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In gas flow measurement, the density of the gas changes as pressure and temperature change. This change in density can affect the accuracy of the measured flow rate if it is uncompensated. There are two exceptions however where uncompensated density change will not affect the flow measurement:

(1) A direct mass flow measurement made with a mass meter – coriolis or thermal mass.

(2) An actual volumetric flow measurement made by velocity type meters – Vortex, Turbine, Ultrasonic, Positive Displacement etc.

The accuracy of all other types of flow measurements are affected by changes in gas density.

**Relationship between Volume, Density, Pressure & Temperature**

From the real gas law:

Where:

P = pressure of gas

V = volume of gas

T = Temperature

n = number of moles of gas

R = Universal gas constant

Z = Compressibility factor

From the above equation, we determine the volume as:

As can be seen from the above relationship, any change in temperature and pressure will affect gas volume measurements. In terms of gas density, putting V = m/ρ, where ρ = gas density , and n = m/M, where m = mass of gas and W = molecular mass of gas, we have:

As seen above, since gas density is a function of absolute pressure and absolute temperature, the change in density is proportional to the change in pressure or temperature.

How much this change in density affects the flow measurement depends on the type of meter. Velocity type measurements have a direct relationship between flow error and density change. DP flowmeters have a square root relationship between flow error and density change. Consequently, velocity type meters are more sensitive to density variations than DP flow meters.

**How to Correct for Density Changes during Gas Flow Measurments**

Given that in gas flow measurements any change in density affects measurement, it has to be compensated to avoid errors in flow measurements. One way to eliminate this flow measurement error is to continuously measure line pressure and temperature by the aid of a multivariable transmitter. The transmitter measures line pressure and temperature to dynamically compensate for density changes in the flow measurements