Free Airs Volume Values Under Pressure

The Rule Behind the Free Air Volume Under Pressure Table

The whole table follows one relation at constant temperature: the free air volume under pressure equals the free volume multiplied by atmospheric pressure and divided by the absolute pressure it is compressed to. Written out, V = V_free × 1.013 / (p + 1.013), with p the gauge reading in bar. Take 1000 dm³ of free air at 7 bar: 1000 × 1.013 / 8.013 gives 126.4 dm³, which is the figure in the 7 bar column. The atmospheric value used throughout is 1.013 bar rather than a rounded 1 bar, which is why the free air volume under pressure figures sit slightly above a simple division by eight.

Gauge Pressure Is Not Absolute Pressure

The most frequent mistake when working out free air volume under pressure by hand is to divide by the gauge reading. A line at 7 bar is at 8.013 bar absolute, and dividing by 7 instead of 8.013 overstates the compressed volume by about 14 %. Every column heading in this table is a gauge pressure, as it would be read on the receiver, so the conversion to absolute is already built into the free air volume under pressure figures.

The Table Is Isothermal

Compression heats air, and hot air takes more space. The free air volume under pressure values here describe air that has been compressed and then allowed to return to ambient temperature, which is what has happened in a receiver a few minutes after the compressor stops. Immediately at the compressor discharge the volume is larger and these figures do not apply. For receiver and pipe sizing the isothermal values are the right ones, because the air is nearly always used long after it has cooled.

Sizing an Air Receiver

A receiver is sold by its physical volume, but what matters in service is how much free air it gives up between the cut-out and cut-in pressures of the compressor. Reverse the free air volume under pressure relation for that: a 500 dm³ receiver falling from 7 bar to 6 bar releases 500 × (7 − 6) / 1.013, roughly 494 dm³ of free air. That is the buffer available to cover a short peak before the compressor has to start, and it is the honest way to compare two receiver sizes.

Pneumatic Actuators and Valve Duty

The same conversion sizes the supply to a pneumatic valve actuator. A double-acting actuator with a swept volume of 10 dm³ working at 6 bar draws 10 × 7.013 / 1.013 of free air per stroke — about 69 dm³ — and twice that for a full open-close cycle. Multiplying by the number of cycles per hour turns the free air volume under pressure figures straight into a compressor duty, which is the number that decides whether an existing plant can carry another automated valve.

Stored Air Is Stored Energy

The right-hand columns are also a safety note. A 500 dm³ receiver at 7 bar holds close to 4000 dm³ of free air, and that expansion happens in an instant if the vessel fails or a joint is broken while still under pressure. Depressurise and lock off before opening any connection: the free air volume under pressure figures describe exactly how much air is waiting to escape.

Where the Table Ends

The columns stop at 7 bar because that is where most industrial systems work. Above roughly 10 bar air stops behaving quite like an ideal gas and the real free air volume under pressure falls a few per cent below the simple calculation; by 30 bar the gap is large enough that compressibility factors are needed. Across the 4 to 7 bar range covered here the ideal relation is accurate to well under one per cent, so the table can be treated as exact for plant work. Below 4 bar the same formula still holds — at 2 bar gauge, for instance, the free volume is divided by 2.97.

Moisture Leaves the Air on the Way In

Compression also squeezes out water. Free air at 20 °C and 70 % relative humidity carries around 12 g of water in every cubic metre, and most of it condenses as soon as that air is compressed and cooled in the receiver. The free air volume under pressure figures are volumes of air only, so the litres of condensate drained every day are additional to them — which is why a receiver needs a working drain and a slope on the take-off, not just the correct volume.

Reading It with the Capacity Table

Volume and flow are different questions. Once the required free air volume under pressure is known, the compressed air pipe capacity table gives the pipe size that can actually deliver it, and the recommended pipe flow velocity bands keep that line at a speed the system can live with. A receiver sized correctly behind an undersized main still starves the tool.