Talk:Reynolds number

broken link
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)

Reynolds Numbers Vary as a function of elevation?
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).

Typical Reynolds Numbers?
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 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)

Inertial force?
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 &mu;/L nor the quantity vs&rho; 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 $$l$$, a time scale $$t$$, and a velocity scale $$v \equiv l / t$$, the dimension of the inertial term (i.e., the term which represents the time rate of change of momentum per unit volume) is $$\rho v / t = \rho v^2/l$$, while the dimension of the viscous term (i.e., the term represented by the divergence of the viscous stress tensor) is $$\mu v/l^2$$. A Reynolds number is properly the ratio of these terms, $$Re \equiv \frac{\rho v^2/l}{\mu v/l^2} = \frac{\rho v l}{\mu}$$. Note that the dimension of the terms in the equations of motion have units of force per unit volume, so that, if multiplied by $$l^3$$, they will yield forces. If you must define a Reynolds number as a ratio of forces, then, your "inertial force" should be $$\rho l^3 v^2$$ and your viscous force should be $$\mu l v$$.

--71.98.78.28 04:04, 11 June 2007 (UTC)


 * How about "inertial effects to viscous effects"? - EndingPop 12:36, 12 June 2007 (UTC)


 * I'm really not sure what the best way to define the Reynolds number is, for an encyclopedia entry. The definition should be comprehensible to the general reader, so defining it in terms of a proper scaling of the equations of motion is probably not a good idea.  I'll check some of my old textbooks.  I seem to recall that there was a nice description in Bird, Stewart, and Lightfoot's Transport Phenomena.  This has been the standard undergraduate textbook for chemical engineers studying transport phenomena for the last 50 years, and hence might not be a bad reference for the article.  By the way, the "inertial force" in the note above should be $$\rho l^2 v^2$$.--71.98.78.28 00:07, 13 June 2007 (UTC)


 * Another way to define the Reynolds number is in terms of energies, btw. The kinetic energy per unit volume characteristic of a flow is $$\rho v^2$$, and the characteristic scale for viscous dissipation per unit volume is $$\mu v / l$$.  Hence, the Reynolds number is $$Re \equiv \frac{\rho v^2}{\mu v / l} = \frac{\rho v l}{\mu}$$.--71.98.78.28 00:18, 13 June 2007 (UTC)


 * However, the first paragraph says, "a measure of the ratio of inertial forces $$\rho v^2$$ to viscous forces $$\mu v / l$$", so it is explicitly referring to forces, not energies. Consequently, it SHOULD say the inertial forces are $$\rho v^2 / l$$, and the viscous forces $$ \mu v / l^2$$ 27 January 2010 (UTC) —Preceding unsigned comment added by 18.124.4.39 (talk)


 * The Reynolds number is the ratio of advection of momentum (velocity transport) to the diffusion of angular momentum (vorticity transport). From a dimensional analysis standpoint, diffusion coefficients have units of $$ l^2/t $$. 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). Hope this helps. --Allen314159 18:58, 21 August 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)

Reynolds number boundaries of flow regimes
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)


 * If you go ask your fluid mechanics professor, he/she will likely tell you that this is a rule of thumb. It is not a hard and fast rule.  That is likely the source of the different numbers.  Perhaps the article should express this? - EndingPop 15:21, 26 February 2007 (UTC)


 * Definately 0-2100 for laminar region and above 4000 is turbulent region. Between 2100-4000there transition region by Mcabe & Smith - —Preceding unsigned comment added by 144.177.50.6 (talk • contribs)

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)


 * Both of those options are a little off (although yours is closer). I assume you're talking about the paragraph describing the transition in the flow within a pipe. This is a rather special consideration, because the behavior of the fluid in a pipe is somewhat different than a fluid flowing around an object. The main factors affecting these are pre-flow perturbations, wall roughness, diameter and length, to name a couple. Reynolds himself predicted this transition would always occur at Re 2300. However, experimental data didn't quite line up with the mathematical predictions.


 * In short, flow through a pipe that is under Re 2300 will generally be continuously laminar. At Re 2300, the transition from laminar to turbulent begins to take place. At this point a very long length (many thousands of times the diameter) is needed to produce a turbulent flow downstream from the inlet. What actually begins to happen is something called "intermittent flow". (Keep in mind this is strictly for pipes.) At numbers above Re 2300, the flow begins to transition from laminar to turbulent and then back again, at very irregular intervals. This is due to the flow in the center of the pipe being mostly laminar and flowing faster, while the flow near the wall is slower and mostly turbulent. The overall flow in the pipe alternates from one state to the other.


 * As the Reynolds number increases, the distance from the inlet to the continuous turbulent-flow decreases and the "intermittency" increases. Above Re 2600, the flow within the entire pipe will have transitioned to fully turbulent. This can all be found in the book Boundary-Layer Theory, by Herrmann Schlichting and Klaus Gersten (the "bible of fluid dynamics" which is often quoted or misquoted in other sources) pages 416--419. Zaereth (talk) 23:32, 13 July 2017 (UTC)

$$Re$$ vs. $$R_e$$
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)

Euler number used in Similarity of flows section
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)


 * There are a whole host of dimensionless numbers that are used in similitude analyses. If you add heat transfer to the list, it'll more than double in size (at least in number that are used often).  The important thing is that Re is used almost always, along with whatever other dimensionless number is required.  Perhaps it would be better to explain this using just Re and then have a list of commonly used dimensionless numbers with their equations.  Eu, Fr, Ma, We, then with heat transfer you also have Pr, Nu, Ra, etc.  Anyway, my point is that there are many that are useful in their own areas, but Re is the only one that is used in almost every situation. - EndingPop 17:18, 17 March 2006 (UTC)

Reynold's / Reynolds number
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)


 * This is a valid point, The theory was named after Osborne Reynolds and so is his theory. In english the apostrophe indicating possession comes after the name and so in this case the correct name of the number should be Reynolds' number --Cleverbum 15:49, 5 June 2006 (UTC)


 * I think it should be "Reynolds number" with no implication of posession. Most named dimensionless numbers are not posessives, e.g. "the Mach number", not "Mach's number". The same goes for Nusselt number, Weber number, Prandtl number, etc.


 * well it's done now. I added them to the actual artical now. change it back if you feel strongly Fegor 22:45, 25 September 2006 (UTC)


 * I googled on it. Theres 161,000 "Reynold's number" and over 20,000,000 "Reynolds number". AFAIK Reynolds is a not an uncommon English name, and the evidence is that it was the guy's name, not Reynold. Also one of the first hits is efunda and wolfram, who are likely to correct, and they both used no apostrophe. So I'm inclined to change it back unless there's a violent objection, and rename the article.WolfKeeper 23:10, 25 September 2006 (UTC)


 * you seem to be missing the point. we are not debating about his name (which, yes, is Reynolds), but whether his number Reynolds' number should be have an apostrophe after the s or not have one at all. eFunda is a reputable website but I doubt they are hardly an authority on grammar. Fegor 00:10, 26 September 2006 (UTC)


 * With all due respect, you are the one missing the point. What major verifiable source do you have that this is correctly or usually spelled with an apostrophe? Incidentally, I also checked Encyclopedia Britannica, no apostrophe.WolfKeeper 00:29, 26 September 2006 (UTC)


 * So yes, I violently object, and yes I've moved it all back. When 100x more hits do it one way, and all the major sources do it the same way, IMHO it's a bit of a clue.WolfKeeper 00:45, 26 September 2006 (UTC)

Effects of Small Reynolds Number
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?


 * I've not heard about that, so I can't confirm or deny it. The example I heard about in class is bull semen. -EndingPop 11:41, 8 August 2006 (UTC)


 * I've heard this enough times that it may be worth addressing here on talk. Reynolds number is "the ratio of inertial (resistant to change of motion) forces to viscous (heavy and gluey) forces." A large airplane has a large amount of inertia behind it, so the gluey, viscous forces of the air do not have much effect. A model airplane, of the exact same type, shape and configuration, will have drastically different flight characteristics because of it's lower Reynolds number. To the model with lower inertia, the viscosity of the air plays a much bigger role.


 * To an insect, the very low Reynolds number means that the insect doesn't have the inertial forces to easily overcome the viscous forces. It has no glide potential, and must constantly provide thrust to keep moving against the viscosity. This also means that the flow across the insect is mostly laminar flow, and the large boundary layer produced gives a very large effective area, as opposed to the actual area of the wing. In this way, a comparison to "swimming" through a heavier fluid seems OK, but inadequate. It's a little more like the resistance you'd feel if you tried to run or flap your arms under water.


 * That is where the comparison ends. The compressibility and density of the air are not affected by inertia. (Well, at least not when talking about subsonic flow.) The insect is no more buoyant, and so must maintain lift as well as thrust. In this way, the insect is definitely not swimming, but flying. Zaereth (talk) 19:47, 18 May 2011 (UTC)

L
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)
 * Maybe it makes more sense to have a separate section on common characteristic lengths. This could include a discussion on the hydraulic diameter. - EndingPop 18:58, 27 November 2006 (UTC)

Engineers
"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)
 * The only reason I can see for doing this is to allow accurate modelling of flow patterns. It is very difficult (if not impossible) to model the transition phase. Of course, you can define the bounds easily enough - one would be a fully turbulent model, the other fully laminar. So long as it doesn't matter where in that region the flow is, there is no reason to avoid the turbulent region - this will generally be true for home piping, however in situations where the magnitude of the pressure drop or the degree of mixing are important the transition phase may be undesirable. It's not always possible to avoid though - certain process engineering applications have a nasty habit of having Re ~2000-4000. Adacore (talk) 16:23, 30 July 2008 (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)

Viscosity
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 suggest you look at the Wikipedia article on viscosity. Chemical Engineer (talk) 11:20, 8 October 2011 (UTC)

Definition
I'm proposing some changes to the definition section, because I think it would be clearer:

Typically it is given as follows:


 * $$ \mathit{Re} = {\rho v_{s}^2/L \over \mu v_{s}/L^2} = {\rho v_{s} L\over \mu} = {v_{s} L\over \nu} = \frac{\mbox{Inertial forces}}{\mbox{Viscous forces}}$$

where $$v_S$$ is the mean fluid velocity, $$L$$ is the characteristic length, $$\mu$$ is the (absolute) dynamic fluid viscosity, $$\nu$$ is the kinematic fluid viscosity, defined as $$\nu = \mu/\rho$$, and $$\rho$$ 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:!jimtalk contribs 18:49, 22 October 2007 (UTC)


 * The definition is WRONG. It is a common misapprehension (and common on the Internet) that Re = ratio of inertial to viscous forces, though it may be said to be proportional to this ratio (or to effects, rather than forces). This can be seen by the fact that the critical value of Re is different for a pipe, sphere in fluid and stirred tank.  The choice of "characteristic dimension" is to some extent arbitrary.  For a pipe the radius or diameter would do, giving a possible factor of 2.  In a typical stirred tank, using the diameter of the impeller or the vessel gives a factor of 3. For a rotating object such as the impeller in a stirred tank, or a cylinder viscometer, the rotational speed could logically be in radians per second or revolutions per second, giving a factor of 2 pi.  (In some conventions the speed in rpm was used with customary values of density and viscosity.)  For various geometric arrangements of fluid moving relative to a body, the Reynolds number is defined as an agreed combination of fluid properties, a characteristic dimension and a velocity.  In papers on agitation or using non-Newtonian fluids, the authors are generally careful to say "The Reynolds Number, defined as.....".  It is NOT defined as a force ratio.Chemical Engineer (talk) 16:34, 17 March 2008 (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)


 * This is all very great if you happen to be a mathamatician, but can we get a definition here that is better translated into common language. My understanding of Reynold's Number is that it is a dimensionless number, whose parmeters are defined by the ratio of dynamic pressure to shearing stress. (eg: At what scale does viscosity overcome shear, or visa-versa.) Is this correct? Zaereth (talk) 17:20, 2 October 2008 (UTC)


 * The math I find to define Re is:


 * Re = (ρ u2) / (μ u / L)
 * = ρ u L / μ
 * = u L / ν   (1)


 * where


 * Re = Reynolds Number (non-dimensional)
 * ρ = density (kg/m3, lbm/ft3 )
 * u = velocity (m/s, ft/s)
 * μ = dynamic viscosity (Ns/m2, lbm/s ft)
 * L = characteristic length (m, ft)
 * ν = kinematic viscosity (m2/s, ft2/s)


 * But since I am no mathamatician, I still think a good English definition is neededZaereth (talk) 18:09, 2 October 2008 (UTC)


 * I think this is a good idea - it should not be defined in terms of flow in a pipe, a very specific (if the original) application. Mirams (talk) 15:46, 4 June 2009 (UTC)


 * Thanks for the response. Reynold's number is a rather important topic when explaining aerodynamic fluid flows, such as the boundary layer of air that surrounds an aircraft wing, which actually alters the shape of the wing, making lift possible. (ie: Too much angle of attack will shear the boundary layer away, and the plane will areodynamically stall.) This effect at a much smaller scale helps explain why a bumble bee can fly, but at a scale any larger it would not be able to, or how an ant can become stuck like glue in a single drop of water.


 * I think the first thing that could use a little "dumbing down for the rest of us" would be the opening paragraph, which is confusing to me. To quote, "In fluid mechanics and heat transfer, the Reynolds number Re is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces (μ / L) and, consequently, it quantifies the relative importance of these two types of forces for given flow conditions." Any ideas on how to translate this into something that is a little more understandable to the masses? Zaereth (talk) 18:42, 4 June 2009 (UTC)


 * I also have to agree with the comment on the top of this page, that the use of a fictitious force, "inertial force", is probably not the best definition, although may be valid under certain circumstances ... I don't know. Zaereth (talk) 19:37, 4 June 2009 (UTC)


 * Just to be clear, the use of "inertial force" does not mean the same thing as coriolis or centrifugal forces, that are "ficticious" (I hate that description, "virtual" would be better) due to rotation of a frame of reference. When used with Reynolds numbers, it means the force (or stresses, really) that come about because the fluid is accelerating as it moves around the object.  Literally, it refers to the forces to accelerate the inertia of the fluid.  The stresses due to these inertial motions can be divided by the viscous shear stresses due to shearing of the flow to construct a Reynolds number.

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)

Dynamic similitude
I found this comment in the text of the article, but without a response (Jdpipe (talk) 05:39, 10 September 2008 (UTC)):


 * expert needed. From above: "When two geometrically similar flow patterns...have the same values [=THE CAUSE]...they...have similar flow geometry. [=THE EFFECT]" -- Isn't this saying geometrically-similar things may have similar geometry? (like furry bears may have fur) Is "similar flow" part of the cause, or the effect? 10/27/07


 * Assuming this refers to similitude, I think the intent of the statement (perhaps it needs rewording) is to say that flows with similar geometry (but different in other ways) have similar flow characteristics if you match Re. Is that the section you're referring to, because I can't find the part you quoted. - EndingPop (talk) 12:52, 10 September 2008 (UTC)

Adimensional vs. Non-dimensional vs. Dimensionless
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)
 * I believe adimensional is the Spanish word for non-dimensional. see Spanish Wikipedia. It is not in the Oxford English Dictionary.Chemical Engineer (talk) 21:53, 29 June 2009 (UTC)


 * Wouldn't it be better to just use the correct term: "Dimensionless"? And what is with that funky character for density? That's not a rho, can we switch it back please?24.120.32.180 (talk) 04:33, 8 August 2009 (UTC)


 * I agree. I think I use "dimensionless" and "non-dimensional" interchangeably, but "dimensionless" seems more cleaner. I also agree on rho ($$\rho$$) versus varrho ($$\varrho$$). I've never seen $$\varrho$$ used for density; it's always $$\rho$$. —Ben FrantzDale (talk) 18:09, 8 August 2009 (UTC)

Why Doesn't Anyone Do the Corrections?
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)
 * If you teach classes you should be in a position to help. Wikipedia is a collaborative effort.  Why not register and see how you can help to improve it.  However, please note that the articles should not come from personal knowledge (however good) but from cited sources.  The "ratio of forces" description is a perennial argument with several sides.  However, note that an encyclopedia is not really the place for a rigorous intellectual dissection of theoretical concepts but a short and (intended to be) helpful brief explanation of facts.  Many of us have day jobs and thus not enough time to do all we would like. Your input would be most welcome, please bring your textbooks! Chemical Engineer (talk) 17:48, 11 October 2009 (UTC)
 * And I do some work in fluid dynamics and we use the terms "force" quite loosely (e.g., in the Navier-Stokes equations we use "force" even after converting everything to accelerations). And since it is a nondimensional number, the top and bottom have different units depending on how the variables are arranged. I second Chemical Engineer - it is ironic to ask why people don't make changes that they point out and then point out an error without changing it - if it is that much of a problem to your students, by all means, contribute on the article page! Awickert (talk) 18:00, 11 October 2009 (UTC)

D
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)

Article needs diagram showing effects of varying reynolds
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)

Example of the importance of the Reynolds number
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)

remarks - geometry of the system; attached vs separated flows
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)
 * You probably understand the subject better than I, (I only know Reynolds as far as it applies to aircraft), you are most welcome to make the changes that would improve this article. Just remember to cite a source for your information, so others can verify it, and try to put it in your own words, to avoid plagiarism. Diagrams are always helpful, but you may have to get permission from the owner, or just make your own to avoid copyright problems. Thanks for your comments, and any assistance you can provide. Zaereth (talk) 16:22, 1 August 2012 (UTC)
 * On a side note, (which is somewhat related to your comment), one thing I do find interesting is that Reynolds number is often described as "the relationship between pressure and shear forces, yet the word "shear" is never used in this article. Here is one source describing it in those terms. Zaereth (talk) 22:24, 1 August 2012 (UTC)

Lower limit for vortex street?
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)


 * Most sources I've seen agree with Re 49 to be the lower limit. However, I think the book Hydrodynamics Around Cylindrical Structures provides one of the best explanations. Between Re 0 and 5, the flow will be laminar. Between Re 5 and 40, there are a fixed pair of vortices, with laminar flow around them. Between Re 40 and 200, the laminar flow forms a vortex street. Between Re 200 and 300, the wake becomes turbulent. Between re 300 and 30,000 (subcritical range), the boundary layer begins to separate, and the wake is completely turbulent. Between 30,000 and 35,000 (critical range), the boundary layer becomes turbulent as it separates, but the boundary layer itself is laminar. Between Re 35,000 and 150,000 (supercritical range), the boundary layer becomes partially laminar and partially turbulnet. Between Re 150,000 and 400,000, the boundary layer is completely turbulent on only one side, but, at Re higher than 400,000 (transcritical), and the boundary layerlayer will be completely turbulent on both sides. Zaereth (talk) 21:17, 13 August 2012 (UTC)

Unilluminating (to me) article
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)

u r wrong
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)


 * I agree that this article could use a lede and introduction with a simplified approach. In general, I would start by saying that "Reynolds number ia a ratio that defines the turbulence of a fluid in motion. This turbulence is often referred to as "eddy currents" and is caused by fluctuations in the flow. These eddy currents occur at many different size scales, which are determined by the Reynolds number. At low Reynolds number, the eddies are very small and the flow is mostly laminar, causing the fluid to shear cleanly past non-moving fluids or surfaces. At high Reynolds number, the eddies become larger and the flow becomes more tubulent than laminar, rolling and spinning past other fluids or surfaces..." or something like that. Zaereth (talk) 02:10, 10 October 2013 (UTC)
 * I wouldn't say that the ratio defines the turbulence, but that it describes the turbulence or that it is a measure of the turbulence. --Izno (talk) 03:07, 10 October 2013 (UTC)
 * Yeah, "describes." That sounds pretty good. Zaereth (talk) 16:26, 10 October 2013 (UTC)


 * Unfortunately, it's not as simple as that, the general shape and surface of the object that the flow is going past is also very important; you can get both smooth flow or turbulent behaviour over a wide range of reynolds numbers, just by changing tiny details of the object. Also, mainly at high Reynolds number, some of the eddies are very, very small. Fluid flow is, in general, chaotic. So there's a big danger here of oversimplifying things.GliderMaven (talk) 20:49, 10 October 2013 (UTC)


 * I understand what you're saying, but you can't put that all in the first sentence. A good many readers are only going to read that first sentence, so it should give the most basic of definitions that can generally encompass the entire article. These people probably ran across the term in some other article, and just want to get the gist-of-it in the fewest amount of words possible. Then it should expand on that definition within just a few paragraphs, touching on many of the finer point as you've just mentioned. (I was only trrying to offer a starting point, that people could build on.) Zaereth (talk) 21:32, 10 October 2013 (UTC)
 * (On a side note: Personally, for me, its often easiest to visualize some of these concepts by using analogies between hydraulics and electronics. In the case of Reynolds number, an analogy can be made between Re and the combination of inductance and resistance in electrical flow, which leads to the concept of magnetic Reynolds number.) Zaereth (talk) 22:06, 10 October 2013 (UTC)
 * On problem I see with the approach this article takes is that it deals too much with Reynolds number in relation to solid surfaces. While important, it tends to ignore Re with respect to fluid-on-fluid flows. I doesn't describe in great detail the relation between Re and boundary layer, nor does it describe how Re is used in the study of cloud formations and meteorology, plate tectonics, plasma physics, ocean currents, or astrophysics, etc... Zaereth (talk) 14:40, 11 October 2013 (UTC) he sagla khota ahe

Mathematical formulæ
The typesetting of formulæ in this article at present is haphazard, being neither internally consistent, nor consistent with standard recommendations."  . —DIV (137.111.13.4 (talk) 07:03, 21 August 2015 (UTC))
 * This is the domain of WP:MOSMATH, not of anything external. If you see specific problems which, after referencing MOSMATH, you think you can fix, then you should do so. If, after referencing MOSMATH, you identify no issues with this article regards MOSMATH, you should seek change at WT:MOSMATH, not here. --Izno (talk) 16:04, 21 August 2015 (UTC)

Lead clean-up
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)

Stokes
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)

Use of "flow situation"
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)


 * My gut reaction is to agree with the use of simpler terminology. However, when reading the article, I find that there are three instances where "flow situation" is used. Within the context where this term is used, the term "fluid flow" is too broad. The fluid doesn't just flow, but also interacts with its surrounding, such as a chimney, a pipe, an airplane wing, or rocks in a river. In these cases, it is not just the mere flowing of fluid that has to be considered, but the entire situation involved with the flow. Therefore, my answer in this case is to use the term "flow situation", which is the more precise one. Zaereth (talk) 19:19, 17 May 2017 (UTC)

Please revert edits that changed v to s
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)
 * I have restored the previous definition, which was with u, which is consistent with the article on viscosity s is commonly used for distance in physics. However, the article is not consistent overall, using different fonts of u and v.  The 1908 symbology is of historical interest only.  I think for the benefit of users, these articles should made consistent throughout.Chemical Engineer (talk) 17:04, 28 January 2018 (UTC)

Derivation
A large portion of explanatory text was removed seemingly arbitrarily from the Derivation section towards the top of the article, as a part of an edit by.

The "derivation" proposed can't go unqualified, for reasons that were given in the removed text, namely:
 * cross-sectional position ($y$,) which is used as an actual variable, is only a vague notion
 * there's no rigorous physical meaning to the mass, volume, etc. that have been re-expressed using $L$, due to the arbitrary choice of that length
 * $$u_0$$ (a lengthwise velocity) is substituted as a proxy for $${\textstyle \frac {dy} {dt}}$$ (a transverse velocity)
 * there is no transverse velocity in the setup in the first place
 * there's no rigorous mathematical sense to the transformations on the differential quantities

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.


 * While I don't necessarily agree with all of Attic Salt's edits or reasoning (I think it's better to gear the text to be more comprehensible to the layman, and one can certainly change a fluids viscosity, by temperature for example), I fully agree with this removal. I am not well versed in the math but rather have a Tesla-like ability to visualize it in my head, but I am well versed in writing and this is just a bunch of commentary, full of iffy phrases such as "could also be considered", "is not so much a", "some insight into the possible meaning", "which doesn't make much sense", "doesn't need to make sense", etc... Not to mention the writing is poor and much too informal to be encyclopedic.


 * The comment on the "derivation" _was_ hand-wavy (as you pointed out correctly,) but this was mostly due to the sloppiness of the "derivation" itself, and the comment was as specific as allowed by the subject matter (as you obviously fail to comprehend.) I'll dare any Fluid Dynamics expert to go deeper than that (and was actually hoping for it; writing style gurus need not apply.)


 * That said, according to your argument, this kind of hand-waving arising out of cautiousness seems to be objectionable, while the kind that serves pseudo-intellectual bullying (see below) seems to be OK. I wonder why.


 * Reynolds number makes perfect sense. The viscous forces try to hold the fluid together while the inertial forces try to tear it apart. When the viscous forces overcome the inertial forces, the flow is laminar, but when the inertial forces overpower them, turbulence results. Reynolds number is used to predict where this will happen (how far from the inlet or output). It's no more mysterious than other dimensionless numbers and ratios such as efficiency or pi. Zaereth (talk) 23:10, 1 April 2019 (UTC)


 * "Reynolds number makes perfect sense. The viscous forces try to hold the fluid together while the inertial forces try to tear it apart."


 * This statement is so self-evidently ridiculous that it shouldn't really need any comment, but it creates the illusion of a valid argument, so:


 * 1) Since this is purportedly a de-mystification of Re, you need to define "viscous forces" and "inertial forces". The exercise is far from trivial, and I've seen no _definitions_ -- neither in this article, nor in any text on Fluid Dynamics that I've come across.  Hand-waving doesn't count for a definition, of course.


 * 2) It's far from obvious how the the ones "try to hold the fluid together" or how the others "try to tear it apart". Please enlighten us, preferably in the body text of the article.


 * 3) Re is very different from pi. There's a very precise meaning of what pi actually means, and it is very clear what lengths it relates and how it relates them.  On the other hand, Re relates, among other things, _a characteristic velocity_ and _a characteristic length_ -- as in, any such quantity of your choosing that you find characteristic of the flow.  Particularly, for pipe flows, Re uses the pipe diameter (a transverse measure), whereas for airfoils, for example, it usually uses a lengthwise measure (e.g. chord length of an arbitrary section -- but you could also choose to use wing span.)  In other words, Re is pretty arbitrary, and doesn't make _any_ physical sense (mystery and imagination set aside.)


 * 4) No matter how deeply you feel you grok Re, the fact remains that what is presented as derivation is just some loosely coupled formulas that relate only superficially to one another. It's good enough for e.g. dimensional analysis, but it's _not a derivation_ of a meaningful quantity.  No one so far has proposed a sensible way to connect the dots in the specific places where this "derivation" breaks down, namely:


 * a) The first proportionality sign -- how are the very specific volume and area related to an arbitrarily chosen length?


 * b) First simplification -- even provided that combining (du/dt) / (du/dy) into dy/dt makes mathematical and physical sense (though it makes neither), then what does (dy/dt) mean?


 * c) Substitution of u_0 -- how is an arbitrarily chosen lengthwise velocity (u_0) related to an undefined (and seemingly non-physical) transverse velocity (dy/dt)?


 * Before you solve these issues (or before someone else does,) this is _not_ a derivation, and it remains accessible only to those with "Tesla-like" abilities (i.e., pretty mysterious.)


 * No offense, but I think your logic might be a bit flawed. You seem to be trying to end with what you begin. Characteristic length is not an arbitrary measurement. It's volume divided by area. That's a common measurement is physics to define a scale of a system, where the total length of a flow may be indefinite. Characteristic velocity is a term you only hear about in rocket-propulsion science. This is exhaust velocity divided by thrust coefficient.


 * Viscosity is the fluid friction, or resistance to flow. In particular, it is resistance to shear, and is related to the cohesive forces in th fluid. Inertia/momentum is resistance to a change in motion, which is a property of mass. (In a pipe there is more inertia near the wall and more momentum at the center; eg: the same force opposing itself). The inertia works to shear the fluid while the viscosity tries to prevent shear from happening.


 * Reynolds number is the ratio of these two forces acting against each other for any particular flow situation. It is not a measure of quantity or intensity, but a proportionality between two dynamic forces fighting each other. And as with any dynamic situation, the entire situation must be considered in order to define the forces involved. That includes the very real fluid-velocity and characteristic length for any given system. For the best book on the matter, I'd suggest Boundary Layer Theory, which is basically the "bible" of fluid mechanics.


 * If you have any sources that can explain this mystery of yours any better, you are welcome to replace it with something that reads like an encyclopedic entry. Perhaps there is something I'm not seeing, like the mystery of the double-slit experiment or thin-film interference (which can be explained by quantum mechanics but will never makes sense when explained in classical terms, and since we can only explain things in classical terms (according to Richard Feynman) it will never make sense). But as it was it just read like confused, unsourced commentary that didn't really tell us anything of value. Zaereth (talk) 19:05, 10 May 2019 (UTC)


 * Amigo, I have put forth some very specific objections here (see (a) - (c) above,) presented as clearly as the light of day. You, from your end, keep piling vagueness and obtuseness on top of the argument, haven't offered one single statement that comes in touch with objective reality in any quantifiable way, and seem to be deeply confused about quantification and reasoning in general.  Also, by now it's utterly clear that, as far as FM is concerned, you're just throwing the bull.  Therefore, I strongly suggest, for the benefit of everyone involved, that you leave quantitative matters alone, and stick with your writing style expertise.

Proposed merger
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)
 * I'd oppose any merger of biog content to Reynolds number. This article doesn't need that here. A para at most. But if the work is really notable, we should keep that article as was. It's a terrible close to merge unrelated content into a vital article without even raising it for discussion first at this target article. Andy Dingley (talk) 23:06, 11 December 2019 (UTC)

Derivation 1
Section "Derivation 1" has multiple issues and should be removed.


 * 1) Some transitions along the presented sequence are superficial and not warranted by any rigorous mathematical or physical reasoning.
 * 2) The sequence of formulas does not match the one at the source, neither does it follow from it in an obvious way.
 * 3) At the source, the claims about "inertial forces" and "viscous forces" that lead to the first step seem to be missing essential and non-obvious intermediate reasoning that cannot be recovered easily (if at all) from the given references.  The material at the source page may be considered some sort of insight into the subject, but it does a very poor job as a derivation.

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)
 * I removed it. This is like what an undergraduate student does when they have absolutely not studied the material, thinking they could just rely on the formulas sheet.--Jasper Deng (talk) 20:01, 28 March 2020 (UTC)

Re vs. Re
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)


 * That's odd, because Reynolds number is not a quantity nor a unit. It's a unitless number, being a product of counteracting forces. It's like efficiency, which is another unitless number. But either way, that is not how WP:Manual of style says to do it, so you'd have to take this up over there. In the field of writing, italics often serve one of a few very specific purposes, and that's almost never units or unitless numbers alike. The exception would be a foreign measurement, such as kanme, which is a Japanese unit of weight. Zaereth (talk) 08:56, 28 April 2022 (UTC)
 * I am not sure, Surely, the Reynolds number is not a unit but it fulfills (like all other characteristic numbers) the definition of quantity from Electropedia:
 * ([Https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=112-01-01 https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=112-01-01] IEV 112-01-01: quantity - property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed by means of a number and a reference
 * In Electropedia, Reynolds number is defined as an item 113-03-36 and written in italic, too: [Https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=113-03-36 https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=113-03-36]
 * Also, an ISO standard, ISO 8000-11:2019(E) says in Introduction a.o.: Characteristic numbers are physical quantities of dimension number 1, although commonly and falsely called "dimensionless" quantities. They are used in the studies of natural and technical processes, and [can] present information about the behaviour of the process, or reveal similarities between different processes.
 * Electropedia mentioned above is an official document of IEC, being an online form of IEC 60050, as said there:
 * 'Electropedia is produced by the IEC, the world’s leading organization that prepares and publishes International Standards for all electrical, electronic and related technologies – collectively known as “electrotechnology”. Electropedia (also known as the "IEV Online") contains all the terms and definitions in the International Electrotechnical Vocabulary or IEV which is published also as a set of publications in the IEC 60050 series that can be ordered separately from the IEC webstore.' JOb (talk) 13:25, 28 April 2022 (UTC) JOb (talk) 13:27, 28 April 2022 (UTC)


 * Well, maybe it's just how one defines the words, I guess. When I think of a quantity number, I think of things like energy. This is a specific quantity that doesn't change unless you add or subtract from it. Power, on the other hand, is a product of energy and time, or a measure of intensity. For example, if I have a flashtube charged with 100 joules of energy, and I release that energy in one second, I have a flash equaling 100 watts of power. If I release that same energy in one microsecond, I have a flash of 100,000,000 watts, yet it is still only 100 joules of energy, so I get the same quantity of work only it's crammed into a shorter time.


 * Still, we're an encyclopedia for a general audience, so we don't always follow the conventions of specific industries or institutes. Our guidelines are more like those of Reuters Manual of Style, or the Chicago Manual of Style, where there are specific rules about the use of italics. The purpose is to cause the least amount of confusion for the reader, and putting this in italics makes it look odd, like it's a foreign term or a word that is being discussed as a word rather than the thing it represents (for example, "The term weld originated with the Swedish Vikings..."). Italics are also used for certain scientific names, such as genera. In most writing conventions, however, you don't find them used for units or quantities like Kelvin, millimeters, radians, watts, etc... It would just be confusing to readers, who may think it's a foreign term or being discussed as a word. That is why you should take this discussion to the manual of style talk page and try to gain consensus there, because if we do it for one, we'd have to do it for all. Zaereth (talk) 18:56, 28 April 2022 (UTC)

Image of the water tap is wrong?
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)
 * Hey. I noticed this as well and agree that a better example could be used. added the images; perhaps they can comment on this. CoronalMassAffection (talk) 17:06, 30 January 2023 (UTC)


 * I wanted it to be something like this. Since the pictures are misleading, you may remove them. ~Shubjt
 * That makes sense, and I think replacing the image of the aerated water with another image showing turbulent flow from a faucet without an aerator would be more clear, both figuratively and literally. I will do this shortly; however, I think it would be best if both images showed flow from the same faucet. I have yet to find a set of images on the Commons that shows this phenomenon, so I will use images of different faucets for now. CoronalMassAffection (talk) 03:31, 31 January 2023 (UTC)


 * Do you think this is good for laminar flow? Tap-gb0fe5d2cc 1920.jpg~Shubjt
 * IMO, it is better than the one currently. You can see the stream tapering, which would only really occur in a laminar flow. I can put this in the article shortly. CoronalMassAffection (talk) 13:16, 31 January 2023 (UTC)

"Smallest scales of turbulent motion"
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)


 * Don't worry. Nobody is going to crucify you for trying to improve an article on Wikipedia. Especially not for fixing that mess. That looks like something someone dreamed up while watching a chimney one day. People come here with all kinds of theories that are often plausible-sounding on the surface but end up being complete bunk, like this gem here: Talk:Potential energy/Archive 1. I've never noticed that section, but there's a certain point in this article, where it begins to wander, that I kind of stop reading. I'd probably just delete it as nonsense, myself. It has no sources, but you are certainly welcome to try and fix it.


 * That said, the one flaw I see in your logic is that not every system has a container, at least not in the traditional sense. Currents in the ocean, for example. Flows in solar-system formation, in galaxies, accretion disks around black holes, gases and particles in the heliosphere, etc... I think that's more along the lines of what the author was thinking about; smoke from a chimney after it has left the stack. What's the limiting factor in flows when the only container is the pressure and direction of the surrounding fluids? Just something to think about.


 * Also, to avoid anybody getting into an uproar over your changes, please provide sources for them. Well-sourced information is rarely challenged. An encyclopedia is written in the third-person objective, so I'd suggest avoiding the second person, unlike the author of that section did. You might wait a week or two to give people a chance to respond here, but that's not a requirement or anything. If anyone disagrees with your changes, the worst that can happen is they might revert you, and then we'll have something to really discuss here. Zaereth (talk) 22:33, 1 March 2023 (UTC)
 * Thanks for the agreement. I will make edits when I have time, with references.
 * The limiting factor of largest eddy size in unconfined flows is the size of the disturbance that caused them... in the case of the chimney smoke, that would be the exit of the chimney. For clouds, I suppose it's like, mountain ranges and pressure fronts and stuff like that, but I'm no meteorologist. HelpfulWitch (talk) 18:58, 2 March 2023 (UTC)


 * Well, I'm no expert on the subject. You probably know more than I do. I first learned about the term in aviation, but encounter it a lot in everything from hydraulics and plumbing to the study of astrophysics. I just thought I'd point out that flows are not always contained by a solid, but quite often their sole containment is another fluid. I suppose the picture of the candle flame would be a better example, and eddies can range from tiny to galactic in size. They occur in solar system formation and likely result in the formation of planets. They're found in massive amounts in the accretion disks around black holes, where the flow is highly viscous, incredibly hot, and constantly switching from subsonic to transonic and back again, before finally going supersonic at nearly the speed of light at the event horizon. (People often think space is a total vacuum, but it's not. Better vacuums have been created here on Earth than are found in space, and Reynolds number plays a big role in determining how these things form and grow, and what limits their size.) Anyhow, I'm just throwing that out there, because I've no doubt that if you limit the section to solid containment then someone else will come along with the same questions. Like I said, just something for you to to consider. Otherwise, by all means, feel free to fix that section. I hope that helps, and happy editing. Zaereth (talk) 20:54, 2 March 2023 (UTC)

Is turbulence related to velocity?
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 source you provided doesn't say what you seem to think it does. It doesn't say anything about where the turbulence develops. I'd suggest checking the already cited source, the book Boundary Layer Theory, which has basically been the bible of fluid dynamics since the 1960s. It gives very detailed descriptions, and has an entire chapter on the laminar/turbulent transition in pipes starting on page 415, with pictures, diagrams and everything.


 * Keep in mind we're talking about the transition from laminar to turbulent, not for fully developed turbulence.


 * For any type of flow there are two parts, called the free stream and the boundary layer. In the free stream friction is not much of a factor, and the entire mass tends to move as one, almost like a solid would. The free stream is in the center of the pipe. The boundary layer is near he wall. In the boundary layer, the flow near the wall of the pipe is basically zero, while farther away from the wall the fluid speeds up, like sheets passing over one another at different speeds. The boundary layer only extends a short distance from the wall, and then you get into the free stream where fluid speed is basically uniform.


 * Turbulence always begins in the boundary layer, not out in the free stream. It's not the velocity of the fluid, per se, but the momentum of it that is the key factor working in opposition to its viscosity. Velocity and momentum are related but not the same. Turbulence develops in the boundary layer not solely because of the speed of the fluid, but because those sheets in the layer are moving at different speeds, from zero to free-stream velocity. For example, imagine what happens if you drag a long sheet across the top of several other sheets. It will try to drag those other sheets with it, and if you pull hard and fast enough the sheets underneath may just bunch up and start rolling themselves up. The same thing happens in the boundary layer when the velocity or momentum of the faster sheets overcome the viscosity holding them neatly together.


 * The turbulence always begins near the wall, but once it starts it will quickly spread out into the free streams, creating turbulence there as well. At first it's intermittent, but as momentum is increased it will turn into fully developed turbulence at around 2900 Re. But this is all described in depth and great detail in the book, and the source you provided does not disagree with it in the slightest, but it also does not say what you are trying to put in the article. Zaereth (talk) 03:01, 27 April 2023 (UTC)


 * To help clarify the difference between speed and momentum/inertia, maybe the analogy of an airplane would be helpful. A large airplane has a lot of inertia behind it, so it has high a Reynolds number and a small boundary layer. A small model airplane, of the same type and configuration --and even flying at the same speed-- will have a much lower Reynolds number simply because its momentum is lower, thus it has a much larger boundary layer and drastically different flight characteristics even though everything else is the same. Zaereth (talk) 03:31, 27 April 2023 (UTC)

Caption of first picture (Schlieren image of a candle)

 * The plume from this candle flame goes from laminar to turbulent. The Reynolds number can be used to predict where this transition will take place.

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)