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I wondered if anyone could provide a bit of guidance.

I have a Helium cannister at 500bar pressure with a flow restrictor supplying Helium at 8 bar pressure to a room of 24m^3 at 1 bar pressure. The Helium flows down a 50m pipe. I want to calculate the pressure increase in the room due to the Helium in the event that the flow restrictor fails and the entire 500bar pressure is exerted on the pipe.

I have used the Hagen-Poiseuille equation to get an expression for the volume flow rate and the pressure drop, however I have not performed these kinds of calculations before and so I am unsure if I am going down the correct path.

My initial thoughts were to take the normal pressure drop between the cannister and the room as 7 bar, then calculate the volume flow rate due to this pressure drop. In a given time of an hour, the pressure in the room should increase from Pair to Pair + Phelium. The pressure of the helium can be calculated using the ideal gas law equation PV=nRT. The process can then be repeated with the higher pressure of 500 bar.

This route seems riddled with holes to me. Is there a more simple/accurate approach to the problem?