Talk:Choked flow

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Mass flow rate of a gas is not limited under choked conditions[edit]

This article needs re-writing to make clear that: (a) the flow of a gas through a restriction attains a maximum linear velocity (i.e., m/s or ft/s) under choked conditions and that velocity cannot be increased by reducing the downstream pressure, but (b) the mass flow rate (i.e., kg/s or lb/s) is not limited under choked conditions ... it can still be increased by increasing the upstream pressure. That is easily shown by the equation for mass flow rate under choked conditions:

Q\;=\;C\;A\;P\;\sqrt{\bigg(\frac{\;\,k\;M}{Z\;R\;T}\bigg)\bigg(\frac{2}{k+1}\bigg)^{(k+1)/(k-1)}}

where:  
Q = mass flow rate, kg/s
C = discharge coefficient, dimensionless (usually about 0.72)
A = discharge hole area, m²
k = cp/cv of the gas
cp = specific heat of the gas at constant pressure
cv = specific heat of the gas at constant volume
P = absolute upstream pressure, Pa
PA = absolute ambient or downstream pressure, Pa
M = gas molecular weight, dimensionless
R = the Universal Gas Law Constant = 8314.5 ( Pa·m³ ) / ( kgmol·°K )
T = absolute gas temperature, °K
Z = the gas compresibility factor at P and T, dimensionless


References:

  • Handbook of Chemical Hazard Analysis Procedures, Appendix B, Federal Emergency Management Agency, U.S. Dept. of Transportation, and U.S. Environmental Protection Agency, 1989.
Handbook of Chemical Hazard Procedures
  • "Methods For The Calculation Of Physical Effects Due To Releases Of Hazardous Substances (Liquids and Gases)", PGS2 CPR 14E, Chapter 2, The Netherlands Organization Of Applied Scientific Research, The Hague, 2005. PGS2 CPR 14E

Finished a complete revision[edit]

I just finished the complete revision of this article. - mbeychok 21:39, 18 March 2006 (UTC)


Some corrections[edit]

I clarified some of the terminology:

  • there was confusion over upstream vs. ambient pressure
  • It was not clear that choked flow occurs in fluids as well as ideal gases
  • The equations deal with molecular ideal gases. Non-ideal gases have significant nonlinearities in the equation of state (ie they differ from the "PV=nRT" form, including higher powers of T, P, and V). In one place, real vs ideal was contrasted incorrectly -- the correct contrast is molecular vs. monatomic ideal gases.

I also generalized the discussion a bit -- Mbeychok's nice treatment dealt primarily with gas venting from a closed system, but choked flow holds for many more systems than just that.

Cheers, zowie 19:19, 23 March 2006 (UTC)

Zowie, thanks for your two lead-in paragraphs. I only see one problem with them and that is the use of the word "flow" without qualifying whether we are talking about volumetric flow (i.e., linear velocity times cross-secdtional area) or about mass flow. I believe that one cannot stress the point enough that "choked flow" pertains to the linear velocity or the volumetric flow rate, but not to the mass flow rate which can still be increased by increasing the upstream pressure ... at least, for gases. Do you think that you could perhaps add a sentence to your lead-in paragraphs stressing the distinction between volumetric flow rate and mass flow rates?
I have yet to find or read a clear presentation concerning choked liquid flows or to find any relevant, precise equations defining choked liquid flows.- mbeychok 01:29, 24 March 2006 (UTC)
No problem, thanks for the updates. There's a nice presentation here: [1]. In engineering circles single-phase choked fluid flow is often called "critical flow"; it might be easier to spot by that name (and, come to think of it, we should mention that in the article...) It's set by the same condition as choked gas flow -- zero pressure in the choke plane -- but as the motion is incompressible some of the terms are different.
Hmm... I might not understand what you mean about mass flow vs volumetric flow, since I'm used to thinking more about fluids than gases. By increasing the upstream pressure in a gas, you increase the sound speed, which in turn increases the linear flow rate in the choke plane -- isn't that the mechanism for increased rate if the upstream pressure is increased? Since KE = 1/2 mv^2, in the choke plane, all of the internal PE is converted to KE, and the PE is linear in the pressure, one should expect the flow rate to vary as the square root of the pressure, at constant density -- which is exactly what you have in your equations.
Cheers, zowie 05:17, 24 March 2006 (UTC)
I think our problem in one of semantics. I have been a practicing engineer for over 50 years and you're an astrophysicist. We simply don't speak the same language. So please bear with me as I try to clarify the difference between mass flow rate and volumetric flow rate. And also for the moment, let us forego using the word "fluid" and talk only of gases and liquids.
By mass flow rate, I mean gas mass per unit time (e.g., kg/s) and by volumetric flow rate, I mean gas volume per unit time (e.g., m³/s). By linear velocity (or speed), I mean distance per unit time (e.g., m/s).
Now, take another look at my opening comment on this talk page and also at the choked flow equation for a gas (which is one of the two equivalent forms I've presented in the choked flow article itself). When the ratio of upstream pressure to downstream pressure across a flow aperture is sufficient to cause choking, it is the gas linear velocity that becomes choked when that velocity reaches sonic velocity. When the linear velocity chokes, the volumetric flow rate also becomes choked because the volumetric velocity is simply the linear velocity multiplied by the area of the aperture (i.e., volume = area × velocity).
But the mass flow rate does not become choked!! As plainly shown in the choked flow equation for calculating the mass flow rate (in my opening comment), increasing the pressure will increase the mass flow rate even though the volumetric flow rate can not increase at choked conditions. Why? Primarily because increasing the pressure, increases the density of a gas and a higher gas density results in a higher mass flow rate without any change in the volumetric flow rate (e.g., mass flow rate = density × volume flow rate).
Why did I think this is important information to impart? Because over the years, I've encountered literally dozens of engineers who thought choked flow conditions limited their ability to increase the mass flow rate through their calibrated orifices and other flow control devices ... when, in fact, only the volumetric flow rate is limited.
Since the effect of pressure on the density of liquids is almost negligible (compared to the effect of pressure on gas density), the choked flow of liquids is probably very much different than that of gases. That is why I felt simply using the words "flow" and "fluids" isn't specific enough and we should always be very careful to make the distinction between "mass flow rate" and "volumetric flow rate" ... as well as between "compressible fluids" and "incompressible" fluids.
Please excuse me for being so long-winded and for perhaps dwelling on what is obvious to you, but I did want to get us talking the same language. - mbeychok 07:18, 24 March 2006 (UTC)
No, no, thank you for taking the time!
Hmmm... I had some more thought about gas pressure, and I think I've been wrong-headed about it. After all, in an ideal gas, zero pressure -> zero density -> zero mass flow, so I've apparently been thinking wrongly about the gas case. Even in the fluid case, "zero pressure" can't really be zero pressure since then you get a two-phase flow as the water boils, and the flow clearly isn't strictly choked then.
I think I've also been thinking something different than you as the definition of "choked" -- it seems obvious to me that changing the pressure upstream should change the flow rate; the surprising and interesting thing is that changing the pressure downstream doesn't change it, and I've been mentally labeling that condition "choked"! But now I understand, I think. Increasing gas pressure at uniform temperature doesn't increase the sound speed (which depends only on temperature and molecular mass), so the linear flow rate can't change as the pressure changes -- but the density changes, so the mass flow rate can vary. Yes?
I must apologize -- this is really quite far outside my realm of expertise, as you noticed, so I must defer to you on definitions and such. zowie 16:40, 24 March 2006 (UTC)
Yes, I think that we now understand each other much better. Under choked flow conditions, any further decrease of the downstream pressure will indeed not change the mass flow rate or the volumetric flow rate. However, increasing the upstream pressure will result in an increase in the mass flow rate. That is precisely what the choke flow equations are saying in their own language.
So, it would be kind of you if you would please emphasize that point in the opening paragraphs that you added ... and also emphasize the point that choked flow in gases is quite different from choked flow in liquids.
The reason that I did not write about choked flow in liquids is, quite frankly, that I lack enough knowledge about that aspect. I don't believe in reading a few books or articles and becoming an instant "expert". Perhaps, someone truly knowledgeable will add a section on that subject. - mbeychok
Okay, I updated the introduction. Is that suitable? Thanks again for taking the time to hash this out! zowie 18:48, 24 March 2006 (UTC)
In a word, yes. If you are ever in Newport Beach, California, I'd like to meet you. - mbeychok 19:16, 24 March 2006 (UTC)
I'd like that too. I live in Boulder, Colorado but I travel to California from time to time. Please look me up if you make it to the front range. zowie 20:11, 24 March 2006 (UTC)
  • Hello. Indeed, that is a very good point that you make about choked velocity vs. choked mass flow rate. Although it may be not as important, I´d like to add, as an aside note, that -according to the equations- the velocity may be increased, under choked conditions and same upstream and downstream pressures, by increasing the source (upstream) temperature. This would lead to a higher temperature and higher speed of sound, downstream, where the flow is sonic (Mach = 1) and, therefore, the flow velocity is equal to the sound speed. Such an increase of the flow velocity, however, would not increase the mass flow rate because the density would be decreased by the higher temperature; actually, the net effect would be a decrease of the mass flow rate (as explained in the article where the presence of the term "1/sqrt(T)" is pointed out). Do you concur? Regards ReedRich (talk) 13:51, 16 December 2008 (UTC)
ReedRich, you asked me (via email) to respond and I said in my reply that the question you raised was perhaps getting too deeply into fluid dynamics for an article intended simply to provide the choked flow equations and that it might be confusing to many readers. You then agreed. Thanks, mbeychok (talk) 16:46, 22 December 2008 (UTC)
  • Hi. Yes, Mbeychok - I concur. Regards. ReedRich (talk) 20 January 2009 (UTC)

Sailoday28, please furnish a citation[edit]

Greetings, Sailoday28: Please furnish a reference citation for the statement about choked isothermal flow occurring when the Mach number equals the square root of Cp/Cv. If you are not familiar with how to format a reference for a Wikipedia article, simply provide your reference just below here and I will format it and install it for you. If possible, an online reference would be preferable. Regards, - mbeychok 05:54, 14 February 2007 (UTC)

Ho=stagnation enthalpy, h=enthalpy, V=spec vol, U=velocity,
P=pressure, G=mass flux, gamma=cp/cv, a=sound speed, a^2=gammaRT
M=U/a
subscript 1 refers to upstream conditions
dHo=dQ and also dQ=dh-VdP
dU^2/2+dh = dQ = dh-VdP
dU^2/2 + VdP=0
For isothermal process and perfect gas:
dU^2/2 - RTdV/V = 0
Integrate U^2/2 - U1^2/2 - RT ln(V/V1) = 0
But U=GV, so (GV)^2 -(G1V1)^2 - 2RT ln(V/V1) = 0
Differentiate G wrt V and set=0 to maximize mass flux
2V(G^2)-2RT/V =0
But GV=u
U^2 = RT, M^2 = U/a)^2, M^2=RT/a^2 = RT/(gammaRT)
M^2=1/gamma
—Preceding unsigned comment added by 69.140.39.229 (talkcontribs) 14 February (UTC)
Thanks, 69.140.39.229, whomever you may be, for the contribution of your derivation. But when I asked Sailoday28 for a reference, I meant a book, journal article or online article ... in other words, a verifiable, valid reference. This article still needs that. - mbeychok 19:30, 14 February 2007 (UTC)
Sailoday28 provided a valid reference on his Talk page in response to my request and I have now added the reference into this article. All is well. - mbeychok 05:17, 16 February 2007 (UTC)

Choked flow discussion.[edit]

Mbeychok. I think some discussion would help as to the focus of your original write up. I don't wish to take away all the good work that you have put into this article. As you have demonstrated, you are a good writer and probably can incorporate some comments of mine which I think are worthwhile. My email is sailoday_28@yahoo.com PS, The equations that looked like jibberish for isothermal flow were mine and thank you for straightening them out. Regards```` —The preceding unsigned comment was added by Sailoday28 (talkcontribs) 22:59, 22 February 2007 (UTC).

Sailoday28, I would be pleased to hear from you. Just go to my user page by clicking here ==>mbeychok. Then in the left hand frame scroll down to the link at "Email this user" and click on it. Be sure to include "Wiki email" in the subject so that it won't be deleted as spam. When I subsequently reply to you, then you will have my regular email address.
By the way, if you would just create a user page of your own, then your name would henceforth appear in blue rather than red. You could also automatically sign your comments on any Discussion page (as explained in the box at the top of this page) by simply typing 4 tildes at the end of your comments like this: ~~~~. As I think I said before, if you expect to do much on the Wikipedia, it is worth taking the time to at least learn how to create pages, how to edit them correctly, how to create internal Wiki links, and how to use Discussion pages. Regards, - mbeychok 23:47, 22 February 2007 (UTC)
Sailoday28: I sent you an email (at your Yahoo address) on Saturday, Feb 25th, discussing how we could collaborate on your suggestions ... and I am waiting of your reply. - mbeychok 19:41, 25 February 2007 (UTC)

Purpose of "choked" flow[edit]

If you agree that choked flow is that resulting from given upstream conditions to the point where downstream backpressue will not effect flow then you might want to rearrange article to different types of choked flow not necessarily in the following order: 1- choking due to the area change--ie venturi effect 2. adiabatic choking in pipes 3 isothermal choking 4-choking with heat addition to pipe

You have started with perfect gas using a Cd. Perhaps a real gas formulation such as a "Generalized" Beattie-Bridgeman or others could be included. By Generalized, I am refering to type of equation of state (EOS)which is reasonably accurate for a number of gases.

The EOS could also be applied to items 2, 3 and 4 above.

Give one example for each discussion.

Main focus for all of above would be for a non-condensing gas.

Regards Sailoday28 22:45, 23 February 2007 (UTC)

A suggestion on nomenclature[edit]

Currently this article uses Q to denote mass flow rate. Usually m(dot) is used for mass flow rate, and Q is used for volumetric flow rate. For example, refer to the wiki page on Orifice Plates. Can I suggest changing the nomenclature in this article, to be consistent and to avoid confusion? Logicman1966 (talk) 03:01, 15 October 2008 (UTC)

I reluctantly agree. The symbol used in the article on mass flow rate is m(dot). Unhappily, the m(dot) symbol is:
  1. Cryptic to those unfamiliar with the use of the notation in calculus, and
  2. Not available as a single glyph in the English alphabet. - Ac44ck (talk) 03:29, 15 October 2008 (UTC)
OK, as there were no objections to my suggestion, I have changed Q to m(dot); It only appears 3 times in the article. I am happy that now there is consistency with other pages. Logicman1966 (talk) 11:39, 16 October 2008 (UTC)

Real gas[edit]

I removed the note at the end of the "Mass flow rate of a gas at choked conditions" section which said, "The above equations are for a real gas."

This page

http://exploration.grc.nasa.gov/education/rocket/snddrv.html

suggests the exact formula:

m(dot) = A_c.sqrt(k rho_c P_c)
Where rho_c is the density where the flow is sonic.

The last equation in the section has a factor involving 'k' which seems to be an isentropic relation based on ideal gas behavior. -Ac44ck (talk) 23:55, 7 November 2008 (UTC)

  • Hi. It seems that the flow area of the sonic section A_c is missing in the above equation. Also, the pressure should be taken at that same section - P_c.
m(dot) = A_c.sqrt(k rho_c P_c). Please, verify; thanks.
ReedRich (talk) 21:01, 10 December 2008 (UTC)
  • How is A_c related to "CA"? How is P_c is related to P? How is rho_c is related to rho? Please substitute into your formula and compare with the one in the article. -Ac44ck (talk) 22:17, 10 December 2008 (UTC)


  • Ok, I will try to clarify what I meant, and also discuss the questions you posed in the paragraph above.

Firstly, I would like to point out that the first two equations for m(dot) presented in the article are quite fine; and that my comment was directed solely at the m(dot) equation presented here, under the discussion section REAL GAS, referenced by the -nasa.gov site.

Secondly, I believe that the original equation at the nasa.gov site is correct, and that there was an error while copying it from there to here. To make it short, let us just observe that all equations must be dimensionally correct, but the copied equation is not.

Summarizing:

(Eq.1) m(dot) = sqrt(k rho_c P) - is incorrect.
(Eq.2) m(dot) = A_c.sqrt(k rho_c P_c) - is correct: it gives the mass flow rate (mass per time).

Regarding the posed questions:

(1) How is A_c related to "C.A"?
- "A_c" is the same as "A" - the discharge hole area. I just wanted to emphasize that the flow is sonic there (Mach = 1); that´s why I added the lowercase "c" subscript to "A". The uppercase "C" is the discharge coefficient - an empirical quantity. It is not present in equations 1 and 2 above, because those are purely theoretical equations resulting from thermodynamics and fluid mechanics. "C" is a factor determined experimentally, actually to fit the equation to the real data obtained from measurements (we may call it "professional cheating" - pardon me for the humor).
(2) How is P_c is related to P
- P_c is the pressure AT the discharge hole area, while P is the upstream "source" pressure. The relationship between them is given under the section "Minimum pressure ratio required for choked flow to occur" of the article - where the pressure ratio (Pu/Pd) is given by a formula and presented in table format for different gases. For consistency, Pu = P (upstream) and Pd = P_c (downstream).
(3) How is rho_c is related to rho?
- rho_c is the gas density AT the discharge hole area. Nasa.gov equation also uses rho_c.
(4) Please substitute into your formula and compare with the one in the article.
- that´s quite a challenge; not difficult but time consuming. I will provide at least one reference from course books used by engineering schools. After all, these results for choked flow are well known since 1950 at least. Ok?
*Ref.: "The Dynamics and Thermodynamics of Compressible Fluid Flow" by Dr. Ascher H. Shapiro from the M.I.T.; Pub. John Wiley & Sons Inc, 1953, ISBN 0-471-06691-5. (This is a classic!)

I hope these remarks helped to advance the understanding of the issues. Regards ReedRich (talk) 16:23, 11 December 2008 (UTC)

Thanks for clarifying. I misunderstood your objection. I am at a loss to find "the original equation at the nasa.gov site" which was copied "from there to here".
The document at http://exploration.grc.nasa.gov/education/rocket/snddrv.html contains:
  • Eq 1: mdot = r * u * A
  • Eq 8a, which can be rearranged and transliterated to: c = sqrt(k P / rho)
Combining the two (substituting u=c and r=rho) and measuring everything at the sonic section gives the form you suggested:
  • m(dot) = A_c.sqrt(k rho_c P_c)
It wasn't clear to me that you were employing this courtesy:
Talk_page_guidelines#Others.27_comments
Never edit someone's words to change their meaning
I have changed the formula in my original remarks to your corrected version. Thanks.
The reference was erroneous anyway because it does not give an "exact" formula — it also contains the factor "k", from an idealized derivation of "c". So I struck through the word "exact" in my original remarks.
In that the legend in this choked flow article says "A = discharge hole cross-sectional area" (as opposed to "minimum nozzle area"), it seems to have orifice plates in mind. The article on orifice plates says "the point of maximum convergence actually occurs shortly downstream of the physical orifice". I wouldn't necessarily equate "A_c" and "A". -Ac44ck (talk) 20:53, 11 December 2008 (UTC)


  • Hi.
By "original equation at the Nasa.gov" I meant (the same as you) - - Eq.1 mdot = r*u*A. (which I agree is correct!)
I should have said "error while transporting (the equation) from there (Nasa) to here (Wiki Discussion - Real Gas)" and I should have remarked that the error was the missing area "A", resulting in the incorrect statement mdot = r*u, which ultimately lead to the equation that I deemed incorrect (because it is dimensionally wrong).
Your mathematical development, starting from Eq.1 and using Eq.8a to obtaing the final expression - - m(dot) = A_c.sqrt(k rho_c P_c), is quite flawless, and follows the same reasoning that I did at home (given all the simplifying assumptions made so far).
Regarding the discussion guidelines, I am still very very new at Wiki protocols, so I hope my beginer mistakes will be forgiven (but not overlooked, please point them out, because I wish to learn).
Eq.1 is indeed exact - and general in many contexts. But the final form is not exact, as you correctly remarked, because some simplifications (such as isentropic and ideal gas assumptions) were employed for the speed "c", which led to the appearance of "k" (the "cp/cv" ratio of specific heats) - as you pointed out: c = sqrt(k.P/rho) and c = sqrt(k.R.T).
Just for future reference, the more general and exact expression is... c = sqrt( dP/drho ) - where, dP/drho stands for the derivative of P with respect to rho. One must be carefull to take the derivative under the proper flow proccess conditions.
Regarding the flow area, you are correct. I had in mind (correctly) that the "discharge hole area" was geometrically at the end of an ideal convergent nozzle (the exit area). Nevertheless, it may also be the throat of a convergent-divergent nozzle, as you remarked ("minimum area"). For plate orifices, the ideal formulation employed in the article is a shaky stretch of the theory, but is the basis for useful empirical correlations - in this case, experimentally determined factors, such as the discharge coefficient "C", represent attempts to correct the theoretical formula.
This is indeed a rich and interesting subject. ReedRich (talk) 17:39, 12 December 2008 (UTC)

Wrong units?[edit]

 The mass flow rate caluclation seems to have the wrong units under the square root sign.

The units would need to be kg-sq per second-sq. They are not. —Preceding unsigned comment added by 206.190.70.135 (talk) 19:41, 2 March 2010 (UTC)

Which calculation? There is more than one. What units do you think it has under the square root sign? -Ac44ck (talk) 03:45, 13 October 2010 (UTC)
 The units for molecular mass seem wrong too.  

They are given as kg/kmole, but other equations, for example on the article [Orifice_plate], they are kg/mol. The summary at the top of the discussion page then states that the same value is dimensionless. At least 2 of these 3 places must be wrong! I am no expert in this field, so I am only going to point out the error, not correct it! Dave t uk (talk) 01:12, 11 December 2010 (UTC)

Is there an equation to calculate choked flow of a liquid??[edit]

159.245.32.2 (talk) 19:34, 18 May 2011 (UTC)Martin

Recent deletion of formula for 'real gas'[edit]

So far, the objections I have heard don't hold a lot of water:

  1. One calculation was off by 15%. Were there no mistakes made? Was the "right" value for compressibilty used? How close is "close enough?"
  2. The equation was derived for ideal gases. And the compressibility factor was introduced to make some (not perfect) allowance for the behavior of real gasses. What is wrong with that?

Then, the denunciation of a practical-for-some-purposes formula and the proposed alternative are unsourced. - Ac44ck (talk) 03:20, 1 June 2011 (UTC)

Error?[edit]

I can read: At choked flow the mass flow rate can be increased by increasing the upstream pressure, or by decreasing the upstream temperature. I think the first part of this statement is true, but the second is false. ? — Preceding unsigned comment added by CharlesCo (talkcontribs) 18:10, 12 October 2011 (UTC)

And if I am mistaken, then this becomes wrong: depending ONLY on the temperature and pressure on the upstream side of the restriction.

So in both cases there is something to modify to make it clearer. — Preceding unsigned comment added by CharlesCo (talkcontribs) 18:14, 12 October 2011 (UTC)

This does seem wrong to me as well, but only based on highschool and college physics background. If you increase something's pressure to gain an effect, generally you can get the same effect by increasing temperature. If this is not the case, there should be a section explaining why this is so to non-experts. Perhaps I can add a citation needed to it while we wait for an expert.131.107.0.81 (talk) 21:31, 25 July 2012 (UTC)

An expert writes: If you look at the second equation in the article - m =CA etc. - you can see that the mass flow rate is increased by increasing the upstream density, rhosubscriptzero. If the upstream pressure is constant, then the way to increase rhozero is to reduce the temperature. 86.183.12.111 (talk) 18:04, 20 January 2014 (UTC)

Centering numbers in a table[edit]

A recent edit removed the centering of numbers in a table. Now the numbers are left-justified in the cell. Why is this better? The WP:MOS seems to be silent on this issue. - Ac44ck (talk) 02:44, 11 October 2012 (UTC)

An explanation would be nice[edit]

I would like an explanation on top of the facts. Why does the speed not increase (much)? I suspect it is because the gas laws for v>1M and those for v<1M are different. In one area it favors a change in speed and in the other a change in density? Somehow in the narrowing it can not meet both behaviors in a continues way? --77.1.163.208 (talk) 09:54, 5 February 2013 (UTC)

Error in Specific Heat Ratio Formula[edit]

There may be an error in the calculation of the specific heat formula:

[2/(1+k)]^[k/(k-1)]

When I calculate the formula with dry air (k = 1.4), I get a value of about 0.5, not somewhere between 1.7 and 2.1 or so. Please check my math and comment.

Scirocco84 (talk) 19:27, 1 March 2013 (UTC)

No error. In the table we are talking about upstream p / throat p and in the equation for pstar/pzero we are talking about throat p / upstream p. 86.183.12.111 (talk) 18:14, 20 January 2014 (UTC)

Comment moved from led[edit]

This comment was in the led of the article. It belongs on the talk page:

The formula shown below appears to be incorrect; choked flow in other references is linearly proportional to pressure; for example see J. M. Lafferty (ed.), Foundations of Vacuum Science and Technology, Wiley, 1998 p. 116; and J. J. Sullivan et al, Mass flow measurement and control of low vapor pressure sources, J. Vac. Sci. Technol. A7, p. 2387 (1989)

- Ac44ck (talk) 17:27, 9 March 2013 (UTC)

Critical flow[edit]

Hi all. Critical flow used to direct to this page. It doesn't any more. I've switched the link back to refer to Froude numbers, on the basis that:

  • That definition is definitely right;
  • A previously copyvio'd article initiation at Critical flow definitely referred to the Froude meaning;
  • This page makes no mention of Froude numbers, nor does it ever use the phrase "Critical flow".

If anyone here thinks I've been too bold, please set up a disambiguation at Critical flow, not just a redirect, so we can have both meanings. And please also make it clear that this page is about a technical use of the phrase too! If someone drops me a note at my talkpage, I'm happy to provide the Froude number contextual info for the redirect. Thanks. DanHobley (talk) 04:49, 6 August 2013 (UTC)

Possible error[edit]

In the section that starts: Choking in change of cross section flow[edit] Assuming ideal gas behaviour, steady-state choked flow occurs when the ratio of the downstream pressure p_0 falls below a critical value p^{*}. I believe that p_0 should be deleted. It seems to say the downstream pressure is p_0, but this is actually the upstream pressure, right? — Preceding unsigned comment added by 207.121.73.2 (talk) 15:18, 24 March 2014 (UTC)

I think it was confusing by virtue of trying to say too many things at the same time. I eliminated some words to simplify it. - Ac44ck (talk) 03:32, 25 March 2014 (UTC)