Flow calculator 4–20 mA

With orifice-plate (and most other DP) flow measurement, differential pressure is proportional to the square of flow: Δp ~ Q². The transmitter measures Δp and transmits it linearly as 4–20 mA, so the signal itself is linear with respect to Q², not Q. Converting back to volumetric flow therefore requires a square root: Q = Q_max · √((I-4)/16). A linear conversion would significantly underestimate flow at low readings and overestimate it in the mid-range — visible above as the gap between the dotted and dashed curves.

At low Δp (the bottom of the range) the measurement carries relatively large noise and sensor inaccuracy. The square-root scale amplifies this further — a small absolute change in Δp near zero causes a large relative change in the calculated flow. This is why a low-flow cut-off is defined: a threshold (typically 3–10% of Q_max) below which the calculated flow is no longer considered reliable, and the transmitter reports and displays it as zero.

The cut-off threshold is specified in % of flow, but the mA scale is linear with respect to Δp = (Q/Q_max)², so converting it to mA requires squaring: I_cutoff = 4 + 16 · (cutoff% / 100)². Below this current, the transmitter reports zero flow — visible in the chart as a vertical jump on the solid curve exactly at I_cutoff.