# A pressure-packed situation

###### Comparison of specific gravity of mercury and water

Pressure is one of the primary measurements used in instrumentation and control.

Its meaning, units, and measuring devices are important to a proper understanding of not only what is occurring in a process but also how instruments and controls serve to monitor the process.

The atmosphere consists of gases and liquids. These gases and liquids have weight and exert a pressure on the surface of the earth. Pressure is force exerted over a unit area. Mathematically, pressure is expressed as P = F/A where P = pressure, F = force, A = area. Therefore, the amount of force exerted by a substance directly affects the amount of pressure. Note that pressure is not a fundamental quantity but is derived from force and area, which in turn are derived from mass, length, and time, the latter three being fundamental quantities.

## Liquid force and pressure

###### Illustration of Boyle's law

A liquid occupies the space in and conforms to the shape of the tank or vessel. To measure pressure, it is necessary to determine the forces exerted on the walls and the bottom of the tank. The amount of force a specific volume of liquid in an open tank exerts over a specific area depends on (1) the height of liquid above the measurement point, (2) the specific gravity, or density, of the liquid, and (3) the temperature of the liquid.

Consider the following example, which addresses these three factors. The first is height. If the water level in a tank is 30 centimeters (cm) and the weight of water at 16°C is 1 kilogram (kg) per cubic decimeter, then the water column exerts a force of 0.3 kg per square centimeter or 29.42 kilopascals at the bottom. If the level rises to 90 cm, the force exerted will be 88.26 kilopascals.

The second factor is weight, which must be determined in order to ascertain the pressure of the liquid. One usually works with specific gravity, which is a reference number that compares the weight of a specific volume-to-liquid to the same volume of water, and a specific volume of gas to air at the same temperature. Water and air are assigned specific gravity constants of one. These values serve as references for determining the specific gravity of other liquids and gases.

A cubic decimeter (dm3 ) of mercury weighs 13.57 kg, while the same volume of water weighs 1 kg at 4°C. Thus, mercury weighs 13.57 times as much as water and has a specific gravity of 13.57.

The third factor is temperature, which affects the pressure of a liquid in an open tank or vessel. If the temperature of the liquid changes, its specific gravity also changes. This is because changes in the temperature will cause the liquid to expand or contract, depending on whether the temperature rises above or falls below the specific standard. When the temperature falls, the liquids expand, which causes the force per unit area to increase.

## Force exerted by gases

###### A U-tube manometer reading pressure by the difference in height (h)

Gases have no definite shape. They expand to occupy the full volume of the vessel that contains them. As a result, a gas will exert an equal amount of pressure on all surfaces of the vessel that contains it.

Boyle's law: The force a gas exerts depends on the volume of the vessel and the temperature of the gas. It's Boyle's law that expresses the relationship between the pressure of the gas and the volume of the vessel in which the gas resides.

Boyle's law states if the temperature stays constant, the force exerted by the gas on the walls of a containing vessel varies inversely with the volume of the vessel, provided the mass remains unchanged.

This means if the volume of the vessel increases, the force exerted by the gas decreases and vice versa. Thus, P1V1 = P2V2 (temperature constant), where P1 and V1 are the initial pressure and volume, respectively, and P2 and V2 are the final steady state pressure and volume, respectively.

Since pressure can be transduced to force by allowing it to act on a known area, the methods of measuring force and pressure are essentially the same, except for high vacuums for which a variety of special methods are used.

Pressure-measuring instruments can broadly break out as either mechanical or electrical/electronic. This includes manometers, which are widely used in laboratories for the calibration of secondary instruments.

Nicholas Sheble (nsheble@isa.org ) edits the Control Fundamentals department. The source for this critique is Fundamentals of Industrial Control, ISA Press 2005, D.A. Coggan, Editor.

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