How Do Subatmospheric Pressures Affect Flow Rates?

A customer’s mass flow meter isn’t measuring correctly at half an atmosphere. What gives? Measuring mass flow under subatmospheric pressures can be challenging because it changes volumetric flow rates. In this post, we examine what exactly happens in these conditions and how you can ensure that your mass or volumetric flow meter is properly sized for your application.

Pressure Effects on Mass and Volume for Static Gases

Pressure is a measure of the force exerted upon a surface. According to the Ideal Gas Law (PV=nRT), as pressure (P) increases, the volume of space that the gas occupies (V) decreases. This happens because gases are compressible, and their molecules get closer to each other as pressure increases. If the pressure decreases, then the molecules get further apart and occupy a greater volume. However, in each case, the number of air molecules within the volume (n, molar mass) remains constant.

Air at 2 atm
Mass: 500 scm3
Volume: 250 cm3

Let’s picture a flexible, non-elastic container like a mylar balloon. We fill it with 500 cm3 of air at atmospheric pressure (1 atm, about 14.696 psia) and standard ambient temperature (25­°C). If we double the pressure to 2 atm, the air molecules get closer together, and the volume is compressed to 250 cm3. If we halve the original pressure to 0.5 atm, the volume doubles to 1000 cm3. If we halve the pressure again to 0.25 atm, the volume increases to 2000 cm3. In each instance, we have neither removed nor added any air, and so the molar mass of air inside the container remains 500 scm3 of air.

Air at 0.25 atm
Mass: 500 scm3
Volume: 2000 cm3

Air at 1 atm
Mass: 500 scm3
Volume: 500 cm3

Line Pressure Effects on Gases in Motion

When air is put into motion, its volume continues to vary with pressure as we have seen above. Doubling the line pressure halves the volumetric flow rate, and decreasing line pressure increases the volumetric flow rate. However, the number of molecules of air that flow (mass flow rate) does not change.

Sizing Flow Meters for Subatmospheric Pressures

Differential pressure-based mass flow meters have internal flow channels that are sized for the highest volumetric flow rates that are expected to pass through them. When these meters are used in subatmospheric applications, they may need to be oversized in order to handle the increased volumetric flow rates.

Take for example an Alicat mass flow meter built for 500 sccm (scm3) at full scale (M-500SCCM-D). If we flow 500 sccm at double the pressure (2 atm), the volumetric flow rate decreases to 250 ccm. This decrease in the actual volume of air flow poses no challenges to flow measurement because the meter can handle twice that amount.

Now, if we intend to flow the same 500 sccm at 0.5 atm, we know that the volumetric flow rate will double to 1000 ccm. Our flow meter sized for 500 sccm is too small; instead, we should use a meter sized for 1000 sccm (M-1SLPM-D). To maintain greatest mass flow resolution, we would specify custom ranges of 500 sccm (mass) and 1000 ccm (volumetric). Similarly, at 0.25 atm the meter would be built for four times the intended mass flow (M-2SLPM-D) and ranged for 500 sccm and 2000 ccm.

Generally speaking, Alicat mass flow meters can be used down to 0.8 atm/11.5 psia without being oversized. We can oversize flow meters for use at pressures as low as 0.2 atm/2.9 psia.

Sizing Flow Controllers for Vacuum and Subatmospheric Pressures

Unlike meters, differential pressure-based mass flow controllers do not need to be oversized for use in subatmospheric conditions. For these applications, we locate the proportional control valve at the downstream side of the controller. This forms a sonic barrier that shields the flow sensor from the volumetric expansion of the gas. In the example below, the measurement head inside the flow controller always sees flow rates at ambient air pressure (1 atm). The gas enters the subatmospheric condition (0.25 atm) and expands only after it passes through the valve. As in the previous examples, the mass flow rate remains constant as the gas transitions from 1 atm to 0.25 atm.