Pressure measurement

• Altimeter
• Barometer
• Depth gauge
• MAP sensor
• Pitot tube
• Sphygmomanometer

Hydrostatic gauges (such as the mercury column manometer) compare pressure to the hydrostatic force per unit area at the base of a column of fluid. Hydrostatic gauge measurements are independent of the type of gas being measured, and can be designed to have a very linear calibration. They have poor dynamic response.

Piston-type gauges counterbalance the pressure of a fluid with a spring (for example tire-pressure gauges of comparatively low accuracy) or a solid weight, in which case it is known as a deadweight tester and may be used for calibration of other gauges.

The difference in fluid height in a liquid-column manometer is proportional to the pressure difference: ${\displaystyle h={\frac {P_{a}-P_{o}}{g\rho }}}$

Ring balance manometer

Liquid-column gauges consist of a column of liquid in a tube whose ends are exposed to different pressures. The column will rise or fall until its weight (a force applied due to gravity) is in equilibrium with the pressure differential between the two ends of the tube (a force applied due to fluid pressure). A very simple version is a U-shaped tube half-full of liquid, one side of which is connected to the region of interest while the reference pressure (which might be the atmospheric pressure or a vacuum) is applied to the other. The difference in liquid levels represents the applied pressure. The pressure exerted by a column of fluid of height h and density ρ is given by the hydrostatic pressure equation, P = hgρ. Therefore, the pressure difference between the applied pressure P_a and the reference pressure P₀ in a U-tube manometer can be found by solving P_a − P₀ = hgρ. In other words, the pressure on either end of the liquid (shown in blue in the figure) must be balanced (since the liquid is static), and so P_a = P₀ + hgρ.

In most liquid-column measurements, the result of the measurement is the height h, expressed typically in mm, cm, or inches. The h is also known as the pressure head. When expressed as a pressure head, pressure is specified in units of length and the measurement fluid must be specified. When accuracy is critical, the temperature of the measurement fluid must likewise be specified, because liquid density is a function of temperature. So, for example, pressure head might be written "742.2 mm_Hg" or "4.2 in_H2O at 59 °F" for measurements taken with mercury or water as the manometric fluid respectively. The word "gauge" or "vacuum" may be added to such a measurement to distinguish between a pressure above or below the atmospheric pressure. Both mm of mercury and inches of water are common pressure heads, which can be converted to S.I. units of pressure using unit conversion and the above formulas.

If the fluid being measured is significantly dense, hydrostatic corrections may have to be made for the height between the moving surface of the manometer working fluid and the location where the pressure measurement is desired, except when measuring differential pressure of a fluid (for example, across an orifice plate or venturi), in which case the density ρ should be corrected by subtracting the density of the fluid being measured.[7]

Although any fluid can be used, mercury is preferred for its high density (13.534 g/cm³) and low vapour pressure. Its convex meniscus is advantageous since this means there will be no pressure errors from wetting the glass, though under exceptionally clean circumstances, the mercury will stick to glass and the barometer may become stuck (the mercury can sustain a negative absolute pressure) even under a strong vacuum.[8] For low pressure differences, light oil or water are commonly used (the latter giving rise to units of measurement such as inches water gauge and millimetres H₂O). Liquid-column pressure gauges have a highly linear calibration. They have poor dynamic response because the fluid in the column may react slowly to a pressure change.

When measuring vacuum, the working liquid may evaporate and contaminate the vacuum if its vapor pressure is too high. When measuring liquid pressure, a loop filled with gas or a light fluid can isolate the liquids to prevent them from mixing, but this can be unnecessary, for example, when mercury is used as the manometer fluid to measure differential pressure of a fluid such as water. Simple hydrostatic gauges can measure pressures ranging from a few torrs (a few 100 Pa) to a few atmospheres (approximately 1000000 Pa).

A single-limb liquid-column manometer has a larger reservoir instead of one side of the U-tube and has a scale beside the narrower column. The column may be inclined to further amplify the liquid movement. Based on the use and structure, following types of manometers are used[9]

1. Simple manometer
2. Micromanometer
3. Differential manometer
4. Inverted differential manometer

A McLeod gauge, drained of mercury

A McLeod gauge isolates a sample of gas and compresses it in a modified mercury manometer until the pressure is a few millimetres of mercury. The technique is very slow and unsuited to continual monitoring, but is capable of good accuracy. Unlike other manometer gauges, the McLeod gauge reading is dependent on the composition of the gas, since the interpretation relies on the sample compressing as an ideal gas. Due to the compression process, the McLeod gauge completely ignores partial pressures from non-ideal vapors that condense, such as pump oils, mercury, and even water if compressed enough.

Useful range: from around 10⁻⁴ Torr[10] (roughly 10⁻² Pa) to vacuums as high as 10⁻⁶ Torr (0.1 mPa),

0.1 mPa is the lowest direct measurement of pressure that is possible with current technology. Other vacuum gauges can measure lower pressures, but only indirectly by measurement of other pressure-dependent properties. These indirect measurements must be calibrated to SI units by a direct measurement, most commonly a McLeod gauge.[11]

Aneroid gauges are based on a metallic pressure-sensing element that flexes elastically under the effect of a pressure difference across the element. "Aneroid" means "without fluid", and the term originally distinguished these gauges from the hydrostatic gauges described above. However, aneroid gauges can be used to measure the pressure of a liquid as well as a gas, and they are not the only type of gauge that can operate without fluid. For this reason, they are often called mechanical gauges in modern language. Aneroid gauges are not dependent on the type of gas being measured, unlike thermal and ionization gauges, and are less likely to contaminate the system than hydrostatic gauges. The pressure sensing element may be a Bourdon tube, a diaphragm, a capsule, or a set of bellows, which will change shape in response to the pressure of the region in question. The deflection of the pressure sensing element may be read by a linkage connected to a needle, or it may be read by a secondary transducer. The most common secondary transducers in modern vacuum gauges measure a change in capacitance due to the mechanical deflection. Gauges that rely on a change in capacitance are often referred to as capacitance manometers.

Membrane-type manometer

The Bourdon pressure gauge uses the principle that a flattened tube tends to straighten or regain its circular form in cross-section when pressurized. (A party horn illustrates this principle.) This change in cross-section may be hardly noticeable, involving moderate stresses within the elastic range of easily workable materials. The strain of the material of the tube is magnified by forming the tube into a C shape or even a helix, such that the entire tube tends to straighten out or uncoil elastically as it is pressurized. Eugène Bourdon patented his gauge in France in 1849, and it was widely adopted because of its superior simplicity, linearity, and accuracy; Bourdon is now part of the Baumer group and still manufacture Bourdon tube gauges in France. Edward Ashcroft purchased Bourdon's American patent rights in 1852 and became a major manufacturer of gauges. Also in 1849, Bernard Schaeffer in Magdeburg, Germany patented a successful diaphragm (see below) pressure gauge, which, together with the Bourdon gauge, revolutionized pressure measurement in industry.[12] But in 1875 after Bourdon's patents expired, his company Schaeffer and Budenberg also manufactured Bourdon tube gauges.

An original 19th century Eugene Bourdon compound gauge, reading pressure both below and above atmospheric with great sensitivity

In practice, a flattened thin-wall, closed-end tube is connected at the hollow end to a fixed pipe containing the fluid pressure to be measured. As the pressure increases, the closed end moves in an arc, and this motion is converted into the rotation of a (segment of a) gear by a connecting link that is usually adjustable. A small-diameter pinion gear is on the pointer shaft, so the motion is magnified further by the gear ratio. The positioning of the indicator card behind the pointer, the initial pointer shaft position, the linkage length and initial position, all provide means to calibrate the pointer to indicate the desired range of pressure for variations in the behavior of the Bourdon tube itself. Differential pressure can be measured by gauges containing two different Bourdon tubes, with connecting linkages (but is more usually measured via diaphragms or bellows and a balance system).

Bourdon tubes measures gauge pressure, relative to ambient atmospheric pressure, as opposed to absolute pressure; vacuum is sensed as a reverse motion. Some aneroid barometers use Bourdon tubes closed at both ends (but most use diaphragms or capsules, see below). When the measured pressure is rapidly pulsing, such as when the gauge is near a reciprocating pump, an orifice restriction in the connecting pipe is frequently used to avoid unnecessary wear on the gears and provide an average reading; when the whole gauge is subject to mechanical vibration, the case (including the pointer and dial) can be filled with an oil or glycerin. Typical high-quality modern gauges provide an accuracy of ±1% of span (Nominal diameter 100mm, Class 1 EN837-1), and a special high-accuracy gauge can be as accurate as 0.1% of full scale.[13]

Force-balanced fused quartz Bourdon tube sensors work on the same principle but uses the reflection of a beam of light from a mirror to sense the angular displacement and current is applied to electromagnets to balance the force of the tube and bring the angular displacement back to zero, the current that is applied to the coils is used as the measurement. Due to the extremely stable and repeatable mechanical and thermal properties of quartz and the force balancing which eliminates nearly all physical movement these sensors can be accurate to around 1 PPM of full scale.[14] Due to the extremely fine fused quartz structures which must be made by hand these sensors are generally limited to scientific and calibration purposes.

In the following illustrations of a compound gauge (vacuum and gauge pressure), the case and window has been removed to show only the dial, pointer and process connection. This particular gauge is a combination vacuum and pressure gauge used for automotive diagnosis:

Indicator front with pointer and dial

Mechanical side with Bourdon tube

• The left side of the face, used for measuring vacuum, is calibrated in inches of mercury on its outer scale and centimetres of mercury on its inner scale
• The right portion of the face is used to measure fuel pump pressure or turbo boost and is scaled in pounds per square inch on its outer scale and kg/cm² on its inner scale.

Mechanical details

Stationary parts:

• A: Receiver block. This joins the inlet pipe to the fixed end of the Bourdon tube (1) and secures the chassis plate (B). The two holes receive screws that secure the case.
• B: Chassis plate. The dial is attached to this. It contains bearing holes for the axles.
• C: Secondary chassis plate. It supports the outer ends of the axles.
• D: Posts to join and space the two chassis plates.

Moving parts:

1. Stationary end of Bourdon tube. This communicates with the inlet pipe through the receiver block.
2. Moving end of Bourdon tube. This end is sealed.
3. Pivot and pivot pin
4. Link joining pivot pin to lever (5) with pins to allow joint rotation
5. Lever, an extension of the sector gear (7)
6. Sector gear axle pin
7. Sector gear
8. Indicator needle axle. This has a spur gear that engages the sector gear (7) and extends through the face to drive the indicator needle. Due to the short distance between the lever arm link boss and the pivot pin and the difference between the effective radius of the sector gear and that of the spur gear, any motion of the Bourdon tube is greatly amplified. A small motion of the tube results in a large motion of the indicator needle.
9. Hair spring to preload the gear train to eliminate gear lash and hysteresis

A second type of aneroid gauge uses deflection of a flexible membrane that separates regions of different pressure. The amount of deflection is repeatable for known pressures so the pressure can be determined by using calibration. The deformation of a thin diaphragm is dependent on the difference in pressure between its two faces. The reference face can be open to atmosphere to measure gauge pressure, open to a second port to measure differential pressure, or can be sealed against a vacuum or other fixed reference pressure to measure absolute pressure. The deformation can be measured using mechanical, optical or capacitive techniques. Ceramic and metallic diaphragms are used.

Useful range: above 10⁻² Torr[15] (roughly 1 Pa)

For absolute measurements, welded pressure capsules with diaphragms on either side are often used.

shape:

• Flat
• Corrugated
• Flattened tube
• Capsule

A pile of pressure capsules with corrugated diaphragms in an aneroid barograph

In gauges intended to sense small pressures or pressure differences, or require that an absolute pressure be measured, the gear train and needle may be driven by an enclosed and sealed bellows chamber, called an aneroid. (Early barometers used a column of liquid such as water or the liquid metal mercury suspended by a vacuum.) This bellows configuration is used in aneroid barometers (barometers with an indicating needle and dial card), altimeters, altitude recording barographs, and the altitude telemetry instruments used in weather balloon radiosondes. These devices use the sealed chamber as a reference pressure and are driven by the external pressure. Other sensitive aircraft instruments such as air speed indicators and rate of climb indicators (variometers) have connections both to the internal part of the aneroid chamber and to an external enclosing chamber.

These gauges use the attraction of two magnets to translate differential pressure into motion of a dial pointer. As differential pressure increases, a magnet attached to either a piston or rubber diaphragm moves. A rotary magnet that is attached to a pointer then moves in unison. To create different pressure ranges, the spring rate can be increased or decreased.

The spinning-rotor gauge works by measuring how a rotating ball is slowed by the viscosity of the gas being measured. The ball is made of steel and is magnetically levitated inside a steel tube closed at one end and exposed to the gas to be measured at the other. The ball is brought up to speed (about 2500 or 3800 rad/s), and the deceleration rate is measured after switching off the drive, by electromagnetic transducers.[16] The range of the instrument is 5⁻⁵ to 10² Pa (10³ Pa with less accuracy). It is accurate and stable enough to be used as a secondary standard. During the last years this type of gauge became much more user friendly and easier to operate. In the past the instrument was famous to requires some skill and knowledge to use correctly. For high accuracy measurements various corrections must be applied and the ball must be spun at a pressure well below the intended measurement pressure for five hours before using. It is most useful in calibration and research laboratories where high accuracy is required and qualified technicians are available.[17] Insulation vacuum monitoring of cryogenic liquids is a perfect suited application for this system too. With the inexpensive and long term stable, weldable sensor, that can be separated from the more costly electronics/read it is a perfect fit to all static vacuums.

Generally, as a real gas increases in density -which may indicate an increase in pressure- its ability to conduct heat increases. In this type of gauge, a wire filament is heated by running current through it. A thermocouple or resistance thermometer (RTD) can then be used to measure the temperature of the filament. This temperature is dependent on the rate at which the filament loses heat to the surrounding gas, and therefore on the thermal conductivity. A common variant is the Pirani gauge, which uses a single platinum filament as both the heated element and RTD. These gauges are accurate from 10⁻³ Torr to 10 Torr, but their calibration is sensitive to the chemical composition of the gases being measured.

Pirani vacuum gauge (open)

A Pirani gauge consists of a metal wire open to the pressure being measured. The wire is heated by a current flowing through it and cooled by the gas surrounding it. If the gas pressure is reduced, the cooling effect will decrease, hence the equilibrium temperature of the wire will increase. The resistance of the wire is a function of its temperature: by measuring the voltage across the wire and the current flowing through it, the resistance (and so the gas pressure) can be determined. This type of gauge was invented by Marcello Pirani.

In two-wire gauges, one wire coil is used as a heater, and the other is used to measure temperature due to convection. Thermocouple gauges and thermistor gauges work in this manner using a thermocouple or thermistor, respectively, to measure the temperature of the heated wire.

Ionization gauges are the most sensitive gauges for very low pressures (also referred to as hard or high vacuum). They sense pressure indirectly by measuring the electrical ions produced when the gas is bombarded with electrons. Fewer ions will be produced by lower density gases. The calibration of an ion gauge is unstable and dependent on the nature of the gases being measured, which is not always known. They can be calibrated against a McLeod gauge which is much more stable and independent of gas chemistry.

Thermionic emission generates electrons, which collide with gas atoms and generate positive ions. The ions are attracted to a suitably biased electrode known as the collector. The current in the collector is proportional to the rate of ionization, which is a function of the pressure in the system. Hence, measuring the collector current gives the gas pressure. There are several sub-types of ionization gauge.

Useful range: 10⁻¹⁰ - 10⁻³ torr (roughly 10⁻⁸ - 10⁻¹ Pa)

Most ion gauges come in two types: hot cathode and cold cathode. In the hot cathode version, an electrically heated filament produces an electron beam. The electrons travel through the gauge and ionize gas molecules around them. The resulting ions are collected at a negative electrode. The current depends on the number of ions, which depends on the pressure in the gauge. Hot cathode gauges are accurate from 10⁻³ Torr to 10⁻¹⁰ Torr. The principle behind cold cathode version is the same, except that electrons are produced in the discharge of a high voltage. Cold cathode gauges are accurate from 10⁻² Torr to 10⁻⁹ Torr. Ionization gauge calibration is very sensitive to construction geometry, chemical composition of gases being measured, corrosion and surface deposits. Their calibration can be invalidated by activation at atmospheric pressure or low vacuum. The composition of gases at high vacuums will usually be unpredictable, so a mass spectrometer must be used in conjunction with the ionization gauge for accurate measurement.[18]

Bayard–Alpert hot-cathode ionization gauge

A hot-cathode ionization gauge is composed mainly of three electrodes acting together as a triode, wherein the cathode is the filament. The three electrodes are a collector or plate, a filament, and a grid. The collector current is measured in picoamperes by an electrometer. The filament voltage to ground is usually at a potential of 30 volts, while the grid voltage at 180–210 volts DC, unless there is an optional electron bombardment feature, by heating the grid, which may have a high potential of approximately 565 volts.

The most common ion gauge is the hot-cathode Bayard–Alpert gauge, with a small ion collector inside the grid. A glass envelope with an opening to the vacuum can surround the electrodes, but usually the nude gauge is inserted in the vacuum chamber directly, the pins being fed through a ceramic plate in the wall of the chamber. Hot-cathode gauges can be damaged or lose their calibration if they are exposed to atmospheric pressure or even low vacuum while hot. The measurements of a hot-cathode ionization gauge are always logarithmic.

Electrons emitted from the filament move several times in back-and-forth movements around the grid before finally entering the grid. During these movements, some electrons collide with a gaseous molecule to form a pair of an ion and an electron (electron ionization). The number of these ions is proportional to the gaseous molecule density multiplied by the electron current emitted from the filament, and these ions pour into the collector to form an ion current. Since the gaseous molecule density is proportional to the pressure, the pressure is estimated by measuring the ion current.

The low-pressure sensitivity of hot-cathode gauges is limited by the photoelectric effect. Electrons hitting the grid produce x-rays that produce photoelectric noise in the ion collector. This limits the range of older hot-cathode gauges to 10⁻⁸ Torr and the Bayard–Alpert to about 10⁻¹⁰ Torr. Additional wires at cathode potential in the line of sight between the ion collector and the grid prevent this effect. In the extraction type the ions are not attracted by a wire, but by an open cone. As the ions cannot decide which part of the cone to hit, they pass through the hole and form an ion beam. This ion beam can be passed on to a:

• Faraday cup
• Microchannel plate detector with Faraday cup
• Quadrupole mass analyzer with Faraday cup
• Quadrupole mass analyzer with microchannel plate detector and Faraday cup
• Ion lens and acceleration voltage and directed at a target to form a sputter gun. In this case a valve lets gas into the grid-cage.

Penning vacuum gauge (cut-away)

There are two subtypes of cold-cathode ionization gauges: the Penning gauge (invented by Frans Michel Penning), and the inverted magnetron, also called a Redhead gauge. The major difference between the two is the position of the anode with respect to the cathode. Neither has a filament, and each may require a DC potential of about 4 kV for operation. Inverted magnetrons can measure down to 1×10⁻¹²  Torr.

Likewise, cold-cathode gauges may be reluctant to start at very low pressures, in that the near-absence of a gas makes it difficult to establish an electrode current - in particular in Penning gauges, which use an axially symmetric magnetic field to create path lengths for electrons that are of the order of metres. In ambient air, suitable ion-pairs are ubiquitously formed by cosmic radiation; in a Penning gauge, design features are used to ease the set-up of a discharge path. For example, the electrode of a Penning gauge is usually finely tapered to facilitate the field emission of electrons.

Maintenance cycles of cold cathode gauges are, in general, measured in years, depending on the gas type and pressure that they are operated in. Using a cold cathode gauge in gases with substantial organic components, such as pump oil fractions, can result in the growth of delicate carbon films and shards within the gauge that eventually either short-circuit the electrodes of the gauge or impede the generation of a discharge path.

Comparison of pressure measurement instruments[19]

Physical phenomena	Instrument	Governing equation	Limiting factors	Practical pressure range	Ideal accuracy	Response time
Mechanical	Liquid column manometer	${\displaystyle \Delta P=\rho gh}$		atm. to 1 mbar
Mechanical	Capsule dial gauge		Friction	1000 to 1 mbar	±5% of full scale	Slow
Mechanical	Strain gauge			1000 to 1 mbar		Fast
Mechanical	Capacitance manometer		Temperature fluctuations	atm to 10−6 mbar	±1% of reading	Slower when filter mounted
Mechanical	McLeod	Boyle's law		10 to 10−3 mbar	±10% of reading between 10−4 and 5⋅10−2 mbar
Transport	Spinning rotor (drag)			10−1 to 10−7 mbar	±2.5% of reading between 10−7 and 10−2 mbar 2.5 to 13.5% between 10−2 and 1 mbar
Transport	Pirani (Wheatstone bridge)		Thermal conductivity	1000 to 10−3 mbar (const. temperature) 10 to 10−3 mbar (const. voltage)	±6% of reading between 10−2 and 10 mbar	Fast
Transport	Thermocouple (Seebeck effect)		Thermal conductivity	5 to 10−3 mbar	±10% of reading between 10−2 and 1 mbar
Ionization	Cold cathode (Penning)		Ionization yield	10−2 to 10−7 mbar	+100 to -50% of reading
Ionization	Hot cathode (ionization induced by thermionic emission)		Low current measurement; parasitic x-ray emission	10−3 to 10−10 mbar	±10% between 10−7 and 10−4 mbar ±20% at 10−3 and 10−9 mbar ±100% at 10−10 mbar

• US Navy (1 December 2016). U.S. Navy Diving Manual Revision 7 SS521-AG-PRO-010 0910-LP-115-1921 (PDF). Washington, DC.: US Naval Sea Systems Command. Archived (PDF) from the original on Dec 28, 2016.