Pressure, Level and Flow Sensors
Gauge, absolute and differential pressure, level by hydrostatic, ultrasonic and radar methods, and flow by differential pressure, magnetic and vortex meters.
Pressure: types and units
Pressure is force per area. Three kinds are measured: gauge pressure (relative to the atmosphere, the most common), absolute pressure (relative to a perfect vacuum, needed for altitude, vacuum and gas calculations) and differential pressure (between two points, used for flow, filters and level in a closed tank).
| Unit | In one bar | Notes |
|---|---|---|
| kPa | 100 kPa | SI-derived; 1 Pa = 1 N/m² |
| psi | 14.50 psi | Pounds per square inch; psig is gauge, psia absolute |
| mmHg (torr) | 750 mmHg | Vacuum and medicine |
| inH2O | 401.5 inH2O | Low pressures and air flow |
| Atmosphere | 0.987 atm | Standard atmosphere is 1.01325 bar |
Pressure sensors and installation
- Piezoresistive (strain-gauge) sensors bond strain gauges to a steel or silicon diaphragm and measure the bridge output (see Force, Load Cells and Vibration). They are the standard for 0.1 to 1000 bar, with accuracies of 0.1 to 0.5 percent.
- Capacitive sensors measure the change in capacitance of a diaphragm; they are excellent at low pressures and for differential measurements.
- Piezoelectric sensors respond only to changes of pressure (dynamic), used for combustion, blast and vibration.
- Pressure switches give an on/off output at a set pressure with an adjustable hysteresis (see Sensor Basics and Selection).
- Ratings: the working range, the overpressure (the most that can be applied without a lasting change) and the burst pressure. Choose a range about 1.5 times the maximum working pressure, and an overpressure rating well above any surge or water hammer.
- Process media: wetted materials must suit the fluid (stainless steel, Hastelloy, ceramic). For viscous, hot, corrosive or hygienic media use a diaphragm seal with a fill fluid, or a flush diaphragm.
- Install it right: mount above a liquid line so that air bubbles escape, below a gas line so that condensate drains, and with a snubber or a damper if there are pulsations. Keep the impulse line short; trapped air or a plug of solids in the line gives a slow or false reading.
- Zero and orientation: a sensor can read a small error if mounted in a different orientation from the one it was calibrated in (the weight of the fill fluid); re-zero it after mounting.
- Temperature: check the compensated temperature range, and use a cooling element (a siphon or a pigtail) for steam.
Level measurement
| Method | Principle | Strengths | Limits |
|---|---|---|---|
| Hydrostatic (pressure) | The pressure at the bottom is ρ g h | Simple, robust, cheap; works in many tanks | Needs the density; the tank vent and the temperature matter |
| Ultrasonic (top-mounted) | Time of flight of sound to the surface | Non-contact, no moving parts | Foam, vapor, dust, a blocked path, the dead zone, and the temperature (see Proximity Sensors) |
| Radar (free-space, 26 or 80 GHz) | Time of flight of a microwave pulse | Not affected by temperature, vapor or pressure, very accurate | Costlier; needs a clear beam path; low-reflection liquids |
| Guided-wave radar | A pulse travels down a probe to the liquid | Works in vessels with internals, foam and interfaces | Build-up on the probe; the length of the probe |
| Float and magnetic float | A float rises with the liquid, with a magnet or a lever | Simple, reliable, switches or continuous | Moving parts, sticking with sludge |
| Capacitance probe | The capacitance between the probe and the tank changes with the level | No moving parts, continuous or point | Needs a stable dielectric; build-up |
| Vibrating fork (point level) | A tuning fork stops vibrating when covered | Independent of density, foam, build-up | Point level only |
| Load cells on the tank | Weigh the tank and compute the level | Works for any tank, includes the contents’ mass | Needs a free-standing tank; the piping loads the cells |
| Optical and conductive probes | Detect the liquid at the probe tip | Cheap point-level switches | Limited to clean or conductive liquids |
Hydrostatic level from pressure
The pressure at the bottom of a liquid column is P = ρ × g × h, with ρ the density (kg/m³), g = 9.81 m/s² and h the height (m), in pascals. A pressure transmitter at the bottom of an open tank gives the level directly; in a closed tank a differential sensor subtracts the pressure above the liquid.
Worked example: a 3 m water tank
- Water (ρ = 1 000 kg/m³) at h = 3.0 m: P = 1 000 × 9.81 × 3.0 = 29 430 Pa = 29.4 kPa = 0.294 bar. A 0 to 0.5 bar sensor suits it, using 59 percent of the range.
- Resolution: 0.1 percent of the 0.5 bar range is 0.001 bar, equal to 5 mm of water: a 3 m tank is measured to about 5 mm.
- A different liquid: an oil of density 850 kg/m³ gives only 25.0 kPa at the same height. If the transmitter is calibrated for water, the reading is wrong by the density ratio: the same pressure from water of 3 m means 3.53 m of oil. Always set the density.
- Temperature changes the density (about 0.02 percent per °C for water near room temperature) and the level reading with it, which matters for tank gauging and custody transfer.
- Closed pressurized tank: use a differential-pressure transmitter, with the low side connected to the tank top (a dry leg, or a wet leg filled with a reference fluid, with the range suppressed or elevated accordingly).
Worked example: an ultrasonic level sensor
An ultrasonic sensor mounted at the top of a 4.0 m tank measures the distance to the surface: 1.2 m. The level is 4.0 − 1.2 = 2.8 m. The sensor’s blind distance (for example 0.35 m) means the tank cannot be filled above 3.65 m as measured by it: mount it high enough, and set the high-level alarm with a separate switch.
Choosing a level sensor
| Situation | Good choice | Why |
|---|---|---|
| Clean water, an open tank, low cost | Submersible or bottom-mounted pressure sensor | Simple and stable |
| Foaming, steam or vapor above the liquid | Guided-wave radar or a pressure sensor | Unaffected by the layer above |
| Corrosive or hygienic | Radar (non-contact) or a flush diaphragm sensor | No dead space to clean |
| Solids and powders | Radar, ultrasonic, or load cells | Continuous measurement of the pile |
| A simple high or low alarm | A float, fork or capacitive switch | Cheap and reliable |
| A very accurate measurement (custody transfer) | High-accuracy radar or servo gauges | Accuracy of 1 mm or better |
Flow measurement
Flow is measured as a volume flow (m³/h, L/min) or a mass flow (kg/h). A volume flow is the flow velocity times the area of the pipe, Q = A × v; the mass flow multiplies by the density.
| Type | Principle | Strengths | Limits |
|---|---|---|---|
| Differential pressure (orifice, venturi, pitot) | A constriction creates a pressure drop proportional to the square of the flow | Well established, no moving parts, any clean fluid | Pressure loss; the square-root relation limits the turndown (about 3:1 to 5:1) |
| Magnetic (electromagnetic) | A conductive liquid moving through a magnetic field induces a voltage proportional to the velocity | No obstruction, wide range, any conductive liquid, slurries | Liquid must be conductive (above about 5 µS/cm); not for gas or oil |
| Vortex | A bluff body sheds vortices at a frequency proportional to the velocity | Steam, gas and liquid; no moving parts | Needs a minimum velocity; sensitive to vibration |
| Coriolis | Vibrating tubes twist in proportion to the mass flow | Direct mass flow and density, very accurate | Costly; pressure drop; large sizes are heavy |
| Ultrasonic (transit time or Doppler) | Sound travels faster with the flow than against it | Clamp-on, no contact with the fluid | Needs a clean, uniform pipe wall; accuracy lower |
| Turbine | A rotor’s speed is proportional to the flow | Accurate, fast, cheap for clean liquids | Moving parts, bearings, wear |
| Thermal mass | A heated element cooled by the gas flow | Direct mass flow of gases, low flows | Gas composition affects it |
| Positive displacement | Fixed volumes counted by gears or pistons | Viscous liquids, accurate at low flow | Pressure drop, wear |
Worked example: three flow calculations
- Differential pressure. Flow is proportional to √ΔP. If an orifice gives 25 kPa at full flow, at 50 percent flow the ΔP is only 25 percent of that: 6.25 kPa. At 20.0 percent of full flow the ΔP is just 1 kPa, below the sensor’s resolution: this is why a DP flowmeter works well only above about 30 percent of its range.
- Magnetic flowmeter. Water at 2.0 m/s in a DN50 pipe (inside diameter 50 mm): A = π × 0.05² ÷ 4 = 19.63 cm², so Q = A × v = 14.1 m³/h (236 L/min). The voltage is E = B × D × v = 0.01 T × 0.05 m × 2.0 m/s = 1.0 mV: small, hence the shielded cable and the sensor’s dedicated electronics.
- Vortex. The shedding frequency is f = St × v ÷ d with St ≈ 0.2 and a bluff body d = 15 mm: at 2.0 m/s f = 0.2 × 2.0 ÷ 0.015 = 26.7 Hz. The count of pulses is proportional to the volume that passed.
- Straight pipe: most meters need a straight length before and after (typically 10 pipe diameters upstream and 5 downstream for a DP or vortex meter, less for a magnetic meter) to give a regular velocity profile.
- Full pipe: a magnetic, ultrasonic or Coriolis meter must be full of liquid; install it in a rising section or a low point, never at the top of a pipe where air collects.
- Temperature and pressure compensation convert a volume flow of gas to a standard volume or a mass flow.
- Totalisers and outputs: 4 to 20 mA, pulse, HART or a fieldbus; the transmitter also shows the total.
Choosing a flowmeter
| Fluid | Good choices |
|---|---|
| Clean water, conductive liquids, slurries | Magnetic; ultrasonic for a retrofit |
| Steam and gas | Vortex, DP with temperature and pressure compensation, thermal mass (gas) |
| Oil and non-conductive liquids | Coriolis, turbine, positive displacement |
| Very accurate mass flow, density, concentration | Coriolis |
| Low-cost indication or check | A rotameter (variable-area flow tube) or a paddlewheel |
| Open channels | A flume or weir with an ultrasonic level sensor |
Troubleshooting
| Symptom | Likely cause | Check |
|---|---|---|
| Pressure reading drifts or is wrong at zero | Zero shift (orientation, temperature, overpressure damage) | Vent to atmosphere and re-zero; compare with a calibrator |
| Noisy or oscillating pressure | Pump pulsations, water hammer, a long impulse line | A snubber, a damping setting, a shorter line |
| Slow response | A blocked or air-filled impulse line, a thick fill fluid | Flush and vent the line |
| Level reading wrong when the liquid changes | The density setting, temperature | Set the density; compensate for temperature |
| Ultrasonic level jumps | Foam, an agitator, an obstruction in the beam, a vapor | Move or shield the sensor; try radar |
| Flow reads high or low | Air in the pipe, partly filled pipe, no straight run, a wrong pipe size entered | Full-pipe check, upstream disturbances, parameters |
| Magnetic meter erratic | Poor grounding of the liquid, a low conductivity, electrode fouling | Grounding rings, conductivity, clean the electrodes |
| No flow signal | A dry pipe, a fouled sensor, a wiring fault | Pipe full? The sensor and wires |
Related
- Sensors and Field Devices: the overview of this guide.
- Force, Load Cells and Vibration: the strain-gauge technology inside pressure sensors, and load cells for level.
- Temperature Sensors: temperature compensation of density and flow.
- Sensor Outputs and Wiring: 4-20 mA and HART wiring.
- Material Properties: compatibility of wetted materials.
- Pneumatic and Hydraulic Actuators: pressure in fluid power circuits.
FAQ
What range of pressure sensor should I buy?
About 1.5 times the maximum working pressure, but not much more: the accuracy is a percentage of the full range, so an oversized sensor reads poorly at the normal pressure. Check the overpressure rating against any surges.
Do I need to know the liquid density for a hydrostatic level?
Yes. The pressure depends on the density, so the level reading is only as good as the density you enter, and it changes with temperature and with the product.
Why does my magnetic flowmeter need grounding?
The signal is a few millivolts. The liquid must be connected to the meter’s reference through the grounding rings or electrodes, or electrical noise and stray currents corrupt the reading.
Can I fit a flowmeter anywhere in the pipe?
No: it needs the right straight run, a full pipe and the right orientation. The data sheet’s installation drawing is as important as its specification.
References
- ISA, Instrument Engineers’ Handbook, vol. 1: Process Measurement and Analysis, CRC Press.
- Miller, R. W., Flow Measurement Engineering Handbook, McGraw-Hill; ISO 5167 (differential pressure flowmeters).
- Endress+Hauser, Emerson (Rosemount), Siemens and VEGA application guides for pressure, level and flow.
Last reviewed: October 2026. Formulas and figures are typical; use the manufacturer’s data and the applicable standards for real installations.