Fluid Mechanics Lesson 15B: Compressible Flow and Choking in Converging Ducts

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You are a god amongst men. My Gpa is single handedly being saved by these lectures

[@johncimbala]

Glad to be of help, but I would not use the word "god." Rather, I say that I stand on the shoulders of giants.

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@@johncimbalaAgreed, apologies. Believe me I've spread the word, you've made what our fluid prof taught so complicated seem easy and straightforward. Thanks again

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thank you for the videos, they've been so helpful. would really appreciate if you can finish the rest of the chapter soon

[@johncimbala]

Taking a few days off for Thanksgiving. Will resume videos on Monday.

[@jacobw..6788]

Thank you for the video, there's one confusion I have, how did you get the p*/po to be 0.5283 in the example when calculating p*? Is there a property table? My college program is not covering these particular concepts. Also, I'm building a self landing rocket with CO2 cartridges as a propellant source for school capstone project. I'm trying to calculate the mass flow out of those small cartridges, and the choked flow that basically puts a cap on how much thrust force I can get out of them. The thing bothers me the most is the pressure of them (800psi to 3000psi) and the freezing cold temp.(~ -70C) when it's being released. I doubt that these are nearly isentropic nor adiabatic. Will it still be worth it to try to figure out the choked flow when I have to assume and accommodate tons of properties.

[@johncimbala]

It's from the equation on page 2 of the notes for the case when k = 1.4 (air). Yes, your flow is definitely choked at those high pressures!

[@johncimbala]

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[@jacobw..6788]

@@johncimbala A thousand thanks! I definitely will!

[@raniaraihan4562]

Good day, sir. What will be the case when Ma>1? Do we equate the critical properties to the exit values?

[@johncimbala]

Ma cannot be > 1 at the exit of a converging nozzle. The most it can to is Ma = 1; in other words, it is choked. If you watch the next couple of videos in this series, you will see that in order to get Ma > 1, you need to have a converging then diverging nozzle.

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[@miguelmartins4703]

At 1:29 you say the flow must remain subsonic in a converging duct. What if we have a converging duct with supersonic flow, followed by a diverging duct (after the throat) with a subsonic flow? Is it even possible? I saw it in an exercise and it isn´t making much sense to me... Thank you in advance!

[@johncimbala]

Not possible if the flow is coming from a pressurized tank upstream. The flow cannot become supersonic without going through a throat.

[@miguelmartins4703]

@@johncimbala what if we have 2 converging-diverging ducts in a row? That way, when the flow leaves the first diverging duct with Ma>1, it immediatly encounters the second converging duct. Is it possible in this case? Or will there be a shock in the beginning of the second converging duct, not allowing the flow to enter it with Ma>1. Thank you.

[@johncimbala]

Yes it is theoretically possible. What usually happens, though, is you get a shock wave just downstream of the second throat, and then the flow is subsonic after that. Many supersonic wind tunnels use this effect because it makes the flow in the supersonic test section more stable - not influenced by downstream noise. Also, if done correctly, it greatly reduces the amount of pressure loss in the wind tunnel, thus leading to reduced power consumption. I teach this in a later section of my course, but have not created a video about it yet.... maybe some day.

[@miguelmartins4703]

@@johncimbala Thank you very much! God bless you! Greetings from Portugal!

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[@halarmad]

How does it work when the pressure in the container is lower than the ambient air? Thank you

[@johncimbala]

If that were the situation at time zero, the flow would go backwards into the tank until the pressures equalized.

[@johncimbala]

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[@michaelgarcia812]

Dont you have to establish that the stagnation conditions in the tank (e.g. pressure, exit area) will be sufficient before analyzing for compressible flow conditions? What are these conditions?

[@johncimbala]

You can always apply the compressible flow analysis even if the flow is nearly incompressible, In that case, the results will asymptote to incompressible analysis results. The conditions for significant compressibility are that the pressure needs to be high enough in the tank to give reasonably high Mach numbers at the end of the converging duct, such as 0.4, 0.8, 0.9, etc. The max is Ma = 1 as I state in the video (choked). If Mach number is really small at the exit, like 0.2, incompressible analysis is a reasonable approximation.

[@johncimbala]

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[@michaelgarcia812]

Thank you, will do. Your textbooks are excellent as well!

[@alihosseiniroknabadi4828]

Thanks alot professor

[@johncimbala]

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[@Samsa3289]

A great explanation 😮😊

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[@Sam-dh9fn]

I would like to ask in the nozzle is it possible that the Ma is greater than 1?

[@Sam-dh9fn]

And if let's say the Ma in a duct is greater than 1, the max mass flow rate will still be calculated using Ma = 1?

[@johncimbala]

No, not possible unless the nozzle has a throat and then the area grows larger beyond the throat. See the next lessons for more discussion about this.

[@johncimbala]

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[@johncimbala]

@@Sam-dh9fn If it is a converging-diverging nozzle and the Mach number is 1 at the throat, then yes you can calculate the mass flow rate at the throat. If it is just a converging nozzle, then the flow will achieve max flow rate when the flow at the throat is sonic (Ma = 1), and then you can use sonic conditions at the throat to calculate mass flow rate, which will be the maximum max flow rate for a converging nozzle.

[@user-le3oy9gd2f]

whats the difference in back pressure and exit pressure? Back pressure what causes the fluid to flow due to the pressure gradient but I don't get how thats different from pressure at the exit. is pressure at the exit not also the same thing?

[@johncimbala]

Yes if the flow is subsonic, but if the flow is choked, the Mach number is 1 right at the throat. In that case the two pressures can differ. Think about a perfect vacuum, for example. Pback = 0, but Pexit is some pressure much greater than zero. Thank you for your comment. Please tell your friends and colleagues about my KZbin channel where there are more than 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

[@Gingerneer80]

What happens in the nozzle if you achieve choke flow before the throat? How sensitive are nozzles to this occurring?

[@johncimbala]

That is impossible. Choked flow, if it is to occur, must occur in the throat in a converging duct

[@Gingerneer80]

@@johncimbala Tha k you for the reply. So, if a nozzle has a throat smaller than is necessary to achieve sonic flow, it will still only achieve sonic flow in the throat?

[@johncimbala]

@@Gingerneer80 Correct. All that will happen is that the mass flow rate will go down. The flow will adjust itself such that it is sonic at the throat if there is enough pressure difference from upstream to downstream of the throat.

[@Gingerneer80]

@@johncimbala Amazing thank you. I've not been able to find this answer anywhere else. I greatly appreciate your help

[@johncimbala]

@@Gingerneer80 The throat size does not really matter. If the pressure ratio (stagnation pressure upstream divided by downstream pressure) is sufficiently high, it will choke at the throat regardless of throat area. All the area does is determine the mass flow rate (bigger for bigger throat), but it will be Mach 1 and choked regardless.