# Basics

Pressure is defined as the force exerted over a unit area. Force may be exerted by liquids, gases, and solids. Pressure is governed by the following equation:

P = F/A

where:

P = Pressure

F = Force

A = Area

# Force Exerted by Liquids

The amount of force a specific volume of liquid in an open tank exerts over a specific area depends on three factors: the height of the liquid above the measurement point, the specific gravity, or weight, of the liquid, and the temperature of the liquid.

If force is measured on the side of the tank, the measurable force exerted on the side of a tank will depend on the height of the liquid above the measuring instrument.

Specific gravity is a reference number that compares the weight of a specific volume of liquid to the same volume of water at 60 Deg. F, and a specific volume of gas at a specific temperature to the same volume of air at the same temperature. Water and air are assigned specific gravity constants of 1. The weight of water at 60 Deg. F is 62.34 pounds per cubic foot. The specific gravity, or mass density, of most liquids is calculated at a standard temperature. If the temperature of the liquid changes, its specific gravity may change. This is because changes in temperature will cause the liquid to expand or contract.

As the temperature of a liquid increases, the liquid expands and becomes lighter per volume. As the temperature of a liquid decreases, the liquid contracts and becomes heavier per volume. Pascal's Law states that when a force is applied to a confined fluid, the force will be transferred undiminished throughout the fluid to all surfaces of the containing vessel.

# Force Exerted by Gases

A gas will exert an equal amount of pressure on all surfaces of the vessel that contains it. Two factors that affect the force a gas exerts are the volume of the vessel and the temperature of the gas.

The relationship between the force exerted by the gas and the volume of the vessel is expressed in Boyle's Law. Boyle's Law states that if temperature is held at a constant, the force exerted by the gas on the walls of a containing vessel varies inversely with the volume of a containing vessel, provided the mass remains unchanged.

The relationship between temperature and the force a gas exerts is expressed in Charles' Law. This law states that if the volume of the vessel holding a gas is constant, the force exerted by the gas on the walls of the vessel will vary directly with the temperature of the gas.

# Units of Measurement

The standard unit of pressure in the English or foot-pounds-second ( FPS ) system is pounds per square inch, or PSI. Once force has been accurately measured, pressure can be determined by dividing the force by the area it is exerted over ( P = F/A ). At sea level, the gases and liquids that make up the atmosphere exert a pressure of approximately 14.696 pounds per square inch. Atmospheric pressure will decrease by about .036 PSI for each 1000 feet of elevation. In some process systems, it may be necessary to know if an indicated pressure includes or excludes atmospheric pressure.

To distinguish this, two specific pressure units are used - pounds per square inch gage, or PSIG, and pounds per square inch absolute, or PSIA. PSIG is reference to atmospheric pressure and the measurement instrument will indicate zero when not connected to the process pressure, with the sensing element exposed to atmospheric pressure. PSIA is referenced to absolute zero. Absolute zero is the pressure measurement when all the pressure exerted by the atmosphere has been removed. A pressure measuring instrument designed to indicate PSIA will read 14.696 pounds per square inch at sea level, when it is not connected to process pressure, and the sensing element is exposed to atmospheric pressure.

Vacuum is often measured in inches of water ( In H2O ) or mercury ( In Hg ). A practically perfect vacuum would be indicated as 407.513 In H2O or 29.9213 In Hg.

# Converting Measurement Units

Pressure measurements may be converted from one unit to another by using charts or by using mathematical formulas. When a process is exposed to pressures below atmospheric pressure, the term "vacuum" is commonly used to indicate the measurement. Vacuum measurements are frequently used in steam systems.

In order to convert measurements between PSIG and PSIA, the value for atmospheric pressure at sea level is added or subtracted to a given measurement.

PSIA = PSIG + 14.7

PSIG = PSIA - 14.7

In addition, PSIG and PSIA measurements can be converted to inches of mercury and inches of water.

In Hg = PSIG x 2.036

In Hg = PSIA x 2.036

In H2O = PSIG x 27.684

In H2O = PSIA x 27.684

# Differential Pressure

Differential pressure is the difference in pressure measurements taken at two related points. It is calculated by subtracting the lower port pressure reading from the high port pressure reading. Differential pressure may be either absolute or gage pressure, as long as both points are measured in the same units.

# Manometers

All manometers operate on the principle that change in pressure will cause a liquid to rise or fail in a tube.

# Basic Manometers

A basic manometer includes a reservoir that is filled with a liquid. The reservoir is usually enclosed with a connection point that can be attached to a source in order to measure its pressure. A transparent tube, or column, is attached to the reservoir. The top of the column may be open, exposing it to atmospheric pressure. Or, the column may be sealed and evacuated. Manometers that have open columns are usually used to measure gage pressure, or pressure in reference to atmospheric pressure. Manometers with sealed columns are used to measure absolute pressure, or pressure in reference to absolute zero. Manometers with sealed columns are also used to measure vacuum.

When a manometer is connected to a process, the liquid in the column will rise or fall according to the pressure of the source it is measuring. In order to determine the amount of pressure, it is necessary to know the type of liquid in the column, and the height of the liquid. The type of liquid in the column of a manometer will affect how much it rises or falls in response to pressure, its specific gravity must be known in order to accurately measure pressure.

Manometers are accurate, they are often used as calibration standards. The shape of the liquid at the interface between the liquid and air in the column affects the accuracy of the manometer. This level is called the meniscus. The shape of the meniscus is determined by the type of liquid used. In order to minimize the errors that result from the shape of the meniscus, the reading must be taken at the surface of the liquid in the center of the column.

The quality of the fill liquid will also affect the accuracy of pressure measurements. The fill liquid must be clean and have a known specific gravity.

# Types of Manometers

A Well Manometer has a glass column that contains the liquid that extends from a well. To measure pressure with this type of manometer, the process is connected to a fitting on the well. A barometer is a well manometer. A barometer has a seal and an evacuated measuring column. this type of manometer detects and measures changes in atmospheric pressure.

A variation of the well manometer is the inclined manometer. This manometer also has a well that contains the liquid and a transparent column. However, on an inclined manometer the tube is mounted at an angle. A small change in pressure will cause greater movement of the liquid in the column.

A U-Tube manometer has a tube bent into the shape of a U and is not connected to a well. Instead, the tub itself is the reservoir. To measure pressure, one leg of the tube is connected to the process and the other leg is left open and exposed to the atmosphere. Pressure is indicated by the amount the liquid that falls in one leg and rises in the other leg. The total movement of the liquid in both legs is the pressure measured by the U-Tube manometer. U-Tube manometers can also be used for vacuum measurements by sealing one leg and connecting the other leg to the process.

A McLeod gage is used as the fundamental standard for measuring vacuum. It measures vacuum by trapping and compressing a volume of gas. A specific volume of mercury is contained in the gage reservoir and the connection point is connected to the vacuum source. When the connection is securely made, the gage is rotated 90 degrees. Measured vacuum is determined by reading the level of the mercury on the scale.

Capacitance manometers use the electrical characteristic of a capacitor to measure pressure.

# Safety

Some types of liquids used in manometers are toxic and can be damaging to the environment. Therefore, when using manometers to measure or indicate pressure, do not connect any manometer to a pressure that has the potential to exceed the range of the manometer. This could cause the liquid to be forced out of the tube. In addition, since the tubes in many manometers are made of glass and can be easily broken, it is important to use care in handling these manometers. If the liquid is accidentally spilled from a manometer, follow your facility's procedures for containing and cleaning hazardous materials.

# Mechanical sensors

Mechanical pressure transducers are devices that convert force exerted by fluids into motion that can be measured to indicate the amount of pressure.

# Bourdon Tubes

There are three common types of Bourdon tubes: C tube, helical tube, and the spiral tube. The most common type of Bourdon tube is the C type. This instrument is an oval tube, shaped to resemble the letter C. One end of the tube is open while the other end is sealed and free to move. The open end is attached to the frame or case of the transducer. Then, the pressure to be measured is applied through the open end. As pressure is applied, the tube will start to straighten slightly. This mechanical response is related to the pressure formula ( P = F/A ). Since the outside surface of the C tube is longer than the inside, the outside has a greater area. Consequently, the force exerted on the outside surface is greater than the force exerted on the inside, causing the tube to straighten. As the tube straightens, the sealed tip will move, providing an indication of pressure changes.

The scales on the dials of some pressure gages include readings below zero. These gages are referred to as compound gages and are often used to indicate vacuum.

A helical tube is an oval tube that is wound into a helix. Its shape resembles a coil. A helical tube pressure element operates on the same principle as the C tube. One end of the tube is closed and is free to move while the other end is open and firmly attached to the transducer case or frame. The pressure to be measured is applied through the open end, causing the tube to try to uncoil. The tip of the tube moves in response to the movement of the coil caused by the pressure. The advantage of the helical tube is that is produces more tip movement than the C tube.

In a spiral tube transducer, the oval tube is wound in a spiral. The major advantage of this type of Bourdon tube is that the tip produces more motion than both C and helical tubes.

# Bellows

A bellows is a cylindrical device that is usually ribbed and very flexible. Bellows are usually made of phosphor, bronze, or brass. A pair of matched bellows can be used to measure absolute pressure or differential pressure. Usually one end of the bellows is attached to the transducer case and the other end if free to move. When pressure is applied to the inside of the bellows, it will expand, causing the free end to move. The movement of the movable end is measured in order to identify the amount of pressure.

# Diaphragms

A diaphragm is a mechanical pressure transducer that is used to detect slight changes in pressure. A diaphragm is a single disk that is exposed to a process. Since process pressure is exerted over a relatively large area, this instrument is more sensitive to small changes in pressure. This principle is based on the basic pressure equation, P = F/A. If a small pressure is exerted over a large area, the force will be relatively large, and will cause the diaphragm to flex. A mechanical device, such as a pin, rod, or bar, is usually connected to the diaphragm so that the amount of flex can be measured in order to determine the amount of pressure exerted. Diaphragm capsules are frequently used as isolation devices.

# Electrical sensors

Electro-mechanical pressure transducer convert the motion produced by mechanical sensing elements into changes in electrical signals.

# The Wheatstone Bridge

One common design of an electrical pressure transducer circuit is the Wheatstone bridge. This configuration has two parallel legs that form a bridge. A voltage source is connected to the bridge so that current will flow through each leg. A typical Wheatstone bridge also has a measuring circuit installed across the bridge. This circuit provides a path for current flow if the bridge is not balanced. The bridge circuit includes four resistors. It is designed so that when the resistance of all four resistors is exactly equal, the current flow through each leg is equal and there is no current flow through the circuit across the bridge. At this point the bridge is balanced. With this design, if the resistance of one of the resistors changes, the current flow through each leg will no longer be equal. This situation creates an imbalance in the bridge. Current will flow through the measuring circuit connected across the bridge. When a Wheatstone bridge is used as a pressure measuring instrument, one of the resistors in the bridge circuit is replaced with a resistance that is connected to a pressure sensing element. If pressure changes, the pressure sensing element will respond to the change in pressure and will change the resistance in the bridge. The change in resistance will cause an imbalance in the bridge circuit. When this happens, the measuring instrument will indicate the pressure change.

# Potentiometric Transducers

This transducer usually utilizes a Wheatstone bridge circuit in which one of the bridge resistors is replaced by a potentiometer. A potentiometer is a wire-wound resistor with a movable slide on it. The slide is usually connected to some type of mechanical pressure sensing element.

# Linear Variable Capacitor Transducers

A capacitor is a device that opposes current flow in an AC circuit. On a linear variable capacitor electric transducer, the distance between the plates is adjusted to detect and indicate changes in process pressure. In this case, the capacitor is connected in a circuit. A meter or system control device is connected to the circuit output to measure the changes in current flow that result from changes in capacitance. One plate of the capacitor remains stationary. The other plate is movable and is connected to a mechanical pressure element, such as a diaphragm.

# Linear Variable Differential Transformer Transducers

Another widely used electrical pressure transducer is the linear variable differential transformer or LVDT. When this device is used to measure pressure, an AC voltage is connected to the primary winding of the transformer. The secondary winding consists of two windings that are connected so that their outputs are at opposite polarities. A movable core is attached to a mechanical pressure sensing device, such as a bellows or diaphragm. If process pressure changes, the mechanical sensing element will move, causing the movable core to move. If an instrument is connected to the voltage induced output of the transformer, it will indicate pressure.

# Variable Inductor Pressure Sensors

In this type of sensor, two coils are wired in opposition to form two legs of an AC bridge. A diaphragm made of a magnetic material is placed between the two coils. Pressure from the measured process is applied to one side of the diaphragm while the other side of the diaphragm is exposed to a reference pressure, such as atmospheric pressure. Changes in process pressure will cause the diaphragm to flex and move toward one of the coils and away from the other. This creates a small air gap between the diaphragm and the coils. As the diaphragm moves, the relative inductance of the coils changes. These changes in relative inductance change the circuit output. Therefore, the circuit output can be measured as pressure.

# Strain Gage Transducers

Strain gages consist of a series of wires that are supported by some type of insulation. The basic principle of a strain gage is that the cross sectional area of the wire will affect its resistance. If the cross sectional area is changed, the wire's resistance will also change. A wire's resistance can be manually adjusted by stretching or straining the wire. The resulting changes in resistance allow strain gages to indicate changes in process pressure.

There are two types of strain gages: unbonded strain gages and bonded strain gages. Unbonded strain gage consists of a stationary member and a movable armature. Both the stationary member and the movable armature have insulated pins that support a series of small wires. These wires are connected so that they will respond to change in pressure. The movable armature of an unbonded strain gage is connected to a mechanical sensing element such as a bellows or a diaphragm. When pressure changes, the mechanical pressure element will move the movable armature to change the tension on the wires in the strain gage. Changing the tension on the wires will change the resistance. In this way, the gage indicates changes in pressure. Bonded strain gages suffer less from long term instability, they are only half as sensitive as unbonded gages.

In bonded strain gages, small wires or pieces of foil are bonded to a piece of insulating material with adhesive, Usually, bonded strain gages have two sets of wires or foil. One set is called the active strain gage element and will be subjected to strain. The other set is the slip, or dummy, element and will not be strained. When used to measured pressure, a bonded strain gage is fastened to some movable part of a mechanical pressure sensing element. Bonded gages are often glued to diaphragms or force beams that will bend or flex when pressure changes. The slip, or dummy, is glued to some part of the pressure element that does not move. The deflection of the diaphragm alters the gage resistance and unbalances an associated bridge. Strain gage transducers are usually part of a bridge circuit, such as the Wheatstone bridge.

# Piezoelectric Transducers

When pressure or strain is applied to crystals such as quartz, rochelle salt, and barium-titanate, the crystals will produce a measurable voltage. This voltage can be monitored to measure pressure. Two types of thermal transfer gages are in wide usage: thermocouple and Pirani gage. The thermocouple gage wire element is made of a fine wire or ribbon heated electrically and immersed in a gas whose pressure is to be measured. The thermal conductivity of the gas varies with pressure in a range of vacuum conditions. The thermocouple gage measures the temperature of the strip with a thermocouple.

The wire element of the Pirani gage is made into an electrical resistance with two wire elements, one of which is sealed in a vacuum as a reference. The two elements are two electrical resistances forming two legs of a Wheatstone bridge.

One type of ionization gage is the hot-cathode ionization gage. In hot-cathode ionization gages, electrons emitted from a cathode move towards a grid. Some of the electrons collide with molecules of the gas whose pressure is to be measured. The gas molecules lose electrons as a result of the collisions, producing positive ions. The remaining electrons are collected on the grid. The positive ions, however, are attracted to the negatively charged collector. Each ion so collected causes a pulse of current to flow in the collector circuit. The number of ions produced depends on the molecular density of the gas. This means that collector current is proportional to gas molecular density, or pressure. The cold-cathode gage consists of an open anode loop between two cathode surfaces with a high voltage impressed between them. A magnetic field deflects electrons from traveling directly to the anode and causes them to oscillate among the magnetic lines of flux. With the increased mean free path, a significant number of ionizing collisions with gas molecules occur. The charge on the field builds up to an equibrium, where each ion leaving the field causes an ion to enter. This current is then a measure of molecular density, or pressure.

# Installation notes

While pressure measurement is usually accomplished by placing the measuring device in direct contact with the process, some process conditions can damage the sensing element. When potentially damaging conditions exist in a process, special installation precautions must be taken to protect the measuring instrument. The method of mounting a measuring instrument will affect its accuracy.

# Protective Devices

Common devices include seal pots, mechanical pressure seals, and pulsation dampers. A Seal pot acts as a condensate chamber, and provides a large area of liquid contact between the process and measuring instrument. In steam service applications, the seal pots may be cooled with water or some other coolant to reduce the time required for the vapor to form condensate. In some cases, the seal pot, lines, and instrument are filled with a sealing fluid to prevent freezing.

In systems where the process fluid is corrosive or highly viscous, mechanical pressure seals are typically used to protect pressure measuring instruments from damage. A standard mechanical seal consists of a bottom housing that is connected to the process, a diaphragm capsule that is filled with oil, and a top housing to which the measuring instrument is connected. The top housing connection lines and sending element contain a fill liquid which is added under vacuum to ensure that there are no air bubbles that could adversely affect the accuracy of the measurement. The bottom housing contains a flushing connection through which process fluid can be drained when maintenance is required.

The type of fill liquid used in a mechanical seal will depend on the particular application. However, in all cases, the liquid should have a low freezing point, a high boiling point, low viscosity, and a low coefficient of thermal expansion. The oil filled capsule is threaded into the top housing. Since seal diaphragms are exposed to the process fluid, they are generally constructed of a corrosion resistant metal or a metal coated with a material such as teflon.

A pig tail is another commonly used mechanical seal. This device consists of a complete turn in a section of tubing or pipe (usually 1/4 inch ID) and is used to connect the pressure instrument to the process. A pig tail is used to protect pressure gages from thermal shock in high process temperatures. Most pig tail are mounted vertically to prevent thermal shock. When mounted horizontally, the pig tail will absorb some mechanical shock and vibration, protecting the measuring instrument from possible damage and excessive wear.

A pulsation damper, or snubber is typically used in applications where there is rapid fluctuation of process pressure. Sudden changes in pressure make it difficult to read the actual value of the pressure measurement and cause unnecessary wear on the instrument. The effect of pressure fluctuation can be minimized by placing a restriction in the impulse line to reduce the response rate of the instrument. Pulsation dampers are available in a variety of designs.