Choked and sonic flow 5

[robjoenz]

The definition of choked flow is when a reduction in downstream pressure does not result in an increase in flow through an orifice. In the case of a tiny hole in a pipe if flow becomes sonic it will also be choked.

My question is... if you have choked flow does it necessarily mean you will have sonic flow? i.e. can choked flow exist for sub-sonic velocities?

Thanks,
Rob

 

[Latexman]

I don't understand what that means. I just want to establish that the only parameter or condition that changes from Case #1 to Case #2 is the inlet pressure. Keep it simple.

Good luck,
Latexman

 

[rbcoulter]

Yes. Only the inlet "stagnation" pressure changes with all the assumptions mentioned earlier. This is "P" in Milton's equation which assumes a zero approach velocity.

It sounds like your trying to remove the constraint of zero approach velocity going from case #1 to case #2. In this way you can claim that the kinetic energy of approach is greater in case #2 because of the higher pressure then saying that the stagnation temperature is higher and then that the throat temperature is higher then that the choke velocity is higher. This model doesn't allow for this (Milton's equations). Other more realistic models may (please provide one or a reference).

My only point is that if you use Milton's equations, without deviating from the assumptions in which it was derived, then the choke velocity does not change if only "P" is increased.

 

[sailoday28]

rbcoulter (Chemical)
"Miltons equations........"
I believe the basic topic is steady state flow.
The "accidental release" equations are at best an APPROXIMATION used in "quasi steady flow"
Of course you can have a large container with a small break and approxmate zero velocity within the container. Initial conditions would set the starting(initial conditions) pressure and tempearture. The relation between the stagnation conditions would be related to heat transfer to the vessel and mass removed. For each step of the "quasi steady" analysis, "Miltons first equation can be used. (I question the second with regard to calculation of gamma),
However, I don't see how you are tying this in with sonic velocity other than the simple relation between the upstream and throat conditions of the flow.

 

[mbeychok]

Regarding the many references in this thread to "Milton's equations", I would like to make it clear that the equations I presented in this thread are not "my" equations. Although I have thoroughly checked their derivation, as stated above they are the equations given in:

(1) "Risk Management Program Guidance For Offsite Consequence Analysis", U.S. EPA publication EPA-550-B-99-009, April 1999
(2) "Handbook of Chemical Hazard Analysis Procedures", Appendix B, Federal Emergency Management Agency, U.S. Dept. of Transportation, and U.S. Environmental Protection Agency, 1989
(3) "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

I could also add:

(4) Equations 5.20 and 5.21 on page 5-14 of the Sixth Edition of Perry's Chemical Engineers' Handbook, 1984. (Perry's equations include the local acceleration constant, g, because they are in the U.S. Customary units rather than SI Metric units).

(5) For those of you who may be in the United Kingdom, exactly the same results are obtained by using Ramskill's equation. Ramskill, P.K., "Discharge Rate Calculation Methods for Use in Plant Safety Assessments", Safety and Reliability Directory, UK Atomic Energy Authority.

I would also point out that the equations are not merely "accidental release" equations. As far back as the 1950's, when we were designing Exxon's Model IV fluid catalytic crackers in refineries, those equations were used to size the choked flow orifices that injected steam into the catalyst circulation system to fluidize the catalyst ... and if we needed to increase the mass flow rate of steam injection, we simply raised the inlet steam pressure. The point being that the equations I presented have been in use for over 60 years.

In my humble opinion, 67 postings in this thread is beginning to get somewhat ridiculous.

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[sailoday28]

mbeychok (Chemical)
Equations being used for 60 years is fine, if the user understands that the upstream Pressure and Temps are stagnation.
With reference to the 2nd equation, I still would like to know why the definition of k as used with compressibility is not spelled out.



Regards