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What the DCS/PLC/SCADA sees and calculates in both configurations for your DP flow meter:
Instrument DP range: 0–2500 mm H₂O
Process flow range: 0–105,000 kg/h

Configuration 1: Square Root Extraction at Transmitter (most common modern setup)
→ In this case, DCS/PLC uses linear scaling directly
* Instrument range (DP span): 0–2500 mm H₂O (corresponds to 0–100% flow)
* Process range (flow span): 0–105000 kg/h (maximum flow at 100% DP)
* Configuration: Square root extraction at the transmitter
4–20 mA signal is linear with flow (not DP).
Key relationships:
* Flow (Q) = Process span × (Flow %) / 100
* DP = Instrument span × (Flow % / 100)² * mA = 4 +(16 ×(Flow % /100)) (linear to flow %)

Step-by-Step Example for 50% Flow
1. Flow rate: 105,000 kg/h × (50 / 100) = 52,500 kg/h
2. DP value: 2,500 mm H₂O × (50 / 100)² = 2,500 × 0.25 = 625 mm H₂O
3. mA output: 4 mA + 16 mA × (50 / 100) = 4 + 8 = 12 mA
(In DCS/PLC: Scale mA directly to flow % with no square root.)

Square root at transmitter → mA is linear with flow %
At 0% flow: 4.00 mA → 0 kg/h → 0 mm H₂O
At 25% flow: 8.00 mA → 26,250 kg/h → 156.25 mm H₂O
At 50% flow: 12.00 mA → 52,500 kg/h → 625 mm H₂O
At 75% flow: 16.00 mA → 78,750 kg/h → 1,406.25 mm H₂O
At 100% flow: 20.00 mA → 105,000 kg/h → 2,500 mm H₂O

Configuration 2: Square Root Extraction in the DCS/PLC (linear in field transmitter)
The DP transmitter outputs 4-20 mA linear to differential pressure (standard "linear" or "pressure" mode, no square root enabled).
Result:
mA is proportional to DP %.
4 mA = 0% DP = 0% flow
8 mA = 25% DP → flow = √25% = 50%
12 mA = 50% DP → flow = √50% ≈ 70.7%
16 mA = 75% DP → flow ≈ 86.6%
20 mA = 100% DP = 100% flow
In the DCS/PLC: You must apply the square root function (typically sqrt(input/100) × 100% or equivalent scaling block) to get correct flow %.
Advantages sometimes preferred:
DCS has better/faster computation and easier low-flow cut-off or filtering logic.
Consistent treatment if many loops use the same square root algorithm.
Quick check in field: Apply 50% of the DP span → output should be ~12 mA (but this corresponds to ~70.7% flow in DCS after sqrt).
mA = 4 + (16 × (DP % / 100))
DP % = (Flow % / 100)² × 100
At 0% flow: DP = 2500 × (0)² = 2500 × 0 = 0 mm H₂O
→ DP % = 0% → mA = 4 + 16 × 0 = 4.00 mA
At 25% flow: DP = 2500 × (0.25)² = 2500 × 0.0625 = 156.25 mm H₂O
→ DP % = 6.25% → mA = 4 + 16 × 0.0625 = 5.00 mA
At 50% flow: DP = 2500 × (0.50)² = 625 mm H₂O
→ DP % = 25% → mA = 4 + 16 × 0.25 = 8.00 mA
At 75% flow: DP = 2500 × (0.75)² = 1406.25 mm H₂O
→ DP % = 56.25% → mA = 4 + 16 × 0.5625 = 13.00 mA
At 100% flow: DP = 2500 × (1)² = 2500 mm H₂O
→ DP % = 100% → mA = 4 + 16 × 1 = 20.00 mA

Quick Field Confirmation Test:
Apply a test DP of 625 mm H₂O (25% of your 2500 span):
If the transmitter outputs ≈ 8.00 mA→ it is linear (square root in DCS)
If it outputs ≈12.00 mA→ square root is done in the transmitter (linear to flow)