An unfortunate consequence of this quadratic relationship is that a pressure-sensing instrument
connected to such a flow element will not directly sense flow rate. Instead, the pressure instrument
will be sensing what is essentially the square of the flow rate. The instrument may register correctly
at the 0% and 100% range points if correctly calibrated for the flow element it connects to, but
it will fail to register linearly in between. Any indicator, recorder, or controller connected to the
pressure-sensing instrument will likewise register incorrectly at any point between 0% and 100% of
range, because the pressure signal is not a direct representation of flow rate.
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 number9, taking the
square-root of the differential pressure signal – which is itself a function of flow squared – yields a
signal directly representing flow.