Fundamentally, pressure-based meters measure kinetic energy density. Bernoulli's equation (used above) relates this to mass density and volumetric flow:
where constant terms are absorbed into k. Using the definitions of density (), molar concentration (), and molar mass (), one can also derive mass flow or molar flow (i.e. standard volume flow):
However, measurements outside the design point must compensate for the effects of temperature, pressure, and molar mass on density and concentration. The ideal gas law is used to relate actual values to design values:
Substituting these two relations into the pressure-flow equations above yields the fully compensated flows:
Q, m, or n are easily isolated by dividing and taking the square root. Note that pressure-, temperature-, and mass-compensation is required for every flow, regardless of the end units or dimensions. Also we see the relations: