Differential pressure accuracy

The error lives in pressure units, set by the URL

A pressure transmitter’s datasheet states its accuracy as a percentage, but the physics behind it is an absolute error in pressure, fixed by the sensor’s upper range limit. A 2000 mbar sensor declared at 0.1 % of URL errs by 2 mbar whether it is calibrated for 2000 mbar or for 200 mbar. Calibrating a narrower span does not shrink the error; it only makes the same error a larger percentage.

The tool therefore works internally in pascals, converts every input from the one global pressure unit chosen on screen, and only converts back at the end. A single unit for all fields is deliberate: mixing bar and mbar between URL and span is the classic thousand-fold mistake.

Electronic dP against the conventional cell

In an electronic dP two independent transmitters sit on the high- and low-pressure taps and the electronics subtract them. Each one errs on its own URL, and because both must be ranged for the full static pressure, that URL is typically much larger than the differential span. The two errors combine — by RSS or linear sum — and the tool reports which sensor dominates. When the contributions are balanced, improving only one sensor buys little.

In a conventional dP a single cell sees only the differential. The base accuracy is declared on the calibrated span, but most datasheets add a turndown rule of the form A[%span] = a + k·TD above a stated limit. Rewritten in pressure units that is a·span + k·URL, and the tool takes the larger of the base accuracy and the rule. Its thermal effect uses the two-term form, one part on URL and one on span. Either way the thermal term is scaled by m = 1 in band mode, or by |T_process − T_ref|/ΔT_ref when the coefficient is declared per degree interval.

From pressure error to level, density and flow

The pressure error only becomes a decision once it is expressed in the measured quantity. For level, h = ΔP/(ρ·g): the error in millimetres is the same at the bottom and at the top of the range, and the liquid density uncertainty enters one for one on top of it. (When a non-contact sensor is chosen instead, the question becomes geometric — see radar level transmitter mounting position.) For density, ρ = ΔP/(g·H): the divisor g·H is small, because H is typically 1–3 m, which makes this the most demanding application — and the static head of the fluid often suppresses a zero far larger than the useful range.

For flow, Q ∝ √ΔP halves the relative error, but ΔP falls with the square of flow. With a conventional cell of 1000 mbar URL calibrated to 250 mbar (0.1 % of span base accuracy, thermal 0.05 % URL + 0.1 % span), the total is 0.79 mbar. Across the range, on an orifice plate with β = 0.65 under ISO 5167-2, the combined flow uncertainty goes 0.69 % at 100 % of Qmax, 0.74 % at 70 %, 0.92 % at 50 %, 1.60 % at 33 % and 2.62 % at 25 %. The transmitter part alone grows from 0.16 % to 2.53 % — the 1/Q² law in numbers. A magnetic flow meter has no square root in its signal, which is why it is the usual alternative when the turndown is wide.

The ISO 5167-2 mode

For an orifice plate (the orifice plate lesson covers the device itself) the tool can break the flow uncertainty into the terms of ABNT NBR ISO 5167-2:2011. u(C) comes from clause 5.3.3.1 as a function of β, with the two arithmetic additions the standard specifies for small pipes and low Reynolds; u(ε) is 3.5·ΔP/(κ·p₁) for gas and exactly zero for liquid, evaluated point by point because it also varies with ΔP. The bore and pipe diameter uncertainties are weighted by sensitivity coefficients derived from the flow equation, 2/(1−β⁴) and 2β⁴/(1−β⁴).

The limits of clause 5.3.1 — d ≥ 12.5 mm, 50 ≤ D ≤ 1000 mm, 0.10 ≤ β ≤ 0.75 and the Reynolds minimum that depends on the tap type — are checked explicitly. Outside them the standard’s uncertainty does not apply and the tool raises an error; with Re_D left blank it reports applicability as not assessed rather than as passed. If u(C) is missing, the budget is incomplete and the verdict is undefined, following the GUM: an unknown term is not a zero term.

What this tool does not cover

The result is reference accuracy plus thermal effect. Static pressure effect, long-term stability, mounting position, power supply effect and, on an electronic dP, the static head error between taps at different elevations are outside it, as are wet-leg and seal effects and the uncertainty of the tap separation H in density service. The tool embeds no manufacturer data: every coefficient is read by the engineer from the instrument datasheet. In flow it does not size the primary element or compute the discharge coefficient itself — only its uncertainty; for that, follow how to size an orifice plate step by step.