Pressure compensation

absolute compares to a vacuum, the pressure of a vacuum never changes.
gauge compares to the ambient, the pressure of ambient will change.

Your formula is better written as:
P_gauge = P_absolute - P_ambient

ambient is the same as atmospheric.

There are two topics running in this thread: (1) how to set up an instrument per the manufacturer's instructions, and (2) how direct process measurements are used to compute a derived measurement.

In the case of #1, regarding the Endress & Hauser Prowirl 200 vortex flowmeter, one can purchase application options such that the instrument will compute derived measurements from multiple inputs. For the derived measurement to be accurate (within capability of the instruments and estimation technique), the instrument must be set up to correctly convert those external inputs to values used by the estimation technique. This is where it is essential for the external scaling and units to be agreed upon by the producer (pressure transducer) and consumer (enhanced flow meter).

The second topic seems related to computing derived measurements -- in this case mass flow. Since the Prowirl 200 is a vortex flowmeter, its base measurement is volumetric (actual) flow. Using external inputs such as temperature and pressure, it will compute estimates for values such as standard flow, mass flow, and energy flow. These estimates are based on industry standards, using equations requiring the external inputs. The equations will use measurements in engineering units based on the standard, and may require an internal conversion (e.g., psig to psia) to match the standard. So the manufacturer's choice of external input units is somewhat arbitrary as long as the values are internally converted consistent with the expression of the standard.

In the case of mass flow of steam, the Prowirl 200 specifies that it uses the IAPWS-IF97/ASME standard. Further investigation down this path will show that fluid density is the critical requirement, and depends on temperature and pressure (if superheated).

Mispeld is correct. Here is the theoretical basis.

Most flow meters actually measure velocity. Multiply by pipe area and you get volumetric flow rate. Multiply that by specific weight or density and you get mass flow rate. For many applications that is what you need to know for process monitoring.

Boyles Law and Charles Law state that for a given mass, the volume and density is a function of both temperature and pressure. Hotter makes the mass take up more room, high pressure makes the mass take up less room. The ratio of volume and density is determined by the ratio of pressure and temperature.

BUT, these ratios must be based on absolute values, not arbitrary mid-range ones. Ordinary temperature, assuming °C, is relative to a randomly chosen repeatable point like the freezing of water. Ordinary gauge pressure is relative to a randomly chosen repeatable point, the average barometric pressure at sea level. If you used a different point for the basis you'd get different ratios - for example using °F instead of °C.

The answer is to use absolute values for all ratio calculations. For temperature, the basis is absolute zero. For pressure, the basis is a full vacuum.

Thank you guys for clearing that up for me. Greatly appreciated