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

  1. Aug 20, 2015 #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!
  2. jcsd
  3. Aug 20, 2015 #2
    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).

  4. Aug 20, 2015 #3


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    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 .
  5. Aug 20, 2015 #4


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    Hello MS1, welcome to PF :smile: !

    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 !
  6. Aug 21, 2015 #5


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    I would think that maintaining a constant flow could be important for the experiment, implying a regulator should be used.
  7. Aug 22, 2015 #6


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