2.2 Flow, Counter, and Motion Sensors

Flowmeters the PE exam actually specifies

Flow questions on PE Control Systems are almost never 'what is Bernoulli's equation.' They are: which meter survives this phase, which one is linear at this Reynolds number, and whether you can afford Coriolis or must live with an orifice plus a density correction. Treat mass flow and volumetric flow as different PVs. An orifice infers volume (actually a discharge through an area) from DP; mass is inferred only after density. Coriolis reports mass from tube twist and density from tube frequency.

DP primary elements

Orifice plates (concentric, eccentric, segmental) are the lowest-capital DP primary. Permanent pressure loss is high (a large fraction of the measured DP does not recover). Uncalibrated discharge-coefficient uncertainty is often on the order of 0.5–2% of rate depending on β, tap type, and International Organization for Standardization (ISO) 5167 / ASME MFC-3M compliance. They need straight run (commonly 10–30 diameters upstream after a disturbance, plus downstream recovery). Square-root extraction is in the transmitter or distributed control system (DCS); at 10% of max flow you have 1% of max DP, so noise and zero error explode—this is why DP flow has poor rangeability unless you stack transmitters or use characterization carefully.

A venturi recovers most of the DP, so permanent loss is low; it handles dirty fluids better than a sharp-edged orifice and costs more to install. A flow nozzle sits between orifice and venturi: common on steam, intermediate recovery, still a DP device. A pitot tube is a point-velocity sensor; a traverse is required if the profile is unknown. An averaging pitot (multiple ports across the pipe) reduces ΔP versus an orifice on large ducts and still needs density for mass. All DP primaries need impulse-line discipline: condensate pots on steam, purges on dirty gas, and no gas trapped in liquid legs.

Magnetic, vortex, turbine, and variable area

A magnetic flowmeter uses Faraday's law (E = B·L·v) in a conductive liquid. Conventional magmeters want roughly ≥ 5 μS/cm (special designs go lower; hydrocarbons and gases are still out). There is essentially no permanent pressure drop, the pipe must be full, and liners (polytetrafluoroethylene (PTFE), rubber, ceramic) are a materials choice. Magmeters do not have a vortex-style high-Reynolds floor; they do have a velocity window (often about 0.3–12 m/s) and fail on empty pipe, gas breakout, and nonconductive fluids.

A vortex meter sheds von Kármán vortices; frequency f = St · v / d with Strouhal number near 0.2 in the linear range. Steam, gas, and many liquids work. Conductivity is irrelevant. The killer is Reynolds number: manufacturers typically want Re on the order of 10,000–20,000 or higher. Below the low-flow cutoff the meter is not 'a little less accurate'—it is off. High viscosity and oversized meters are how you fail a vortex application that looked fine at nameplate flow.

Turbine meters give a pulse train with a K-factor (pulses per gallon or per cubic meter). Accuracy on clean, lubricating liquids can be 0.15–0.5%, which is why they still appear in custody and fuel. Bearings and solids are the failure mode. The pulse train feeds a counter or totalizer—the same hardware idea as a turbine pickup on a pump or compressor shaft.

Variable-area meters (rotameters) are local, inexpensive, must be vertical, and are viscosity- and density-sensitive. Use them for purge indication, not as the custody PV.

Ultrasonic, Coriolis, thermal mass, positive displacement

Transit-time ultrasonic meters compare upstream and downstream flight times. They need an acoustically clean path: little solids, little bubbles, known pipe ID. Doppler ultrasonic meters need scatterers (particles or bubbles); they are the wrong meter on a clean, degassed liquid and the right one on many slurries. Neither requires electrical conductivity. Clamp-on uncertainty is worse than spool-piece uncertainty; do not claim 0.5% on a clamp-on without a calibration story.

Coriolis meters measure mass from oscillating-tube Coriolis force and density from natural frequency. Typical liquid mass accuracy is 0.1% class. Straight-run requirements are usually minimal. Pressure drop can be high on bent-tube designs; straight-tube designs drain and clean better. Gas Coriolis is possible but density (signal) is low—size carefully. Capital cost is several times an orifice run.

Thermal-mass meters infer gas mass from heated-velocity sensors. They are strong on clean gases and weak on changing composition, moisture, and liquids. Positive-displacement (PD) meters (oval gear, rotary) shine on viscous liquids and custody where moving parts are acceptable. They add pressure drop and maintenance.

Counters and motion sensors

A pulse counter totalizes K-factor or pickup pulses for inventory and flow. Debounce, pull-up, and NAMUR (process-industry sensor interface) versus transistor-transistor logic (TTL) levels belong on the loop sheet. Proximity probes (inductive for metals, often in American Petroleum Institute (API) 670 machinery protection); capacitive for some nonmetals) give gap or pass/fail presence. Encoders (incremental or absolute) give shaft angle and, by differentiation, speed. A tachometer or magnetic pickup on a toothed wheel is frequency proportional to speed. A linear variable differential transformer (LVDT) is an AC-excited transformer whose core position (valve stem, damper) sets the secondary voltages—no sliding contact, good for dirty stem position compared with a potentiometer.

Meter versus process (phase, conductivity, accuracy, ΔP)

Worked example: when Coriolis beats orifice plus densitometer

A 2-inch finished acetic-acid line, 12,000 lb/h, 80 °C, liquid, Re ≈ 80,000, customer custody target ±0.2% mass, fluid worth about $1.20/lb. An orifice (β ≈ 0.6) plus DP infers volumetric-like flow; mass needs density. Density of acetic acid moves several percent from 20 °C to 80 °C. A separate densitometer (vibrating element or nuclear) adds capital, another failure mode, and stacked uncertainty. Combined mass uncertainty of 0.5–1% is common if the orifice is not proving-quality and the density loop is ordinary.

A 0.5% mass error is 60 lb/h. Annualized: 60 × 8760 × $1.20 ≈ $630,000/year of measurement money, even before contract penalties. A liquid Coriolis at 0.1% mass, with density from the same tubes, typically costs on the order of $12,000–$25,000 installed versus $3,000–$6,000 for an orifice run. The Coriolis is justified. The same plant's cooling-water header at ±2% for energy balance is not a Coriolis project—use an orifice or magmeter (conductivity of treated water is usually ample).

Reynolds versus conductivity, mag versus vortex. A 2-inch full-pipe water line, 50 μS/cm, flow that swings from Re ≈ 8,000 to 80,000: the magmeter is in conductivity range and does not shut off at Re = 8,000. A vortex meter may be below its linear Re cutoff at the low end even though the high end looks perfect. Do not pick vortex 'because steam plants use vortex' when this service is low-Re liquid. Do not pick a magmeter for dry steam or hydrocarbon condensate with no conductivity.

Motion and exam traps

Specify an LVDT or a qualified positioner feedback for stem position; a cheap pot on a sticky stem is a loop-sheet lie. Do not use a Doppler meter on clean condensate. Do not claim orifice ±0.1% without a proving story. Square-root DP at 10% flow is a noise trap. Thermal mass on a composition-changing vent is a composition trap, not a flow trap.