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Say I have a gas cylinder filled with nitrogen to some volume at some pressure. On that cylinder I have a regulator so that I get a steady pressure out. I wish to discharge the cylinder. How many hours until that cylinder is exhausted?

I would assume the 'new volume' would be Vl=(Ph*Vh)/Pl. However, I don't understand how the flow rate is determined.

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If pressure is constant, then how do you have two variables, Ph and Pl that represent pressure? There would be two volumes, the difference between them is the volume extracted. Flow rate is volume extracted times density over time. Oh, and your regulator has to do work. –  AlanSE Jul 24 '12 at 17:21
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Based on the initial cylinder volume and pressure, you can calculate the mass of the nitrogen in the cylinder. Now, calculate the mass of nitrogen release in a quantity of time at the pressure / flow rate that the cylinder is discharging. As there is a regulator, this might be constant or close to constant, thus you can simply multiply this loss of mass per unit of time for the time period in which the valve is open. Assuming a constant cylinder volume, you can then subtract this loss of mass from the initial mass and recalculate for pressure.

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