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Help With Understanding Shock Waves And Supersonic Flow

fluid flow mach number

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#1 winchester427


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Posted 08 September 2019 - 04:53 PM

Hi all


I have been studying Coulson & Richardson Volume 1 part 1 chapter 4 (Flow of compressible fluids). 


In section 4.6 it talks about shock waves where the Mach number can exceed 1. Unfortunately I have read through this section 3 or 4 times and I do not understand it :(


This concept seems alien to me and it seems to conflict with earlier chapters which explain how flow through a nozzle/Orifice is maximised when throat velocity is equal to speed of sound in the fluid and the pressure wave cannot propagate upstream any faster (4.2 & 4.3) and also maximum flow through a pipe (4.5) where flow does not increase at outlet pressure below a critical value. 


I was always under the thought process that once we hit choked flow - that's it and you cannot increase velocity beyond the speed of sound. (I guess maybe the fluid can continue to expand downstream and the velocity will increase as density drops?)


Is anyone able to explain how we can exceed Mach 1 in simple terms? or do you have any more simplified resources to explain it from the perspective of a chemical engineer interested in pipe flow? I have looked online at some resources from NASA etc; but they are more relating to an object moving through a gas rather than flow of compressible fluids in pipes.


Many thanks in advance



#2 Bobby Strain

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Posted 08 September 2019 - 06:13 PM

So, how about the Concord? And military aircraft? They fly at Mach > 1.



Edited by Bobby Strain, 08 September 2019 - 06:13 PM.

#3 Pilesar


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Posted 08 September 2019 - 10:32 PM   Best Answer

You are not the only person who finds Coulson & Richardson's explanation of supersonic velocity of fluids to be suspicious. I much prefer to think that supersonic velocity of fluids is impossible. See an excellent explanation by Doug McDaniel here:
(A thank you to Art Montemayor for pointing me to this resource just a few months ago.)

Edited by Pilesar, 08 September 2019 - 11:00 PM.

#4 breizh


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Posted 09 September 2019 - 02:23 AM



Consider the link above together with attachments to support your work .


Another good reference in fluid mechanic is the following :

Pipe flow a practical and comprehensive guide by Donald  Rennels and Hobart Hudson  (Wiley)


Good luck 


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Edited by breizh, 09 September 2019 - 02:38 AM.

#5 winchester427


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Posted 09 September 2019 - 04:59 PM

Thank you very much for the responses!


@Bobby - Yes, I could stretch my brain to that with the jet engines accelerating the plane but couldn't wrap my head around gas molecules accelerating themselves beyond mach 1 in a pipe.


@Pilesar - Thank you so much for that document it was exactly what I was after!! Mr McDaniel's explanations certainly make a lot more sense to me! And it also makes me feel better that I'm not the only one confused.


@breizh - thank you for those resources!

#6 Bobby Strain

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Posted 09 September 2019 - 06:22 PM

One must use a nozzle properly designed to get above mach 1 in a conduit. It won't happen without such a device.




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