# Pressure measurement

Posted 24 Nov 2018 by Nikolay

Pressure is the force applied by gases and liquids due to their weight, such as the pressure of the atmosphere on the surface of the earth or the pressure liquids apply on the bottom and walls of a container.

Pressure units are a measure of the force acting over a specified area. It is most commonly expressed in pounds per square inch (psi), sometimes pounds per square foot (psf), or pascals (Pa or kPa) in metric units.

Pressure = force / area

The bar is a metric unit of pressure, but it is not approved as part of the International System of Units (SI), nevertheless it is one of the most popular pressure units particularly in European countries. It is defined as exactly equal to 100 000 Pa, which is slightly less than the current average atmospheric pressure on Earth at sea level.

There are some basic terms applied to pressure measurements:

Total vacuum–which is zero pressure or lack of pressure, as would be experienced in outer space.

Vacuum is a pressure measurement made between total vacuum and normal atmospheric pressure.

Atmospheric pressure is the pressure on the earth’s surface due to the weight of the gases in the earth’s atmosphere. It dependants on atmospheric conditions and drops above sea level.

Absolute pressure is the pressure measured with respect to a vacuum (pressure compared to zero pressure of empty space or vacuum).

Gauge pressure is the pressure measured with respect to atmospheric pressure.

Differential pressure is the pressure measured with respect to another pressure and is expressed as the difference between the two values. This would represent two points in a pressure or flow system - delta p (Δp).

Density - r is defined as the mass per unit volume of a material, i.e., pound (slug)per cubic foot (lb (slug)/ft3) or kilogram per cubic meter (kg/m3).

Specific weight - g is defined as the weight per unit volume of a material, i.e., pound per cubic foot (lb/ft3) or newton per cubic meter (N/m3).

Static pressure is the pressure of fluids or gases that are stationary or not in motion (Figure 1). Point 1 is considered as static pressure although the fluid above it is flowing.

Dynamic pressure is the pressure exerted by a fluid or gas when it impacts on a surface or an object due to its motion or flow – the dynamic pressure is 2-1.

Impact pressure (total pressure) is the sum of the static and dynamic pressures on a surface or object. Point 2 depicts the impact pressure.

Figure 1. Static, dynamic and impact pressures.

### Pressure measurement

Main pressure measurement units:

1. Pounds per square foot (psf) or pounds per square inch (psi)
2. Atmospheres (atm)
3. Pascals (N/m2) or kilopascal (1000Pa)*
4. Torr = 1 mm mercury
5. Bar (1.013 atm) = 100 kPa

Pressure measuring Instruments

Manometers are good examples of pressure measuring instruments, though they are not as common as they used to be because of the development of new, smaller, more rugged, and easier to use pressure sensors.

U–tube manometers consist of U-shaped glass tubes partially filled with a liquid. When there are equal pressures on both sides, the liquid levels will correspond to the zero point on a scale as shown in Figure 2a. The scale is graduated in pressure units. When a pressure is applied to one side of the U-tube that is higher than on the other side, as shown in Figure 2b, the liquid rises higher in the lower pressure side, so that the difference in the heights of the two columns of liquid compensates for the difference in pressure.

Figure 2. U-tube manometer.

Inclined manometers were developed to measure low pressures. The low pressure arm is inclined, so that the fluid has a longer distance to travel than in a vertical tube for the same pressure change. This gives a magnified scale as shown in Figure 3a.

Well manometers are alternatives to inclined manometers for measuring low pressures using low-density liquids. In the well manometer, one leg has a much larger diameter than the other leg, as shown in Figure 3b. When there is no pressure difference the liquid levels will be at the same height for a zero reading.

Figure 3. Inclined manometer (a). Well tube manometer (b).

An increase in the pressure in the larger leg will cause a larger change in the height of the liquid in the smaller leg. The pressure across the larger area of the well must be balanced by the same volume of liquid rising in the smaller leg. The effect is similar to the balance of pressure and volume in hydraulic jacks.

The basic pressure sensing element can be configured as a C-shaped Bourdon tube, helical Bourdon tube, flat diaphragm, convoluted diaphragm, capsule or a set of bellows.

Figure 4. Basic pressure sensing elements.

Gauges are a major group of pressure sensors that measure pressure with respect to atmospheric pressure. They are used for local indication and are the most common type of pressure-measurement instrument used in process industries. Pressure gauges consist of a dial or indicator and a pressure element. A pressure element converts pressure into a mechanical motion.

Most mechanical pressure elements rely on the pressure that acts on a surface area inside the element to produce a force that causes a mechanical deflection. Most common are Bourdon tubes diaphragms and bellows elements.

Bourdon tubes are hollow, cross-sectional beryllium, copper, or steel tubes, shaped into a three quarter circle. They may be rectangular or oval in cross section, but the operating principle is that the outer edge of the cross section has a larger surface than the inner. When pressure is applied, the outer edge has a proportionally larger total force applied because of its larger surface area, and the diameter of the circle increases. To detect the movement the circle can be mechanically coupled to a pointer, which when calibrated, will indicate pressure as a line of sight indicator, or it can be coupled to a potentiometer to give a resistance value proportional to the pressure for electrical signals. The Bourdon tube dates from the 1840s.

Bourdon tubes can withstand overloads of up to 30 to 40 percent of their maximum rated load without damage, but if overloaded may require recalibration.

Most common are the “C” shaped Bourdon tubes. The tubes can also be shaped into helical or spiral shapes to increase their range. The Bourdon tube is normally used for measuring positive gauge pressures, but can also be used to measure negative gauge pressures. If the pressure on the Bourdon tube is lowered, then the diameter of the tube reduces. This movement can be coupled to a pointer to make a vacuum gauge. Bourdon tubes can have a pressure range of up to 100,000 psi (700 MPa).

Figure 5. “C” type Bourdon tube pressure gage.

- inexpensive
- wide operating range
- fast response
- good sensitivity
- direct pressure measurement

- primarily intended for indication only
- non linear transducer, linearised by gear mechanism
- hysteresis on cycling
- sensitive to temperature variations
- limited life when subject to shock and vibration

A diaphragm is another device that is commonly used to convert pressure into a physical movement. A diaphragm is a flexible membrane. When two are fastened together they form a container called a capsule. In pressure- measuring instruments, the diaphragms are normally metallic. Pressure applied inside the diaphragm capsule causes it to expand and produce motion along its axis. A diaphragm acts like a spring and will extend or contract until a force is developed that balances the pressure difference force.

A diaphragm consists of a thin layer or film of a material supported on a rigid frame. Pressure can be applied to one side of the film for gauge sensing or pressures can be applied to both sides of the film for differential or absolute pressure sensing. A wide range of materials can be used for the sensing film, from rubber to plastic for low-pressure devices, silicon for medium pressures, to stainless steel for high pressures.

The membrane movement can be sensed using a strain gauge, piezoelectric, or changes in capacitance techniques (older techniques included magnetic and carbon pile devices). The deformation in the above sensing devices uses transducers to give electrical signals.

Figure 6. Diaphragm pressure sensor and pressure gauge.

- provide isolation from process fluid
- good for low pressure
- inexpensive
- wide range
- reliable and proven
- used to measure gauge, atmospheric and differential pressure

Capsules are two diaphragms joined back to back (Figure 4). Pressure can be applied to the space between the diaphragms forcing them apart and thus measure gauge pressure. The expansion of the diaphragm can be mechanically coupled to an indicating device. The deflection in a capsule depends on its diameter, material thickness, and elasticity. Materials used are phosphor bronze, stainless steel, and iron nickel alloys. The pressure range of instruments using these materials is up to 50 psi (350 kPa). Capsules can be joined together to increase sensitivity and mechanical movement.

Bellows are similar to capsules, except that the diaphragms instead of being joined directly together, are separated by a corrugated tube or tube with convolutions (Figure 4). When pressure is applied to the bellows it elongates by stretching the convolutions and not the end diaphragms. The materials used for the bellows type of pressure sensor are similar to those used for the capsule, giving a pressure range for the bellows of up to 800 psi (5 MPa). Bellows devices can be used for absolute and differential pressure measurements.

Figure 6. Bellows.

Differential measurements can be made by using two bellows connected mechanically, opposing each other when pressure is applied to them. When pressures are applied to the bellows a differential scale reading is obtained.

The bellows are the most sensitive of the mechanical devices for low-pressure measurements - 0 to 210 kPa.

### Vacuum instruments

Vacuum instruments are used to measure pressures less than atmospheric pressure. The Bourdon tube, diaphragms, and bellows can be used as vacuum gauges, they measure negative pressures with respect to atmospheric pressure.

### Mounting of the pressure instruments

Some basic principles should be considered before installing the pressure instruments.

- Distance between sensor and source should be kept to a minimum.
- Sensors should be connected via valves for ease of replacement.
- Overrange protection devices should be included at the sensor.
- To eliminate errors due to trapped gas in sensing liquid pressures, the sensor should be located below the source.
- To eliminate errors due to trapped liquid in sensing gas pressures, the sensor should be located above the source.
- When measuring pressures in corrosive fluids and gases, an inert medium is necessary between the sensor and the source or the sensor must be corrosion resistant.
- The weight of the liquid in the connection line of a liquid pressure sensing device located above or below the source will cause errors in the zero, and a correction must be made by the zero adjustment, or otherwise compensated for in measurement systems.

### Location of Process Connections

Process connections should be located on the top of the process line for gases, and on the side of the lines for other fluids.

### Isolation Valves

Many pressure devices require tapping points into the process. Isolation valves should be considered between the process fluid and the measuring equipment if the device is required to be taken out of service for replacement or calibration.

Figure 7 . Instrument isolation valves.

### Use of Impulse Lines

Using impulse lines allows the sensor to be mounted away from the process equipment. The pressure is static, so there is no significant pressure loss over the length of the line. An instrument can be mounted in a location based on easier access, away from a hot or dangerous process, or proximity to both ends of a differential measurement.
Impulse piping should be as short as possible. Instruments in gas applications should be self draining. Self draining can be achieved by sloping the lines towards the process to avoid trapping condensables and liquids. Instruments used in liquid and condensable applications should be self-venting. Self-venting is performed by sloping the lines towards the instrument to avoid trapping gas.
If solids can accumulate in the impulse line, tees and plug fittings should be installed in the place of elbows to allow for “rodding” of plugged lines.

Figure 8. Impulse line.

### Test And Drain Valves

Apart from the isolation valve at the process connection, the need for test and drain valves must be evaluated. If the fluid to be measured is toxic or corrosive, a blowdown valve line should be provided.

For maintenance reasons, all valves must be accessible from either the ground or suitable platforms.

### Sensor Construction

The sensor may need to be isolated mechanically, electronically and thermally from the process medium and the external environment.

Mechanical and thermal isolation can be achieved by moving the sensor away from the process flange. Designs of this type relieve mechanical stress on the cell. This can result in improved static pressure performance and removes the sensor from direct heat.

### Temperature Effects

High temperatures and large temperature variations can affect pressure measuring equipment.

Temperature measurement and correction within the device is another form of compensation for thermal effects, but is the more expensive choice.

### Calibration

Pressure-sensing devices are calibrated at the factory. In cases where a sensor is suspect and needs to be recalibrated, the sensor can be returned to the factory for recalibration, or it can be compared to a known reference.

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