Instrumentation
Differential Pressure Flow and Square Root Extraction
Flow from a differential pressure signal with square root extraction, including the low-flow cutoff and the resolution penalty near zero.
Calculated reference results
- Flow
- 707.107gpm
- Percent of full scale flow
- 70.71%
- Differential as percent of DP span
- 50.00%
- Flow change per 1% of signal here
- 7.036gpm
The arithmetic
- Normalized signal = (12.000 mA - 4) / 16 = 0.50000
- Flow fraction = sqrt(0.50000) = 0.70711
- Flow = 0.70711 x 1,000.00 = 707.107 gpm
What this does not account for
- Decide where extraction happens, write it on the loop sheet, and verify at 50% of flow. Applying it twice is wrong everywhere except at zero and full scale, which is exactly where people check.
- Square root extraction amplifies noise badly near zero. Without a low flow cutoff, a still pipe reports a wandering trickle and the totalizer accumulates flow that never happened.
- Differential pressure flow accuracy depends on the primary element, the straight run, the fluid density, and the impulse lines. This calculation covers only the signal relationship.
How this is calculated
Differential pressure flow measurement produces a signal proportional to the square of flow, so flow is the square root of the normalized differential multiplied by the full-scale flow. Applying extraction twice, once in the transmitter and again in the controller, gives a reading that is wrong everywhere except at zero and full scale.
Formulas
Flow = sqrt((mA - 4) / 16) x Flow_full_scale
Assumptions and limitations built into this calculator
- Ideal square-law relationship between differential pressure and flow.
- Ignores fluid density compensation, which matters on gas and steam.
- Ignores primary element discharge coefficient and installation effects.
Frequently asked questions
- How do I tell whether extraction is already happening in the transmitter?
- Check the transmitter configuration, with a HART communicator if it has one. Then verify at 50% of flow: if the reading is about 25% of full scale, extraction is being applied twice.
Direct contact
Have a controls question?
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