Pressure increase in room connected to cannister

[alibo]

Hello,

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?

 

[edgepflow]

Welcome to PF.

You could probably get a reasonably accurate answer as follows.

If you know the volume of your helium canister, use the perfect gas law to figure out the total mass of helium in the canister. You can use the 'Z' compressibility factor for improved accuracy.

Assume that eventually all this helium will end up in the 24 m^3 room. Find the partial pressure of helium from PV = mRT. Then add Pair + Phelium to get your final pressure.

 

[alibo]

Thanks, that's the solution I hit on in the end!

The next issue is that I want to add a flow restrictor to reduce the pressure in the pipe. The room can evacuate 50m3/hr of gas, which equates to 0.014 m3/s. I want to restrict the flow entering the room to this level to prevent the pressure increasing.

I thought that the Hagen-Poiseuille equation would work, but it appears to be only useful for laminar flow. The Reynold's number for this setup puts it firmly in the turbulent category, so should I use the Darcy-Weisbach equation?

 

[edgepflow]

For your flow restriction, were you going to use an orifice, a valve, or just striaght pipe? Both compressibility and viscous effect will be important.

With your pressure differences, your flow will likely be choked (limited by the speed of sound). For any component, if the downstream pressure drops below about 50% of the inlet pressure, the flow will be choked.

So let me know your arrangement, and we can go from there.

 

[alphy]

Dear researcher,

Thank you for reaching out for guidance. Your approach using the Hagen-Poiseuille equation and the ideal gas law is a good start. However, there are a few other factors that should be considered in your calculations.

Firstly, the flow restrictor may not fail completely, so there will likely still be some restriction in the flow of Helium. This means that the entire 500 bar pressure will not be exerted on the pipe and subsequently on the room. It would be helpful to know the level of restriction in the flow restrictor in order to accurately calculate the pressure increase in the room.

Secondly, the 50m pipe will also have an impact on the pressure increase in the room. The longer the pipe, the higher the pressure drop will be. It would be beneficial to include the length and diameter of the pipe in your calculations.

Lastly, the temperature of the Helium will also affect its pressure. As the gas flows through the pipe and into the room, it will undergo adiabatic expansion and its temperature will decrease. This will result in a decrease in pressure, so it is important to take this into account in your calculations.

In summary, your approach is a good starting point, but it would be helpful to consider the level of restriction in the flow restrictor, the length and diameter of the pipe, and the temperature of the Helium in order to accurately calculate the pressure increase in the room. I would also recommend consulting with a colleague or a specialist in fluid dynamics to ensure the accuracy of your calculations. Best of luck in your research!

Sincerely,