Pressure Equalization Calculations

(For a properly formatted version you can download, copy this URL to your browser:
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Two initial conditions add up to a third condition, and each of these conditions is represented mathematically by a constant like PV/T.

The combined gas law is P1V1/T1 = P2V2/T2 = P3V3T3 etc.

The shortcut version, derived from a chain of steps, that pertains to pressure equalization, is:

P1V1/T1 + P2V2/T2 = PV/T for full equalization.

Unbalanced equalization has the same sum constant PV/T but the thermal effects don’t equalize as fast as the pressure effects:

PaVa/Ta + PbVb/Tb = PcVc/Tc + PdVd/Td = PV/T

Once the six values of the initial condition of the two air masses to be mixed are filled in on the equation, the next step is to find the equalized pressure. This is the same for both tank and equalizer. The advantage of the in-tank equalizer is that this pressure is reached quicker in thisway; compression heat becomes a savable quantity.

The next step is to use the adiabatic equation to find the final tank temperature, after unbalanced equalization—not waiting for thermal equalization. The form of the adiabatic equation to use is the one that solves for final temperature in terms of pressure change and the index n = 1.406. The pressure change is known since full pressure equalization is a stopping place.

With final tank temperature known and reflecting adiabatic compression, there is only one more unknown and it can be found using the combined gas laws or preferably the shortcut version derived for mixing problems. This gives final equalizer temperature.

With these instructions and examples shown in the worksheet, anyone can design a miracle machine that compresses air WITH the tank pressure instead of AGAINST IT.

The equalization engine relies on a large difference between the volume of the tank and the equalizer, so with all else being equal, using a smaller equalizer or a larger tank will increase the COP.

COP is the proportion of work made available compared to the work used to make it available. A Coefficient of Performance over 1 indicates success.

Let me know if you have any questions, criticism, suggestions, or improvements that you want to see added to the Pneumatic Options Research Library.

Luther