Orifice Explorer — the Square-Root Trap

1 · The meter run

PIPE BORE D BETA RATIO β = d/D FULL-SCALE FLOW Q_max (URV) DENSITY ρ

2 · The operating point & the transmitter

ACTUAL FLOW (% of full scale) DP MEASUREMENT ERROR (% of DP span) UPSTREAM FITTING STRAIGHT RUN AVAILABLE UPSTREAM

—% FLOW ERROR AT THIS FLOW

Q ∝ √ΔP ⇒ δQ/Q = ½ · δΔP/ΔP

ORIFICE BORE d

ΔP AT FULL SCALE

ΔP NOW (% FLOW)

DP ERROR vs READING

PERMANENT LOSS

USABLE TURNDOWN (±1 %)

STRAIGHT RUN REQUIRED

DOWNSTREAM REQUIRED

3 · Where does the √ live?

Exactly one square-root extraction may exist in the chain. Either the transmitter outputs a linearised (flow) signal and the DCS block is set to linear, or the transmitter outputs raw DP and the DCS does the extraction. Do it in both and you get:

TRUE FLOW

DCS WOULD DISPLAY

Model notes. Discharge coefficient fixed at C = 0.60 (flange taps, fully turbulent) and expansibility ε = 1, so the gas presets are indicative only — a real calculation iterates C from Reader-Harris/Gallagher at the running Reynolds number and applies ε. Permanent loss uses the ISO 5167-2 relation. Straight-run lengths are indicative values in the spirit of ISO 5167-2 Table 3 (zero-additional-uncertainty column); always work from the current standard, and remember ISO allows half those lengths at the price of an extra 0.5 % uncertainty.