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{{about|pressure in the physical sciences}}
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{{Infobox physical quantity
| name = Pressure
| unit = [[Pascal (unit)|Pascal]] (Pa)
| basequantities = 1&nbsp;[[kilogram|kg]]/([[metre|m]]·[[second|s]]<sup>2</sup>)
| symbols = ''P''


| derivations = ''P'' = [[force|F]] / [[area|A]]
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[[Image:Pressure exerted by collisions.svg|thumb|right|250px|alt=A figure showing pressure exerted by particle collisions inside a closed container. The collisions that exert the pressure are highlighted in red.|Pressure as exerted by particle collisions inside a closed container.]]
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{{Thermodynamics|cTopic=[[List of thermodynamic properties|System properties]]}}
 
'''Pressure''' (symbol: ''P'' or ''p'') is the ratio of [[force]] to the [[area]] over which that force is distributed.
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Pressure is force per unit area applied in a direction [[perpendicular]] to the surface of an object. [[Gauge pressure]] (also spelled ''gage'' pressure)<ref group=lower-alpha>The preferred spelling varies by country and even by industry. Further, both spellings are often used ''within'' a particular industry or country. Industries in British English-speaking countries typically use the "gauge" spelling. Many of the largest US manufacturers of pressure transducers and instrumentation use the spelling "gage pressure" in their most formal documentation [http://www.sensotec.com/pressurefaq.shtml sensotec.com] Honeywell-Sensotec's FAQ page and [http://us.fluke.com/usen/Home/Search.asp?txtSearchBox=%22gage+pressure%22&x=0&y=0 fluke.com], Fluke Corporation's product search page.</ref> is the pressure relative to the local atmospheric or ambient pressure. Pressure is measured in any unit of force divided by any unit of area.  The [[International System of Units|SI]] unit of pressure is the [[newton (unit)|newton]] per [[square metre]], which is called the ''[[Pascal (unit)|pascal]]'' (Pa) after the seventeenth-century philosopher and scientist [[Blaise Pascal]]. A pressure of 1 Pa is small; it approximately equals the pressure exerted by a dollar bill resting flat on a table. Everyday pressures are often stated in kilopascals (1 kPa = 1000 Pa).
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Pressure is the amount of force acting perpendicularly per unit area. The symbol of pressure is ''p''.<ref group=lower-alpha>The usage of P vs p is context-driven. It depends on 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.</ref><ref>{{Cite book |last=Giancoli |first=Douglas G. |coauthors= |title=Physics: principles with applications |year=2004 |publisher=Pearson Education |location=Upper Saddle River, N.J. |isbn=0-13-060620-0 |pages=}}</ref>
 
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{{Conjugate variables (thermodynamics)}}
[[File:Pressure force area.svg|200px|right]]
Mathematically:
:<math>p = \frac{F}{A}\ \mbox{or}\ p = \frac{dF_n}{dA}</math>


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


The minus sign comes from the fact that the force is considered towards the surface element, while the normal vector points outward.
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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.
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Pressure is transmitted 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]].
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===Units===
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[[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 special 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 |date= |accessdate=2012-03-27}}</ref> before that, pressure in SI was expressed simply as N/m<sup>2</sup>.


Non-SI measures such as [[pound-force per square inch|pounds per square inch]] and ''[[bar (unit)|bars]]'' are used in some parts of the world, primarily in the United States of America. The [[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/cm<sup>2</sup>, or as 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 expressly forbidden in SI. The [[technical atmosphere]] (symbol: at) is 1&nbsp;kgf/cm<sup>2</sup> (98.0665&nbsp;kPa or 14.223&nbsp;psi).
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Since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume measured in J·m<sup>−3</sup>, related to energy density.
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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, where the hecto- prefix is rarely used. The [[inch of mercury]] is still used in the United States. Oceanographers usually measure underwater pressure in [[decibar]]s (dbar) because an increase in pressure of 1&nbsp;dbar is approximately equal to an increase in depth of 1&nbsp;meter.
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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 follows:
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:standard atmosphere = 101,325&nbsp;[[pascal (unit)|Pa]] = 101.325&nbsp;kPa = 1,013.25&nbsp;hPa.
 
 
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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., [[centimeters of water]], mm 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|''p ''{{=}}'' ρgh''}}. 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 [[torr|millimeters of mercury]] or [[inHg|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.{{Citation needed|date=January 2013}} One mmHg (millimeter of mercury) is 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 millimeters of mercury in most of the world, and lung pressures in centimeters of water are still common.
 
 
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[[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 standard 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 bar, and is not the same as a linear metre of depth, and 33.066&nbsp;fsw = 1&nbsp;atm.<ref name="usn T2.10"/> Note that 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
 
 
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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' 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>{{cite web |accessdate=2009-07-07 |publisher=NIST |url=http://physics.nist.gov/Pubs/SP811/sec07.html#7.4 |title=Rules and Style Conventions for Expressing Values of Quantities}}</ref> For example, {{nowrap|"''P''<sub>g</sub> {{=}} 100 psi"}} rather than {{nowrap|"''P'' {{=}} 100 psig"}}.
 
 
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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.
 
 
</ul>
Presently or formerly popular pressure units include the following:
*[[atmosphere (unit)|atmosphere]] (atm)
*manometric units:
**centimeter, inch, and millimeter of mercury ([[torr]])
**{{anchor|H2O}}Height of equivalent column of water, including millimeter (mm H<sub>2</sub>O), [[centimeter of water|centimeter]] (cm H<sub>2</sub>O), meter, inch, and foot of water
*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 centimeter ([[technical atmosphere]])
**gram-force and tonne-force (metric ton-force) per square centimeter
**[[barye]] ([[dyne]] per square centimeter)
**kilogram-force and tonne-force per square meter
**[[sthene]] per square meter ([[pieze]])
 
{{Pressure Units}}
 
===Examples===
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]].
 
Another example is of a common knife. If we try to cut a fruit with the flat side it obviously will not cut. But if we take the thin side, it will cut smoothly. The reason is that the flat side has a greater surface area (less pressure) and so it does not cut the fruit. When we take the thin side, the surface area is reduced and so it cuts the fruit easily and quickly. This is one example of a practical application of pressure.
 
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 "220&nbsp;[[pascal (unit)|kPa]] (32&nbsp;psi)", 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 320&nbsp;kPa (46.7&nbsp;psi). 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 220&nbsp;kPa (32&nbsp;psi)". 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 plates]], 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. 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 32&nbsp;psi 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>NIST, [http://physics.nist.gov/Pubs/SP811/sec07.html#7.4 ''Rules and Style Conventions for Expressing Values of Quantities''], Sect. 7.4.</ref>
 
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 100&nbsp;kPa, a gas (such as helium) at 200&nbsp;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.-->) (300&nbsp;kPa [absolute]) is 50% denser than the same gas at 100&nbsp;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.-->) (200&nbsp;kPa [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.
 
===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 we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to a very small point (becoming less true as we approach the atomic scale), and 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 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.
 
A closely related quantity is the [[stress (physics)|stress]] tensor ''σ'', which relates the vector force '''F''' to the [[vector area]] '''A''' via
:<math>\mathbf{F}=\mathbf{\sigma 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.
 
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 web|url=http://www.springerlink.com/content/c3540l4q9nr17627/ |title=Einstein's gravity under pressure |publisher=Springerlink.com |date= |accessdate=2012-03-27}}</ref>
 
==Types==
 
===Fluid pressure===
'''Fluid pressure''' is the pressure at some point within a [[fluid]], such as [[water]] or [[Atmosphere of Earth|air]] (for more information specifically about liquid pressure, see [[Pressure#Liquid pressure|section below]]).
 
Fluid pressure occurs in one of two situations:
<ol><li>an open condition, called "open channel flow"</li>
<ol style="list-style-type: lower-latin;">
<li>the ocean, or</li>
<li>swimming pool, or</li>
<li>the atmosphere.</li></ol>
<li>a closed condition, called closed conduits</li>
<ol style="list-style-type: lower-latin;">
<li>water line, or</li>
<li>gas line.</li></ol></ol>
 
Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only [[negligible]] changes in the pressure. Such conditions conform with principles of [[fluid statics]]. The pressure at any given point of a non-moving (static) fluid is called the '''hydrostatic pressure'''. <!--For bolding note that this page is the target of redirection from "hydrostatic pressure"-->
 
Closed bodies of fluid are either "static", when the fluid is not moving, or "dynamic", when the fluid can move as in either a pipe or by compressing an air gap in a closed container. The pressure in closed conditions conforms with the principles of [[fluid dynamics]].
 
The concepts of fluid pressure are predominantly attributed to the discoveries of [[Blaise Pascal]] and [[Daniel Bernoulli]]. [[Bernoulli's equation]] can be used in almost any situation to determine the pressure at any point in a fluid. The equation makes some assumptions about the fluid, such as the fluid being ideal<ref name=Finnemore>{{cite book |last=Finnemore, John, E. and Joseph B. Franzini |title=Fluid Mechanics: With Engineering Applications |year=2002 |publisher=McGraw Hill, Inc. |location=New York, NY |isbn=978-0-07-243202-2 |pages=14–29}}</ref> and incompressible.<ref name=Finnemore/> An ideal fluid is a fluid in which there is no friction, it is [[inviscid]],<ref name=Finnemore/> zero [[viscosity]].<ref name=Finnemore/> The equation is written between any two points ''a'' and ''b'' in a system that contain the same fluid.
:<math>\frac{p_a}{\gamma}+\frac{v_a^2}{2g}+z_a=\frac{p_b}{\gamma}+\frac{v_b^2}{2g}+z_b</math><ref name=NCEES>{{cite book|last=NCEES|title=Fundamentals of Engineering: Supplied Reference Handbook|year=2011|publisher=NCEES|location=Clemson, SC|isbn=978-1-932613-59-9|page=64}}</ref>
 
where:
:''p'' = pressure of the fluid
:''γ'' = ''ρg'' = density·acceleration of gravity = [[specific weight]] of the fluid.<ref name=Finnemore/>
:''v'' = velocity of the fluid
:''g'' = [[acceleration of gravity]]
:''z'' = elevation
:<math>\frac{p}{\gamma}</math> = pressure head
:<math>\frac{v^2}{2g}</math> = velocity head
 
====Applications====
* (Hydraulics brakes)
* [[Artesian well]]
* [[Blood pressure]]
* [[Hydraulic head]]
* [[Turgor pressure|Plant cell turgidity]]
* [[Pythagorean cup]]
 
===Explosion or deflagration pressures===
[[Explosion]] or [[deflagration]] pressures are the result of the ignition of explosive [[gas]]es, mists, dust/air suspensions, in unconfined and confined spaces.
 
===Negative pressures===
[[File:13-07-23-kienbaum-unterdruckkammer-33.jpg|thumb|negative pressure chamber in [[Bundesleistungszentrum Kienbaum]], Germany]]
While '''pressures''' are, in general, positive, there are several situations in which negative pressures may be encountered:
*When dealing in relative (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.-->) pressures. For instance, an absolute pressure of 80&nbsp;kPa may be described as 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 −21&nbsp;kPa (i.e., 21&nbsp;kPa below an atmospheric pressure of 101&nbsp;kPa).
*When attractive forces (e.g., [[van der Waals force]]s<!--"van", see [[Talk:Van der Waals#Van should be capitalized unless preceded by first name]] rebuttal-->) between the particles of a fluid exceeds repulsive forces due to thermal motion. These forces explain [[ascent of sap]] in tall plants. Negative pressure must exist at the top of any tree taller than 10&nbsp;m, which is the [[pressure head]] of water that balances the atmospheric pressure. Van der Waals forces maintain cohesion of columns of sap that run continuously in [[xylem]] from the roots to the top leaves.
*The [[Casimir effect]] can create a small attractive force due to interactions with [[vacuum energy]]; this force is sometimes termed "vacuum pressure" (not to be confused with the negative ''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 a vacuum).
*Depending on how the orientation of a surface is chosen, the same distribution of forces may be described either as a positive pressure along one [[Normal (geometry)|surface normal]], or as a negative pressure acting along the opposite surface normal.
*In the [[cosmological constant]].
 
===Stagnation pressure===<!--This section is linked from [[Drag equation]]-->
[[Stagnation pressure]] is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower [[static pressure]], it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by the [[Mach number]] of the fluid. In addition, there can be differences in pressure due to differences in the elevation (height) of the fluid. See [[Bernoulli's equation]].
 
The pressure of a moving fluid can be measured using a [[Pitot tube]], or one of its variations such as a [[Kiel probe]] or [[Cobra probe]], connected to a [[manometer]]. Depending on where the inlet holes are located on the probe, it can measure static pressures or stagnation pressures.
 
===Surface pressure===
There is a two-dimensional analog of pressure – the lateral force per unit length applied on a line perpendicular to the force.
 
Surface pressure is denoted by π and shares many similar properties with three-dimensional pressure. Properties of surface chemicals can be investigated by measuring pressure/area isotherms, as the two-dimensional analog of [[Boyle's law]], {{nowrap|''πA'' {{=}} ''k''}}, at constant temperature.
:<math>\pi = \frac{F}{l}.</math>
 
===Pressure of an ideal gas ===
{{main|Ideal gas law}}
In an [[ideal gas]], molecules have no volume and do not interact. Pressure varies linearly with temperature, volume, and quantity according to the [[ideal gas law]],
:<math>P=\frac{nRT}{V}</math>
 
where:
:''P'' is the absolute pressure of the gas
:''n'' is the [[amount of substance]]
:''T'' is the absolute temperature
:''V'' is the volume
:''R'' is  the [[ideal gas constant]].
 
[[Real gas]]es exhibit a more complex dependence on the variables of state.<ref>P. Atkins, J. de Paula ''Elements of Physical Chemistry'', 4th Ed, W.H. Freeman, 2006. ISBN 0-7167-7329-5.</ref>
 
===Vapor pressure===
{{main|Vapor pressure}}
Vapor pressure is the pressure of a [[vapor]] in [[thermodynamic equilibrium]] with its condensed [[Phase (matter)|phase]]s in a closed system. All [[liquid]]s and [[solid]]s have a tendency to [[evaporate]] into a gaseous form, and all [[gas]]es have a tendency to [[condense]] back to their liquid or solid form.
 
The [[atmospheric pressure]] [[boiling point]] of a liquid (also known as the [[normal boiling point]]) is the temperature at which the vapor pressure equals the ambient atmospheric pressure. With any incremental increase in that temperature, the vapor pressure becomes sufficient to overcome atmospheric pressure and lift the liquid to form vapor bubbles inside the bulk of the substance. [[liquid bubble|Bubble]] formation deeper in the liquid requires a higher pressure, and therefore higher temperature, because the fluid pressure increases above the atmospheric pressure as the depth increases.
 
The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called [[partial pressure|partial vapor pressure]].
 
===Liquid pressure===
{{See also|Fluid statics#Pressure in fluids at rest}}
{{Continuum mechanics}}
When a person swims under the water, water pressure is felt acting on the person's eardrums. The deeper that person swims, the greater the pressure. The pressure felt is due to the weight of the water above the person. As someone swims deeper, there is more water above the person and therefore greater pressure. The pressure a liquid exerts depends on its depth.
 
Liquid pressure also depends on the density of the liquid. If someone was submerged in a liquid more dense than water, the pressure would be correspondingly greater. The pressure due to a liquid in liquid columns of constant density or at a depth within a substance is represented by the following formula:
:<math>P=\rho gh</math>
 
where:
:''P'' is liquid pressure
:''g'' is gravity at the surface of overlaying material
:ρ is [[density]] of liquid
:''h'' is height of liquid column or depth within a substance
 
Another way of saying this <u>same</u> formula is the following:
 
:<math>P = \text{weight density} \times \!\, \text{depth}</math>
 
{| class="toccolours collapsible collapsed" width="60%" style="text-align:left"
!Derivation of this equation
|-
|This is derived from the definitions of pressure and weight density. Consider an area at the bottom of a vessel of liquid. The weight of the column of liquid directly above this area produces pressure. From the definition:
 
:<math>\text{Weight density} = \frac{\text{weight}}{\text{volume}}</math>
 
we can express this weight of liquid as
 
:<math>\text{Weight} = \text{weight density} \times \!\, \text{volume}</math>
 
where the volume of the column is simply the area multiplied by the depth. Then we have
 
:<math>\text{Pressure} = \frac{\text{force}}{\text{area}} = \frac{\text{weight}}{\text{area}} = \frac{\text{weight density} \times \!\, \text{volume}}{\text{area}}</math>
 
:<math>\text{Pressure} = \frac{\text{weight density} \times \!\, \text{(area} \times \!\, \text{depth)}}{\text{area}}</math>
 
With the "area" in the numerator and the "area" in the denominator canceling each other out, we are left with:
 
:<math>\text{Pressure} = \text{weight density} \times \!\, \text{depth}</math>
 
Written with symbols, this is our original equation:
:<math>P=\rho gh</math>
|}
 
The pressure a liquid exerts against the sides and bottom of a container depends on the density and the depth of the liquid. If atmospheric pressure is neglected, liquid pressure against the bottom is twice as great at twice the depth; at three times the depth, the liquid pressure is threefold; etc. Or, if the liquid is two or three times as dense, the liquid pressure is correspondingly two or three times as great for any given depth. Liquids are practically incompressible - that is, their volume can hardly be changed by pressure (water volume decreases by only 50 millionths of its original volume for each atmospheric increase in pressure). Thus, except for small changes produced by temperature, the density of a particular liquid is practically the same at all depths.
 
Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the ''total'' pressure acting on a liquid. The total pressure of a liquid, then, is ρ''gh'' + the pressure of the atmosphere. When this distinction is important, the term ''total pressure'' is used. Otherwise, discussions of liquid pressure refer to pressure without regard to the normally ever-present atmospheric pressure.
 
It is important to recognize that the pressure does not depend on the ''amount'' of liquid present. Volume is not the important factor - depth is. The average water pressure acting against a dam depends on the average depth of the water and not on the volume of water held back. For example, a large, shallow lake with a height of 3 m exerts only half the average pressure that the 6 m-tall small, deep pond does. A person will feel the same pressure whether his/her head is dunked a meter beneath the surface of the water in a small pool or to the same depth in the middle of a large lake. If four vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimeters under the surface will be acted on by water pressure that is the same in any of the vases. If the fish swims a few centimeters deeper, the pressure on the fish will increase with depth and be the same no matter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater, but it makes no difference what vase it is in. All vases are filled to equal depths, so the water pressure is the same at the bottom of each vase, regardless of its shape or volume. If water pressure at the bottom of a vase were greater than water pressure at the bottom of a neighboring vase, the greater pressure would force water sideways and then up the narrower vase to a higher level until the pressures at the bottom were equalized. Pressure is depth dependent, not volume dependent, so there is a reason that water seeks its own level.
 
===Direction of liquid pressure===
An experimentally determined fact about liquid pressure is that it is exerted equally in all directions.<ref name="Hewitt">Hewitt 251 (2006)</ref> If someone is submerged in water, no matter which way that person tilts his/her head, the person will feel the same amount of water pressure on his/her ears. Because a liquid can flow, this pressure isn't only downward. Pressure is seen acting sideways when water spurts sideways from a leak in the side of an upright can. Pressure also acts upward, as demonstrated when someone tries to push a beach ball beneath the surface of the water. The bottom of a boat is pushed upward by water pressure ([[buoyancy]]).
 
When a liquid presses against a surface, there is a net force that is perpendicular to the surface. Although pressure doesn't have a specific direction, force does. A submerged triangular block has water forced against each point from many directions, but components of the force that are not perpendicular to the surface cancel each other out, leaving only a net perpendicular point.<ref name="Hewitt" /> This is why water spurting from a hole in a bucket initially exits the bucket in a direction at right angles to the surface of the bucket in which the hole is located.Then it curves downward due to gravity. If there are three holes in a bucket (top, bottom, and middle), then the force vectors perpendicular to the inner container surface will increase with increasing depth - that is, a greater pressure at the bottom makes it so that the bottom hole will shoot water out the farthest. The force exerted by a fluid on a smooth surface is always at right angles to the surface. The speed of liquid out of the hole is <math>\scriptstyle \sqrt{2gh}</math>, where ''h'' is the depth below the free surface.<ref name="Hewitt" /> Interestingly, this is the same speed the water (or anything else) would have if freely falling the same vertical distance ''h''.
 
===Kinematic pressure===
:<math>P=p/\rho_0</math>
is the kinematic pressure, where <math>p</math> is the pressure and <math>\rho_0</math> constant mass density. The SI unit of ''P'' is m<sup>2</sup>/s<sup>2</sup>. Kinematic pressure is used in the same manner as [[kinematic viscosity]] <math>\nu</math> in order to compute [[Navier-Stokes equation]] without explicitly showing the density <math>\rho_0</math>.
 
;Navier-Stokes equation with kinematic quantities
:<math> \frac{\partial u}{\partial t} + (u \nabla) u = - \nabla P + \nu \nabla^2 u </math>
 
==See also==
{{portal|Underwater diving}}
{{cmn|3|
*[[Atmospheric pressure]]
*[[Blood pressure]]
*[[Boyle's Law]]
*[[Combined gas law]]
*[[Conversion of units]]
*[[Critical point (thermodynamics)]]
*[[Dynamic pressure]]
*[[Hydraulics]]
*[[Internal pressure]]
*[[Kinetic theory#Pressure|Kinetic theory]]
*[[Microphone]]
*[[Orders of magnitude (pressure)]]
*[[Partial pressure]]
*[[Pressure measurement]]
*[[Pressure sensor]]
*[[Sound pressure]]
*[[Spouting can]]
*[[Timeline of temperature and pressure measurement technology]]
*[[Units conversion by factor-label]]
*[[Vacuum]]
*[[Vacuum pump]]
*[[Vertical pressure variation]]
}}
 
==Notes==
{{Reflist|group=lower-alpha}}
 
==References==
{{reflist|1
<ref name="usn T2.10">{{cite book |title=US Navy Diving Manual, 6th revision |pages=2–32 |year=2006 |publisher=US Naval Sea Systems Command |location=United States |url=http://www.supsalv.org/00c3_publications.asp?destPage=00c3&pageID=3.9 |accessdate=2008-06-15 |author=US Navy }}</ref>
}}
 
==External links==
*[http://www.physnet.org/modules/pdf_modules/m48.pdf ''Introduction to Fluid Statics and Dynamics''] on [http://www.physnet.org/ Project PHYSNET]
*[http://www.grc.nasa.gov/WWW/K-12/airplane/pressure.html Pressure being a scalar quantity]
*[http://www.sengpielaudio.com/calculator-densityunits.htm Online pressure converter for 15 different pressure units]
*[http://www.cressto.cz/unit-converter How to convert pressure units]
*[http://amrita.olabs.co.in/?sub=1&brch=1&sim=71&cnt=1 Pressure Exerted by a Solid Iron Cuboid on Sand], instructions for performing classroom experiment
 
{{Diving medicine, physiology and physics}}
 
[[Category:Atmospheric thermodynamics]]
[[Category:Underwater diving physics]]
[[Category:Concepts in physics]]
[[Category:Fluid dynamics]]
[[Category:Fluid mechanics]]
[[Category:Hydraulics]]
[[Category:Pressure| ]]
[[Category:Thermodynamics]]
[[Category:State functions]]

Latest revision as of 11:36, 4 March 2014

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