How Fast Does Air Escape from a Pressurized Container?

[pranj5]

Suppose there is an enclosed container having air inside at say 4 barA pressure. Now, a hole has been made at one of the walls of the container and by another hole, air is continuously injecting inside so that the pressure wouldn't fall. Now, with what speed the air from the container will come out. In short, there is a pressure difference of 3 barA (4 barA - 1 barA), how much velocity that pressure difference can create with a compressible fluid?

 

[DrClaude]

http://www.pipeflowcalculations.net/nozzle.xhtml

 

[pranj5]

http://www.pipeflowcalculations.net/nozzle.xhtml

It's about nozzles and what I have said is about just an orifice at the wall.

 

[boneh3ad]

Are you familiar with the concept of choked flow?

 

[pranj5]

Choked flow in nozzles? Yes!

 

[boneh3ad]

Choked flow applies to essentially any pressurized container with a hole in it. In other words, your first order of business here is to determine if your pressure ration results in choked flow through your orifice. Once you answer that, you will have a good idea of how to calculate the speed.

 

[pranj5]

Choked flow will occur when the speed of the gas will become equal to the speed of sound. The speed of sound can be calculated but how to calculate the speed with which the gas will come out?

 

[boneh3ad]

You have to determine if the flow will be choked in your orifice through which gas is escaping. If it is, then you know it is moving with exactly the speed of sound, which is easy to calculate. If it is not choked, then you can typically use isentropic approximations to get a good estimate of the parameters at the exit and then use those to calculate velocity.

 

[pranj5]

Can you give an example?

 

[boneh3ad]

An example of what? You said you are familiar with choked flow, right? That implies, to me, that you know how to determined if a flow is choked.

 

[russ_watters]

An example of what? You said you are familiar with choked flow, right? That implies, to me, that you know how to determined if a flow is choked.

...and even if you aren't quite as familiar as you let on, @pranj5 , I'm sure Google is. Why don't you give a shot at calculating if you have choked flow for us.

 

[boneh3ad]

Well I think the important thing to distinguish here is the difference between being familiar with a simple textbook definition (achieving sonic conditions at a throat) and what the concept actually means.

Choked flow can occur even without a converging or diverging section attached to the throat are (which really can just mean a hole in this case). There are also very specific pressure considerations for determining whether a flow is choked.

 

[malemdk]

Use Bernoullis equation to find the exit speed

 

[russ_watters]

Use Bernoullis equation to find the exit speed

The pressure/speed is too high for Bernoulli's equation to work.

 

[pranj5]

Seems that there are different opinion here and now I want to go on my own way. First, for simplicity I consider the flow to be subsonic so that no choking can occur. And I want to deduct the speed directly from the First law of Thermodynamics. It's the enthalpy of the gas that will be converted into motion here. As the tank is always replenished with new supply so that the pressure inside wouldn't decrease, that means the temperature inside wouldn't change too and that means only the PV will be converted into motion.
So, by simple equation; PV = ½ mv²
Where m is the mass of 1 gm-mole of the gas.
So, v = Square root (2RT/m)

 

[boneh3ad]

No, that equation is not correct. If it was, you would have to convert every ounce of energy contained in a pressurized flow into an organized flow with no more random molecular motions.

There really aren't different opinions here, either. There are people who don't know what they are talking about and suggest using Bernoulli's equation in a compressible flow, and then there are people who study compressible flows for a living and are telling you to first determine if the flow is choked (it's an easy calculation if you really are familiar with choked flow) and then use that to determine the velocity.

 

[pranj5]

No, that equation is not correct. If it was, you would have to convert every ounce of energy contained in a pressurized flow into an organized flow with no more random molecular motions.

Random molecular motion results in internal heat/energy and I hope you have noticed that I haven't considered that into factor. If flow going out have the same U, then how every ounce of energy contained in the gas has been converted. It's the pressure part i.e. PV has been converted into the velocity. No change in internal energy i.e. random motion of molecules.

There really aren't different opinions here, either. There are people who don't know what they are talking about and suggest using Bernoulli's equation in a compressible flow, and then there are people who study compressible flows for a living and are telling you to first determine if the flow is choked (it's an easy calculation if you really are familiar with choked flow) and then use that to determine the velocity.

As far as I know, choked flow occurs when the velocity reached M. I have already stated that the velocity is subsonic.

 

[russ_watters]

As far as I know, choked flow occurs when the velocity reached M. I have already stated that the velocity is subsonic.

You can't make things be true just by stating them: you must calculate it. This isn't optional, pranj5.

 

[boneh3ad]

Random molecular motion results in internal heat/energy and I hope you have noticed that I haven't considered that into factor. If flow going out have the same U, then how every ounce of energy contained in the gas has been converted. It's the pressure part i.e. PV has been converted into the velocity. No change in internal energy i.e. random motion of molecules.

The thermodynamic pressure is a measure of the rms kinetic energy per unit volume of a continuous fluid as a result of molecular motions. If you use the equation you proposed there, it's probably easiest to divide through by $V$ and look at it as

p = \dfrac{1}{2}\rho v^2.

By using your method you assumed that all of the energy associated with $p$ is converted to $v$. All of it. This isn't the case. This equation is essentially an oversimplification of the energy equation. I already showed you the proper interpretation of the energy equation in your other thread, which you seem to have ignored.

As far as I know, choked flow occurs when the velocity reached M. I have already stated that the velocity is subsonic.

That's the textbook definition of choked flow. Is that the depth of your knowledge on the topic? Do you understand all the imications of choked flow or do you just know the definition as it is printed after the bold print in a textbook? Do you understand that a flow may be choked or not depending of the specifics of that flow?

These things are basic to compressible flows and I am trying to determine whether you actually already understand them or not. That's important to the answer.

 

[pranj5]

You can't make things be true just by stating them: you must calculate it. This isn't optional, pranj5.

It's a well known fact and process and can be found in wikipedia. Why should I waste me time?
@ boneh3ad; just found this link[/PLAIN] and calculated and found what I need.

 

[boneh3ad]

It's a well known fact and process and can be found in wikipedia. Why should I waste me time?
@ boneh3ad; just found this http://1.http//www.tlv.com/global/TI/calculator/air-flow-rate-through-orifice.html and calculated and found what I need.

If this is your attitude, then this thread should be closed right now because you obviously don't want to learn. The concept of choked flow is obviously not very well known because you obviously don't have a clue what that concept should even apply in the case you are trying to discuss here (hint: your flow is choked! You need to understand why and how you can tell).

That calculator, I think you will find, is useless to you. It cites equations at the bottom but doesn't give a source and doesn't give you the assumptions under which it works, so there's no telling if the calculator can handle compressible flows or not.

 

[pranj5]

If this is your attitude, then this thread should be closed right now because you obviously don't want to learn. The concept of choked flow is obviously not very well known because you obviously don't have a clue what that concept should even apply in the case you are trying to discuss here (hint: your flow is choked! You need to understand why and how you can tell).

Seems that you have considered that whenever a gas will be released through an orifice, the flow will be choked. I just can't understand how it can be. There may be scenarios when the flow will be choked, but I just can say that that will not be the case everytime.

That calculator, I think you will find, is useless to you. It cites equations at the bottom but doesn't give a source and doesn't give you the assumptions under which it works, so there's no telling if the calculator can handle compressible flows or not.

The calculator says about air which is a compressible fluid.

 

[boneh3ad]

Seems that you have considered that whenever a gas will be released through an orifice, the flow will be choked. I just can't understand how it can be. There may be scenarios when the flow will be choked, but I just can say that that will not be the case everytime.

I never said it would be choked every time. I said that you need to understand when a flow will be choked, then determine if your flow is choked, and then determine the velocity. In your case, given the pressures you cited, your flow will be choked. It is clear to me that you don't actually understand choked flow as you claim.

The calculator says about air which is a compressible fluid.

Air is a compressible medium. That does not mean a flow of air is a compressible flow. For example, Bernoulli's equation can be applied to the flow of air if it is slow enough, and therefore behaves incompressibly. On the other hand, if it is moving fast enough, then Bernoulli's equation cannot be used. It's still air, but the situation in the flow changes.

Have you ever taken a fluid mechanics course? It seems you have never taken a compressible flow/gas dynamics class, but what about basic level fluids?

 

[russ_watters]

Why should I waste me time?

You shouldn't - and you shouldn't waste our time either. Thread locked.