Through my invistigatiation to a mismatch issue whic occured in my gas plant between two different flow meters, i cam across two different flow compensation formulas configured in our DCS.

The first formula:

F compensated = Flow transmitter readings * Square root(14.7 + Pressure transmitter/ 14.7 + design pressure) * Square root(459.67 + design temperature / 459.67 + temperature transmitter)

The second formulas:

F compensated = Flow transmitter readings * Square root( (0.0931842 * moleculer weight * (14.7 + Pressure transmitter)) / ( Gas compressibility * Gas density * (459.67 + temperature transmitter ) ))

My question is what is the difference between these formulas? and when I should use each one of them? because after using both of them thier results are not matching.