Square-Root Extraction: Configure It in the Right Place
A DP flow measurement is nonlinear at birth: the differential pressure grows with the square of flow, so something in the loop must take a square root before the number means flow. The trap is that three devices in a typical chain - the transmitter, the PLC or flow computer, and the SCADA system - can each do it, and a loop where two of them do it, or none, produces readings that look fine at the ends of the scale and lie everywhere else. This page is about putting the extraction in exactly one deliberate place.
Where to Apply Square-Root Extraction in one line: To configure square-root extraction in the right place, trace the signal chain from transmitter to SCADA tag, decide which single device linearizes the DP signal, configure every other device in the chain as linear, and record the decision in the loop documentation. Custody and gas measurement conventionally leave the transmitter linear and let the flow computer apply the full flow calculation; simple monitoring loops often extract in the transmitter. The symptom of getting it wrong is a flow that matches at zero and full scale but disagrees mid-range.
The Rule: Exactly One Square Root in the Chain
The mathematics is unforgiving. Extract once and the signal is proportional to flow. Extract twice and mid-range readings run high - both curves agree at zero and at full scale, so the error hides from the casual checks people actually do, which happen at no-flow and near design flow. Skip extraction entirely and mid-range readings run low with the same deceptive agreement at the endpoints. This is why the failure survives commissioning so often: the loop checks pass at the ends, and the lie lives in the middle where the plant operates.
The background on why DP flow needs the square root at all is covered in square-root extraction for flow. The configuration question this page answers is purely one of placement: transmitter, controller or flow computer, or SCADA - one of them, never two, never zero, and written down.
What You Need
Access and documentation for every link in the chain: the transmitter's output-characterization setting, the PLC, RTU, or flow computer's input configuration for that channel, and the SCADA tag's scaling math. The loop sheet should state where extraction happens; if it does not, that omission is the first finding of the exercise. You are also going to want a way to inject or simulate a known mid-range DP, because mid-range is where placement errors show themselves.
Know the service class before deciding. If the meter run feeds custody transfer or regulatory gas measurement, the flow computer applies the full flow equation - compressibility, temperature, and pressure corrections along the lines of AGA and API methods - and it expects raw, linear DP as its input. In that world the transmitter stays linear as a matter of convention and auditability, and the decision is effectively made for you.
Walk the Chain and Pick the Place
Extracting in the transmitter makes the 4-20 mA signal itself proportional to flow: everything downstream treats it as a plain linear input, indicators on the loop read flow directly, and no downstream device needs to know the measurement was ever nonlinear. That simplicity suits standalone monitoring and simple control loops. Its cost is at the low end: the square root steepens the curve near zero, so tiny DP noise becomes large indicated-flow noise, which is why a low-flow cutoff accompanies extraction wherever it happens.
Extracting in the PLC or flow computer keeps the transmitted signal as raw DP, which preserves the measurement for diagnostics, retains resolution where the DP lives, and matches the custody convention where the computer owns the whole flow calculation. Extracting in SCADA is the last resort - it works arithmetically, but it leaves every device upstream carrying a nonlinear signal that anyone can misread as flow, and it buries a measurement-critical function in tag configuration where instrument techs rarely look. Wherever you extract, configure the other two stages explicitly linear and note the choice on the loop sheet.
Verifying the Result and Common Mistakes
Prove the placement with a mid-range test, because the endpoints cannot catch the error. Inject or simulate a known DP at some middle value and confirm the indicated flow matches the expected value from the flow equation - a double extraction reads distinctly high at mid-scale and a missing extraction distinctly low, while both agree with the truth at zero and full scale. Check the low-flow cutoff too: it belongs logically with the extraction, and a cutoff configured in a device that is not doing the extraction often does nothing.
The recurring mistakes: a replacement transmitter arriving configured square-root where the old one was linear, silently stacking a second extraction on the flow computer's; SCADA tag math applying a square root to a signal the transmitter already linearized; nobody writing the placement on the loop sheet, so every subsequent tech guesses; and validating only at zero and full scale, where the two wrong configurations are mathematically indistinguishable from the right one. A mid-range check and one line of documentation prevent all of them.
Frequently Asked Questions
How do I tell if square-root extraction is being applied twice?
Compare an indicated mid-range flow against the value calculated from the raw DP. Double extraction reads high in the middle of the range while agreeing at zero and full scale, because the fourth-root curve sits above the square-root curve between the endpoints. The confirming check is configuration: walk the transmitter's output characterization, the controller or flow computer channel, and the SCADA tag math, and count the square roots. There should be exactly one.
Where should extraction go for custody transfer measurement?
In the flow computer, with the transmitter configured linear. Custody and regulatory gas measurement uses the full flow equation with compressibility and temperature and pressure corrections per AGA and API methods, and the computer needs raw DP as its input. Extraction in the transmitter would pre-distort that input and break the auditability of the calculation. The transmitter-linear convention is one of the things an auditor will expect to see on the meter run.
What is a low-flow cutoff and why does it belong with the extraction?
The square-root curve is extremely steep near zero, so the tiny DP noise present at no-flow becomes large, jittery indicated flow. A low-flow cutoff forces the flow output to zero below a configured threshold to suppress that noise, and totalizers depend on it to avoid accumulating phantom volume. It belongs in the device doing the extraction because that is where the steepened signal exists; configured elsewhere it may act on the wrong signal or not at all.
Automation services
Need help turning this into a working system?
Merobix integrates SCADA, programs Allen-Bradley and Siemens PLCs, and designs and fabricates industrial control panels.
Meeting requests are reviewed before confirmation.