How long will it take for a gas cylinder to empty?

[Infinity_a]

The main aim of my question is to find time taken by gas filled tank while emptying (from full to zero) it into atmosphere?
I require a set of equations which might be used in the calculation of such a situation.

Known parameters are:
1. Pressure inside the gas tank.
2. Dimension and shape of the gas tank.
3. Temperature in and outside the gas tank.
4. Volume of gas inside the gas tank.
5. Density of gas

Assumptions that can be made is:-
1. The gas tank is cylindrical in shape.
2. The valve is located exactly at the bottom of the gas tank (height of the valve from the bottom is zero).
3. The valve is completely open without any regulators( etc.) in the valve.
No regulation is being made to the flow rate, flow rate is not constant.
4. Size of the opening is fixed from which the gas is coming out.

Some ideas that I got regarding this situation are:
1. The above situation will keep taking place until the pressure inside the gas tank gets equal to the atmospheric pressure.
2. The flow rate of the gas coming out of the gas tank will decrease with the decrease in pressure inside the gas tank.
3. It could be similar to the case of unsteady flow of fluids.

I have tried this equation below as a start but I know this doesn't feel right to calculate the time.
Since we know
Flow rate = Volume / Time
so changing sides
Time = Volume / Flow rate

So please anyone if you have an idea to find out time taken by a gas tank in emptying it into atmosphere it might be helpful. Also if you get anything regarding in the case of liquids ( or fluids) it might be helpful too.

The following things that I have already seen before posting this thread which are not much helpful are:
https://www.physicsforums.com/threads/how-long-will-it-take-for-a-gas-tank-to-empty.828527/
https://www.elgas.com.au/blog/2042-how-do-i-calculate-the-lpg-propane-consumption-per-hour

(this link below was helpful but the calculations were done in case of liquids)
https://www.haywardflowcontrol.com/images/flowcontrol/PDF/VessTime.pdf

 

[mfb]

You'll probably need a numerical simulation. Keep track of the temperature in the tank as it will change over time. The flow rate mainly depends on the pressure difference, the density of the gas inside and of course the size of the opening.

 

[BvU]

Hello $\infty_a\;,\quad$

The following things that I have already seen before posting this thread which are not much helpful

Why weren't they helpful ?

I wonder if you realize this is not a trivial problem. They way you state it isn't very helpful for potential helpers. Are we dealing with a bursting disk scenario, or with a small leak, something completely different ? How accurate do you need the answer (I expect this is not homework; is it hazop or something ?)

Known parameters are:
1. Pressure inside the gas tank.
2. Dimension and shape of the gas tank.
3. Temperature in and outside the gas tank.
4. Volume of gas inside the gas tank.

If they are know to you, why not let us know them too ?
Your 3. (at all $t$ ?) can mean you can assume this is an isothermic process -- ever seen a gas bottle empty full throttle with some violence ?
Why do you specifically state 4. after 2. ?

A gas tank with a valve at the bottom center ?

 

[Infinity_a]

Hello $\infty_a\;,\quad$

I will be answering the situation line by line.

Why weren't they helpful ?
Ans. They weren't helpful because I feel my case is different than the case provided in the above links.

I wonder if you realize this is not a trivial problem. They way you state it isn't very helpful for potential helpers. Are we dealing with a bursting disk scenario, or with a small leak, something completely different ?
Ans. Well its not a leak or burst scenario, its just just the valve we have in the container is open completely without any control in the flow rate.

How accurate do you need the answer (I expect this is not homework; is it hazop or something ?)
Ans. Its regarding a computer program that I'm trying to develop (It is just a small part of a software that I'm trying to make using data science)

If they are know to you, why not let us know them too ?
Ans. It would be helpful if you could assume any value required about the dimensions, pressure, temperature etc that you feel is required
.
Your 3. (at all $t$ ?) can mean you can assume this is an isothermic process -- ever seen a gas bottle empty full throttle with some violence ?
Why do you specifically state 4. after 2. ?
Ans. I'm not sure about the thermodynamic process. I specified the state 4 after 2 because the volume of gas inside the gas tank might not be equal to the actual capacity of the gas tank. I'm not sure about it

A gas tank with a valve at the bottom center ?
Ans. Yeah you can assume that.

P.S.: I'm from a Computer Science engineering background It would be really helpful if I could get to know about the equations required in calculations.

 

[Infinity_a]

You'll probably need a numerical simulation. Keep track of the temperature in the tank as it will change over time. The flow rate mainly depends on the pressure difference, the density of the gas inside and of course the size of the opening.

So how do I find the equations that I need to calculate the time?

 

[BvU]

You google 'orifice flow' or 'orifice plate'

P.S.: I'm from a Computer Science engineering background It would be really helpful if I could get to know about the equations required in calculations.

There are good textbooks. If you are serious, you acquire some domain knowledge .

 

[Infinity_a]

You google 'orifice flow' or 'orifice plate'

There are good textbooks. If you are serious, you acquire some domain knowledge .

Well I would really like to read some books. But I'm not sure what I'm looking for in my current scenario and I don't have several months to spent on this part only :(

I do have these books already.
1. Fluid Mechanics: Fundamentals and Applications Book by John Cimbala and Yungus A. Cengel.
https://g.co/kgs/ajsHZp
2. Gas pipeline hydraulics Book by E. Shashi Menon
https://g.co/kgs/ga4nPK
3. Engineering Thermodynamics by P.K. Nag
https://books.google.co.in/books/about/Engineering_Thermodynamics.html?id=91MZ2ZOb3n8C

 

[BvU]

Well, that's a good start.
So this is homework ? Comp Sci or Comp Phys ? How simple are you allowed to make it ?
What about the links ? Plenty equations !

PF can't be a substitute for a curriculum: we try to help when folks are stuck at some point by asking and hinting.
What stops you from getting started ?

 

[Infinity_a]

Well, that's a good start.
So this is homework ? Comp Sci or Comp Phys ? How simple are you allowed to make it ?
What about the links ? Plenty equations !

PF can't be a substitute for a curriculum: we try to help when folks are stuck at some point by asking and hinting.
What stops you from getting started ?

So this is homework ? Comp Sci or Comp Phys ?

Ans. No its not a homework, Its just a sub-part of the software that I'm working on.

How simple are you allowed to make it ?

Ans. Well as simple as possible but considering the above conditions which I have mentioned in my post.

What about the links ? Plenty equations !

Ans. Well they might be helpful if you could share some. :)

PF can't be a substitute for a curriculum: we try to help when folks are stuck at some point by asking and hinting.

Ans. I really appreciate it but its not a part of my curriculum, its part of the outside curriculum that I'm working on developing a computer program.

What stops you from getting started ?

Ans. I'm confused, I do not know what I'm looking for with respect to my scenario and I do not know the correct path to look for. I also do not know in which domain I should search.

 

[BvU]

Well they might be helpful if you could share some. :)

" You google 'orifice flow' or 'orifice plate' "

The blue words are hyperlinks - just click on them. But you know that.

 

[mfb]

If they are know to you, why not let us know them too ?
Ans. It would be helpful if you could assume any value required about the dimensions, pressure, temperature etc that you feel is required

You will need some approximations, but which approximations are useful depends on your parameters. It doesn't help if we invent parameters suitable for some approximation that cannot be made in your setup.
As one big example: If the opening is large the gas temperature will drop a lot and there won't be much heat exchange with the environment, we can neglect the heat transfer. If the opening is small the gas temperature will keep the temperature of the environment, we can neglect temperature changes. In between it gets complicated.

 

[Nik_2213]

We had a high pressure nitrogen cylinder shed its semi-flexible outlet pipe at the equipment end, a clunky HPLC column packer. The regulator was a high-pressure type, so the big cylinder emptied quite rapidly. We could not get near due to the flailing hose. After that blow-down, the steel nitrogen cylinder and its valve were rather cold...

 

[Infinity_a]

You will need some approximations, but which approximations are useful depends on your parameters. It doesn't help if we invent parameters suitable for some approximation that cannot be made in your setup.
As one big example: If the opening is large the gas temperature will drop a lot and there won't be much heat exchange with the environment, we can neglect the heat transfer. If the opening is small the gas temperature will keep the temperature of the environment, we can neglect temperature changes. In between it gets complicated.

So could you tell me the equations which are used to calculate the time ?

 

[Infinity_a]

" You google 'orifice flow' or 'orifice plate' "

The blue words are hyperlinks - just click on them. But you know that.

I have seen that reply here.

You google 'orifice flow' or 'orifice plate'

There are good textbooks. If you are serious, you acquire some domain knowledge .

I need an equation in which I get a time as output. what is the time taken by this process of emptying the gas tank?
I need some equations to calculate the time.

 

[mfb]

So could you tell me the equations which are used to calculate the time ?

The universal gas law probably: pV=nkT
If your gas is not close to an ideal gas, you might need some modifications. And I can't tell you more because you still refuse to give numbers.
Equations for adiabatic or isothermal compression/expansion maybe. Again it depends on things you refuse to tell.
Equations for heat flow maybe.
Torricelli's law probably.

A combination of these things will give you the change of mass, temperature, pressure and so on in the container, and calculating it step by step in time will tell you when you fall below some given overpressure (it will never reach exactly the same pressure with your calculations, but come arbitrarily close).

 

[BvU]

You are in the wrong restaurant. Here at PF you have to do something yourself. You have been pointed at sets of equations and are now supposed to set up something, anything, by yourself.

The alternative is that you hire someone to do your work for you.

 

[BvU]

Another hint (last one). Study some of the results you get when googling 'draining of a tank'. eq (6) here has a t on its own, on the left hand side of the equation.

I need some equations to calculate the time.

Read the guidelines.

Just in case you don't realize: we do try to help you.

 

[Infinity_a]

You are in the wrong restaurant. Here at PF you have to do something yourself. You have been pointed at sets of equations and are now supposed to set up something, anything, by yourself.

The alternative is that you hire someone to do your work for you.

Thank you for your reply and effort. I am trying my best here.

 

[Infinity_a]

The universal gas law probably: pV=nkT
If your gas is not close to an ideal gas, you might need some modifications. And I can't tell you more because you still refuse to give numbers.
Equations for adiabatic or isothermal compression/expansion maybe. Again it depends on things you refuse to tell.
Equations for heat flow maybe.
Torricelli's law probably.

A combination of these things will give you the change of mass, temperature, pressure and so on in the container, and calculating it step by step in time will tell you when you fall below some given overpressure (it will never reach exactly the same pressure with your calculations, but come arbitrarily close).

Thank you for your reply and effort.