Equalization Pressure - Calculation, Explanation & Examples

Описание: Very often we will find two volumes of gas under different conditions. Take an example of a vacuum packing machine which has vented to the atmosphere connected by a valve to a vacuum tank ready to start the next cycle. We want to know when we open the valve what will happen?

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⦿ 00:42 The long route to calculate Equalization Pressure.
⦿ 01:08 Simplifying the process to calculate Equalization Pressure
⦿ 02:11 Central Vacuum Systems

If we open the valve we know that molecules from the higher pressure atmospheric process chamber will flow into the lower pressure vacuum vessel until the pressure equalizes at some middle level. Calculating this equalization point is a very practical application of the ideal-gas law.

The long route is we could use the pressure, temperature, and volume of each container to work out how many gas molecules there are in each chamber. Then we can sum those two moles of gases so we know the total quantity of gas and finally we can take the new volume which is the total size of both containers and calculate the pressure that the full quantity of gas would have if it filled that volume.

Simplifying that process and assuming the temperature remains constant throughout we can reduce the steps down to very simple operation.
P1V1 + P2V2 = P3V3 (Pressure 1 times volume 1 plus pressure 2 times volume 2 equals the total pressure times the total volume).

▸ So if our process chamber is 50 liters vented to atmosphere and the vacuum tank is 2,000 liters volume held at 100 mbar absolute, we can very quickly calculate what the equalization pressure would be.
(1013 x 50) + (100 x 2000) = P3 x 2050
P3 = 122 mbara

In practical terms this arrangement allows the chamber evacuation to happen quickly during a short section of the total cycle time. The vacuum vessel would then be isolated and pumped back down to a 100 mbara while the next pack is being prepared.

Central vacuum systems are designed based on knowledge of the cycle times of the plant machinery. The whole vacuum system pipework must be sized so that the vacuum manifold never equalizes outside of the allowable operating pressure region. Of course, the introduction of variable speed vacuum pumps has made controlling the pressure in central vacuum systems significantly easier in recent years.

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