The physics of pressure

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• Pressure is proportional to force and inversely related to the area over which the force is applied.
• Pressure is caused by two forces-gravity and compression.
• Pressure values lower than atmospheric are referred to as vacuum or negative gage pressure.
By Donald R. Gillum

Pressure is a fundamental measurement from which other variables can be inferred. Pressure values rank with those of voltage and temperature in defining the energy (primarily potential) or state of matter. Temperature is the potential for doing thermodynamic work, voltage is the potential for doing electrical work, and pressure is the potential for doing fluidic work. The importance of pressure measurement is demonstrated by the need for transmitting signals powering equipment, inferring fluid flow in pipes, and using filled thermal systems in some temperature applications. Liquid levels in tanks and other vessels also can be inferred from pressure quantities. Pressure can be best understood through Pascal's law, which describes the behavior of fluids at rest. According to this law, pressure is proportional to force and inversely related to the area over which the force is applied.

In this discussion, the term "fluid" refers to liquids and gases. Both occupy the container in which they are placed; however, a liquid, if it does not completely fill the container, will present a free liquid surface, whereas a gas will fill the volume of its container. When a gas is confined in a container, molecules of the gas strike the container walls. This collision results in a force exerted against the surface area of the container. Pressure is equal to the force applied to an object (here, the walls of the container) divided by the area perpendicular to the force. The relationship between pressure, force, and area is expressed as:

P = F/A

Where P is pressure, F is force, and A is area-in other words, pressure is equal to force per unit area.

For a liquid at rest, the pressure exerted by the fluid at any point will be perpendicular to the boundary point. In addition, whenever an external pressure is applied to any confined fluid at rest, the pressure is increased at every point in the fluid by the amount of the external pressure. The practical consequences of Pascal's law are apparent in hydraulic presses and jacks, hydraulic brakes, and pressure instruments used for measurement and calibration.

Pressure is caused by two forces-gravity and compression. The pressure exerted by a volume of liquid is proportional to the vertical height, the mass density of the liquid, and the value of gravity at the local point. Work performed on a volume of contained fluid compresses the fluid, causing the pressure to rise in direct proportion to the work performed. Likewise, a compressed fluid is capable of doing work at the expense of pressure release. In liquids, the gravitational effects are the primary source of pressure, and in gases the work effects predominate. Both effects are always present to some degree in the physics of fluids and are significant considerations in the science of pressure measurement.

We live in an environment of about 1 atm (atmospheric) pressure produced by the effect of gravity on the air molecules that surround the earth. This pressure is an unnoticeable, permanent condition, and thus it is a natural reference to which higher or lower pressures can be compared. This situation is particularly useful since many pressure-measuring instruments actually measure differential pressure. These devices, such as the familiar Bourdon tube, yield an output proportional to the applied pressure minus the value of the environmental pressure surrounding the instrument. The pressure indicated by any instrument referenced to the local atmosphere is called "gage" pressure. The corresponding units, such as psi, are postscripted with the letter "g." Thus, "psig" means pounds per square inch gage pressure.

Pressure values lower than atmospheric are referred to as vacuum or negative gage pressure. If, by diligent pumping, all free molecules are removed from a volume, then there is no longer an agent within the volume that could exert a force on any area. A perfect vacuum exists, and the pressure is true or "absolute" zero. The value of this pressure is independent of the pressure in the atmosphere surrounding the evacuated vessel and hence is the true zero point on any pressure scale, regardless of unit.

An absolute pressure scale is of major significance in many engineering and scientific endeavors because it eliminates the need to measure and perform calculations for the value of a local atmosphere. If the local atmosphere does affect a pressure measurement, then its conversion to absolute terms by adding the locally measured value of atmospheric pressure (as is done with a barometer) yields a number-that is, an absolute pressure-which can be compared with similar measurements made in different places and at different times without the varying atmospheric pressure further entering the comparisons.

Pressure measurements can be referenced to atmospheric pressure, which is 14.696 psi at sea level, to zero pressure, which is a vacuum (no positive pressure is expended). When referenced to atmospheric pressure, the unit is gage pressure and is designated psig; when referenced to absolute zero pressure or a vacuum, the term psia is used. Most pressure gages, transmitters, and other pressure-measuring devices indicate a zero reading when the measuring point is exposed to atmosphere. This is 0 psig. However, measuring devices designed to produce readings referenced to absolute pressure indicate a reading of 0 psia when a perfect vacuum is applied to the measuring point. Such devices indicate a reading of 14.7 when the measuring point is exposed to atmospheric pressure because a pressure of 14.7 psi is applied to the input. The relationship between absolute and gage pressure can be expressed as:

psia = psig + Atmospheric pressure (Patm)

when P > Patm

In the above equation, the relationship between absolute and gage pressure is a function of the local atmospheric pressure. A change in atmospheric pressure will cause a change in absolute pressure. Thus, a change in atmospheric pressure would cause a change in an absolute pressure-measuring instrument but not in a gage pressure-measuring instrument. This is true because atmospheric pressure represents a variable point on the absolute pressure scale. Pressure measurements are referenced to standard conditions that can be mutually established by consenting parties, but which are usually expressed as atmospheric pressure (1 atm) at sea level and 60°F.

Source: Industrial Pressure, Level, and Density Measurement, Second Edition by Donald R. Gillum (ISBN: 978-1-934394-34-2) www.isa.org/pressureleveldensity