Square Root Extraction – Why DP Flow Is Non-Linear

Understanding the mathematical relationship between differential pressure and flow rate — and how incorrect scaling causes real plant errors.

Why Square Root Is Required

Differential pressure flow measurement follows Bernoulli’s principle:

Flow ∝ √(ΔP)

• ΔP increases with the square of flow
• If flow doubles, ΔP becomes four times
• Therefore, square root must be applied

Without square root extraction, flow reading will be incorrect.

Visual Representation

The relationship is curved — not linear.

Where Square Root Extraction Is Applied

Option 1: In the Transmitter

• Transmitter outputs linear flow signal
• 4 mA = 0% flow
• 20 mA = 100% flow

Option 2: In the DCS / PLC

• Transmitter sends linear DP signal
• DCS performs square root calculation
• Engineering scaling applied afterward

Never apply square root twice.

Common Field Mistakes

• Square root enabled in both transmitter and DCS
• Square root not applied anywhere
• Wrong low/high DP range configuration
• Flow scaled as linear DP

Example – Practical Scenario

Suppose:

• DP range: 0–100 mbar
• Flow range: 0–1000 Nm³/h

If ΔP = 25 mbar:

√(25/100) = √0.25 = 0.5 → Flow = 50% = 500 Nm³/h

Without square root, DCS would incorrectly show 25% flow.

Failure Symptoms in Plant

• Flow looks too low at low DP
• Control valve behaves abnormally
• Flow trend not matching process conditions
• Calibration mismatch between field and DCS

Troubleshooting Logic

1. Check transmitter configuration (linear DP or linear flow)
2. Check DCS block configuration
3. Confirm only one square root applied
4. Verify LRV and URV match design data

Many flow control issues are scaling configuration errors — not hardware failures.

Related Flow Topics

• Impulse Line Installation
• Manifold Valves & Equalization
• DP Flow Troubleshooting Master Guide