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<div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Scalar nature</span> </div> </a> <ul id="toc-Scalar_nature-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Types" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Types"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Types</span> </div> </a> <button aria-controls="toc-Types-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Types subsection</span> </button> <ul id="toc-Types-sublist" class="vector-toc-list"> <li id="toc-Fluid_pressure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fluid_pressure"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Fluid pressure</span> </div> </a> <ul id="toc-Fluid_pressure-sublist" class="vector-toc-list"> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Applications</span> </div> </a> <ul id="toc-Applications-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Explosion_or_deflagration_pressures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Explosion_or_deflagration_pressures"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Explosion or deflagration pressures</span> </div> </a> <ul id="toc-Explosion_or_deflagration_pressures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Negative_pressures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Negative_pressures"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Negative pressures</span> </div> </a> <ul id="toc-Negative_pressures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stagnation_pressure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stagnation_pressure"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Stagnation pressure</span> </div> </a> <ul id="toc-Stagnation_pressure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Surface_pressure_and_surface_tension" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Surface_pressure_and_surface_tension"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Surface pressure and surface tension</span> </div> </a> <ul id="toc-Surface_pressure_and_surface_tension-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pressure_of_an_ideal_gas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pressure_of_an_ideal_gas"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Pressure of an ideal gas</span> </div> </a> <ul id="toc-Pressure_of_an_ideal_gas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vapour_pressure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vapour_pressure"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Vapour pressure</span> </div> </a> <ul id="toc-Vapour_pressure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liquid_pressure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liquid_pressure"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.8</span> <span>Liquid pressure</span> </div> </a> <ul id="toc-Liquid_pressure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Direction_of_liquid_pressure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Direction_of_liquid_pressure"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.9</span> <span>Direction of liquid pressure</span> </div> </a> <ul id="toc-Direction_of_liquid_pressure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kinematic_pressure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kinematic_pressure"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.10</span> <span>Kinematic pressure</span> </div> </a> <ul id="toc-Kinematic_pressure-sublist" class="vector-toc-list"> <li id="toc-Navier–Stokes_equation_with_kinematic_quantities" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Navier–Stokes_equation_with_kinematic_quantities"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.10.1</span> <span>Navier–Stokes equation with kinematic quantities</span> </div> </a> <ul id="toc-Navier–Stokes_equation_with_kinematic_quantities-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Pressure</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 112 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-112" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">112 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Druk" title="Druk – Afrikaans" lang="af" hreflang="af" data-title="Druk" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Druck_(Physik)" title="Druck (Physik) – Alemannic" lang="gsw" hreflang="gsw" data-title="Druck (Physik)" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B6%D8%BA%D8%B7" title="ضغط – Arabic" lang="ar" hreflang="ar" data-title="ضغط" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Presi%C3%B3n" title="Presión – Asturian" lang="ast" hreflang="ast" data-title="Presión" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/T%C9%99zyiq" title="Təzyiq – Azerbaijani" lang="az" hreflang="az" data-title="Təzyiq" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A8%D8%A7%D8%B3%D9%82%DB%8C" title="باسقی – South Azerbaijani" lang="azb" hreflang="azb" data-title="باسقی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9A%E0%A6%BE%E0%A6%AA" title="চাপ – Bangla" lang="bn" hreflang="bn" data-title="চাপ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ap-le%CC%8Dk" title="Ap-le̍k – Minnan" lang="nan" hreflang="nan" data-title="Ap-le̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A6%D1%96%D1%81%D0%BA" title="Ціск – Belarusian" lang="be" hreflang="be" data-title="Ціск" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A6%D1%96%D1%81%D0%BA" title="Ціск – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Ціск" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Presyon" title="Presyon – Central Bikol" lang="bcl" hreflang="bcl" data-title="Presyon" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9D%D0%B0%D0%BB%D1%8F%D0%B3%D0%B0%D0%BD%D0%B5" title="Налягане – Bulgarian" lang="bg" hreflang="bg" data-title="Налягане" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Pritisak" title="Pritisak – Bosnian" lang="bs" hreflang="bs" data-title="Pritisak" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Pressi%C3%B3" title="Pressió – Catalan" lang="ca" hreflang="ca" data-title="Pressió" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Tlak" title="Tlak – Czech" lang="cs" hreflang="cs" data-title="Tlak" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Puresha" title="Puresha – Shona" lang="sn" hreflang="sn" data-title="Puresha" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Gwasgedd" title="Gwasgedd – Welsh" lang="cy" hreflang="cy" data-title="Gwasgedd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Tryk_(fysik)" title="Tryk (fysik) – Danish" lang="da" hreflang="da" data-title="Tryk (fysik)" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%B6%D8%BA%D8%B7" title="ضغط – Moroccan Arabic" lang="ary" hreflang="ary" data-title="ضغط" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Druck_(Physik)" title="Druck (Physik) – German" lang="de" hreflang="de" data-title="Druck (Physik)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/R%C3%B5hk" title="Rõhk – Estonian" lang="et" hreflang="et" data-title="Rõhk" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%AF%CE%B5%CF%83%CE%B7" title="Πίεση – Greek" lang="el" hreflang="el" data-title="Πίεση" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%9B%D0%B5%D0%BF%D1%88%D1%82%D1%8F%D0%BC%D0%BE" title="Лепштямо – Erzya" lang="myv" hreflang="myv" data-title="Лепштямо" data-language-autonym="Эрзянь" data-language-local-name="Erzya" class="interlanguage-link-target"><span>Эрзянь</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Presi%C3%B3n" title="Presión – Spanish" lang="es" hreflang="es" data-title="Presión" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Premo" title="Premo – Esperanto" lang="eo" hreflang="eo" data-title="Premo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Presio" title="Presio – Basque" lang="eu" hreflang="eu" data-title="Presio" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D8%B4%D8%A7%D8%B1" title="فشار – Persian" lang="fa" hreflang="fa" data-title="فشار" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Pression" title="Pression – French" lang="fr" hreflang="fr" data-title="Pression" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Br%C3%BA" title="Brú – Irish" lang="ga" hreflang="ga" data-title="Brú" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Presi%C3%B3n" title="Presión – Galician" lang="gl" hreflang="gl" data-title="Presión" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%95%EB%A0%A5" title="압력 – Korean" lang="ko" hreflang="ko" data-title="압력" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%83%D5%B6%D5%B7%D5%B8%D6%82%D5%B4" title="Ճնշում – Armenian" lang="hy" hreflang="hy" data-title="Ճնշում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A6%E0%A4%BE%E0%A4%AC" title="दाब – Hindi" lang="hi" hreflang="hi" data-title="दाब" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Tlak" title="Tlak – Croatian" lang="hr" hreflang="hr" data-title="Tlak" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Preso" title="Preso – Ido" lang="io" hreflang="io" data-title="Preso" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Tekanan" title="Tekanan – Indonesian" lang="id" hreflang="id" data-title="Tekanan" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Pression" title="Pression – Interlingua" lang="ia" hreflang="ia" data-title="Pression" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Pressione" title="Pressione – Italian" lang="it" hreflang="it" data-title="Pressione" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9C%D7%97%D7%A5" title="לחץ – Hebrew" lang="he" hreflang="he" data-title="לחץ" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%92%E0%B2%A4%E0%B3%8D%E0%B2%A4%E0%B2%A1" title="ಒತ್ತಡ – Kannada" lang="kn" hreflang="kn" data-title="ಒತ್ತಡ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-krc mw-list-item"><a href="https://krc.wikipedia.org/wiki/%D0%91%D0%B0%D1%81%D1%8B%D0%BC" title="Басым – Karachay-Balkar" lang="krc" hreflang="krc" data-title="Басым" data-language-autonym="Къарачай-малкъар" data-language-local-name="Karachay-Balkar" class="interlanguage-link-target"><span>Къарачай-малкъар</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AC%E1%83%9C%E1%83%94%E1%83%95%E1%83%90" title="წნევა – Georgian" lang="ka" hreflang="ka" data-title="წნევა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%D8%AF%D9%8E%D8%A8%D8%A7%D9%88" title="دَباو – Kashmiri" lang="ks" hreflang="ks" data-title="دَباو" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="Kashmiri" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D2%9A%D1%8B%D1%81%D1%8B%D0%BC" title="Қысым – Kazakh" lang="kk" hreflang="kk" data-title="Қысым" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Shinikizo" title="Shinikizo – Swahili" lang="sw" hreflang="sw" data-title="Shinikizo" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Presyon" title="Presyon – Haitian Creole" lang="ht" hreflang="ht" data-title="Presyon" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%91%D0%B0%D1%81%D1%8B%D0%BC_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D0%BA)" title="Басым (физикалык) – Kyrgyz" lang="ky" hreflang="ky" data-title="Басым (физикалык)" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Pressio" title="Pressio – Latin" lang="la" hreflang="la" data-title="Pressio" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Spiediens" title="Spiediens – Latvian" lang="lv" hreflang="lv" data-title="Spiediens" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Sl%C4%97gis" title="Slėgis – Lithuanian" lang="lt" hreflang="lt" data-title="Slėgis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Dr%C3%B6k" title="Drök – Limburgish" lang="li" hreflang="li" data-title="Drök" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Nyom%C3%A1s" title="Nyomás – Hungarian" lang="hu" hreflang="hu" data-title="Nyomás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D1%82%D0%B8%D1%81%D0%BE%D0%BA" title="Притисок – Macedonian" lang="mk" hreflang="mk" data-title="Притисок" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Tsindry_(fizika)" title="Tsindry (fizika) – Malagasy" lang="mg" hreflang="mg" data-title="Tsindry (fizika)" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AE%E0%B5%BC%E0%B4%A6%E0%B5%8D%E0%B4%A6%E0%B4%82" title="മർദ്ദം – Malayalam" lang="ml" hreflang="ml" data-title="മർദ്ദം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%A6%E0%A4%BE%E0%A4%AC" title="दाब – Marathi" lang="mr" hreflang="mr" data-title="दाब" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%D8%B3%DB%8C%D8%A8" title="سیب – Mazanderani" lang="mzn" hreflang="mzn" data-title="سیب" data-language-autonym="مازِرونی" data-language-local-name="Mazanderani" class="interlanguage-link-target"><span>مازِرونی</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tekanan" title="Tekanan – Malay" lang="ms" hreflang="ms" data-title="Tekanan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%94%D0%B0%D1%80%D0%B0%D0%BB%D1%82" title="Даралт – Mongolian" lang="mn" hreflang="mn" data-title="Даралт" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%96%E1%80%AD%E1%80%A1%E1%80%AC%E1%80%B8" title="ဖိအား – Burmese" lang="my" hreflang="my" data-title="ဖိအား" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Druk_(grootheid)" title="Druk (grootheid) – Dutch" lang="nl" hreflang="nl" data-title="Druk (grootheid)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%9A%E0%A4%BE%E0%A4%AA" title="चाप – Nepali" lang="ne" hreflang="ne" data-title="चाप" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%9A%E0%A4%BE%E0%A4%AA" title="चाप – Newari" lang="new" hreflang="new" data-title="चाप" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%9C%A7%E5%8A%9B" title="圧力 – Japanese" lang="ja" hreflang="ja" data-title="圧力" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Druk" title="Druk – Northern Frisian" lang="frr" hreflang="frr" data-title="Druk" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Trykk" title="Trykk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Trykk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Trykk" title="Trykk – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Trykk" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Pression" title="Pression – Occitan" lang="oc" hreflang="oc" data-title="Pression" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Dhiibbaa" title="Dhiibbaa – Oromo" lang="om" hreflang="om" data-title="Dhiibbaa" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Bosim" title="Bosim – Uzbek" lang="uz" hreflang="uz" data-title="Bosim" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-blk mw-list-item"><a href="https://blk.wikipedia.org/wiki/%E1%80%90%E1%80%AD%E1%80%80%E1%80%BA%EA%A9%BB%E1%80%94%E1%80%BB%EA%A9%BB%E1%80%A1%E1%80%AC%E1%82%8F" title="တိက်ꩻနျꩻအာႏ – Pa'O" lang="blk" hreflang="blk" data-title="တိက်ꩻနျꩻအာႏ" data-language-autonym="ပအိုဝ်ႏဘာႏသာႏ" data-language-local-name="Pa'O" class="interlanguage-link-target"><span>ပအိုဝ်ႏဘာႏသာႏ</span></a></li><li class="interlanguage-link interwiki-pap mw-list-item"><a href="https://pap.wikipedia.org/wiki/Preshon" title="Preshon – Papiamento" lang="pap" hreflang="pap" data-title="Preshon" data-language-autonym="Papiamentu" data-language-local-name="Papiamento" class="interlanguage-link-target"><span>Papiamentu</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Pression" title="Pression – Piedmontese" lang="pms" hreflang="pms" data-title="Pression" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Druck_(Physik)" title="Druck (Physik) – Low German" lang="nds" hreflang="nds" data-title="Druck (Physik)" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ci%C5%9Bnienie" title="Ciśnienie – Polish" lang="pl" hreflang="pl" data-title="Ciśnienie" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Press%C3%A3o" title="Pressão – Portuguese" lang="pt" hreflang="pt" data-title="Pressão" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Presiune" title="Presiune – Romanian" lang="ro" hreflang="ro" data-title="Presiune" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/%C3%91it%27iy" title="Ñit'iy – Quechua" lang="qu" hreflang="qu" data-title="Ñit'iy" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B0%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Давление – Russian" lang="ru" hreflang="ru" data-title="Давление" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Pressur" title="Pressur – Scots" lang="sco" hreflang="sco" data-title="Pressur" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Shtypja" title="Shtypja – Albanian" lang="sq" hreflang="sq" data-title="Shtypja" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Prissioni" title="Prissioni – Sicilian" lang="scn" hreflang="scn" data-title="Prissioni" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B4%E0%B7%93%E0%B6%A9%E0%B6%B1%E0%B6%BA" title="පීඩනය – Sinhala" lang="si" hreflang="si" data-title="පීඩනය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Pressure" title="Pressure – Simple English" lang="en-simple" hreflang="en-simple" data-title="Pressure" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%AF%D9%BB%D8%A7%D8%A1%D9%8F_(%D9%81%D8%B2%DA%AA%D8%B3)" title="دٻاءُ (فزڪس) – Sindhi" lang="sd" hreflang="sd" data-title="دٻاءُ (فزڪس)" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Tlak" title="Tlak – Slovak" lang="sk" hreflang="sk" data-title="Tlak" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Tlak" title="Tlak – Slovenian" lang="sl" hreflang="sl" data-title="Tlak" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Cadaadis" title="Cadaadis – Somali" lang="so" hreflang="so" data-title="Cadaadis" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%BE%DB%95%D8%B3%D8%AA%D8%A7%D9%86" title="پەستان – Central Kurdish" lang="ckb" hreflang="ckb" data-title="پەستان" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D1%82%D0%B8%D1%81%D0%B0%D0%BA" title="Притисак – Serbian" lang="sr" hreflang="sr" data-title="Притисак" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Tlak" title="Tlak – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Tlak" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Tekenan" title="Tekenan – Sundanese" lang="su" hreflang="su" data-title="Tekenan" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Paine" title="Paine – Finnish" lang="fi" hreflang="fi" data-title="Paine" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Tryck" title="Tryck – Swedish" lang="sv" hreflang="sv" data-title="Tryck" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Presyon" title="Presyon – Tagalog" lang="tl" hreflang="tl" data-title="Presyon" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%B4%E0%AF%81%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="அழுத்தம் – Tamil" lang="ta" hreflang="ta" data-title="அழுத்தம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Adad" title="Adad – Kabyle" lang="kab" hreflang="kab" data-title="Adad" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%91%D0%B0%D1%81%D1%8B%D0%BC" title="Басым – Tatar" lang="tt" hreflang="tt" data-title="Басым" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" 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data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Force distributed over an area</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about pressure in the physical sciences. For other uses, see <a href="/wiki/Pressure_(disambiguation)" class="mw-disambig" title="Pressure (disambiguation)">Pressure (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above">Pressure</th></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:Pressure_exerted_by_collisions.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Pressure_exerted_by_collisions.svg/250px-Pressure_exerted_by_collisions.svg.png" decoding="async" width="250" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Pressure_exerted_by_collisions.svg/375px-Pressure_exerted_by_collisions.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Pressure_exerted_by_collisions.svg/500px-Pressure_exerted_by_collisions.svg.png 2x" data-file-width="246" data-file-height="218" /></a></span><div class="infobox-caption">Pressure exerted by particle collisions inside a closed container. The collisions that exert the pressure are highlighted in red.</div></td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Common symbols</div></th><td class="infobox-data"><span class="texhtml mvar" style="font-style:italic;">p</span>, <span class="texhtml mvar" style="font-style:italic;">P</span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/SI_unit" class="mw-redirect" title="SI unit">SI unit</a></th><td class="infobox-data"><a href="/wiki/Pascal_(unit)" title="Pascal (unit)">pascal</a> (Pa)</td></tr><tr><th scope="row" class="infobox-label">In <a href="/wiki/SI_base_unit" title="SI base unit"><span class="wrap">SI base units</span></a></th><td class="infobox-data"><a href="/wiki/Kilogram" title="Kilogram">kg</a>⋅<a href="/wiki/Metre" title="Metre">m</a><sup>−1</sup>⋅<a href="/wiki/Second" title="Second">s</a><sup>−2</sup></td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Derivations from<br />other quantities</div></th><td class="infobox-data"><span class="texhtml"><i>p</i> = <a href="/wiki/Force" title="Force"><i>F</i></a> / <a href="/wiki/Area" title="Area"><i>A</i></a></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Dimensional_analysis#Formulation" title="Dimensional analysis">Dimension</a></th><td class="infobox-data"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {M}}{\mathsf {L}}^{-1}{\mathsf {T}}^{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">T</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {M}}{\mathsf {L}}^{-1}{\mathsf {T}}^{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26435c142d9215c2834f037ef49d75c85a2f0e4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.542ex; height:2.676ex;" alt="{\displaystyle {\mathsf {M}}{\mathsf {L}}^{-1}{\mathsf {T}}^{-2}}" /></span></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title" style="padding-bottom:0.3em;border-bottom:1px solid #aaa;"><a href="/wiki/Thermodynamics" title="Thermodynamics">Thermodynamics</a></th></tr><tr><td class="sidebar-image" style="display:block;margin:0.3em 0 0.4em;"><span class="mw-default-size skin-invert-image" typeof="mw:File/Frameless"><a href="/wiki/Carnot_heat_engine" title="Carnot heat engine"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/250px-Carnot_heat_engine_2.svg.png" decoding="async" width="220" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/330px-Carnot_heat_engine_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/500px-Carnot_heat_engine_2.svg.png 2x" data-file-width="840" data-file-height="370" /></a></span><div class="sidebar-caption">The classical <a href="/wiki/Carnot_heat_engine" title="Carnot heat engine">Carnot heat engine</a></div></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c">Branches</div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Thermodynamics" title="Thermodynamics">Classical</a></li> <li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical</a></li> <li><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical</a></li> <li><a href="/wiki/Quantum_thermodynamics" title="Quantum thermodynamics">Quantum thermodynamics</a></li></ul> </div> <ul><li><a href="/wiki/Equilibrium_thermodynamics" title="Equilibrium thermodynamics">Equilibrium</a> / <a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">Laws</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Zeroth_law_of_thermodynamics" title="Zeroth law of thermodynamics">Zeroth</a></li> <li><a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">First</a></li> <li><a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">Second</a></li> <li><a href="/wiki/Third_law_of_thermodynamics" title="Third law of thermodynamics">Third</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Thermodynamic_system" title="Thermodynamic system">Systems</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Closed_system" title="Closed system">Closed system</a></li> <li><a href="/wiki/Thermodynamic_system#Open_system" title="Thermodynamic system">Open system</a></li> <li><a href="/wiki/Isolated_system" title="Isolated system">Isolated system</a></li></ul> <table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_state" title="Thermodynamic state">State</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Equation_of_state" title="Equation of state">Equation of state</a></li> <li><a href="/wiki/Ideal_gas" title="Ideal gas">Ideal gas</a></li> <li><a href="/wiki/Real_gas" title="Real gas">Real gas</a></li> <li><a href="/wiki/State_of_matter" title="State of matter">State of matter</a></li> <li><a href="/wiki/Phase_(matter)" title="Phase (matter)">Phase (matter)</a></li> <li><a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">Equilibrium</a></li> <li><a href="/wiki/Control_volume" title="Control volume">Control volume</a></li> <li><a href="/wiki/Thermodynamic_instruments" title="Thermodynamic instruments">Instruments</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_process" title="Thermodynamic process">Processes</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Isobaric_process" title="Isobaric process">Isobaric</a></li> <li><a href="/wiki/Isochoric_process" title="Isochoric process">Isochoric</a></li> <li><a href="/wiki/Isothermal_process" title="Isothermal process">Isothermal</a></li> <li><a href="/wiki/Adiabatic_process" title="Adiabatic process">Adiabatic</a></li> <li><a href="/wiki/Isentropic_process" title="Isentropic process">Isentropic</a></li> <li><a href="/wiki/Isenthalpic_process" title="Isenthalpic process">Isenthalpic</a></li> <li><a href="/wiki/Quasistatic_process" title="Quasistatic process">Quasistatic</a></li> <li><a href="/wiki/Polytropic_process" title="Polytropic process">Polytropic</a></li> <li><a href="/wiki/Free_expansion" class="mw-redirect" title="Free expansion">Free expansion</a></li> <li><a href="/wiki/Reversible_process_(thermodynamics)" title="Reversible process (thermodynamics)">Reversibility</a></li> <li><a href="/wiki/Irreversible_process" title="Irreversible process">Irreversibility</a></li> <li><a href="/wiki/Endoreversible_thermodynamics" title="Endoreversible thermodynamics">Endoreversibility</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_cycle" title="Thermodynamic cycle">Cycles</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Heat_engine" title="Heat engine">Heat engines</a></li> <li><a href="/wiki/Heat_pump_and_refrigeration_cycle" title="Heat pump and refrigeration cycle">Heat pumps</a></li> <li><a href="/wiki/Thermal_efficiency" title="Thermal efficiency">Thermal efficiency</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/List_of_thermodynamic_properties" title="List of thermodynamic properties">System properties</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div style="font-size:90%;padding-bottom:0.2em;border-bottom:1px solid #aaa;">Note: <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">Conjugate variables</a> in <i>italics</i></div> <table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none;margin-top:0.4em;"><tbody><tr><td class="sidebar-content" style="padding-bottom:0.7em;"> <ul><li><a href="/wiki/Thermodynamic_diagrams" title="Thermodynamic diagrams">Property diagrams</a></li> <li><a href="/wiki/Intensive_and_extensive_properties" title="Intensive and extensive properties">Intensive and extensive properties</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Process_function" title="Process function">Process functions</a></th></tr><tr><td class="sidebar-content" style="padding-bottom:0.7em;;padding-bottom:0.4em;"> <div class="hlist"> <ul><li><a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">Work</a></li> <li><a href="/wiki/Heat" title="Heat">Heat</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/State_function" title="State function">Functions of state</a></th></tr><tr><td class="sidebar-content" style="padding-bottom:0.7em;"> <ul><li><a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">Temperature</a> / <i><a href="/wiki/Entropy" title="Entropy">Entropy</a></i> (<a href="/wiki/Introduction_to_entropy" title="Introduction to entropy">introduction</a>)</li> <li><a class="mw-selflink selflink">Pressure</a> / <i><a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">Volume</a></i></li> <li><a href="/wiki/Chemical_potential" title="Chemical potential">Chemical potential</a> / <i><a href="/wiki/Particle_number" title="Particle number">Particle number</a></i></li> <li><a href="/wiki/Vapor_quality" title="Vapor quality">Vapor quality</a></li> <li><a href="/wiki/Reduced_properties" title="Reduced properties">Reduced properties</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Material_properties_(thermodynamics)" title="Material properties (thermodynamics)">Material properties</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Thermodynamic_databases_for_pure_substances" title="Thermodynamic databases for pure substances">Property databases</a></li></ul> <div style="font-size:90%;margin-top:0.4em;border-top:1px solid #aaa;"> <table> <tbody><tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Heat_capacity" title="Heat capacity">Specific heat capacity</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/891d40a9b18752b04065caee655d008b3ec11428" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.46ex; height:1.676ex;" alt="{\displaystyle c=}" /></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}" /></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c609f4d3c5692ea4495479ef47594dc67f9fa464" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.817ex; height:2.176ex;" alt="{\displaystyle \partial S}" /></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}" /></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504aa558fff3d00d10b03cadb1085cb0b7bdc631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.954ex; height:2.176ex;" alt="{\displaystyle \partial T}" /></span></td></tr></tbody></table></td></tr> <tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Compressibility" title="Compressibility">Compressibility</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =-}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mo>−</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =-}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b01c042bf1456bd4d2a8caed1f4912820a7ecbb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.239ex; height:2.509ex;" alt="{\displaystyle \beta =-}" /></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}" /></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cecdd9d069fa84159940068fc11a91b6b3b9ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.105ex; height:2.176ex;" alt="{\displaystyle \partial V}" /></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebc4a48eb2412f08b54fe438b5139c88f9cfa372" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.487ex; height:2.509ex;" alt="{\displaystyle \partial p}" /></span></td></tr></tbody></table></td></tr> <tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Thermal_expansion" title="Thermal expansion">Thermal expansion</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a92d4583d351f08c1c70985f0c843b2fff1b01e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.941ex; height:1.676ex;" alt="{\displaystyle \alpha =}" /></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}" /></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cecdd9d069fa84159940068fc11a91b6b3b9ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.105ex; height:2.176ex;" alt="{\displaystyle \partial V}" /></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504aa558fff3d00d10b03cadb1085cb0b7bdc631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.954ex; height:2.176ex;" alt="{\displaystyle \partial T}" /></span></td></tr></tbody></table></td></tr> </tbody></table></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Thermodynamic_equations" title="Thermodynamic equations">Equations</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Carnot%27s_theorem_(thermodynamics)" title="Carnot's theorem (thermodynamics)">Carnot's theorem</a></li> <li><a href="/wiki/Clausius_theorem" title="Clausius theorem">Clausius theorem</a></li> <li><a href="/wiki/Fundamental_thermodynamic_relation" title="Fundamental thermodynamic relation">Fundamental relation</a></li> <li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></li></ul> </div> <ul><li><a href="/wiki/Maxwell_relations" title="Maxwell relations">Maxwell relations</a></li> <li><a href="/wiki/Onsager_reciprocal_relations" title="Onsager reciprocal relations">Onsager reciprocal relations</a></li> <li><a href="/wiki/Bridgman%27s_thermodynamic_equations" title="Bridgman's thermodynamic equations">Bridgman's equations</a></li> <li><i><a href="/wiki/Table_of_thermodynamic_equations" title="Table of thermodynamic equations">Table of thermodynamic equations</a></i></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Thermodynamic_potential" title="Thermodynamic potential">Potentials</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">Free energy</a></li> <li><a href="/wiki/Free_entropy" title="Free entropy">Free entropy</a></li></ul> </div> <div class="plainlist"><ul><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Internal_energy" title="Internal energy">Internal energy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U(S,V)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U(S,V)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/921f33f9c6551562ec836007b035c2de6323d2d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.912ex; height:2.843ex;" alt="{\displaystyle U(S,V)}" /></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Enthalpy" title="Enthalpy">Enthalpy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H(S,p)=U+pV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(S,p)=U+pV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6407d78e5f39d07f70e2414a92e08e2e068519f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.254ex; height:2.843ex;" alt="{\displaystyle H(S,p)=U+pV}" /></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A(T,V)=U-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(T,V)=U-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e93692f031ba6484d82731c54db83a69daed3f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.867ex; height:2.843ex;" alt="{\displaystyle A(T,V)=U-TS}" /></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G(T,p)=H-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(T,p)=H-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dd7a8f0b8ae04963da133e3b202432e1b6caed4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.614ex; height:2.843ex;" alt="{\displaystyle G(T,p)=H-TS}" /></span></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist"><ul><li>History</li><li>Culture</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> History</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/History_of_thermodynamics" title="History of thermodynamics">General</a></li> <li><a href="/wiki/History_of_entropy" title="History of entropy">Entropy</a></li> <li><a href="/wiki/Gas_laws" title="Gas laws">Gas laws</a></li></ul> </div> <ul><li><a href="/wiki/History_of_perpetual_motion_machines" title="History of perpetual motion machines">"Perpetual motion" machines</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Philosophy_of_thermal_and_statistical_physics" class="mw-redirect" title="Philosophy of thermal and statistical physics">Philosophy</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Entropy_(arrow_of_time)" class="mw-redirect" title="Entropy (arrow of time)">Entropy and time</a></li> <li><a href="/wiki/Entropy_and_life" title="Entropy and life">Entropy and life</a></li> <li><a href="/wiki/Brownian_ratchet" title="Brownian ratchet">Brownian ratchet</a></li> <li><a href="/wiki/Maxwell%27s_demon" title="Maxwell's demon">Maxwell's demon</a></li> <li><a href="/wiki/Heat_death_paradox" title="Heat death paradox">Heat death paradox</a></li> <li><a href="/wiki/Loschmidt%27s_paradox" title="Loschmidt's paradox">Loschmidt's paradox</a></li> <li><a href="/wiki/Synergetics_(Haken)" title="Synergetics (Haken)">Synergetics</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> Theories</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Caloric_theory" title="Caloric theory">Caloric theory</a></li></ul> </div> <ul><li><a href="/wiki/Vis_viva" title="Vis viva"><i>Vis viva</i> <span style="font-size:85%;">("living force")</span></a></li> <li><a href="/wiki/Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">Mechanical equivalent of heat</a></li> <li><a href="/wiki/Power_(physics)" title="Power (physics)">Motive power</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/List_of_important_publications_in_physics" class="mw-redirect" title="List of important publications in physics">Key publications</a></th></tr><tr><td class="sidebar-content"> <ul><li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/An_Inquiry_Concerning_the_Source_of_the_Heat_Which_Is_Excited_by_Friction" title="An Inquiry Concerning the Source of the Heat Which Is Excited by Friction">An Inquiry Concerning the<br />Source ... Friction</a></i></div></li> <li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of<br />Heterogeneous Substances</a></i></div></li> <li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/Reflections_on_the_Motive_Power_of_Fire" title="Reflections on the Motive Power of Fire">Reflections on the<br />Motive Power of Fire</a></i></div></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> Timelines</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Timeline_of_thermodynamics" title="Timeline of thermodynamics">Thermodynamics</a></li> <li><a href="/wiki/Timeline_of_heat_engine_technology" title="Timeline of heat engine technology">Heat engines</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <div class="hlist"><ul><li>Art</li><li>Education</li></ul></div></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">Maxwell's thermodynamic surface</a></li> <li><a href="/wiki/Entropy_(energy_dispersal)" title="Entropy (energy dispersal)">Entropy as energy dispersal</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c">Scientists</div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Boltzmann</a></li> <li><a href="/wiki/Percy_Williams_Bridgman" title="Percy Williams Bridgman">Bridgman</a></li> <li><a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Carathéodory</a></li> <li><a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Carnot</a></li> <li><a href="/wiki/Beno%C3%AEt_Paul_%C3%89mile_Clapeyron" class="mw-redirect" title="Benoît Paul Émile Clapeyron">Clapeyron</a></li> <li><a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Clausius</a></li> <li><a href="/wiki/Th%C3%A9ophile_de_Donder" title="Théophile de Donder">de Donder</a></li> <li><a href="/wiki/Pierre_Duhem" title="Pierre Duhem">Duhem</a></li> <li><a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">von Helmholtz</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Lewis</a></li> <li><a href="/wiki/Fran%C3%A7ois_Massieu" title="François Massieu">Massieu</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Julius_von_Mayer" title="Julius von Mayer">von Mayer</a></li> <li><a href="/wiki/Walther_Nernst" title="Walther Nernst">Nernst</a></li> <li><a href="/wiki/Lars_Onsager" title="Lars Onsager">Onsager</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/William_John_Macquorn_Rankine" class="mw-redirect" title="William John Macquorn Rankine">Rankine</a></li> <li><a href="/wiki/John_Smeaton" title="John Smeaton">Smeaton</a></li> <li><a href="/wiki/Georg_Ernst_Stahl" title="Georg Ernst Stahl">Stahl</a></li> <li><a href="/wiki/Peter_Tait_(physicist)" class="mw-redirect" title="Peter Tait (physicist)">Tait</a></li> <li><a href="/wiki/Benjamin_Thompson" title="Benjamin Thompson">Thompson</a></li> <li><a href="/wiki/Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">van der Waals</a></li> <li><a href="/wiki/John_James_Waterston" title="John James Waterston">Waterston</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c">Other</div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Nucleation" title="Nucleation">Nucleation</a></li> <li><a href="/wiki/Self-assembly" title="Self-assembly">Self-assembly</a></li> <li><a href="/wiki/Self-organization" title="Self-organization">Self-organization</a></li> <li><a href="/wiki/Order_and_disorder" title="Order and disorder">Order and disorder</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below"> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Thermodynamics" title="Category:Thermodynamics">Category</a></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Thermodynamics_sidebar" title="Template:Thermodynamics sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Thermodynamics_sidebar" title="Template talk:Thermodynamics sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Thermodynamics_sidebar" title="Special:EditPage/Template:Thermodynamics sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Pressure</b> (symbol: <i>p</i> or <i>P</i>) is the <a href="/wiki/Force" title="Force">force</a> applied <a href="/wiki/Perpendicular" title="Perpendicular">perpendicular</a> to the surface of an object per unit <a href="/wiki/Area" title="Area">area</a> over which that force is distributed.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 445">: 445 </span></sup> <a href="/wiki/Gauge_pressure" class="mw-redirect" title="Gauge pressure">Gauge pressure</a> (also spelled <i>gage</i> pressure)<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> is the pressure relative to the ambient pressure. </p><p>Various <a href="#Units">units</a> are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the <a href="/wiki/International_System_of_Units" title="International System of Units">SI</a> unit of pressure, the <a href="/wiki/Pascal_(unit)" title="Pascal (unit)">pascal</a> (Pa), for example, is one <a href="/wiki/Newton_(unit)" title="Newton (unit)">newton</a> per <a href="/wiki/Square_metre" title="Square metre">square metre</a> (N/m<sup>2</sup>); similarly, the <a href="/wiki/Pound_(force)" title="Pound (force)">pound-force</a> per <a href="/wiki/Square_inch" title="Square inch">square inch</a> (<a href="/wiki/Pound_per_square_inch" title="Pound per square inch">psi</a>, symbol lbf/in<sup>2</sup>) is the traditional unit of pressure in the <a href="/wiki/Imperial_units" title="Imperial units">imperial</a> and <a href="/wiki/United_States_customary_units" title="United States customary units">US customary</a> systems. Pressure may also be expressed in terms of <a href="/wiki/Standard_atmosphere_(unit)" title="Standard atmosphere (unit)">standard atmospheric pressure</a>; the unit <a href="/wiki/Atmosphere_(unit)" class="mw-redirect" title="Atmosphere (unit)">atmosphere</a> (atm) is equal to this pressure, and the <a href="/wiki/Torr" title="Torr">torr</a> is defined as <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">760</span></span> of this. <a href="/wiki/Manometric" class="mw-redirect" title="Manometric">Manometric</a> units such as the <a href="/wiki/Centimetre_of_water" class="mw-redirect" title="Centimetre of water">centimetre of water</a>, <a href="/wiki/Millimetre_of_mercury" title="Millimetre of mercury">millimetre of mercury</a>, and <a href="/wiki/Inch_of_mercury" title="Inch of mercury">inch of mercury</a> are used to express pressures in terms of the height of <a href="/wiki/Pressure_measurement#Liquid_column_(manometer)" title="Pressure measurement">column of a particular fluid</a> in a manometer. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Pressure</i> is the amount of force applied <a href="/wiki/Perpendicular" title="Perpendicular">perpendicular</a> to the surface of an object per unit area. The symbol for it is "p" or <i>P</i>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/IUPAC" class="mw-redirect" title="IUPAC">IUPAC</a> recommendation for pressure is a lower-case <i>p</i>.<sup id="cite_ref-IUPACGoldPressure_4-0" class="reference"><a href="#cite_note-IUPACGoldPressure-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> However, upper-case <i>P</i> is widely used. The usage of <i>P</i> vs <i>p</i> depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as <a href="/wiki/Power_(physics)" title="Power (physics)">power</a> and <a href="/wiki/Momentum" title="Momentum">momentum</a>, and on writing style. </p> <div class="mw-heading mw-heading3"><h3 id="Formula">Formula</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=2" title="Edit section: Formula"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><table class="sidebar nomobile nowraplinks wraplinks" style="width:18em;"><tbody><tr><td class="sidebar-above" style="background:lavender; font-size:120%;"> <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">Conjugate variables<br />of thermodynamics</a></td></tr><tr><td class="sidebar-content" style="padding:2px;"> <table class="wikitable" style="width:100%;border-collapse:collapse;border-spacing:0px 0px;border:none;margin:1px 0 0 0;"><tbody><tr style="vertical-align:top"><td> <a class="mw-selflink selflink">Pressure</a></td><td> <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">Volume</a></td></tr><tr style="vertical-align:top"><td> (<a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">Stress</a>)</td><td> (<a href="/wiki/Deformation_(physics)#Strain" title="Deformation (physics)">Strain</a>)</td></tr><tr style="vertical-align:top"><td> <a href="/wiki/Temperature" title="Temperature">Temperature</a></td><td> <a href="/wiki/Entropy" title="Entropy">Entropy</a></td></tr><tr style="vertical-align:top"><td> <a href="/wiki/Chemical_potential" title="Chemical potential">Chemical potential</a></td><td> <a href="/wiki/Particle_number" title="Particle number">Particle number</a></td></tr></tbody></table></td> </tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/File:Pressure_force_area.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Pressure_force_area.svg/200px-Pressure_force_area.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Pressure_force_area.svg/300px-Pressure_force_area.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Pressure_force_area.svg/400px-Pressure_force_area.svg.png 2x" data-file-width="350" data-file-height="350" /></a><figcaption></figcaption></figure> <p>Mathematically:<sup id="cite_ref-Georgia_State_University,_Physics_&_Astronomy_5-0" class="reference"><a href="#cite_note-Georgia_State_University,_Physics_&_Astronomy-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p={\frac {F}{A}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <mi>A</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p={\frac {F}{A}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46bcb6e308d86c8df7f4bbe05df5a44f6c2c2f0d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-left: -0.089ex; width:7.583ex; height:5.343ex;" alt="{\displaystyle p={\frac {F}{A}},}" /></span> where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}" /></span> is the pressure,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}" /></span> is the magnitude of the <a href="/wiki/Normal_force" title="Normal force">normal force</a>,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" /></span> is the area of the surface on contact.</li></ul> <p>Pressure is a <a href="/wiki/Scalar_(physics)" title="Scalar (physics)">scalar</a> quantity. It relates the <a href="/wiki/Vector_area" title="Vector area">vector area</a> element (a vector normal to the surface) with the <a href="/wiki/Normal_force" title="Normal force">normal force</a> acting on it. The pressure is the scalar <a href="/wiki/Proportionality_constant" class="mw-redirect" title="Proportionality constant">proportionality constant</a> that relates these two normal vectors: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d\mathbf {F} _{n}=-p\,d\mathbf {A} =-p\,\mathbf {n} \,dA.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>p</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> <mo>=</mo> <mo>−</mo> <mi>p</mi> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">n</mi> </mrow> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>A</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\mathbf {F} _{n}=-p\,d\mathbf {A} =-p\,\mathbf {n} \,dA.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/326ab5a81d27c5faff9b177ee7c54a10825c621c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.757ex; height:2.509ex;" alt="{\displaystyle d\mathbf {F} _{n}=-p\,d\mathbf {A} =-p\,\mathbf {n} \,dA.}" /></span> </p><p>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 <i>S</i> in contact with the fluid, the total force exerted by the fluid on that surface is the <a href="/wiki/Surface_integral" title="Surface integral">surface integral</a> over <i>S</i> of the right-hand side of the above equation. </p><p>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.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2021)">citation needed</span></a></i>]</sup> </p><p>Pressure is distributed to solid boundaries or across arbitrary sections of fluid <i>normal to</i> these boundaries or sections at every point. It is a fundamental parameter in <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>, and it is <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">conjugate</a> to <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">volume</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> It is defined as a derivative of the <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> of a system:<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=-\left({\frac {\partial U}{\partial V}}\right)_{S,N},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=-\left({\frac {\partial U}{\partial V}}\right)_{S,N},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3947becd781ed025282089f62e57c391cfbb0abb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; margin-left: -0.089ex; width:17.384ex; height:6.509ex;" alt="{\displaystyle p=-\left({\frac {\partial U}{\partial V}}\right)_{S,N},}" /></span></dd></dl> <p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}" /></span> is the internal energy,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span> is the volume of the system,</li> <li>The subscripts mean that the derivative is taken at fixed <a href="/wiki/Entropy" title="Entropy">entropy</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}" /></span>) and <a href="/wiki/Particle_number" title="Particle number">particle number</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}" /></span>).</li></ul> <div class="mw-heading mw-heading3"><h3 id="Units">Units</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=3" title="Edit section: Units"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Barometer_mercury_column_hg.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Barometer_mercury_column_hg.jpg/250px-Barometer_mercury_column_hg.jpg" decoding="async" width="220" height="312" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Barometer_mercury_column_hg.jpg/330px-Barometer_mercury_column_hg.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Barometer_mercury_column_hg.jpg/500px-Barometer_mercury_column_hg.jpg 2x" data-file-width="1704" data-file-height="2415" /></a><figcaption>Mercury column</figcaption></figure> <p>The <a href="/wiki/SI" class="mw-redirect" title="SI">SI</a> unit for pressure is the <a href="/wiki/Pascal_(unit)" title="Pascal (unit)">pascal</a> (Pa), equal to one <a href="/wiki/Newton_(unit)" title="Newton (unit)">newton</a> per <a href="/wiki/Square_metre" title="Square metre">square metre</a> (N/m<sup>2</sup>, or kg·m<sup>−1</sup>·s<sup>−2</sup>). This name for the unit was added in 1971;<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> before that, pressure in SI was expressed in newtons per square metre. </p><p>Other units of pressure, such as <a href="/wiki/Pound-force_per_square_inch" class="mw-redirect" title="Pound-force per square inch">pounds per square inch</a> (lbf/in<sup>2</sup>) and <a href="/wiki/Bar_(unit)" title="Bar (unit)">bar</a>, are also in common use. The <a href="/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_units" title="Centimetre–gram–second system of units">CGS</a> unit of pressure is the <a href="/wiki/Barye" title="Barye">barye</a> (Ba), equal to 1 dyn·cm<sup>−2</sup>, or 0.1 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>") 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 <a href="/wiki/Technical_atmosphere" class="mw-redirect" title="Technical atmosphere">technical atmosphere</a> (symbol: at) is 1 kgf/cm<sup>2</sup> (98.0665 kPa, or 14.223 psi). </p><p>Pressure is related to <a href="/wiki/Energy_density" title="Energy density">energy density</a> and may be expressed in units such as <a href="/wiki/Joule" title="Joule">joules</a> per cubic metre (J/m<sup>3</sup>, which is equal to Pa). Mathematically: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p={\frac {F\cdot {\text{distance}}}{A\cdot {\text{distance}}}}={\frac {\text{work}}{\text{volume}}}={\frac {\text{energy (J)}}{{\text{volume }}({\text{m}}^{3})}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>F</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>distance</mtext> </mrow> </mrow> <mrow> <mi>A</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>distance</mtext> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>work</mtext> <mtext>volume</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>energy (J)</mtext> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>volume </mtext> </mrow> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p={\frac {F\cdot {\text{distance}}}{A\cdot {\text{distance}}}}={\frac {\text{work}}{\text{volume}}}={\frac {\text{energy (J)}}{{\text{volume }}({\text{m}}^{3})}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/258d90b2992ca2caf6b4dd910d3667419fa17246" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-left: -0.089ex; width:45.387ex; height:6.509ex;" alt="{\displaystyle p={\frac {F\cdot {\text{distance}}}{A\cdot {\text{distance}}}}={\frac {\text{work}}{\text{volume}}}={\frac {\text{energy (J)}}{{\text{volume }}({\text{m}}^{3})}}.}" /></span> </p><p>Some <a href="/wiki/Meteorologist" title="Meteorologist">meteorologists</a> prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit <a href="/wiki/Millibar" class="mw-redirect" title="Millibar">millibar</a> (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 <a href="/wiki/Decibar" class="mw-redirect" title="Decibar">decibars</a> (dbar) because pressure in the ocean increases by approximately one decibar per metre depth. </p><p>The <a href="/wiki/Atmosphere_(unit)" class="mw-redirect" title="Atmosphere (unit)">standard atmosphere</a> (atm) is an established constant. It is approximately equal to typical air pressure at Earth <a href="/wiki/Mean_sea_level" class="mw-redirect" title="Mean sea level">mean sea level</a> and is defined as <span class="nowrap"><span data-sort-value="7005101325000000000♠"></span>101<span style="margin-left:.25em;">325</span> Pa</span> (Note: IUPAC recommends the value <span class="nowrap"><span data-sort-value="7005100000000000000♠"></span>100<span style="margin-left:.25em;">000</span> Pa</span>, but prior to 1982 the value <span class="nowrap"><span data-sort-value="7005101325000000000♠"></span>101<span style="margin-left:.25em;">325</span> Pa</span> (= 1 atm) was usually used.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Because pressure is commonly measured by its ability to displace a column of liquid in a <a href="/wiki/Manometer" class="mw-redirect" title="Manometer">manometer</a>, pressures are often expressed as a depth of a particular fluid (e.g., <a href="/wiki/Centimetres_of_water" class="mw-redirect" title="Centimetres of water">centimetres of water</a>, <a href="/wiki/Millimetres_of_mercury" class="mw-redirect" title="Millimetres of mercury">millimetres of mercury</a> or <a href="/wiki/Inches_of_mercury" class="mw-redirect" title="Inches of mercury">inches of mercury</a>). The most common choices are <a href="/wiki/Mercury_(element)" title="Mercury (element)">mercury</a> (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 <i>h</i> and density <i>ρ</i> is given by the hydrostatic pressure equation <span class="nowrap"><i>p</i> = <i>ρgh</i></span>, where <i>g</i> is the <a href="/wiki/Gravitational_acceleration" title="Gravitational acceleration">gravitational acceleration</a>. 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. </p><p>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.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> One millimetre of mercury is approximately equal to one <a href="/wiki/Torr" title="Torr">torr</a>. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These <i>manometric units</i> are still encountered in many fields. <a href="/wiki/Blood_pressure" title="Blood pressure">Blood pressure</a> is measured in millimetres (or centimetres) of mercury in most of the world, and lung pressures in centimetres of water are still common.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2021)">citation needed</span></a></i>]</sup> </p><p><a href="/wiki/Underwater_diving" title="Underwater diving">Underwater divers</a> use the <a href="/wiki/Metre_sea_water" title="Metre sea water">metre sea water</a> (msw or MSW) and <a href="/wiki/Foot_sea_water" class="mw-redirect" title="Foot sea water">foot sea water</a> (fsw or FSW) units of pressure, and these are the units for pressure gauges used to measure pressure exposure in <a href="/wiki/Diving_chamber" title="Diving chamber">diving chambers</a> and <a href="/wiki/Dive_computer" title="Dive computer">personal decompression computers</a>. A msw is defined as 0.1 bar (= 10,000 Pa), is not the same as a linear metre of depth. 33.066 fsw = 1 atm<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2023)">citation needed</span></a></i>]</sup> (1 atm = 101,325 Pa / 33.066 = 3,064.326 Pa). The pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2023)">citation needed</span></a></i>]</sup> </p><p>Gauge 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 <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">National Institute of Standards and Technology</a> recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure.<sup id="cite_ref-pubs_11-0" class="reference"><a href="#cite_note-pubs-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> For example, <span class="nowrap">"<i>p</i><sub>g</sub> = 100 psi"</span> rather than <span class="nowrap">"<i>p</i> = 100 psig"</span>. </p><p>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. </p><p>Presently or formerly popular pressure units include the following: </p> <ul><li><a href="/wiki/Atmosphere_(unit)" class="mw-redirect" title="Atmosphere (unit)">atmosphere</a> (atm)</li> <li>manometric units: <ul><li>centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury,</li> <li><span class="anchor" id="H2O"></span>height of equivalent column of water, including <a href="/wiki/Millimeters,_water_gauge" class="mw-redirect" title="Millimeters, water gauge">millimetre</a> (mm <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span>), <a href="/wiki/Centimetre_of_water" class="mw-redirect" title="Centimetre of water">centimetre</a> (cm <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span>), metre, <a href="/wiki/Inch_of_water" title="Inch of water">inch</a>, and foot of water;</li></ul></li> <li>imperial and customary units: <ul><li><a href="/wiki/Kip_(unit)" title="Kip (unit)">kip</a>, <a href="/wiki/Ton-force#Short_ton-force" title="Ton-force">short ton-force</a>, <a href="/wiki/Ton-force#Long_ton-force" title="Ton-force">long ton-force</a>, <a href="/wiki/Pound-force" class="mw-redirect" title="Pound-force">pound-force</a>, <a href="/wiki/Ounce-force" class="mw-redirect" title="Ounce-force">ounce-force</a>, and <a href="/wiki/Poundal" title="Poundal">poundal</a> per square inch,</li> <li>short ton-force and long ton-force per square inch,</li> <li>fsw (feet sea water) used in underwater diving, particularly in connection with diving pressure exposure and <a href="/wiki/Decompression_(diving)" title="Decompression (diving)">decompression</a>;</li></ul></li> <li>non-SI metric units: <ul><li><a href="/wiki/Bar_(unit)" title="Bar (unit)">bar</a>, decibar, <a href="/wiki/Millibar" class="mw-redirect" title="Millibar">millibar</a>, <ul><li>msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and <a href="/wiki/Decompression_(diving)" title="Decompression (diving)">decompression</a>,</li></ul></li> <li>kilogram-force, or kilopond, per square centimetre (<a href="/wiki/Technical_atmosphere" class="mw-redirect" title="Technical atmosphere">technical atmosphere</a>),</li> <li>gram-force and tonne-force (metric ton-force) per square centimetre,</li> <li><a href="/wiki/Barye" title="Barye">barye</a> (<a href="/wiki/Dyne" title="Dyne">dyne</a> per square centimetre),</li> <li>kilogram-force and tonne-force per square metre,</li> <li><a href="/wiki/Sthene" class="mw-redirect" title="Sthene">sthene</a> per square metre (<a href="/wiki/Pieze" class="mw-redirect" title="Pieze">pieze</a>).</li></ul></li></ul> <div class="mw-heading mw-heading3"><h3 id="Examples">Examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=4" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Aluminium_cylinder.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Aluminium_cylinder.jpg/120px-Aluminium_cylinder.jpg" decoding="async" width="120" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Aluminium_cylinder.jpg/180px-Aluminium_cylinder.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Aluminium_cylinder.jpg/240px-Aluminium_cylinder.jpg 2x" data-file-width="1000" data-file-height="1770" /></a><figcaption>The effects of an external pressure of 700 bar on an aluminum cylinder with 5 mm (0.197 in) wall thickness</figcaption></figure> <p>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 <a href="/wiki/Thumbtack" class="mw-redirect" title="Thumbtack">thumbtack</a> 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 <i>normal to</i> these boundaries or sections at every point. Unlike <a href="/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stress</a>, pressure is defined as a <a href="/wiki/Scalar_(physics)" title="Scalar (physics)">scalar quantity</a>. The negative <a href="/wiki/Gradient" title="Gradient">gradient</a> of pressure is called the <a href="/wiki/Force_density" title="Force density">force density</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>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.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>For gases, pressure is sometimes measured not as an <i>absolute pressure</i>, but relative to <a href="/wiki/Atmospheric_pressure" title="Atmospheric pressure">atmospheric pressure</a>; such measurements are called <i>gauge pressure</i>. An example of this is the air pressure in an <a href="/wiki/Automobile" class="mw-redirect" title="Automobile">automobile</a> <a href="/wiki/Tire" title="Tire">tire</a>, which might be said to be "220 <a href="/wiki/Pascal_(unit)" title="Pascal (unit)">kPa</a> (32 psi)", but is actually 220 kPa (32 psi) above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa (14.7 psi), the absolute pressure in the tire is therefore about 320 kPa (46 psi). In technical work, this is written "a gauge pressure of 220 kPa (32 psi)". </p><p>Where space is limited, such as on <a href="/wiki/Pressure_gauge" class="mw-redirect" title="Pressure gauge">pressure gauges</a>, <a href="/wiki/Name_plate" class="mw-redirect" title="Name plate">name plates</a>, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)", is permitted.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> In non-<a href="/wiki/SI" class="mw-redirect" title="SI">SI</a> technical work, a gauge pressure of 32 psi (220 kPa) is sometimes written as "32 psig", and an absolute pressure as "32 psia", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.<sup id="cite_ref-pubs_11-1" class="reference"><a href="#cite_note-pubs-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on <a href="/wiki/Pressure_vessel" title="Pressure vessel">storage vessels</a> 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 kPa (15 psi), a gas (such as helium) at 200 kPa (29 psi) (gauge) (300 kPa or 44 psi [absolute]) is 50% denser than the same gas at 100 kPa (15 psi) (gauge) (200 kPa or 29 psi [absolute]). Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Scalar_nature">Scalar nature</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=5" title="Edit section: Scalar nature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a static <a href="/wiki/Gas" title="Gas">gas</a>, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant <a href="/wiki/Brownian_motion" title="Brownian motion">random motion</a>. 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 of some sort, or in a gravitational well such as a planet, otherwise known as <i><a href="/wiki/Atmospheric_pressure" title="Atmospheric pressure">atmospheric pressure</a></i>. </p><p>In the case of planetary <a href="/wiki/Atmosphere" title="Atmosphere">atmospheres</a>, the <a href="/wiki/Pressure-gradient_force" title="Pressure-gradient force">pressure-gradient force</a> of the gas pushing outwards from higher pressure, lower altitudes to lower pressure, higher altitudes is balanced by the <a href="/wiki/Gravitational_force" class="mw-redirect" title="Gravitational force">gravitational force</a>, preventing the gas from diffusing into <a href="/wiki/Outer_space" title="Outer space">outer space</a> and maintaining <a href="/wiki/Hydrostatic_equilibrium" title="Hydrostatic equilibrium">hydrostatic equilibrium</a>. </p><p>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.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>A closely related quantity is the <a href="/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stress</a> tensor <i>σ</i>, which relates the vector force <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da18bef8c979f3548bb0d8976f5844012d7b8256" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.683ex; height:2.176ex;" alt="{\displaystyle \mathbf {F} }" /></span> to the <a href="/wiki/Vector_area" title="Vector area">vector area</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0795cc96c75d81520a120482662b90f024c9a1a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.019ex; height:2.176ex;" alt="{\displaystyle \mathbf {A} }" /></span> via the linear relation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} =\sigma \mathbf {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} =\sigma \mathbf {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/794ef3068c311fab0818b0975e4c7c5a5e473e9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.13ex; height:2.176ex;" alt="{\displaystyle \mathbf {F} =\sigma \mathbf {A} }" /></span>. </p><p>This <a href="/wiki/Tensor" title="Tensor">tensor</a> may be expressed as the sum of the <a href="/wiki/Viscous_stress_tensor" title="Viscous stress tensor">viscous stress tensor</a> 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.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>According to the theory of <a href="/wiki/General_relativity" title="General relativity">general relativity</a>, pressure increases the strength of a gravitational field (see <a href="/wiki/Stress%E2%80%93energy_tensor" title="Stress–energy tensor">stress–energy tensor</a>) and so adds to the mass-energy cause of <a href="/wiki/Gravity" title="Gravity">gravity</a>. This effect is unnoticeable at everyday pressures but is significant in <a href="/wiki/Neutron_star" title="Neutron star">neutron stars</a>, although it has not been experimentally tested.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Types">Types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=6" title="Edit section: Types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Fluid_pressure">Fluid pressure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=7" title="Edit section: Fluid pressure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Fluid pressure</i> is most often the compressive stress at some point within a <a href="/wiki/Fluid" title="Fluid">fluid</a>. (The term <i>fluid</i> refers to both liquids and gases – for more information specifically about liquid pressure, see <a href="#Liquid_pressure">section below</a>.) </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Defekter_unterflurhydrant_goettingen.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Defekter_unterflurhydrant_goettingen.jpg/260px-Defekter_unterflurhydrant_goettingen.jpg" decoding="async" width="260" height="390" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Defekter_unterflurhydrant_goettingen.jpg/390px-Defekter_unterflurhydrant_goettingen.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Defekter_unterflurhydrant_goettingen.jpg/520px-Defekter_unterflurhydrant_goettingen.jpg 2x" data-file-width="1200" data-file-height="1800" /></a><figcaption>Water escapes at high speed from a damaged hydrant that contains water at high pressure</figcaption></figure> <p>Fluid pressure occurs in one of two situations: </p> <ul><li>An open condition, called "open channel flow", e.g. the ocean, a swimming pool, or the atmosphere.</li> <li>A closed condition, called "closed conduit", e.g. a water line or gas line.</li></ul> <p>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 <a href="/wiki/Fluid_statics" class="mw-redirect" title="Fluid statics">fluid statics</a>. The pressure at any given point of a non-moving (static) fluid is called the <i>hydrostatic pressure</i>. </p><p>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 <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>. </p><p>The concepts of fluid pressure are predominantly attributed to the discoveries of <a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Blaise Pascal</a> and <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a>. <a href="/wiki/Bernoulli%27s_equation" class="mw-redirect" title="Bernoulli's equation">Bernoulli's equation</a> 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<sup id="cite_ref-Finnemore_18-0" class="reference"><a href="#cite_note-Finnemore-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> and incompressible.<sup id="cite_ref-Finnemore_18-1" class="reference"><a href="#cite_note-Finnemore-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> An ideal fluid is a fluid in which there is no friction, it is <a href="/wiki/Inviscid" class="mw-redirect" title="Inviscid">inviscid</a><sup id="cite_ref-Finnemore_18-2" class="reference"><a href="#cite_note-Finnemore-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> (zero <a href="/wiki/Viscosity" title="Viscosity">viscosity</a>).<sup id="cite_ref-Finnemore_18-3" class="reference"><a href="#cite_note-Finnemore-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> The equation for all points of a system filled with a constant-density fluid is<sup id="cite_ref-NCEES_19-0" class="reference"><a href="#cite_note-NCEES-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {p}{\gamma }}+{\frac {v^{2}}{2g}}+z=\mathrm {const} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <mi>γ</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>g</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {p}{\gamma }}+{\frac {v^{2}}{2g}}+z=\mathrm {const} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d1c445c0cca05fd86d3270b9cc09aeb1055433c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.036ex; height:6.176ex;" alt="{\displaystyle {\frac {p}{\gamma }}+{\frac {v^{2}}{2g}}+z=\mathrm {const} ,}" /></span> </p><p>where: </p> <ul><li><i>p</i>, pressure of the fluid,</li> <li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\gamma }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\gamma }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c5a51bb731eb471125cf853d8c845695870617f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle {\gamma }}" /></span></i> = <i>ρg</i>, density × acceleration of gravity is the (volume-) <a href="/wiki/Specific_weight" title="Specific weight">specific weight</a> of the fluid,<sup id="cite_ref-Finnemore_18-4" class="reference"><a href="#cite_note-Finnemore-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li> <li><i>v</i>, velocity of the fluid,</li> <li><i>g</i>, <a href="/wiki/Gravitational_acceleration" title="Gravitational acceleration">acceleration of gravity</a>,</li> <li><i>z</i>, elevation,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {p}{\gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <mi>γ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {p}{\gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf7442b3179a84a84bb4806d395446ff61314e4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:2.098ex; height:5.343ex;" alt="{\displaystyle {\frac {p}{\gamma }}}" /></span>, pressure head,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {v^{2}}{2g}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>g</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {v^{2}}{2g}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8115229798fd3a3a4ad6dc853e442791232e817e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:3.115ex; height:6.176ex;" alt="{\displaystyle {\frac {v^{2}}{2g}}}" /></span>, velocity head.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Applications">Applications</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=8" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Hydraulic_brakes" class="mw-redirect" title="Hydraulic brakes">Hydraulic brakes</a></li> <li><a href="/wiki/Artesian_well" title="Artesian well">Artesian well</a></li> <li><a href="/wiki/Blood_pressure" title="Blood pressure">Blood pressure</a></li> <li><a href="/wiki/Hydraulic_head" title="Hydraulic head">Hydraulic head</a></li> <li><a href="/wiki/Turgor_pressure" title="Turgor pressure">Plant cell turgidity</a></li> <li><a href="/wiki/Pythagorean_cup" title="Pythagorean cup">Pythagorean cup</a></li> <li><a href="/wiki/Pressure_washing" title="Pressure washing">Pressure washing</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Explosion_or_deflagration_pressures">Explosion or deflagration pressures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=9" title="Edit section: Explosion or deflagration pressures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Explosion" title="Explosion">Explosion</a> or <a href="/wiki/Deflagration" title="Deflagration">deflagration</a> pressures are the result of the ignition of explosive <a href="/wiki/Gas" title="Gas">gases</a>, mists, dust/air suspensions, in unconfined and confined spaces. </p> <div class="mw-heading mw-heading3"><h3 id="Negative_pressures">Negative pressures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=10" title="Edit section: Negative pressures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:13-07-23-kienbaum-unterdruckkammer-33.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/13-07-23-kienbaum-unterdruckkammer-33.jpg/220px-13-07-23-kienbaum-unterdruckkammer-33.jpg" decoding="async" width="220" height="146" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/13-07-23-kienbaum-unterdruckkammer-33.jpg/330px-13-07-23-kienbaum-unterdruckkammer-33.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/13-07-23-kienbaum-unterdruckkammer-33.jpg/440px-13-07-23-kienbaum-unterdruckkammer-33.jpg 2x" data-file-width="4288" data-file-height="2848" /></a><figcaption>Low-pressure chamber in <a href="/wiki/Bundesleistungszentrum_Kienbaum" title="Bundesleistungszentrum Kienbaum">Bundesleistungszentrum Kienbaum</a>, Germany</figcaption></figure> <p>While <i>pressures</i> are, in general, positive, there are several situations in which negative pressures may be encountered: </p> <ul><li>When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of −21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa). For example, <a href="/wiki/Abdominal_decompression" title="Abdominal decompression">abdominal decompression</a> is an <a href="/wiki/Obstetric" class="mw-redirect" title="Obstetric">obstetric</a> procedure during which negative gauge pressure is applied intermittently to a pregnant woman's abdomen.</li> <li>Negative absolute pressures are possible. They are effectively <a href="/wiki/Tension_(physics)" title="Tension (physics)">tension</a>, and both bulk solids and bulk liquids can be put under negative absolute pressure by pulling on them.<sup id="cite_ref-Imre2007_20-0" class="reference"><a href="#cite_note-Imre2007-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Microscopically, the molecules in solids and liquids have attractive interactions that overpower the thermal kinetic energy, so some tension can be sustained. Thermodynamically, however, a bulk material under negative pressure is in a <a href="/wiki/Metastable" class="mw-redirect" title="Metastable">metastable</a> state, and it is especially fragile in the case of liquids where the negative pressure state is similar to <a href="/wiki/Superheating" title="Superheating">superheating</a> and is easily susceptible to <a href="/wiki/Cavitation" title="Cavitation">cavitation</a>.<sup id="cite_ref-liqneg_21-0" class="reference"><a href="#cite_note-liqneg-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> In certain situations, the cavitation can be avoided and negative pressures sustained indefinitely,<sup id="cite_ref-liqneg_21-1" class="reference"><a href="#cite_note-liqneg-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> for example, liquid mercury has been observed to sustain up to <span class="nowrap"><span data-sort-value="2992569368750000000♠"></span>−425 atm</span> in clean glass containers.<sup id="cite_ref-Briggs1953_22-0" class="reference"><a href="#cite_note-Briggs1953-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Negative liquid pressures are thought to be involved in the <a href="/wiki/Ascent_of_sap" title="Ascent of sap">ascent of sap</a> in plants taller than 10 m (the atmospheric <a href="/wiki/Pressure_head" title="Pressure head">pressure head</a> of water).<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li>The <a href="/wiki/Casimir_effect" title="Casimir effect">Casimir effect</a> can create a small attractive force due to interactions with <a href="/wiki/Vacuum_energy" title="Vacuum energy">vacuum energy</a>; this force is sometimes termed "vacuum pressure" (not to be confused with the negative <i>gauge pressure</i> of a vacuum).</li> <li>For non-isotropic stresses in rigid bodies, depending on how the orientation of a surface is chosen, the same distribution of forces may have a component of positive stress along one <a href="/wiki/Normal_(geometry)" title="Normal (geometry)">surface normal</a>, with a component of negative stress acting along another surface normal. The pressure is then defined as the average of the three principal stresses. <ul><li>The stresses in an <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a> are generally non-isotropic, with the stress normal to one surface element (the <a href="/wiki/Normal_stress" class="mw-redirect" title="Normal stress">normal stress</a>) being negative, and positive for surface elements perpendicular to this.</li></ul></li> <li>In <a href="/wiki/Cosmology" title="Cosmology">cosmology</a>, <a href="/wiki/Dark_energy" title="Dark energy">dark energy</a> creates a very small yet cosmically significant amount of negative pressure, which accelerates the <a href="/wiki/Expansion_of_the_universe" title="Expansion of the universe">expansion of the universe</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Stagnation_pressure">Stagnation pressure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=11" title="Edit section: Stagnation pressure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Stagnation_pressure" title="Stagnation pressure">Stagnation pressure</a></div> <p><a href="/wiki/Stagnation_pressure" title="Stagnation pressure">Stagnation pressure</a> 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 <a href="/wiki/Static_pressure" title="Static pressure">static pressure</a>, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{0}={\frac {1}{2}}\rho v^{2}+p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ρ</mi> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{0}={\frac {1}{2}}\rho v^{2}+p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d22539ef55efce4b39e3f353475d564ada18882c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-left: -0.089ex; width:14.804ex; height:5.176ex;" alt="{\displaystyle p_{0}={\frac {1}{2}}\rho v^{2}+p}" /></span> where </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b969ada68a88e2aeba9a2d2096abaf1fd53c21d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.313ex; height:2.009ex;" alt="{\displaystyle p_{0}}" /></span> is the <a href="/wiki/Stagnation_pressure" title="Stagnation pressure">stagnation pressure</a>,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }" /></span> is the density,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}" /></span> is the flow velocity,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}" /></span> is the static pressure.</li></ul> <p>The pressure of a moving fluid can be measured using a <a href="/wiki/Pitot_tube" title="Pitot tube">Pitot tube</a>, or one of its variations such as a <a href="/wiki/Kiel_probe" title="Kiel probe">Kiel probe</a> or <a href="/wiki/Cobra_probe" title="Cobra probe">Cobra probe</a>, connected to a <a href="/wiki/Manometer" class="mw-redirect" title="Manometer">manometer</a>. Depending on where the inlet holes are located on the probe, it can measure static pressures or stagnation pressures. </p> <div class="mw-heading mw-heading3"><h3 id="Surface_pressure_and_surface_tension">Surface pressure and surface tension</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=12" title="Edit section: Surface pressure and surface tension"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There is a two-dimensional analog of pressure – the lateral force per unit length applied on a line perpendicular to the force. </p><p>Surface pressure is denoted by π: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi ={\frac {F}{l}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>F</mi> <mi>l</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi ={\frac {F}{l}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53af29d568d459f139c3881376d4afc6034df1d8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.007ex; height:5.343ex;" alt="{\displaystyle \pi ={\frac {F}{l}}}" /></span> 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 <a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a>, <span class="nowrap"><i>πA</i> = <i>k</i></span>, at constant temperature. </p><p><a href="/wiki/Surface_tension" title="Surface tension">Surface tension</a> is another example of surface pressure, but with a reversed sign, because "tension" is the opposite to "pressure". </p> <div class="mw-heading mw-heading3"><h3 id="Pressure_of_an_ideal_gas">Pressure of an ideal gas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=13" title="Edit section: Pressure of an ideal gas"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></div> <p>In an <a href="/wiki/Ideal_gas" title="Ideal gas">ideal gas</a>, molecules have no volume and do not interact. According to the <a href="/wiki/Ideal_gas_law" title="Ideal gas law">ideal gas law</a>, pressure varies linearly with temperature and quantity, and inversely with volume: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p={\frac {nRT}{V}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mi>R</mi> <mi>T</mi> </mrow> <mi>V</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p={\frac {nRT}{V}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/034869333c760448ff0f20369c81b47bcb708f93" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-left: -0.089ex; width:10.635ex; height:5.343ex;" alt="{\displaystyle p={\frac {nRT}{V}},}" /></span> where: </p> <ul><li><i>p</i> is the absolute pressure of the gas,</li> <li><i>n</i> is the <a href="/wiki/Amount_of_substance" title="Amount of substance">amount of substance</a>,</li> <li><i>T</i> is the absolute temperature,</li> <li><i>V</i> is the volume,</li> <li><i>R</i> is the <a href="/wiki/Ideal_gas_constant" class="mw-redirect" title="Ideal gas constant">ideal gas constant</a>.</li></ul> <p><a href="/wiki/Real_gas" title="Real gas">Real gases</a> exhibit a more complex dependence on the variables of state.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Vapour_pressure">Vapour pressure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=14" title="Edit section: Vapour pressure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Vapour_pressure" class="mw-redirect" title="Vapour pressure">Vapour pressure</a></div> <p>Vapour pressure is the pressure of a <a href="/wiki/Vapour" class="mw-redirect" title="Vapour">vapour</a> in <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a> with its condensed <a href="/wiki/Phase_(matter)" title="Phase (matter)">phases</a> in a closed system. All liquids and <a href="/wiki/Solid" title="Solid">solids</a> have a tendency to <a href="/wiki/Evaporate" class="mw-redirect" title="Evaporate">evaporate</a> into a gaseous form, and all <a href="/wiki/Gas" title="Gas">gases</a> have a tendency to <a href="/wiki/Condense" class="mw-redirect" title="Condense">condense</a> back to their liquid or solid form. </p><p>The <a href="/wiki/Atmospheric_pressure" title="Atmospheric pressure">atmospheric pressure</a> <a href="/wiki/Boiling_point" title="Boiling point">boiling point</a> of a liquid (also known as the <a href="/wiki/Normal_boiling_point" class="mw-redirect" title="Normal boiling point">normal boiling point</a>) 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 vapour bubbles inside the bulk of the substance. <a href="/wiki/Liquid_bubble" class="mw-redirect" title="Liquid bubble">Bubble</a> 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. </p><p>The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called <a href="/wiki/Partial_pressure" title="Partial pressure">partial vapor pressure</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Liquid_pressure">Liquid pressure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=15" title="Edit section: Liquid pressure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Fluid_statics#Pressure_in_fluids_at_rest" class="mw-redirect" title="Fluid statics">Fluid statics § Pressure in fluids at rest</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330" /><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum mechanics</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J=-D{\frac {d\varphi }{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <mo>−</mo> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>φ</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=-D{\frac {d\varphi }{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1856f88def2056f28ed27c7d31180a6240820ea6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.874ex; height:5.509ex;" alt="{\displaystyle J=-D{\frac {d\varphi }{dx}}}" /></span><div class="sidebar-caption"><a href="/wiki/Fick%27s_laws_of_diffusion" title="Fick's laws of diffusion">Fick's laws of diffusion</a></div></td></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Laws</div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;"> Conservations</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Conservation_of_mass" title="Conservation of mass">Mass</a></li> <li><a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">Momentum</a></li> <li><a href="/wiki/Conservation_of_energy" title="Conservation of energy">Energy</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;"> Inequalities</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Clausius%E2%80%93Duhem_inequality" title="Clausius–Duhem inequality">Clausius–Duhem (entropy)</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Solid_mechanics" title="Solid mechanics">Solid mechanics</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Deformation_(physics)" title="Deformation (physics)">Deformation</a></li> <li><a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">Elasticity</a> <ul><li><a href="/wiki/Linear_elasticity" title="Linear elasticity">linear</a></li></ul></li> <li><a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">Plasticity</a></li> <li><a href="/wiki/Hooke%27s_law" title="Hooke's law">Hooke's law</a></li> <li><a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">Stress</a></li> <li><a href="/wiki/Strain_(mechanics)" title="Strain (mechanics)">Strain</a> <ul><li><a href="/wiki/Finite_strain_theory" title="Finite strain theory">Finite strain</a></li> <li><a href="/wiki/Infinitesimal_strain_theory" title="Infinitesimal strain theory">Infinitesimal strain</a></li></ul></li> <li><a href="/wiki/Compatibility_(mechanics)" title="Compatibility (mechanics)">Compatibility</a></li> <li><a href="/wiki/Bending" title="Bending">Bending</a></li> <li><a href="/wiki/Contact_mechanics" title="Contact mechanics">Contact mechanics</a> <ul><li><a href="/wiki/Frictional_contact_mechanics" title="Frictional contact mechanics">frictional</a></li></ul></li> <li><a href="/wiki/Material_failure_theory" title="Material failure theory">Material failure theory</a></li> <li><a href="/wiki/Fracture_mechanics" title="Fracture mechanics">Fracture mechanics</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Fluid" title="Fluid">Fluids</a></th></tr><tr><td class="sidebar-content"> <div class="wraplinks"> <ul><li><a href="/wiki/Hydrostatics" title="Hydrostatics">Statics</a> <b>·</b> <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Dynamics</a></li> <li><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a> <b>·</b> <a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a></li> <li><a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equations</a></li> <li><a href="/wiki/Hagen%E2%80%93Poiseuille_equation" title="Hagen–Poiseuille equation">Poiseuille equation</a> <b>·</b> <a href="/wiki/Pascal%27s_law" title="Pascal's law">Pascal's law</a></li> <li><a href="/wiki/Viscosity" title="Viscosity">Viscosity</a> <ul><li>(<a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian</a> <b>·</b> <a href="/wiki/Non-Newtonian_fluid" title="Non-Newtonian fluid">non-Newtonian</a>)</li></ul></li> <li><a href="/wiki/Buoyancy" title="Buoyancy">Buoyancy</a> <b>·</b> <a href="/wiki/Mixing_(process_engineering)" title="Mixing (process engineering)">Mixing</a> <b>·</b> <a class="mw-selflink selflink">Pressure</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Liquid" title="Liquid">Liquids</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Adhesion" title="Adhesion">Adhesion</a></li> <li><a href="/wiki/Capillary_action" title="Capillary action">Capillary action</a></li> <li><a href="/wiki/Chromatography" title="Chromatography">Chromatography</a></li> <li><a href="/wiki/Cohesion_(chemistry)" title="Cohesion (chemistry)">Cohesion (chemistry)</a></li> <li><a href="/wiki/Surface_tension" title="Surface tension">Surface tension</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Gas" title="Gas">Gases</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Atmosphere" title="Atmosphere">Atmosphere</a></li> <li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a></li> <li><a href="/wiki/Charles%27s_law" title="Charles's law">Charles's law</a></li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a></li> <li><a href="/wiki/Fick%27s_law" class="mw-redirect" title="Fick's law">Fick's law</a></li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a></li> <li><a href="/wiki/Graham%27s_law" title="Graham's law">Graham's law</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></th></tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Rheology" title="Rheology">Rheology</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Viscoelasticity" title="Viscoelasticity">Viscoelasticity</a></li> <li><a href="/wiki/Rheometry" title="Rheometry">Rheometry</a></li> <li><a href="/wiki/Rheometer" title="Rheometer">Rheometer</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Smart_fluid" title="Smart fluid">Smart fluids</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Electrorheological_fluid" title="Electrorheological fluid">Electrorheological</a></li> <li><a href="/wiki/Magnetorheological_fluid" title="Magnetorheological fluid">Magnetorheological</a></li> <li><a href="/wiki/Ferrofluid" title="Ferrofluid">Ferrofluids</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Robert_Boyle" title="Robert Boyle">Boyle</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li> <li><a href="/wiki/Jacques_Charles" title="Jacques Charles">Charles</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Adolf_Eugen_Fick" title="Adolf Eugen Fick">Fick</a></li> <li><a href="/wiki/Joseph_Louis_Gay-Lussac" title="Joseph Louis Gay-Lussac">Gay-Lussac</a></li> <li><a href="/wiki/Thomas_Graham_(chemist)" title="Thomas Graham (chemist)">Graham</a></li> <li><a href="/wiki/Robert_Hooke" title="Robert Hooke">Hooke</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Claude-Louis_Navier" title="Claude-Louis Navier">Navier</a></li> <li><a href="/wiki/Walter_Noll" title="Walter Noll">Noll</a></li> <li><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascal</a></li> <li><a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">Stokes</a></li> <li><a href="/wiki/Clifford_Truesdell" title="Clifford Truesdell">Truesdell</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Continuum_mechanics" title="Template:Continuum mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Continuum_mechanics" title="Template talk:Continuum mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Continuum_mechanics" title="Special:EditPage/Template:Continuum mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>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. </p><p>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. Thus, we can say that the depth, density and liquid pressure are directly proportionate. The pressure due to a liquid in liquid columns of constant density and gravity at a depth within a substance is represented by the following formula: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=\rho gh,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>ρ</mi> <mi>g</mi> <mi>h</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=\rho gh,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52e88d7677c00e22d3c91ce6e1fd69f7b77cb814" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:8.661ex; height:2.676ex;" alt="{\displaystyle p=\rho gh,}" /></span> where: </p> <ul><li><i>p</i> is liquid pressure,</li> <li><i>g</i> is gravity at the surface of overlaying material,</li> <li><i>ρ</i> is <a href="/wiki/Density" title="Density">density</a> of liquid,</li> <li><i>h</i> is height of liquid column or depth within a substance.</li></ul> <p>Another way of saying the same formula is the following: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p={\text{weight density}}\times {\text{depth}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>weight density</mtext> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>depth</mtext> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p={\text{weight density}}\times {\text{depth}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99e736186c9481f7ffa5e4a922b40257ef3ee024" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:28.269ex; height:2.509ex;" alt="{\displaystyle p={\text{weight density}}\times {\text{depth}}.}" /></span> </p> <table class="toccolours collapsible collapsed" width="60%" style="text-align:left"> <tbody><tr> <th>Derivation of this equation </th></tr> <tr> <td>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 <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{weight density}}={\frac {\text{weight}}{\text{volume}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>weight density</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>weight</mtext> <mtext>volume</mtext> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{weight density}}={\frac {\text{weight}}{\text{volume}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b8c4f43632c1b4700f1f534f0b3a1e4559f5a51" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:25.842ex; height:5.509ex;" alt="{\displaystyle {\text{weight density}}={\frac {\text{weight}}{\text{volume}}}}" /></span> we can express this weight of liquid as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{weight}}={\text{weight density}}\times {\text{volume}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>weight</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>weight density</mtext> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>volume</mtext> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{weight}}={\text{weight density}}\times {\text{volume}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1503efa18fc0779e0fa1f1ea4742ada422acec23" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:35.21ex; height:2.509ex;" alt="{\displaystyle {\text{weight}}={\text{weight density}}\times {\text{volume}},}" /></span> where the volume of the column is simply the area multiplied by the depth. Then we have <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{pressure}}={\frac {\text{force}}{\text{area}}}={\frac {\text{weight}}{\text{area}}}={\frac {{\text{weight density}}\times {\text{volume}}}{\text{area}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>pressure</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>force</mtext> <mtext>area</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>weight</mtext> <mtext>area</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>weight density</mtext> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>volume</mtext> </mrow> </mrow> <mtext>area</mtext> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{pressure}}={\frac {\text{force}}{\text{area}}}={\frac {\text{weight}}{\text{area}}}={\frac {{\text{weight density}}\times {\text{volume}}}{\text{area}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8bfdc2fbfa05ded4099da4e6ba14dadf3019dac1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:57.072ex; height:5.343ex;" alt="{\displaystyle {\text{pressure}}={\frac {\text{force}}{\text{area}}}={\frac {\text{weight}}{\text{area}}}={\frac {{\text{weight density}}\times {\text{volume}}}{\text{area}}},}" /></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{pressure}}={\frac {{\text{weight density}}\times {\text{(area}}\times {\text{depth)}}}{\text{area}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>pressure</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>weight density</mtext> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>(area</mtext> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>depth)</mtext> </mrow> </mrow> <mtext>area</mtext> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{pressure}}={\frac {{\text{weight density}}\times {\text{(area}}\times {\text{depth)}}}{\text{area}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf1a0898e1c54dfb23153c92b73d15df987fd34a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:45.071ex; height:5.676ex;" alt="{\displaystyle {\text{pressure}}={\frac {{\text{weight density}}\times {\text{(area}}\times {\text{depth)}}}{\text{area}}}.}" /></span> </p><p>With the "area" in the numerator and the "area" in the denominator canceling each other out, we are left with <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{pressure}}={\text{weight density}}\times {\text{depth}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>pressure</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>weight density</mtext> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>depth</mtext> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{pressure}}={\text{weight density}}\times {\text{depth}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a78b8823055f68a44d5bac854bbf4a7f1009d5df" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:35.316ex; height:2.509ex;" alt="{\displaystyle {\text{pressure}}={\text{weight density}}\times {\text{depth}}.}" /></span> </p><p>Written with symbols, this is our original equation: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=\rho gh.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>ρ</mi> <mi>g</mi> <mi>h</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=\rho gh.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/086d9be5404e1ae1eddadf81ef8c34da53e8fdf0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:8.661ex; height:2.676ex;" alt="{\displaystyle p=\rho gh.}" /></span> </p> </td></tr></tbody></table> <p>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. </p><p>Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the <i>total</i> pressure acting on a liquid. The total pressure of a liquid, then, is <i>ρgh</i> plus the pressure of the atmosphere. When this distinction is important, the term <i>total pressure</i> is used. Otherwise, discussions of liquid pressure refer to pressure without regard to the normally ever-present atmospheric pressure. </p><p>The pressure does not depend on the <i>amount</i> 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 wide but shallow lake with a depth of 3 m (10 ft) exerts only half the average pressure that a small 6 m (20 ft) deep pond does. (The <i>total force</i> applied to the longer dam will be greater, due to the greater total surface area for the pressure to act upon. But for a given 5-foot (1.5 m)-wide section of each dam, the 10 ft (3.0 m) deep water will apply one quarter the force of 20 ft (6.1 m) deep water). A person will feel the same pressure whether their head is dunked a metre beneath the surface of the water in a small pool or to the same depth in the middle of a large lake. </p><p>If four interconnected vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimetres 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 centimetres 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 which 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 neighboring 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. </p><p>Restating this as an energy equation, the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface, <a href="/wiki/Gravitational_energy" title="Gravitational energy">gravitational potential energy</a> is large but liquid pressure energy is low. At the bottom of the vessel, all the gravitational potential energy is converted to pressure energy. The sum of pressure energy and gravitational potential energy per unit volume is constant throughout the volume of the fluid and the two energy components change linearly with the depth.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Mathematically, it is described by <a href="/wiki/Bernoulli%27s_equation" class="mw-redirect" title="Bernoulli's equation">Bernoulli's equation</a>, where velocity head is zero and comparisons per unit volume in the vessel are <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {p}{\gamma }}+z=\mathrm {const} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <mi>γ</mi> </mfrac> </mrow> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {p}{\gamma }}+z=\mathrm {const} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/095b4a65ff277119a4e0d9518f4d5de3948016cf" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.081ex; height:5.343ex;" alt="{\displaystyle {\frac {p}{\gamma }}+z=\mathrm {const} .}" /></span> </p><p>Terms have the same meaning as in <a href="#Fluid_pressure">section Fluid pressure</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Direction_of_liquid_pressure">Direction of liquid pressure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=16" title="Edit section: Direction of liquid pressure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An experimentally determined fact about liquid pressure is that it is exerted equally in all directions.<sup id="cite_ref-Hewitt_26-0" class="reference"><a href="#cite_note-Hewitt-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> If someone is submerged in water, no matter which way that person tilts their head, the person will feel the same amount of water pressure on their ears. Because a liquid can flow, this pressure is not 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 ball is pushed upward by water pressure (<a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a>). </p><p>When a liquid presses against a surface, there is a net force that is perpendicular to the surface. Although pressure does not 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.<sup id="cite_ref-Hewitt_26-1" class="reference"><a href="#cite_note-Hewitt-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> This is why liquid particles' velocity only alters in a <a href="/wiki/Normal_(geometry)" title="Normal (geometry)">normal</a> component after they are collided to the container's wall. Likewise, if the collision site is a hole, water spurting from the 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 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {\sqrt {2gh}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mi>g</mi> <mi>h</mi> </msqrt> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\sqrt {2gh}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5395be40c1dc49442cfefc7173ca81f364dbeb45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.201ex; height:2.509ex;" alt="{\displaystyle \scriptstyle {\sqrt {2gh}}}" /></span>, where <i>h</i> is the depth below the free surface.<sup id="cite_ref-Hewitt_26-2" class="reference"><a href="#cite_note-Hewitt-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> As predicted by <a href="/wiki/Torricelli%27s_law" title="Torricelli's law">Torricelli's law</a> this is the same speed the water (or anything else) would have if freely falling the same vertical distance <i>h</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Kinematic_pressure">Kinematic pressure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=17" title="Edit section: Kinematic pressure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\frac {p}{\rho _{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\frac {p}{\rho _{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59721dfd0d4f508dc38e2023764aebee49fb8aaf" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:7.936ex; height:5.343ex;" alt="{\displaystyle P={\frac {p}{\rho _{0}}}}" /></span> is the kinematic pressure, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}" /></span> is the pressure and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9c04a9d26b86af8c6205ba2a6287fd655b6b714" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.256ex; height:2.176ex;" alt="{\displaystyle \rho _{0}}" /></span> constant mass density. The SI unit of <i>P</i> is m<sup>2</sup>/s<sup>2</sup>. Kinematic pressure is used in the same manner as <a href="/wiki/Kinematic_viscosity" class="mw-redirect" title="Kinematic viscosity">kinematic viscosity</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }" /></span> in order to compute the <a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equation</a> without explicitly showing the density <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9c04a9d26b86af8c6205ba2a6287fd655b6b714" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.256ex; height:2.176ex;" alt="{\displaystyle \rho _{0}}" /></span>. </p> <div class="mw-heading mw-heading4"><h4 id="Navier–Stokes_equation_with_kinematic_quantities"><span id="Navier.E2.80.93Stokes_equation_with_kinematic_quantities"></span>Navier–Stokes equation with kinematic quantities</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=18" title="Edit section: Navier–Stokes equation with kinematic quantities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial u}{\partial t}}+(u\nabla )u=-\nabla P+\nu \nabla ^{2}u.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>u</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mi mathvariant="normal">∇</mi> <mo stretchy="false">)</mo> <mi>u</mi> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mi>P</mi> <mo>+</mo> <mi>ν</mi> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>u</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial u}{\partial t}}+(u\nabla )u=-\nabla P+\nu \nabla ^{2}u.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3cb20970d57739dc562f6cded5d5d14ba7957b2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:30.356ex; height:5.509ex;" alt="{\displaystyle {\frac {\partial u}{\partial t}}+(u\nabla )u=-\nabla P+\nu \nabla ^{2}u.}" /></span> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=19" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 30em;"> <ul><li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a> – Relation between gas pressure and volume</li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a> – Combination of Charles', Boyle's and Gay-Lussac's gas laws</li> <li><a href="/wiki/Conversion_of_units" title="Conversion of units">Conversion of units</a> – Comparison of various scales</li> <li><a href="/wiki/Critical_point_(thermodynamics)" title="Critical point (thermodynamics)">Critical point (thermodynamics)</a> – Temperature and pressure point where phase boundaries disappear</li> <li><a href="/wiki/Dimensional_analysis" title="Dimensional analysis">Dimensional analysis</a> – Analysis of the relationships between different physical quantities</li> <li><a href="/wiki/Dynamic_pressure" title="Dynamic pressure">Dynamic pressure</a> – Kinetic energy per unit volume of a fluid</li> <li><a href="/wiki/Electric_potential" title="Electric potential">Electric potential</a> – Line integral of the electric field</li> <li><a href="/wiki/Electron_degeneracy_pressure" title="Electron degeneracy pressure">Electron degeneracy pressure</a> – Repulsive force in quantum mechanics</li> <li><a href="/wiki/High_pressure" title="High pressure">High pressure</a> – Great force distributed over a small area</li> <li><a href="/wiki/Hydraulics" title="Hydraulics">Hydraulics</a> – Applied engineering involving liquids</li> <li><a href="/wiki/Hydrostatic_stress" title="Hydrostatic stress">Hydrostatic stress</a> – Component of mechanical stress without shear</li> <li><a href="/wiki/Internal_pressure" title="Internal pressure">Internal pressure</a> – measure of how the internal energy of a system changes when it expands or contracts at constant temperature<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Kinetic_theory_of_gases#Pressure_and_kinetic_energy" title="Kinetic theory of gases">Kinetic theory</a> – Understanding of gas properties in terms of molecular motion</li> <li><a href="/wiki/Microphone" title="Microphone">Microphone</a> – Device that converts sound into an electrical signal</li> <li><a href="/wiki/Orders_of_magnitude_(pressure)" title="Orders of magnitude (pressure)">Orders of magnitude (pressure)</a> – Comparison of a wide range of pressures</li> <li><a href="/wiki/Partial_pressure" title="Partial pressure">Partial pressure</a> – Pressure of a component gas in a mixture</li> <li><a href="/wiki/Pressure_measurement" title="Pressure measurement">Pressure measurement</a></li> <li><a href="/wiki/Pressure_sensor" class="mw-redirect" title="Pressure sensor">Pressure sensor</a></li> <li><a href="/wiki/Sound_pressure" title="Sound pressure">Sound pressure</a> – Local pressure deviation caused by a sound wave</li> <li><a href="/wiki/Static_pressure" title="Static pressure">Static pressure</a> – Term in fluid mechanics</li> <li><a href="/wiki/Timeline_of_temperature_and_pressure_measurement_technology" title="Timeline of temperature and pressure measurement technology">Timeline of temperature and pressure measurement technology</a></li> <li><a href="/wiki/Torricelli%27s_law" title="Torricelli's law">Torricelli's law</a> – Theorem in fluid mechanics</li> <li><a href="/wiki/Vacuum_pump" title="Vacuum pump">Vacuum pump</a> – Equipment generating a relative vacuum</li> <li><a href="/wiki/Vertical_pressure_variation" title="Vertical pressure variation">Vertical pressure variation</a> – Variation in pressure as a function of elevation</li></ul></div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=20" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">The preferred spelling varies by country and even by industry. Further, both spellings are often used <i>within</i> a particular industry or country. Industries in British English-speaking countries typically use the "gauge" spelling.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=21" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626" /><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFKnight2007" class="citation book cs1">Knight, Randall D. (2007). "Fluid Mechanics". <a rel="nofollow" class="external text" href="https://books.google.com/books?id=32yzygAACAAJ&q=Physics+for+Scientists+and+Engineers:+A+Strategic+Approach"><i>Physics for Scientists and Engineers: A Strategic Approach</i></a> <span class="cs1-format">(google books)</span> (2nd ed.). San Francisco: Pearson Addison Wesley. p. 1183. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-321-51671-8" title="Special:BookSources/978-0-321-51671-8"><bdi>978-0-321-51671-8</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">6 April</span> 2020</span>. <q><span style="font-size:85%;"><i>Pressure itself is not a Force, even though we sometimes talk "informally" about the "force exerted by the pressure. The correct statement is that the Fluid exerts a force on a surface. In addition, Pressure is a scalar, not a vector.</i> </span></q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Fluid+Mechanics&rft.btitle=Physics+for+Scientists+and+Engineers%3A+A+Strategic+Approach&rft.place=San+Francisco&rft.pages=1183&rft.edition=2nd&rft.pub=Pearson+Addison+Wesley&rft.date=2007&rft.isbn=978-0-321-51671-8&rft.aulast=Knight&rft.aufirst=Randall+D.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D32yzygAACAAJ%26q%3DPhysics%2Bfor%2BScientists%2Band%2BEngineers%3A%2BA%2BStrategic%2BApproach&rfr_id=info%3Asid%2Fen.wikipedia.org%3APressure" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGiancoli2004" class="citation book cs1">Giancoli, Douglas G. (2004). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/physics00doug"><i>Physics: principles with applications</i></a></span>. 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"Einstein's gravity under pressure". <i>Astrophysics and Space Science</i>. <b>321</b> (2): <span class="nowrap">151–</span>156. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0705.0825">0705.0825</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009Ap&SS.321..151V">2009Ap&SS.321..151V</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10509-009-0016-8">10.1007/s10509-009-0016-8</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:218673952">218673952</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astrophysics+and+Space+Science&rft.atitle=Einstein%27s+gravity+under+pressure&rft.volume=321&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E151-%3C%2Fspan%3E156&rft.date=2009&rft_id=info%3Aarxiv%2F0705.0825&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A218673952%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fs10509-009-0016-8&rft_id=info%3Abibcode%2F2009Ap%26SS.321..151V&rft.aulast=Vishwakarma&rft.aufirst=Ram+Gopal&rfr_id=info%3Asid%2Fen.wikipedia.org%3APressure" class="Z3988"></span></span> </li> <li id="cite_note-Finnemore-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-Finnemore_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Finnemore_18-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Finnemore_18-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Finnemore_18-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Finnemore_18-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFinnemore,_John,_E._and_Joseph_B._Franzini2002" class="citation book cs1">Finnemore, John, E. and Joseph B. Franzini (2002). <i>Fluid Mechanics: With Engineering Applications</i>. New York: McGraw Hill, Inc. pp. <span class="nowrap">14–</span>29. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-243202-2" title="Special:BookSources/978-0-07-243202-2"><bdi>978-0-07-243202-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fluid+Mechanics%3A+With+Engineering+Applications&rft.place=New+York&rft.pages=%3Cspan+class%3D%22nowrap%22%3E14-%3C%2Fspan%3E29&rft.pub=McGraw+Hill%2C+Inc.&rft.date=2002&rft.isbn=978-0-07-243202-2&rft.au=Finnemore%2C+John%2C+E.+and+Joseph+B.+Franzini&rfr_id=info%3Asid%2Fen.wikipedia.org%3APressure" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></span> </li> <li id="cite_note-NCEES-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-NCEES_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1"><i>Fundamentals of Engineering: Supplied Reference Handbook</i>. Clemson, South Carolina: NCEES. 2011. p. 64. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-932613-59-9" title="Special:BookSources/978-1-932613-59-9"><bdi>978-1-932613-59-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Engineering%3A+Supplied+Reference+Handbook&rft.place=Clemson%2C+South+Carolina&rft.pages=64&rft.pub=NCEES&rft.date=2011&rft.isbn=978-1-932613-59-9&rfr_id=info%3Asid%2Fen.wikipedia.org%3APressure" class="Z3988"></span></span> </li> <li id="cite_note-Imre2007-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-Imre2007_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFImre2007" class="citation book cs1">Imre, A. R. (2007). "How to generate and measure negative pressure in liquids?". <i>Soft Matter under Exogenic Impacts</i>. NATO Science Series II: Mathematics, Physics and Chemistry. Vol. 242. pp. <span class="nowrap">379–</span>388. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4020-5872-1_24">10.1007/978-1-4020-5872-1_24</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-5871-4" title="Special:BookSources/978-1-4020-5871-4"><bdi>978-1-4020-5871-4</bdi></a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1568-2609">1568-2609</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=How+to+generate+and+measure+negative+pressure+in+liquids%3F&rft.btitle=Soft+Matter+under+Exogenic+Impacts&rft.series=NATO+Science+Series+II%3A+Mathematics%2C+Physics+and+Chemistry&rft.pages=%3Cspan+class%3D%22nowrap%22%3E379-%3C%2Fspan%3E388&rft.date=2007&rft.issn=1568-2609&rft_id=info%3Adoi%2F10.1007%2F978-1-4020-5872-1_24&rft.isbn=978-1-4020-5871-4&rft.aulast=Imre&rft.aufirst=A.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APressure" class="Z3988"></span></span> </li> <li id="cite_note-liqneg-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-liqneg_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-liqneg_21-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFImreMarisWilliams2002" class="citation book cs1">Imre, A. R; Maris, H. J; Williams, P. R, eds. (2002). <i>Liquids Under Negative Pressure (Nato Science Series II)</i>. Springer. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-94-010-0498-5">10.1007/978-94-010-0498-5</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-0895-5" title="Special:BookSources/978-1-4020-0895-5"><bdi>978-1-4020-0895-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Liquids+Under+Negative+Pressure+%28Nato+Science+Series+II%29&rft.pub=Springer&rft.date=2002&rft_id=info%3Adoi%2F10.1007%2F978-94-010-0498-5&rft.isbn=978-1-4020-0895-5&rfr_id=info%3Asid%2Fen.wikipedia.org%3APressure" class="Z3988"></span></span> </li> <li id="cite_note-Briggs1953-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-Briggs1953_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBriggs1953" class="citation journal cs1">Briggs, Lyman J. (1953). "The Limiting Negative Pressure of Mercury in Pyrex Glass". <i>Journal of Applied Physics</i>. <b>24</b> (4): <span class="nowrap">488–</span>490. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1953JAP....24..488B">1953JAP....24..488B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1721307">10.1063/1.1721307</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0021-8979">0021-8979</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Applied+Physics&rft.atitle=The+Limiting+Negative+Pressure+of+Mercury+in+Pyrex+Glass&rft.volume=24&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E488-%3C%2Fspan%3E490&rft.date=1953&rft.issn=0021-8979&rft_id=info%3Adoi%2F10.1063%2F1.1721307&rft_id=info%3Abibcode%2F1953JAP....24..488B&rft.aulast=Briggs&rft.aufirst=Lyman+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APressure" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKaren_Wright2003" class="citation web cs1">Karen Wright (March 2003). <a rel="nofollow" class="external text" href="http://discovermagazine.com/2003/mar/featscienceof">"The Physics of Negative Pressure"</a>. <a href="/wiki/Discover_(magazine)" title="Discover (magazine)">Discover</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150108182004/http://discovermagazine.com/2003/mar/featscienceof">Archived</a> from the original on 8 January 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">31 January</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Physics+of+Negative+Pressure&rft.pub=Discover&rft.date=2003-03&rft.au=Karen+Wright&rft_id=http%3A%2F%2Fdiscovermagazine.com%2F2003%2Fmar%2Ffeatscienceof&rfr_id=info%3Asid%2Fen.wikipedia.org%3APressure" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text">P. Atkins, J. de Paula <i>Elements of Physical Chemistry</i>, 4th Ed, W. H. Freeman, 2006. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7167-7329-5" title="Special:BookSources/0-7167-7329-5">0-7167-7329-5</a>.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text">Streeter, V. L., <i>Fluid Mechanics</i>, Example 3.5, McGraw–Hill Inc. (1966), New York.</span> </li> <li id="cite_note-Hewitt-26"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hewitt_26-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hewitt_26-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Hewitt_26-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Hewitt 251 (2006)<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources"><span title="A complete citation is needed. (July 2020)">full citation needed</span></a></i>]</sup></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pressure&action=edit&section=22" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20190929053038/http://www.physnet.org/modules/pdf_modules/m48.pdf"><i>Introduction to Fluid Statics and Dynamics</i></a> on <a rel="nofollow" class="external text" href="http://www.physnet.org/">Project PHYSNET</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100106203418/http://www.grc.nasa.gov/WWW/K-12/airplane/pressure.html">Pressure being a scalar quantity</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20200311121248/http://www.wikiunits.org/">wikiUnits.org - Convert units of pressure</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output 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