DP Flow Square Root: Check the 4–20 mA Signal at Intermediate Points

First identify what the current represents

A DP-flow loop can send a current linear to differential pressure and calculate flow downstream, or send a current already proportional to calculated flow. Document the configured variable and the calculation location. A display value, HART variable and analogue output must be checked separately; do not infer their mapping from a screen label.

Yokogawa's FieldGuide describes square-root extraction in either the transmitter or the controller, with the operation applied once to the DP-derived value. This is a signal-chain check, not a recommendation for an unverified product feature.

Use a model with explicit limits

For this teaching example, assume zero-based positive DP and flow ranges, constant density and effective flow coefficient, and operation within the primary element's applicable regime. Exclude low-flow transition and cutoff behaviour for the ideal calculation.

Let x = DP / DP_max and y = Q / Q_max. Both are dimensionless fractions. Then y = sqrt(x), or x = y².

• Current linear to DP: I_DP = 4 + 16 × x, in mA.
• Current proportional to flow: I_Q = 4 + 16 × y, in mA.
• If the input current is linear to DP, first obtain x = (I - 4) / 16, then calculate y. Do not take the square root of the current in mA directly.

This is not a complete gas or steam mass-flow calculation. Changing density, discharge coefficient and other process effects need the actual validated model. Offset ranges, reverse flow and device-specific transfer functions require separate treatment.

Build an intermediate-point test sheet

The following values are calculated examples, not WESIVO performance data. Each line states flow fraction, required DP fraction, current linear to DP and current proportional to flow.

• 30% flow: 9% DP; I_DP = 5.44 mA; I_Q = 8.80 mA.
• 60% flow: 36% DP; I_DP = 9.76 mA; I_Q = 13.60 mA.
• 80% flow: 64% DP; I_DP = 14.24 mA; I_Q = 16.80 mA.
• 100% flow: 100% DP; both currents are 20.00 mA.

For a separate check at 16% DP, the ideal flow is 40%. A linear-DP current is 6.56 mA; a flow-proportional current is 10.40 mA. If downstream logic treats the linear-DP input as flow without extraction, it indicates 16%. If it extracts a root from the already flow-proportional input, it indicates about 63.25%. Both errors disappear at the ideal endpoints, so endpoint-only checks can miss them.

Record the check's coverage

An injected current checks the receiving I/O and downstream calculation. Applied DP checks an additional part of the transmitter chain. Neither alone verifies the primary element or proves actual steam flow accuracy. Record the applied quantity, observed current, digital variable, displayed flow, configuration revision and calculation owner.

Near zero, square-root conversion magnifies small DP changes. The cited low-flow note discusses device-specific transition and cutoff behaviour. Record the actual threshold, basis and mode; do not apply a universal cutoff or silently turn negative/fault input into valid zero flow.

For a WESIVO 730E or 780C enquiry, attach the required signal schedule and request confirmation of the ordered output characteristic. The current catalogue is the product reference; this general calculation does not establish built-in square root, compensation or a validated flow system for either model.