This simulator models a classic orifice-plate DP flow meter: a sharp-edged plate in a flanged pipe run, high and low pressure taps feeding impulse tubing and a three-valve manifold, a DP-sensing transmitter and a current-loop receiver. Adjust actual flow, fluid and geometry properties, manifold and impulse-line condition, and where the square-root extraction happens, then watch the true differential, sensed differential and indicated flow diverge or agree.
• A real-time 3D cutaway of the flanged pipe spool, orifice plate, high/low taps, impulse tubing and supports, three-valve manifold, DP transmitter and receiver, with home view, focus-selected-part, full-enclosure/cutaway toggle, exploded view, auto-rotate, expand and show/hide numbered labels matching a companion diagram. • Ten live controls: actual liquid flow, liquid density, pipe bore, orifice/pipe diameter ratio (beta), fixed discharge coefficient, calibrated full-scale flow (range), a square-root-in-transmitter checkbox, a square-root-in-receiver checkbox, manifold mode (measure differential / equalized sensing ports), and impulse-line condition (healthy / high leg blocked / low leg blocked / high and low lines reversed). • Play/pause, single-step (0.1 s) and larger-step (1 s) time controls, plus a playback-speed selector (10x slow motion, real time, 10x faster, 1 minute per second). • A start/stop trial action and a step-actual-flow action, with a live "what is happening" sequence narrative, operating state, switch-state tokens and a scrollable cell-readings table. • Ten live metrics: actual volume flow, true tap differential, sensed differential, high-port pressure, low-port pressure, DP at calibrated full-scale flow, loop signal current, receiver flow estimate, flow indication error and upstream mean velocity. • A Curves & measurements tab with two charts (true vs. measured DP, and actual vs. indicated flow), the full model equations, and snapshot measurements. • An Experiments tab with four guided scenarios (correct receiver extraction, no square root, double extraction, equalized manifold), a model-verification bench of independent automated checks, and a timestamped event log with a copyable trial report. • A Learn & assess tab with guided lessons, a knowledge-check quiz and a written scope/reference statement.
An orifice plate creates a pressure drop that grows with the square of flow, not linearly with it: for this incompressible, fixed-discharge-coefficient model, ΔP is proportional to Q². That means recovering flow from a measured differential requires taking a square root somewhere in the signal chain — either in the transmitter or in the receiver, but not both and not neither. Skip the extraction entirely and a mid-range flow reads far low; extract it twice and the same flow reads high, because the correction has now been applied in a chain that already linearized the signal once.
The three-valve manifold and impulse tubing sit between the physical taps and the transmitter, and they can silently corrupt the reading before any square-root question even arises: equalizing the manifold drives sensed differential to zero regardless of true flow, and a blocked impulse leg simply freezes at whatever pressure was trapped when the blockage occurred, no longer tracking the live tap pressure.
The equations panel gives the orifice relation Q = Cd·Ao·√[2ΔP/(ρ(1−β⁴))] with Ao = π(βD)²/4, its inverse ΔP = (Q/(Cd·Ao))²·ρ(1−β⁴)/2, and the two-stage scaling from linear DP fraction to a single flow-fraction square root. Changing geometry or density also recomputes the calibration DP at the chosen range flow, so the meter's span moves with the physical setup, not just with the range-flow slider.
The stated scope is explicit about what is left out: this is an incompressible-liquid model with a fixed discharge coefficient, no Reynolds-number correction, no cavitation or compressibility effects, and no installation straight-run modeling. A fixed 2000 kPa upstream baseline is imposed and negative differential clips to zero, since this is a unidirectional meter.
For this fixed-geometry, fixed-discharge-coefficient orifice model, differential pressure is proportional to the square of flow (ΔP ∝ Q²). To recover a flow value that scales linearly with the real process flow, exactly one square-root extraction must happen somewhere in the signal chain — either inside the transmitter or inside the receiver.
Applying no square-root extraction under-reports mid-range flow substantially, because a linear DP signal is being read as if it were already flow. Applying the extraction twice over-reports partial-range flow instead, since the second extraction is applied to a signal that has already been linearized. The simulator's preset experiments show both distortions numerically at 30 m³/h actual flow.
Equalizing the three-valve manifold's sensing ports drives the measured differential pressure — and therefore the indicated flow — to zero, even though actual pipe flow continues unchanged. A blocked high or low impulse leg instead freezes at whatever pressure was present at the moment the blockage occurred, so the transmitter keeps reading a stale, no-longer-representative differential rather than failing to zero.
This is an incompressible-liquid model with a fixed discharge coefficient: it does not include Reynolds-number correction, cavitation, gas compressibility, or the effect of insufficient upstream/downstream straight pipe run. A fixed 2000 kPa upstream pressure is imposed as a baseline, and the meter is unidirectional, so negative differential pressure is clipped to zero rather than modeled as reverse flow.