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# Velocity of Gas Under Pressure When Released

09/11/2015 4:40 AM

If a pressurized gas is suddenly released, what will be the velocity?

WILL IT DEPEND ON PRESSURE?

WILL IT DEPEND ON GAS?

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#1

### Re: Velocity of gas under pressure when released

09/11/2015 4:57 AM

Yes, yes, and yes to several unasked questions. (The second yes is less significant than most of the others.)

Shouting doesn't help.

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#2

### Re: Velocity of gas under pressure when released

09/11/2015 6:15 AM

There are 2 regions:

under and over a threshold of the pressures ratio gas source pressure / receiver pressure

If the value is less the threshold velocity depends on the pressure differences, if it is over the threshold velocity is constant.

The threshold depends on the nature of gas molecules i.e. number of atoms in the molecule.

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#3

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 10:24 AM

For gases, the pressure is related to velocity as square of velocity ...
"Keep in mind that the temperature of a gas is actually a measure of its average kinetic energy, and kinetic energy of a particle is related to its velocity according to the following equation:

KE=12mv2

where KE represents kinetic energy of a particle, m equals mass, and v2 is the square of its velocity. As velocity increases so does kinetic energy. Of course the inverse is also true, that as kinetic energy increases so does velocity. You can see from this relationship how a molecule with a higher temperature will be moving faster. The temperature of the system is the average kinetic energy of its particles. Thermal energy is the total kinetic energy of all the particles in a system. Temperature, thermal energy, and the speed of a molecule are all directly related. "

http://chemwiki.ucdavis.edu/Physical_Chemistry/Physical_Properties_of_Matter/Phases_of_Matter/Gases/Kinetic_Theory_of_Gases/Kinetic_Theory_of_Gases

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#4

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 10:55 AM

I may be stupid but I do not relate your answer to the question. Would you please explain how the molecule velocity is related to the gas flow velocity when an orifice is opened between two pressure levels ?

What you wrote is the relationship between molecules velocity and pressure since pressure is the sum of molecules impacts on the container wall and is of course depending on the gas temperature.

But this has not direct relation to the isentropic process of a gas flow through an opening between two pressure levels and this the question as far as I understand with my poor english the question.

Nick

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#5

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 11:42 AM

Perhaps you interpreted the question more specifically than I did....to me the question was ambivalent and non-specific....the type of gas and temperatures involved could have a great deal to do with the answer...I didn't see anything about an orifice...never the less the link provided should provide the tools to answer any remaining questions the OP may have.....

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#23

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 7:36 AM

As I wrote my english is very poor but here is the way I understood the question :

If a pressurized gas is suddenly released, what will be the velocity?

WILL IT DEPEND ON PRESSURE?

WILL IT DEPEND ON GAS?

If a gas is pressurized it means, for m,e that it is in a closed space since in a free space it is not pressurized. If it is released it means, again only for me, that the closed space got an opening to the free space. The mentioned velocity is, again for me, the velocity of the flow from high pressure closed space to free space at lower pressure.

Thus the question is on my opinion (and I do not consider that I am always right) that the right answer is how this velocity depends on high pressure versus low pressure and nature of the considered gas. Again in my humble opinion the kinetic theory of gas is not directly related to the flow velocity so that it is not the right answer to the question.

My reaction i justified by the fact that, unfortunately, too many answers are totally unrelated to the questions- on my opinion- and those are soo many that I start to doubt about my faculty to understand what is the real meaning of questions. I also start to deeply doubt about my understanding of your language. I was many years working for american companies and I had no problems of understanding but it was many years ago and may be the language in its evolution changed soo much that I cannot consider anymore myself up to date.

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#6

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 11:48 AM

If I might chime in....please consider more what Nick name has posted. The limiting velocity is strictly related to the viscosity of the gas, whatever its identity, and when the pressure is high enough to produce the limiting velocity, flow will assume viscosity limit of flow. Gas viscosity is of course, low, thus it takes a high pressure and a relatively small orifice to reach this limit.

http://www.lmnoeng.com/Flow/GasViscosity.php

Here I have pasted a link to a common gas viscosity calculator.

Poisseuille's law provides an account of viscous flow through a tubular (circular) section, as pasted from this link:

http://www.lazzero.com/index.php?option=com_content&id=111&Itemid=116&lang=en

Since I am not "the expert" on this topic, I used my uncanny ability to do research and found something relative to an answer.

These considerations apply to knowing the velocity of a jet of gas from an orifice, flow in a tube, and possibly could be applied (not sure how accurately) to a rocket nozzle model.

By the way, an explosion is simply a sudden release of gas from an initially confined system, where energy is suddenly released into the matrix (forming the gas and heating it to extreme pressures). Brissance of an explosive type is simply a measure of the intensity of the shock wave (velocity front) of the released gases. High brissance is considerably higher in advanced technical explosives than in dynamite or nitrate based "heaving" explosives. Detonation chord is one example of an explosive with a high burn velocity and a high brissance.

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#22

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 5:07 AM

Agreed. Kinetic theory is interesting and no doubt has its uses, but not many I suspect in practical gas flow problems.

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#16

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 6:50 PM

it is not 12mv^2 but 1/2mv^2 or if you take all degrees of freedom then 3/2mv^2.

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#17

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 7:57 PM

"if you take all degrees of freedom"? Here in the U.S.A. we've lost all degree of freedoms and about one step away from Marshall Law, with an extremely large orifice we call our government

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#7

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 12:35 PM

For "sudden release" the velocity would be a product, among other things, of modulus of elasticity for a circular orifice constricted by musculature and would be influenced by demographics and/or criminal background.

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#8

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 12:51 PM

One must also factor in the demographics when also considering the sex of the entity owning the orifice, when considering the shrillness of any audible vibrations of the raspberry.

Criminal background? Really? Last time I checked, one not have to pass a background check to own one of these orifices, or be a "licensed" emitter.

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#11

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 2:22 PM

Yes, but in prison, you would get frequent "Background Checks" resulting in an orificial dimensional change. Or so I gather.....

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#14

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 3:30 PM

LOL, OK you win on that one!

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#30

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 1:01 PM

.....and would be influenced by demographics and/or criminal background.

....and how many beans have been eaten...!

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#9

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 12:55 PM

I do not completely understand what you mean. You could either say through some orifice or the other way - burst/explode.

Only one thing is certain, since in mechanical terms, this is called depressurization process or ΔP = negative.

Looking at Benoulli's Equation (Just focus on V and P parameters, you could disregard enthalpic effect, in your case -note equation is for incompressible liquid, but the same analogy with gas)

One way or another, state one(initial) will balance the outcome of state 2(final) in the equation.

It is obvious what will happen.

Heard of the forecast on the weather when they say "we have a low pressure" - what would usually that will imply?

Yes effects of Pressure, Volume and Temperature will depend on the type of gas.

Read, something about (PVn = const.) for gas undergoing polytropic process and (PV=mRT=constant) ideal gas equation.

Hope this helps.

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#10

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 1:52 PM

I'm wondering what this student's lecture notes say about the laws of gas or did they cut miss class and didn't copy another classmates notes?

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#12

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 2:46 PM

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#13

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 3:01 PM

Perhaps only one student attended the lecture and was so disgusted with his classmates that the student refused to allow copying?

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#15

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 6:39 PM

I am a new member to this forum with a BSME and 45 years of engineering background including 20 years of new product development of ASME Section 8 High Pressure Relief Valves.

With that being said, when I read the resulting posts to your question as well as all online sites and literature addressing the subject of gas flow dynamics and equations, what I found was what I perceive as perfect examples of: "When you ask engineers what time it is, they will start by describing how a watch works".

So here is my effort to give you the best simplest answer to your question. First, as the first posted response states the short answer is Yes and Yes.

Now for a bit more detail without addressing all of issues of ideal gas laws, energy conservation, etc

He best way for me to explain this is by talking about flow through a very simple nozzle, a hole in a plate, with P1 (the pressure on one side) and P2 (the pressure on the other side). As has been stated, there are two basic types of flow that can exist though that hole, they are categorized as Subcritical (Subsonic) Flow and Critical (Sonic) Flow.

The presssure conditons that control which of those flow conditions will exist at our hole is the pressure ratio of P1 to P2 and the characteristics of the gas flowing through the hole.

In this example we will assume that the gas is air. For air, the critical pressure ratio (the point at which the flow characteristics through the hole changes) is the point at which P2= P1/2. As long as P2 > P1/2, then P2 will have an effect on the flow rate and velocity of the air flowing through the hole; but when P2 decreases to the point that P2 = P1/2 then the flow velocity through the hole reaches Mach 1 (the speed of sound), a shock wave forms in the hole and the maximum velocity at which air can flow through the hole has been achieved. Beyond that point, the flow rate and velocity through the hole are no longer affected by P2 no matter how much that pressure decreases. This condition is what is known as "Choked Flow".

To expand this to another case, an explosion of gas is controlled by the same rules; but, in this case, when the pressure created by the ignition is below 2*atmospheric pressure you will feel a flow of air past you. When the pressure is greater than 2*atmospheric pressure you will be struck by an expanding shock wave of compressed gas traveling at Mach 1. No matter how much higher the ignition pressure reaches the speed at which the shock wave strikes you will not be greater than Mach 1, but the stored energy in that shock wave will be intensified proportionally.

I hope this (long worded) explanation helps you understand the basic conditions applying to your question.

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#18

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 8:47 PM

Welcome to CR4. The more you hang around here the more you will find that most questions are terse while demanding the most verbose answers. Unfortunately the attention span of most posters is shorter than their question. Your response was detailed and to the point, making it easy for me (an EE) to get it. It would be great if the OP (Original Poster) would provide some feedback as well.

Now what time is it????

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#19

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 9:12 PM

First, welcome to the mad house. I really love your exquisite, well nuanced answer here that covers all practical scenarios.

There are a very few radical, hyper non-linear scenarios (type II supernova, black hole event horizon, ultra-high vacuum to poor vacuum leaks, phonon effects) that meet the stated OP criteria that your answer is not a completely accurate answer. Most importantly, your answer identifies where the non-linearities start to happen.

GA!!!!

[Now where is that pint.]

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#20

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 10:36 PM

Ahhh at last some clarity.....now what was the question again???

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#27

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 12:00 PM

Wait a minute, if gas flow cannot exceed the speed of sound, which is around 761 mph, then how are jet airplanes, which are basically powered by gas nozzles, able to exceed the speed of sound?

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#28

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 12:55 PM

Because they use a Laval nozzle. This tapers down to the throat, then diameter increases again. The shape of the diverging section is fairly critical. In the throat velocity is sonic, in the diverging section velocity increases, even though area increases. The gas density decreases faster than the velocity increases, as the mass flow per unit area is constant.

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#31

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 1:45 PM

So a gas could escape at supersonic speed by a change in density....but energy has to be added...?

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#32

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 4:25 PM

Yeess, the energy comes from the burning fuel. I don't see a problem.

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#33

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 6:07 PM

Alrighty then.....PREPARE FOR LAUNCH!!!!

SOLAR AWAYYYYyyyyyyeeeeeee,,,....

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#34

### Re: Velocity of Gas Under Pressure When Released

09/14/2015 1:29 AM

You may want to check your right leg as it looks like the making of STS-51L (Challenger) event with a massive gas release!!

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#35

### Re: Velocity of Gas Under Pressure When Released

09/14/2015 6:29 PM
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#41

### Re: Velocity of Gas Under Pressure When Released

09/16/2015 8:28 AM

Thank you for the NASA link dear brother Solar Eagle.

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#42

### Re: Velocity of Gas Under Pressure When Released

09/17/2015 8:57 PM

This is the part of the topic in Thermodynamics, that I and others were absent. Thanks SE for posting.

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#36

### Re: Velocity of Gas Under Pressure When Released

09/15/2015 9:46 AM

Excellent. Try H2O2

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#39

### Re: Velocity of Gas Under Pressure When Released

09/15/2015 3:01 PM

Great Balls Of Fire!

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#40

### Re: Velocity of Gas Under Pressure When Released

09/16/2015 8:18 AM

He was referring to a free expansion shock wave, and that is different from confined gases in a jet nozzle. It is true that an explosion will never exceed Mach 1, however, in space, no one can hear you scream anyway. A rocket nozzle (and some jet engine nozzles) can have gas speeds of Mach 5 (or more). At least so I am told. The speed of the vessel through the medium (air or space) depends on the integral of thrust, nozzle velocity, and drag (and lift).

The reason some most nozzles can exceed Mach 1 is to do with the rate of lateral expansion relative to the velocity of the (plasma) flames escaping from the nozzle.

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#25

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 10:36 AM

Welcome, and congratulations. Not many of us have 100% good answers!

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#21

### Re: Velocity of Gas Under Pressure When Released

09/11/2015 11:23 PM

Yes.

Yes.

Do you mean release through a valve or orifice?

Or perhaps the bursting of a balloon or container?

There are many variables to the question that make it impossible to give a detailed answer.

Better questions will get better answers.

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#24

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 10:25 AM

http://www.engineeringtoolbox.com/bernouilli-equation-d_183.html

The Bernoulli equation describes the relationship between pressure and velocity (kinetic energy), and is derived from the Conservation of Energy law. It can be summed up as "the sum of potential energy, pressure, and kinetic energy is constant".

As can be seen, the kinetic energy is dependent on the type of gas (density ρ) and the velocity squared.

The exact relationship, of course, depends on the geometry, i.e., whether the gas is expanding in free space, through an orifice, etc.

As others have noted, this applies to incompressible flow.

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#26

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 10:52 AM

You did not mention that this is valid ONLY in subcritical domain when flow is not chocked.

Is the conservation law valid only for incompressible fluids ?

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#29

### Re: Velocity of Gas Under Pressure When Released

09/12/2015 1:00 PM

No, sorry, that was a brain f**t. Strike the last sentence. I believe past the subcritical domain the value of ρ would change appropriately.

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#37

### Re: Velocity of Gas Under Pressure When Released

09/15/2015 1:36 PM

What - like a balloon bursting? Sonic velocity. For as long as the bang lasts.

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#38

### Re: Velocity of Gas Under Pressure When Released

09/15/2015 2:19 PM

Yes, as long as the pressure in the balloon is greater than 2x Atmospheric ie > 15 psig; but, since the spherical sonic wave front is driven by the pressure contained within it, the wave it will quickly dissipate due to the spherical volume expansion and resulting rapid internal pressure reduction to below 15 psig.

The higher the initial balloon internal pressure the further the spherical sonic pressure wave will travel.

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