The high and low-pressure taps of the primary device are fed by sensing lines to a differential pressure (D/P) cell. The output of the D/P cell acts on a pressure to milliamp transducer, which transmits a variable 4-20 ma signal. The D/P cell and transmitter are shown together as a flow transmitter.

The relationship between the differential pressure (^P) and flow rate (Q) are not equal. DP is proportional to the square of the flow rate Q.

To convert the signal from the flow transmitter, (figure 9 above) to one that is directly proportional to the flow-rate, one has to obtain or extract the square root of the signal from the flow transmitter.

The square root extractor is an electronic (or pneumatic) device that takes the square root of the signal from the flow transmitter and outputs a corresponding linear flow signal. Several methods are used in the construction of square root extractors.

Square root extractors are usually current operated devices so they can be connected directly to the 4-20 mA current loop of a flow transmitter. The output of the square root extractor is again a 4-20 mA signal. This signal is directly proportional to the flow-rate in the pipe-work.