calculating instantaneous mass flow rate out of air tank

[pgmta4f]

I'm having trouble calculating a mass flow rate out of a pressure vessel at a given instance. I have an air tank at a known volume and temperature at high pressure (>3000psi) connected to a pressure regulator that regulates the pressure down to 100psi on the outlet. I have a process on the 100psi side that consumes a constant, known CFM. My first inclination is to calculate the constant mass flow rate on the outlet side using:

mdot = (rho)(Vdot), where rho = (MolarMass * Pressure)/(R * Temp)
where Vdot=CFM of process, MolarMass=28.96g/mol, and Pressure=100psi (i realize the units don't match...i would convert before calculating)

This mass flowrate would equal the flowrate out of the tank. My problem is that I'm having trouble determining the Temp value after the pressure regulator. I don't think I can use the relationship: T2=T1(P2/P1) because I don't think it can be assumed as a constant volume process due to the end process consuming air and doing work... or can it be assumed that way?

Any help is greatly appreciated.

 

[TD2K]

No, that's not going to give you the right answer.

You need a Mollier chart for air (or nitrogen as air is 78% nitrogen if you can't get one for air). The expansion across the regulator is a constant enthalphy expansion. Take your starting conditions and plot them on the Mollier chart. Follow the constant enthalphy line to your outlet pressure and read off the resulting temperature.

The GPSA data book has Mollier charts as does Perry's Handbook for Chemical Engineers and lots of other sources. You might contact a compressor manufacturer such as Elliott, IR, Atlas Copco, they would have them also. I didn't have much luck finding one on the web.

You could use a process simulator also if you have access to you and the NIST database would also provide you with the necessary data should you want to download it and manipulate it.

 

[sailoday28]

If friction and pipe heat transfer upstream of the pressure regulating valve are being neglected, an approximation for the transient is to assume quasi-steady flow. Conditions in the air tank will be dependent upon heat transfer to the tank air. Further approximations for the heat transfer are: For a very slow process--the air tank is isothermal.
For a fairly rapid process, the air tank is isentropic.
For enthalpy just upstream of the reducing valve, stagnation conditions must be considered. That enthalpy should be reduced by the kinetic energy of the air flowing into the valve.