In order that we may have indicators, recorders, and controllers that actually do register linearly with flow rate, we must mathematically “condition” or “characterize” the pressure signal sensed by the differential pressure instrument. Since the mathematical function inherent to the flow element is quadratic (square), the proper conditioning for the signal must be the inverse of that: square root. Just as taking the square-root of the square of a number yields the original number, taking the
square-root of the differential pressure signal – which is itself a function of flow squared – yields a signal directly representing flow