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

[mary_smith_1]

Hello all,
I have an oxygen tank that is 10 L in volume, pressurized at 500 barr (pressure can be adjusted down to 1 barr out of the tube), and I want to 'bubble' the oxygen into a beaker of water. I will simply use a tube (diameter is around 0.5 cm) connected from the tank and with the other end placed in a beaker. I want to know how long it will take for the oxygen tank to run out.
I thought this was a very trivial problem at first but now I see that it's not so. The flow rate is not constant with time because the pressure in the tank will change and the flow is compressible so I can't use Bernoulli's eqn.
I would really appreciate some insight into how I can calculate the time, or at least the flow rate due to the pressure drop.
Thank you!

 

[Chestermiller]

Hello all,
I have an oxygen tank that is 10 L in volume, pressurized at 500 barr (pressure can be adjusted down to 1 barr out of the tube), and I want to 'bubble' the oxygen into a beaker of water. I will simply use a tube (diameter is around 0.5 cm) connected from the tank and with the other end placed in a beaker. I want to know how long it will take for the oxygen tank to run out.
I thought this was a very trivial problem at first but now I see that it's not so. The flow rate is not constant with time because the pressure in the tank will change and the flow is compressible so I can't use Bernoulli's eqn.
I would really appreciate some insight into how I can calculate the time, or at least the flow rate due to the pressure drop.
Thank you!

The main resistance to gas flow in you system lies in the valve. The pressure drop/flow rate relationship for the valve needs to be established (probably experimentally).

Chet

 

[Nidum]

You'll have to have a proper pressure regulator on the Oxygen tank . One that can be set to give required delivery pressure independent of tank pressure .

Gauge on this will show what that pressure is ie 2 bar , 0.5 bar , 0.1 bar or whatever is needed for application . Probably find right setting by trial and error .

Then :

Calculate mass of Oxygen in tank . Calculate mass flow rate of gas through tube using known area , known inlet pressure and (near enough) atmospheric outlet pressure .

Mass in tank/mass flow rate = time to empty .

 

[BvU]

Hello MS1, welcome to PF !

Your "simply using a tube" can't be the whole story. Usually there is some pressure reducer valve on top of a cylinder to prevent unpleasant events. 500 Bar isn't good for bubbling or blowing up balloons.

And then the calculation becomes easy again: you have a little overpressure (a few tens of mBar or less) and your 10 L at 500 Bar delivers about 5000 L at atmospheric pressure.

My estimate is the liquid level above the tube outlet is more determining for the amount of mBars you need for a sensible flowrate than the diameter of the tube.

In the tube you have a pressure drop that you can calculate with the usual tools (Darcy equation, derived from Bernoulli -- sorry for the units in this last link)


[edit] well well, three responses in a short time !

 

[russ_watters]

I would think that maintaining a constant flow could be important for the experiment, implying a regulator should be used.

 

[Averagesupernova]

Although it was not specifically said that there IS a regulator on the tank, this quote:

(pressure can be adjusted down to 1 barr out of the tube),

implies that there is a regulator.