Talk:Reynolds number

From Wikipedia, the free encyclopedia

Contents

[edit] 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 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 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 ρv / t = ρv2 / l, while the dimension of the viscous term (i.e., the term represented by the divergence of the viscous stress tensor) is μv / l2. 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 l3, they will yield forces. If you must define a Reynolds number as a ratio of forces, then, your "inertial force" should be ρl3v2 and your viscous force should be μlv.

--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 ρl2v2.--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 ρv2, and the characteristic scale for viscous dissipation per unit volume is μv / 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)
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 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). Hope this helps. --Allen314159 18:58, 21 August 2007 (UTC)

[edit] 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)

[edit] Re vs. Re

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)

[edit] 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)

[edit] 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)

[edit] Effects of Small Reynold's Number

I have heard that (due to the effects of small Reynold's 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)

[edit] 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)


[edit] 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)

[edit] 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)

[edit] 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 vS is the mean fluid velocity, L is the characteristic length, μ is the (absolute) dynamic fluid viscosity, ν is the kinematic fluid viscosity, defined as ν = μ / ρ, and ρ 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)