Square Root Extraction Calculator
Differential pressure across an orifice, venturi or pitot tube rises with the square of flow. Use this calculator to convert a linear DP signal into flow, or to find the DP and current you should see at a given flow.
- DP % = (8 − 4) ÷ 16 × 100 = 25.00 %
- Flow % = 10 × √25.00 = 50.00 %
- Flow = 50.00 % × 100 = 50 m³/h
DP percent vs flow percent
| DP (% span) | Flow (% max) | Linear signal | Square rooted signal |
|---|---|---|---|
| 0.00 % | 0.0 % | 4.00 mA | 4.00 mA |
| 1.00 % | 10.0 % | 4.16 mA | 5.60 mA |
| 4.00 % | 20.0 % | 4.64 mA | 7.20 mA |
| 6.25 % | 25.0 % | 5.00 mA | 8.00 mA |
| 10.00 % | 31.6 % | 5.60 mA | 9.06 mA |
| 25.00 % | 50.0 % | 8.00 mA | 12.00 mA |
| 36.00 % | 60.0 % | 9.76 mA | 13.60 mA |
| 50.00 % | 70.7 % | 12.00 mA | 15.31 mA |
| 64.00 % | 80.0 % | 14.24 mA | 16.80 mA |
| 81.00 % | 90.0 % | 16.96 mA | 18.40 mA |
| 100.00 % | 100.0 % | 20.00 mA | 20.00 mA |
Why DP Flow Needs Square Root Extraction
Bernoulli's equation shows that flow through a restriction is proportional to the square root of the differential pressure across it. A DP transmitter measures pressure linearly, so its signal must be square rooted before it represents flow.
Flow % = 10 × √(DP %)
DP % = (I − 4) ÷ 16 × 100
Where Q is flow, ΔP is differential pressure, K is a constant for the primary element and I is the transmitter current in mA.
Worked example
A DP transmitter ranged for a flow of 100 m³/h reads 8 mA. DP = (8 − 4) ÷ 16 × 100 = 25 %. Flow = 10 × √25 = 50 %, so the flow is 50 m³/h. Half the flow gives only a quarter of the DP.
Frequently Asked Questions
Where should square root extraction be done, transmitter or DCS?
Either works, but only in one place. Modern practice is usually to keep the transmitter linear (DP) and extract the root in the DCS, which keeps the DP value available for diagnostics.
Why is a low flow cutoff used with square root extraction?
Near zero, a tiny DP error becomes a large flow error: 0.1 % DP noise reads as about 3 % flow. A cutoff of a few percent flow forces the reading to zero and stops the totaliser counting noise.
What is the rangeability of a DP flow meter?
Because of the square law, a 10:1 flow range needs a 100:1 DP range. That is why a single orifice and DP transmitter is normally limited to about 3:1 or 4:1 turndown for good accuracy.
Learn more on the blog
What factors affect the stability of flow meter readings?
A practical, field focused guide on instrumentationblog.in that explains the theory behind this calculator and how engineers apply it on real plants.
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