Back-pressure in a bubbler is one of the many techniques for measuring level. The back-pressure is the head of the liquid. The pressure sensor measures the back-pressure, and the level is inferred from the equation
P=ρgh
Where P is the pressure in the sensor,
ρ is the density of the liquid
g is the acceleration due to gravity and
h is the height of the liquid, i.e. the level, above the bubbler nozzle.
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I don't know what a pneumerastat is, but a critical component in a bubbler that uses air (pneuma) and is a controller (stat) is the constant flow, differential pressure regulator.
The purpose of the constant flow, differential regulator is to regulate a constant flow rate of gas, because the regulated pressure used to create a constant flow rate will then vary with the back pressure or the head pressure at the outlet of the bubbler tube.
The calculation of level faces the same inherent situation as all head pressure level measurements, an inferred level from head pressure, which varies with the density of the fluid; so a specific gravity calculation is needed for correction.