Pressure

Pressure (symbol: p) is the force applied over an area in a direction perpendicular to the surface of the area.

Pressure is a natural physical phenomenon. It is a scalar quantity and a fundamental parameter in thermodynamics.

Formula and units

Mathematically:

$p={\frac {F}{A}}$

where:

$p$ is the pressure

$F$ is the perpendicular force

$A$ is the area.

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N·m^-2 or kg·m^-1·s^-2). It was given that SI name in 1971. Before that, pressure in SI was expressed simply as N/m².

Pressure Units

	pascal (Pa)	bar (bar)	atmosphere (atm)	torr (torr)	pound-force per square inch (psi)	kilogram-force per square centimeter (kgf/cm2)
1 Pa	≡ 1 N/m2	10−5	9.8692×10−6	7.5006×10−3	145.04×10−6	1.01972×10−5
1 bar	100,000	≡ 106 dyn/cm2	0.98692	750.06	14.504	1.01972
1 atm	101,325	1.01325	≡ 1 atm	760	14.696	1.03323
1 torr	133.322	1.3332×10−3	1.3158×10−3	≡ 1 torr ≈ 1 mmHg	19.337×10−3	1.35951×10−3
1 psi	6,894.76	68.948×10−3	68.046×10−3	51.715	≡ 1 lbf/in2	7.03059×10−2
1 kgf/cm2	98,066.5	0.980665	0.967838	735.5576	14.22357	≡ 1 kgf/cm2

Example reading:  1 Pa = 1 N/m²  = 10⁻⁵ bar  = 9.8692×10⁻⁶ atm  = 7.5006×10⁻³ torr, etc.
Note: mmHg is an abbreviation for millimetre of mercury

Absolute pressure versus gauge pressure

(CC) Diagram: Milton Beychok
Figure 1: The relationship of absolute, gauge and vacuum pressures

Bourdon tube pressure gauges, vehicle tire gauges and many other types of pressure gauges are zero referenced to atmospheric pressure, which means that they measure the pressure above atmospheric pressure. However, absolute pressures are zero referenced to a complete vacuum. Thus, the absolute pressure of any system is the gauge pressure of the system plus the local atmospheric or ambient pressure. Figure 1 illustrates the relationship between gauge and absolute pressure for any pressures above atmospheric pressure.

An example of the difference is between gauge and absolute pressure is the air pressure in a vehicle tire. A tire pressure gauge might read 220 kPa as the gauge pressure, but that means the pressure is 220 kPa above atmospheric pressure. Since atmospheric pressure at sea level is about 101 kPa, the absolute pressure in the tire is therefore about 321 kPa.

In technical writing, this would be written as a gauge pressure of 220 kPa or as an absolute pressure of 321 kPa. Where space is limited, such as on pressure gauge dials, table headings or graph labels, the use of a modifier in parentheses, such as kPa (gauge) or kPa (absolute), is strongly encouraged. The use of kPa(g) or kPa(a) is not recommended. Gauge pressure is also sometimes spelled gage pressure.

As shown in Figure 1, a pressure below atmospheric pressure may be expressed in terms of how much it is below atmospheric pressure or in terms of how much it is above a complete vacuum. For example, if the atmospheric pressure is 101 kPa, point B in Figure 1 might be expressed as being 45 kPa of vacuum, meaning it is 45 kPa below atmospheric pressure. It might also be expressed as 56 kPa (absolute) meaning that it is 56 kPa above zero pressure. In technical writing, it is very important to make clear how any pressures below atmospheric pressure are expressed.

Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the piping components of fluid flow systems. However, whenever equation of state (EOS) properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure is 101 kPa: a gas at 200 kPa (gauge), which is 301 kPa (absolute), is 50 percent more dense than the same gas at 100 kPa (gauge), which is 201 kPa (absolute). Focusing on the gauge values, one might erroneously conclude the gas at 200 kPa (gauge) had twice the density of the same gas at 100 kPa (gauge).

Negative pressures

While pressures are generally positive, when describing a system operating under a vacuum (partial), the system pressure may be stated as being an absolute pressure of 80 kPa (for example) or it may be described as a gauge pressure of −21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa).

A statement such as the system operates at a vacuum of 100 mmHg will lead to confusion because it might mean an absolute pressure 100 mmHg or a gauge pressure of −100 mmHg (i.e., 100 mm below an atmospheric pressure of 760 mmHg).

Example effects of pressure

A finger can be pressed against a wall without making a lasting impression; however, the same finger pushing a thumbtack can easily make a small hole in the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area.

Another example is that of a common knife. The flat side of the knife won't cut an apple. But if we use the thin side, it will easily cut the apple. When we use the thin side, more pressure is applied because the surface area is reduced and so it readily cuts the apple.

If one is at the bottom of a deep pool of water, the water pressure will cause pain in one's ears. That pain cannot be relieved by turning one's head. The water's force on your eardrum is always the same, and is always perpendicular to the surface where the eardrum contacts the water.