be the diameter of the rising column of hot gas.
So there is nothing to predict in the case of a candle. It transitions because it was meta stable to begin with. Am I missing something or is this misleading/wrong? I remove this sentence and change the word "goes" to "transitions". Eheran ( talk) 07:08, 20 December 2023 (UTC)