Editing Pressure (section)

==Definition==
''Pressure'' is the amount of force applied [[perpendicular]] to the surface of an object per unit area. The symbol for it is "p" or ''P''.<ref>
{{Cite book |last=Giancoli |first=Douglas G. |title=Physics: principles with applications |year=2004 |publisher=Pearson Education |location=Upper Saddle River, N.J. |isbn=978-0-13-060620-4 |url-access=registration |url=https://archive.org/details/physics00doug }}</ref>
The [[IUPAC]] recommendation for pressure is a lower-case ''p''.<ref name="IUPACGoldPressure">
{{cite book|url = http://goldbook.iupac.org/P04819.html|title = IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book")|publisher = Blackwell Scientific Publications|author1 = McNaught, A. D.|author2 = Wilkinson, A.|author3 = Nic, M.|author4 = Jirat, J.|author5 = Kosata, B.|author6 = Jenkins, A.|year = 2014|location = Oxford|isbn = 978-0-9678550-9-7|doi = 10.1351/goldbook.P04819|version = 2.3.3|url-status = live|archive-url = https://web.archive.org/web/20160304071856/http://goldbook.iupac.org/E02281.html|archive-date = 2016-03-04}}</ref>
However, upper-case ''P'' is widely used. The usage of ''P'' vs ''p'' depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as [[Power (physics)|power]] and [[momentum]], and on writing style.

===Formula===
{{Conjugate variables (thermodynamics)}}
[[File:Pressure force area.svg|200px|right]]
Mathematically:<ref name="Georgia State University, Physics & Astronomy">{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/press.html |title=Pressure |author=R Nave |website=Hyperphysics |publisher=Georgia State University, Dept. of Physics and Astronomy |access-date=2022-03-05 }}</ref>
<math display="block">p = \frac{F}{A},</math>
where:
*<math>p</math> is the pressure,
*<math>F</math> is the magnitude of the [[normal force]],
*<math>A</math> is the area of the surface on contact.

Pressure is a [[Scalar (physics)|scalar]] quantity. It relates the [[vector area]] element (a vector normal to the surface) with the [[normal force]] acting on it. The pressure is the scalar [[proportionality constant]] that relates these two normal vectors:
<math display="block">d\mathbf{F}_n = -p\,d\mathbf{A} = -p\,\mathbf{n}\,dA.</math>

The minus sign comes from the convention that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface ''S'' in contact with the fluid, the total force exerted by the fluid on that surface is the [[surface integral]] over ''S'' of the right-hand side of the above equation.

It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.{{citation needed|date=October 2021}}

Pressure is distributed to solid boundaries or across arbitrary sections of fluid ''normal to'' these boundaries or sections at every point. It is a fundamental parameter in [[thermodynamics]], and it is [[conjugate variables (thermodynamics)|conjugate]] to [[Volume (thermodynamics)|volume]].<ref>{{cite journal |last1=Alberty |first1=Robert A. |title=USE OF LEGENDRE TRANSFORMS IN CHEMICAL THERMODYNAMICS (IUPAC Technical Report) |journal=Pure Appl. Chem. |date=2001 |volume=73 |issue=8 |pages=1349–1380 |doi=10.1351/pac200173081349 |s2cid=98264934 |url=http://publications.iupac.org/pac/2001/pdf/7308x1349.pdf |access-date=1 November 2021 |quote=See Table 1 Conjugate pairs of variables ... (p.1357)}}</ref> It is defined as a [[derivative]] of the [[internal energy]] of a system:<ref>{{cite book |last1=Salinas |first1=Silvio R. A. |title=Introduction to statistical physics |date=2001 |publisher=Springer |location=New York |isbn=0-387-95119-9 |page=42}}</ref>
:<math display="block">p = -\left(\frac{\partial U}{\partial V}\right)_{S, N},</math>
where:
*<math>U</math> is the internal energy,
*<math>V</math> is the volume of the system,
*The subscripts mean that the derivative is taken at fixed [[entropy]] (<math>S</math>) and [[particle number]] (<math>N</math>).

===Units===
[[File:Barometer mercury column hg.jpg|thumb|right|Mercury column]]
The [[SI]] unit for pressure is the [[Pascal (unit)|pascal]] (Pa), equal to one [[newton (unit)|newton]] per [[square metre]] (N/m<sup>2</sup>, or kg·m<sup>−1</sup>·s<sup>−2</sup>). This name for the unit was added in 1971;<ref>{{cite web |url=http://www.bipm.fr/en/convention/cgpm/14/pascal-siemens.html |title=14th Conference of the International Bureau of Weights and Measures |publisher=Bipm.fr |access-date=2012-03-27 |url-status=dead |archive-url=https://web.archive.org/web/20070630020548/http://www.bipm.fr/en/convention/cgpm/14/pascal-siemens.html |archive-date=2007-06-30 }}</ref> before that, pressure in SI was expressed in newtons per square metre.

Other units of pressure, such as [[pound-force per square inch|pounds per square inch]] (lbf/in<sup>2</sup>) and [[bar (unit)|bar]], are also in common use. The [[Centimetre–gram–second system of units|CGS]] unit of pressure is the [[barye]] (Ba), equal to 1&nbsp;dyn·cm<sup>−2</sup>, or 0.1&nbsp;Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre ("g/cm<sup>2</sup>" or "kg/cm<sup>2</sup>"<!--don't add an f to kg, this is making the point about usage without it-->) and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is deprecated in SI. The [[technical atmosphere]] (symbol: at) is 1&nbsp;kgf/cm<sup>2</sup> (98.0665&nbsp;kPa, or 14.223&nbsp;psi).

Pressure is related to [[energy density]] and may be expressed in units such as [[joule]]s per cubic metre (J/m<sup>3</sup>, which is equal to Pa).
Mathematically:
<math display="block">p = \frac{F \cdot \text{distance}}{A \cdot \text{distance}} = \frac{\text{work}}{\text{volume}} = \frac{\text{energy (J)}}{\text{volume }(\text{m}^3)}.</math>

Some [[meteorologist]]s prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit [[millibar]] (mbar). Similar pressures are given in kilopascals (kPa) in most other fields, except aviation where the hecto- prefix is commonly used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in [[decibar]]s (dbar) because pressure in the ocean increases by approximately one decibar per metre depth.

The [[Atmosphere (unit)|standard atmosphere]] (atm) is an established constant. It is approximately equal to typical air pressure at Earth [[mean sea level]] and is defined as {{val|101325|u=Pa}} (IUPAC recommends the value {{val|100000|u=Pa}}, but prior to 1982 the value {{val|101325|u=Pa}} (= 1 atm) was usually used).<ref>{{cite web |title=IUPAC Quantities, Units and Symbols in Physical Chemistry |url=https://goldbook.iupac.org/terms/view/S05921 |website=IUPAC Gold Book |access-date=29 January 2025}}</ref>

Because pressure is commonly measured by its ability to displace a column of liquid in a [[manometer]], pressures are often expressed as a depth of a particular fluid (e.g., [[centimetres of water]], [[millimetres of mercury]] or [[inches of mercury]]). The most common choices are [[Mercury (element)|mercury]] (Hg) and water; water is nontoxic and readily available, while mercury's high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height ''h'' and density ''ρ'' is given by the hydrostatic pressure equation {{nowrap|1=''p'' = ''ρgh''}}, where ''g'' is the [[gravitational acceleration]]. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely.

When millimetres of mercury (or inches of mercury) are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units.<ref>{{SIbrochure8th|page=127}}</ref> One millimetre of mercury is approximately equal to one [[torr]]. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These ''manometric units'' are still encountered in many fields. [[Blood pressure]] is measured in millimetres (or centimetres) of mercury in most of the world, and lung pressures in centimetres of water are still common.{{citation needed|date=October 2021}}

[[Underwater diving|Underwater divers]] use the [[metre sea water]] (msw or MSW) and [[foot sea water]] (fsw or FSW) units of pressure, and these are the units for pressure gauges used to measure pressure exposure in [[diving chamber]]s and [[Dive computer|personal decompression computers]]. A msw is defined as 0.1&nbsp;bar (= 10,000&nbsp;Pa), is not the same as a linear metre of depth. 33.066&nbsp;fsw = 1&nbsp;atm{{citation needed|date=February 2023}} (1&nbsp;atm = 101,325&nbsp;Pa / 33.066 = 3,064.326 Pa).  The pressure conversion from msw to fsw is different from the length conversion: 10&nbsp;msw = 32.6336&nbsp;fsw, while 10&nbsp;m = 32.8083&nbsp;ft.{{citation needed|date=February 2023}}

Gauge<!--Editors are asked to PLEASE check the discussion page for this article before making changes regarding "gauge" vs. "gage" spelling issues. Much debate has transpired on this issue.--> pressure is often given in units with "g" appended, e.g. "kPag", "barg" or "psig", and units for measurements of absolute pressure are sometimes given a suffix of "a", to avoid confusion, for example "kPaa", "psia". However, the US [[National Institute of Standards and Technology]] recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure.<ref name = pubs>{{cite journal |access-date= 2009-07-07 |journal=NIST |url=http://physics.nist.gov/Pubs/SP811/sec07.html#7.4 |title=Rules and Style Conventions for Expressing Values of Quantities |date=2 July 2009 |url-status=live |archive-url=https://web.archive.org/web/20090710192735/http://physics.nist.gov/Pubs/SP811/sec07.html#7.4 |archive-date=2009-07-10 }}</ref> For example, {{nowrap|1="''p''<sub>g</sub> = 100 psi"}} rather than {{nowrap|1="''p'' = 100 psig"}}.

Differential pressure is expressed in units with "d" appended; this type of measurement is useful when considering sealing performance or whether a valve will open or close.

Presently or formerly popular pressure units include the following:
*[[atmosphere (unit)|atmosphere]] (atm)
*manometric units:
**centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury,
**{{anchor|H2O}}height of equivalent column of water, including [[Millimeters, water gauge|millimetre]] (mm {{chem|H|2|O}}), [[centimetre of water|centimetre]] (cm {{chem|H|2|O}}), metre, [[inch of water|inch]], and foot of water;
*imperial and customary units:
**[[kip (unit)|kip]], [[Ton-force#Short ton-force|short ton-force]], [[Ton-force#Long ton-force|long ton-force]], [[pound-force]], [[ounce-force]], and [[poundal]] per square inch,
**short ton-force and long ton-force per square inch,
**fsw (feet sea water) used in underwater diving, particularly in connection with diving pressure exposure and [[Decompression (diving)|decompression]];
*non-SI metric units:
**[[bar (unit)|bar]], decibar, [[millibar]],
***msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and [[Decompression (diving)|decompression]],
**kilogram-force, or kilopond, per square centimetre ([[technical atmosphere]]),
**gram-force and tonne-force (metric ton-force) per square centimetre,
**[[barye]] ([[dyne]] per square centimetre),
**kilogram-force and tonne-force per square metre,
**[[sthene]] per square metre ([[pieze]]).
<!--

{{Pressure Units}}
[[File:Pressure units.png|alt=A vizualization of pressure units as circles in log scale. A circle is to imagine a bubble, that such pressure would occupy.|thumb|Pressure units as circles in log scale. 4 graphs show scaled P units to unitary mTorr, Pa, mbar, bar. A circle is to imagine a bubble, that such pressure would occupy.]]
-->

===Examples===
[[File:Aluminium cylinder.jpg|120px|thumbnail|right|The effects of an external pressure of 700&nbsp;bar on an aluminum cylinder with {{convert|5|mm|in|3|abbr=on}} wall thickness]]
As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a [[thumbtack]] can easily damage 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. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid ''normal to'' these boundaries or sections at every point. Unlike [[stress (physics)|stress]], pressure is defined as a [[Scalar (physics)|scalar quantity]]. The negative [[gradient]] of pressure is called the [[force density]].<ref>{{cite book |last1=Lautrup |first1=Benny |title=Physics of continuous matter : exotic and everyday phenomena in the macroscopic world |date=2005 |publisher=Institute of Physics |location=Bristol |isbn=9780750307529 |page=50}}</ref>

Another example is a knife. If the flat edge is used, force is distributed over a larger surface area resulting in less pressure, and it will not cut. Whereas using the sharp edge, which has less surface area, results in greater pressure, and so the knife cuts smoothly. This is one example of a practical application of pressure.<ref>{{cite book |last1=Breithaupt |first1=Jim |title=Physics |date=2015 |location=Basingstoke |isbn=9781137443243 |page=106 |edition=Fourth |publisher=Palgrave Macmillan }}</ref>

For gases, pressure is sometimes measured not as an ''absolute pressure'', but relative to [[atmospheric pressure]]; such measurements are called ''gauge<!--Editors are asked to PLEASE check the discussion page for this article before making changes regarding "gauge" vs. "gage" spelling issues. Much debate has transpired on this issue.--> pressure''. An example of this is the air pressure in an [[automobile]] [[tire]], which might be said to be "{{convert|220 |kPa |psi|abbr=on|lk=in}}", but is actually 220&nbsp;kPa (32&nbsp;psi) above atmospheric pressure. Since atmospheric pressure at sea level is about 100&nbsp;kPa (14.7&nbsp;psi), the absolute pressure in the tire is therefore about {{convert|320|kPa|psi|abbr=on}}. In technical work, this is written "a gauge<!--Editors are asked to PLEASE check the discussion page for this article before making changes regarding "gauge" vs. "gage" spelling issues. Much debate has transpired on this issue.--> pressure of {{convert|220|kPa|psi|abbr=on}}".

Where space is limited, such as on [[pressure gauge<!--Editors are asked to PLEASE check the discussion page for this article before making changes regarding "gauge" vs. "gage" spelling issues. Much debate has transpired on this issue.-->]]s, [[name plate]]s, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge<!--Editors are asked to PLEASE check the discussion page for this article before making changes regarding "gauge" vs. "gage" spelling issues. Much debate has transpired on this issue.-->)" or "kPa (absolute)", is permitted.<ref> {{Cite book|author=Institute of Electrical and Electronics Engineers |title=268-1992 |author-link=Institute of Electrical and Electronics Engineers |year=1992}}</ref> In non-[[SI]] technical work, a gauge<!--Editors are asked to PLEASE check the discussion page for this article before making changes regarding "gauge" vs. "gage" spelling issues. Much debate has transpired on this issue.--> pressure of {{convert|32 |psi|kPa|abbr=on}} is sometimes written as "32&nbsp;psig", and an absolute pressure as "32&nbsp;psia", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.<ref name = pubs/>

Gauge<!--Editors are asked to PLEASE check the discussion page for this article before making changes regarding "gauge" vs. "gage" spelling issues. Much debate has transpired on this issue.--> pressure is the relevant measure of pressure wherever one is interested in the stress on [[Pressure vessel|storage vessels]] and the plumbing components of fluidics systems. However, whenever equation-of-state 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 {{convert|100|kPa|psi|abbr=on}}, a gas (such as helium) at {{convert|200|kPa|psi|abbr=on}} (gauge<!--Editors are asked to PLEASE check the discussion page for this article before making changes regarding "gauge" vs. "gage" spelling issues. Much debate has transpired on this issue.-->) ({{convert|300|kPa|psi|abbr=on|disp=or}} [absolute]) is 50% denser than the same gas at {{convert|100|kPa|psi|abbr=on}} (gauge<!--Editors are asked to PLEASE check the discussion page for this article before making changes regarding "gauge" vs. "gage" spelling issues. Much debate has transpired on this issue.-->) ({{convert|200|kPa|psi|abbr=on|disp=or}} [absolute]). Focusing on gauge<!--Editors are asked to PLEASE check the discussion page for this article before making changes regarding "gauge" vs. "gage" spelling issues. Much debate has transpired on this issue.--> values, one might erroneously conclude the first sample had twice the density of the second one.{{citation needed|date=October 2021}}

===Scalar nature===
In a static [[gas]], the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant [[Brownian motion|random motion]]. Because there are an extremely large number of molecules and because the motion of the individual molecules is random in every direction, no motion is detected. When the gas is at least partially confined (that is, not free to expand rapidly), the gas will exhibit a [[hydrostatic pressure]]. This confinement can be achieved with either a physical container, or in the gravitational well of a large mass, such as a planet, otherwise known as [[atmospheric pressure]].

In the case of planetary [[atmosphere]]s, the [[pressure-gradient force]] of the gas pushing outwards from higher pressure, lower altitudes to lower pressure, higher altitudes is balanced by the [[gravitational force]], preventing the gas from diffusing into [[outer space]] and maintaining [[hydrostatic equilibrium]].

In a physical container, the pressure of the gas originates from the molecules colliding with the walls of the container. The walls of the container can be anywhere inside the gas, and the force per unit area (the pressure) is the same. If the "container" is shrunk down to a very small point (becoming less true as the atomic scale is approached), the pressure will still have a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense associated with it. Pressure force acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular (at right angle) to the surface.<ref>{{Cite web |date=2023-03-28 |title=Gas Pressure Study Guide - Inspirit Learning Inc |url=https://www.inspiritvr.com/gas-pressure-study-guide/ |access-date=2024-02-11 |language=en-US}}</ref>

A closely related quantity is the [[stress (physics)|stress]] tensor ''σ'', which relates the vector force <math>\mathbf{F}</math> to the 
[[vector area]] <math>\mathbf{A}</math> via the linear relation <math>\mathbf{F} = \sigma\mathbf{A}</math>.

This [[tensor]] may be expressed as the sum of the [[viscous stress tensor]] minus the hydrostatic pressure. The negative of the stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure.<ref>{{Cite web |title=Thermal-FluidsPedia {{!}} Pressure (Thermodynamics) {{!}} Thermal-Fluids Central |url=https://www.thermalfluidscentral.org/encyclopedia/index.php/Pressure_(Thermodynamics) |access-date=2024-02-11 |website=www.thermalfluidscentral.org}}</ref>

According to the theory of [[general relativity]], pressure increases the strength of a gravitational field (see [[stress–energy tensor]]) and so adds to the mass-energy cause of [[gravity]]. This effect is unnoticeable at everyday pressures but is significant in [[neutron star]]s, although it has not been experimentally tested.<ref>{{cite journal|title=Einstein's gravity under pressure |doi=10.1007/s10509-009-0016-8 |volume=321 |issue=2 |journal=Astrophysics and Space Science |pages=151–156|arxiv=0705.0825 |bibcode=2009Ap&SS.321..151V |year=2009 |last1=Vishwakarma |first1=Ram Gopal |s2cid=218673952 }}</ref>