Calculate pressure of a closed system after a period of gas ingress?!

[chantique84]

Hi I was wondering if there is a formula or spreadsheet kicking about to determine what the pressure (P2) of a closed system may be after a period of gas ingress/injection into the system? I can obtain the information for initial pressure (P1), gas injection rate, diameter of gas inlet/opening, volume of vessel, injection pressure and possibly the gas compressibility. I am interested in approximate numbers so any rough calcs would be sufficient. Any help you may have on this is greatly appreciated!

 

[Bribyk]

How's PV=nRT for a start?

 

[Latexman]

Sounds a lot like homework. R u a student?

Good luck,
Latexman

 

[sailoday28]

If the system is rigid, try the change of internal energy in the system is equal to the sum of product of mass inflow and specific enthalpy of the outside components.

 

[Flareman]

chantique84
There is more than one answer.
You need to look at the rate of inflow. If it holds constant becuase the DeltaP across the control orifice is above critical, then you use PV=nRT.
Once the DeltaP changes as a function of the internal pressure, then you have to go to a logarithmic decay function using Q=Qo * exp(-t/k)
Where Qo = base quantity, t= time and k= time constant (which is based on the initial rate of change) You may need to read up on this.
Good luck
David

 

[sailoday28]

Correction to my last input. As the vessel temperature changes, heat transfer to the surroundings has to be considered.

Simple example: If you puncture an evacuated rigid vessel with say air as the ambient, the vessel will significantly heat up if there is no heat transfer.

 

[willem79]

How about a good old fashioned heat and massbalance?!