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

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1. Aug 20, 2015

### 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!

2. Aug 20, 2015

### Staff: Mentor

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

3. Aug 20, 2015

### 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 .

4. Aug 20, 2015

### 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)

 well well, three responses in a short time !

5. Aug 21, 2015

### Staff: Mentor

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

6. Aug 22, 2015

### Averagesupernova

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