Venturi effect - Wikipedia

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aria-controls="toc-Experimental_apparatus-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 Experimental apparatus subsection</span> </button> <ul id="toc-Experimental_apparatus-sublist" class="vector-toc-list"> <li id="toc-Venturi_tubes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Venturi_tubes"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Venturi tubes</span> </div> </a> <ul id="toc-Venturi_tubes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Orifice_plate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Orifice_plate"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Orifice plate</span> </div> </a> <ul id="toc-Orifice_plate-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Instrumentation_and_measurement" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Instrumentation_and_measurement"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Instrumentation and measurement</span> </div> </a> <button aria-controls="toc-Instrumentation_and_measurement-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 Instrumentation and measurement subsection</span> </button> <ul id="toc-Instrumentation_and_measurement-sublist" class="vector-toc-list"> <li id="toc-Flow_rate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Flow_rate"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Flow rate</span> </div> </a> <ul id="toc-Flow_rate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Differential_pressure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Differential_pressure"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Differential pressure</span> </div> </a> <ul id="toc-Differential_pressure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Compensation_for_temperature,_pressure,_and_mass" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Compensation_for_temperature,_pressure,_and_mass"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Compensation for temperature, pressure, and mass</span> </div> </a> <ul id="toc-Compensation_for_temperature,_pressure,_and_mass-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Examples</span> </div> </a> <button aria-controls="toc-Examples-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 Examples subsection</span> </button> <ul id="toc-Examples-sublist" class="vector-toc-list"> <li id="toc-Machines" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Machines"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Machines</span> </div> </a> <ul id="toc-Machines-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Architecture" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Architecture"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Architecture</span> </div> </a> <ul id="toc-Architecture-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nature" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nature"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Nature</span> </div> </a> <ul id="toc-Nature-sublist" class="vector-toc-list"> </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">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-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">6</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">7</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" > <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">Venturi effect</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 35 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-35" 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">35 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/Venturi-effek" title="Venturi-effek – Afrikaans" lang="af" hreflang="af" data-title="Venturi-effek" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A3%D9%86%D8%A8%D9%88%D8%A8_%D9%81%D9%8A%D9%86%D8%AA%D9%88%D8%B1%D9%8A" title="أنبوب فينتوري – Arabic" lang="ar" hreflang="ar" data-title="أنبوب فينتوري" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D1%84%D0%B5%D0%BA%D1%82_%D0%92%D0%B5%D0%BD%D1%82%D1%83%D1%80%D1%8B" title="Эфект Вентуры – Belarusian" lang="be" hreflang="be" data-title="Эфект Вентуры" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%BD%D0%B0_%D0%92%D0%B5%D0%BD%D1%82%D1%83%D1%80%D0%B8" title="Ефект на Вентури – Bulgarian" lang="bg" hreflang="bg" data-title="Ефект на Вентури" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Efecte_Venturi" title="Efecte Venturi – Catalan" lang="ca" hreflang="ca" data-title="Efecte Venturi" 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/Venturiho_efekt" title="Venturiho efekt – Czech" lang="cs" hreflang="cs" data-title="Venturiho efekt" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Venturi-Durchflussmessung" title="Venturi-Durchflussmessung – German" lang="de" hreflang="de" data-title="Venturi-Durchflussmessung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A6%CE%B1%CE%B9%CE%BD%CF%8C%CE%BC%CE%B5%CE%BD%CE%BF_%CE%92%CE%B5%CE%BD%CF%84%CE%BF%CF%8D%CF%81%CE%B9" title="Φαινόμενο Βεντούρι – Greek" lang="el" hreflang="el" data-title="Φαινόμενο Βεντούρι" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Efecto_Venturi" title="Efecto Venturi – Spanish" lang="es" hreflang="es" data-title="Efecto Venturi" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Venturi_efektua" title="Venturi efektua – Basque" lang="eu" hreflang="eu" data-title="Venturi efektua" 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/%D8%A7%D8%AB%D8%B1_%D9%88%D9%86%D8%AA%D9%88%D8%B1%DB%8C" title="اثر ونتوری – Persian" lang="fa" hreflang="fa" data-title="اثر ونتوری" 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/Effet_Venturi" title="Effet Venturi – French" lang="fr" hreflang="fr" data-title="Effet Venturi" 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/Fead%C3%A1n_Venturi" title="Feadán Venturi – Irish" lang="ga" hreflang="ga" data-title="Feadán Venturi" 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/Efecto_Venturi" title="Efecto Venturi – Galician" lang="gl" hreflang="gl" data-title="Efecto Venturi" 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/%EB%B2%A4%ED%88%AC%EB%A6%AC_%ED%9A%A8%EA%B3%BC" title="벤투리 효과 – Korean" lang="ko" hreflang="ko" data-title="벤투리 효과" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A5%87%E0%A4%82%E0%A4%9A%E0%A5%81%E0%A4%B0%E0%A5%80_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AD%E0%A4%BE%E0%A4%B5" title="वेंचुरी प्रभाव – Hindi" lang="hi" hreflang="hi" data-title="वेंचुरी प्रभाव" 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/Venturijeva_cijev" title="Venturijeva cijev – Croatian" lang="hr" hreflang="hr" data-title="Venturijeva cijev" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Efek_Venturi" title="Efek Venturi – Indonesian" lang="id" hreflang="id" data-title="Efek Venturi" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Effetto_Venturi" title="Effetto Venturi – Italian" lang="it" hreflang="it" data-title="Effetto Venturi" 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%A2%D7%A7%D7%A8%D7%95%D7%9F_%D7%95%D7%A0%D7%98%D7%95%D7%A8%D7%99" title="עקרון ונטורי – Hebrew" lang="he" hreflang="he" data-title="עקרון ונטורי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Venturi_caurule" title="Venturi caurule – Latvian" lang="lv" hreflang="lv" data-title="Venturi caurule" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Venturi-cs%C5%91" title="Venturi-cső – Hungarian" lang="hu" hreflang="hu" data-title="Venturi-cső" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Venturi-effect" title="Venturi-effect – Dutch" lang="nl" hreflang="nl" data-title="Venturi-effect" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%99%E3%83%B3%E3%83%81%E3%83%A5%E3%83%AA" title="ベンチュリ – Japanese" lang="ja" hreflang="ja" data-title="ベンチュリ" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Venturieffekt" title="Venturieffekt – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Venturieffekt" 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/Venturi-effekten" title="Venturi-effekten – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Venturi-effekten" 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/Efi%C3%A8ch_Venturi" title="Efièch Venturi – Occitan" lang="oc" hreflang="oc" data-title="Efièch Venturi" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Efeito_Venturi" title="Efeito Venturi – Portuguese" lang="pt" hreflang="pt" data-title="Efeito Venturi" 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/Efectul_Venturi" title="Efectul Venturi – Romanian" lang="ro" hreflang="ro" data-title="Efectul Venturi" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D1%84%D1%84%D0%B5%D0%BA%D1%82_%D0%92%D0%B5%D0%BD%D1%82%D1%83%D1%80%D0%B8" title="Эффект Вентури – Russian" lang="ru" hreflang="ru" data-title="Эффект Вентури" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Venturi_effect" title="Venturi effect – Simple English" lang="en-simple" hreflang="en-simple" data-title="Venturi effect" 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-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%92%D0%B5%D0%BD%D1%82%D1%83%D1%80%D0%B8%D1%98%D0%B5%D0%B2%D0%B0_%D1%86%D0%B5%D0%B2" title="Вентуријева цев – Serbian" lang="sr" hreflang="sr" data-title="Вентуријева цев" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Venturi-ilmi%C3%B6" title="Venturi-ilmiö – Finnish" lang="fi" hreflang="fi" data-title="Venturi-ilmiö" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%92%D0%B5%D0%BD%D1%82%D1%83%D1%80%D1%96" title="Ефект Вентурі – Ukrainian" lang="uk" hreflang="uk" data-title="Ефект Вентурі" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a 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</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">Reduced pressure caused by a flow restriction in a tube or pipe</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Lead_too_short plainlinks metadata ambox ambox-content ambox-lead_too_short" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/40px-Wiki_letter_w.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/60px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/80px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article's <a href="/wiki/Wikipedia:Manual_of_Style/Lead_section#Length" title="Wikipedia:Manual of Style/Lead section">lead section</a> <b>may be too short to adequately <a href="/wiki/Wikipedia:Summary_style" title="Wikipedia:Summary style">summarize</a> the key points</b>.<span class="hide-when-compact"> Please consider expanding the lead to <a href="/wiki/Wikipedia:Manual_of_Style/Lead_section#Provide_an_accessible_overview" title="Wikipedia:Manual of Style/Lead section">provide an accessible overview</a> of all important aspects of the article.</span> <span class="date-container"><i>(<span class="date">February 2024</span>)</i></span></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Venturi5.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Venturi5.svg/300px-Venturi5.svg.png" decoding="async" width="300" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Venturi5.svg/450px-Venturi5.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Venturi5.svg/600px-Venturi5.svg.png 2x" data-file-width="579" data-file-height="325" /></a><figcaption>The upstream <a href="/wiki/Static_pressure" title="Static pressure">static pressure</a> (1) is higher than in the constriction (2), and the <a href="/wiki/Fluid" title="Fluid">fluid</a> <a href="/wiki/Speed" title="Speed">speed</a> at "1" is lower than at "2", because the cross-sectional area at "1" is greater than at "2".</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:VenturiFlow.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/78/VenturiFlow.png" decoding="async" width="220" height="205" class="mw-file-element" data-file-width="220" data-file-height="205" /></a><figcaption>A flow of air through a <a href="/wiki/Pitot_tube" title="Pitot tube">Pitot tube</a> Venturi meter, showing the columns connected in a <a href="/wiki/Manometer" class="mw-redirect" title="Manometer">manometer</a> and partially filled with water. The meter is "read" as a differential pressure head in cm or inches of water.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Venturi_Tube_en.webm/220px--Venturi_Tube_en.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="75" data-mwtitle="Venturi_Tube_en.webm" data-mwprovider="wikimediacommons" resource="/wiki/File:Venturi_Tube_en.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/58/Venturi_Tube_en.webm/Venturi_Tube_en.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/58/Venturi_Tube_en.webm/Venturi_Tube_en.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/5/58/Venturi_Tube_en.webm" type="video/webm; codecs="vp8, vorbis"" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/58/Venturi_Tube_en.webm/Venturi_Tube_en.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/58/Venturi_Tube_en.webm/Venturi_Tube_en.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/58/Venturi_Tube_en.webm/Venturi_Tube_en.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>Video of a Venturi meter used in a lab experiment</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Venturi.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/Venturi.gif/220px-Venturi.gif" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/Venturi.gif/330px-Venturi.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/16/Venturi.gif/440px-Venturi.gif 2x" data-file-width="640" data-file-height="360" /></a><figcaption>Idealized flow in a Venturi tube</figcaption></figure> <p>The <b>Venturi effect</b> is the reduction in <a href="/wiki/Fluid_pressure" class="mw-redirect" title="Fluid pressure">fluid pressure</a> that results when a moving fluid speeds up as it flows through a constricted section (or choke) of a pipe. The Venturi effect is named after its discoverer, the 18th-century Italian <a href="/wiki/Physicist" title="Physicist">physicist</a> <a href="/wiki/Giovanni_Battista_Venturi" title="Giovanni Battista Venturi">Giovanni Battista Venturi</a>. </p><p>The effect has various engineering applications, as the reduction in pressure inside the constriction can be used both for measuring the fluid flow and for moving other fluids (e.g. in a <a href="/wiki/Vacuum_ejector" title="Vacuum ejector">vacuum ejector</a>). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Background">Background</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=1" title="Edit section: Background"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Inviscid_flow" title="Inviscid flow">inviscid</a> <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>, an incompressible fluid's <a href="/wiki/Velocity" title="Velocity">velocity</a> must <i>increase</i> as it passes through a constriction in accord with the <a href="/wiki/Continuity_equation#Fluid_dynamics" title="Continuity equation">principle of mass continuity</a>, while its <a href="/wiki/Static_pressure" title="Static pressure">static pressure</a> must <i>decrease</i> in accord with the principle of <a href="/wiki/Mechanical_energy#Conservation_of_mechanical_energy" title="Mechanical energy">conservation of mechanical energy</a> (<a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a>) or according to the <a href="/wiki/Euler_equations_(fluid_dynamics)" title="Euler equations (fluid dynamics)">Euler equations</a>. Thus, any gain in <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> a fluid may attain by its increased velocity through a constriction is balanced by a drop in pressure because of its loss in <a href="/wiki/Potential_energy" title="Potential energy">potential energy</a>. </p><p>By measuring pressure, the flow rate can be determined, as in various <a href="/wiki/Flow_measurement" title="Flow measurement">flow measurement</a> devices such as Venturi meters, Venturi nozzles and <a href="/wiki/Orifice_plate" title="Orifice plate">orifice plates</a>. </p><p>Referring to the adjacent diagram, using Bernoulli's equation in the special case of steady, incompressible, inviscid flows (such as the flow of water or other liquid, or low-speed flow of gas) along a streamline, the theoretical pressure drop at the constriction is given by </p><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_{1}-p_{2}={\frac {\rho }{2}}(v_{2}^{2}-v_{1}^{2}),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1}-p_{2}={\frac {\rho }{2}}(v_{2}^{2}-v_{1}^{2}),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e4a810e0c2717a6bb34519b01353f2054dc6c6e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-left: -0.089ex; width:22.174ex; height:4.843ex;" alt="{\displaystyle p_{1}-p_{2}={\frac {\rho }{2}}(v_{2}^{2}-v_{1}^{2}),}"></span> </p><p>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 \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 <a href="/wiki/Density" title="Density">density</a> of the fluid, <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_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98d33f5d498d528bd8c10edc8ac8c34347f32b3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.182ex; height:2.009ex;" alt="{\displaystyle v_{1}}"></span> is the (slower) fluid velocity where the pipe is wider, 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 v_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb04c423c2cb809c30cac725befa14ffbf4c85f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.182ex; height:2.009ex;" alt="{\displaystyle v_{2}}"></span> is the (faster) fluid velocity where the pipe is narrower (as seen in the figure). </p> <div class="mw-heading mw-heading3"><h3 id="Choked_flow">Choked flow</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=2" title="Edit section: Choked flow"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The limiting case of the Venturi effect is when a fluid reaches the state of <a href="/wiki/Choked_flow" title="Choked flow">choked flow</a>, where the <a href="/wiki/Fluid_velocity" class="mw-redirect" title="Fluid velocity">fluid velocity</a> approaches the local <a href="/wiki/Speed_of_sound" title="Speed of sound">speed of sound</a>. When a fluid system is in a state of choked flow, a further decrease in the downstream pressure environment will not lead to an increase in velocity, unless the fluid is compressed. </p><p>The mass flow rate for a compressible fluid will increase with increased upstream pressure, which will increase the density of the fluid through the constriction (though the velocity will remain constant). This is the principle of operation of a <a href="/wiki/De_Laval_nozzle" title="De Laval nozzle">de Laval nozzle</a>. Increasing source temperature will also increase the local sonic velocity, thus allowing increased mass flow rate, but only if the nozzle area is also increased to compensate for the resulting decrease in density. </p> <div class="mw-heading mw-heading3"><h3 id="Expansion_of_the_section">Expansion of the section</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=3" title="Edit section: Expansion of the section"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Bernoulli equation is invertible, and pressure should rise when a fluid slows down. Nevertheless, if there is an expansion of the tube section, turbulence will appear, and the theorem will not hold. In all experimental Venturi tubes, the pressure in the entrance is compared to the pressure in the middle section; the output section is never compared with them. </p> <div class="mw-heading mw-heading2"><h2 id="Experimental_apparatus">Experimental apparatus</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=4" title="Edit section: Experimental apparatus"><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:Green_Hope_High_School_(Physics_Laboratory_Venturi_Tube)_2006.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Green_Hope_High_School_%28Physics_Laboratory_Venturi_Tube%29_2006.jpg/220px-Green_Hope_High_School_%28Physics_Laboratory_Venturi_Tube%29_2006.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Green_Hope_High_School_%28Physics_Laboratory_Venturi_Tube%29_2006.jpg/330px-Green_Hope_High_School_%28Physics_Laboratory_Venturi_Tube%29_2006.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Green_Hope_High_School_%28Physics_Laboratory_Venturi_Tube%29_2006.jpg/440px-Green_Hope_High_School_%28Physics_Laboratory_Venturi_Tube%29_2006.jpg 2x" data-file-width="1280" data-file-height="960" /></a><figcaption>Venturi tube demonstration apparatus built out of PVC pipe and operated with a vacuum pump</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:254px;max-width:254px"><div class="trow"><div class="tsingle" style="width:252px;max-width:252px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Aircraft_venturi_1.JPG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Aircraft_venturi_1.JPG/250px-Aircraft_venturi_1.JPG" decoding="async" width="250" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Aircraft_venturi_1.JPG/375px-Aircraft_venturi_1.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Aircraft_venturi_1.JPG/500px-Aircraft_venturi_1.JPG 2x" data-file-width="3888" data-file-height="2592" /></a></span></div></div></div><div class="trow"><div class="tsingle" style="width:252px;max-width:252px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Aircraft_venturi_2.JPG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Aircraft_venturi_2.JPG/250px-Aircraft_venturi_2.JPG" decoding="async" width="250" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Aircraft_venturi_2.JPG/375px-Aircraft_venturi_2.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Aircraft_venturi_2.JPG/500px-Aircraft_venturi_2.JPG 2x" data-file-width="3888" data-file-height="2592" /></a></span></div></div></div><div class="trow"><div class="tsingle" style="width:252px;max-width:252px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Aircraft_venturi_3.JPG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Aircraft_venturi_3.JPG/250px-Aircraft_venturi_3.JPG" decoding="async" width="250" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Aircraft_venturi_3.JPG/375px-Aircraft_venturi_3.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Aircraft_venturi_3.JPG/500px-Aircraft_venturi_3.JPG 2x" data-file-width="3888" data-file-height="2592" /></a></span></div><div class="thumbcaption">A pair of Venturi tubes on a light aircraft, used to provide airflow for air-driven gyroscopic instruments</div></div></div></div></div> <div class="mw-heading mw-heading3"><h3 id="Venturi_tubes">Venturi tubes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=5" title="Edit section: Venturi tubes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The simplest apparatus is a tubular setup known as a Venturi tube or simply a Venturi (plural: "Venturis" or occasionally "Venturies"). Fluid flows through a length of pipe of varying diameter. To avoid undue <a href="/wiki/Aerodynamic_drag" class="mw-redirect" title="Aerodynamic drag">aerodynamic drag</a>, a Venturi tube typically has an entry cone of 30 degrees and an exit cone of 5 degrees.<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> </p><p>Venturi tubes are often used in processes where permanent pressure loss is not tolerable and where maximum accuracy is needed in case of highly viscous liquids.<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. (April 2016)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Orifice_plate">Orifice plate</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=6" title="Edit section: Orifice plate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Venturi tubes are more expensive to construct than simple <a href="/wiki/Orifice_plate" title="Orifice plate">orifice plates</a>, and both function on the same basic principle. However, for any given differential pressure, orifice plates cause significantly more permanent energy loss.<sup id="cite_ref-wolfram_2-0" class="reference"><a href="#cite_note-wolfram-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Instrumentation_and_measurement">Instrumentation and measurement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=7" title="Edit section: Instrumentation and measurement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Both Venturi tubes and orifice plates are used in industrial applications and in scientific laboratories for measuring the flow rate of liquids. </p> <div class="mw-heading mw-heading3"><h3 id="Flow_rate">Flow rate</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=8" title="Edit section: Flow rate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A Venturi can be used to measure the <a href="/wiki/Volumetric_flow_rate" title="Volumetric flow rate">volumetric flow rate</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 \scriptstyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>Q</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9a68abc18b091bcba3e1a93dd9ed6bb20080f61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.3ex; height:1.843ex;" alt="{\displaystyle \scriptstyle Q}"></span>, using <a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a>. </p><p>Since <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 {\begin{aligned}Q&=v_{1}A_{1}=v_{2}A_{2}\\[3pt]p_{1}-p_{2}&={\frac {\rho }{2}}\left(v_{2}^{2}-v_{1}^{2}\right)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.6em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>Q</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}Q&=v_{1}A_{1}=v_{2}A_{2}\\[3pt]p_{1}-p_{2}&={\frac {\rho }{2}}\left(v_{2}^{2}-v_{1}^{2}\right)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b29832cefc46a783a62acdaa33eacbc9165fd56" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:24.195ex; height:8.509ex;" alt="{\displaystyle {\begin{aligned}Q&=v_{1}A_{1}=v_{2}A_{2}\\[3pt]p_{1}-p_{2}&={\frac {\rho }{2}}\left(v_{2}^{2}-v_{1}^{2}\right)\end{aligned}}}"></span> </p><p>then <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 Q=A_{1}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1}}}}=A_{2}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{1-\left({\frac {A_{2}}{A_{1}}}\right)^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mi>ρ</mi> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mi>ρ</mi> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=A_{1}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1}}}}=A_{2}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{1-\left({\frac {A_{2}}{A_{1}}}\right)^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/164d293785917d5d5bb07cdb01d96bafbc603a61" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.005ex; width:49.11ex; height:9.009ex;" alt="{\displaystyle Q=A_{1}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1}}}}=A_{2}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{1-\left({\frac {A_{2}}{A_{1}}}\right)^{2}}}}}}"></span> A Venturi can also be used to mix a liquid with a gas. If a pump forces the liquid through a tube connected to a system consisting of a Venturi to increase the liquid speed (the diameter decreases), a short piece of tube with a small hole in it, and last a Venturi that decreases speed (so the pipe gets wider again), the gas will be sucked in through the small hole because of changes in pressure. At the end of the system, a mixture of liquid and gas will appear. See <a href="/wiki/Aspirator_(pump)" class="mw-redirect" title="Aspirator (pump)">aspirator</a> and <a href="/wiki/Pressure_head" title="Pressure head">pressure head</a> for discussion of this type of <a href="/wiki/Siphon" title="Siphon">siphon</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Differential_pressure">Differential pressure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=9" title="Edit section: Differential pressure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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">Main article: <a href="/wiki/Pressure_head" title="Pressure head">Pressure head</a></div> <p>As fluid flows through a Venturi, the expansion and compression of the fluids cause the pressure inside the Venturi to change. This principle can be used in <a href="/wiki/Metrology" title="Metrology">metrology</a> for gauges calibrated for differential pressures. This type of pressure measurement may be more convenient, for example, to measure fuel or combustion pressures in jet or rocket engines. </p><p>The first large-scale Venturi meters to measure liquid flows were developed by <a href="/wiki/Clemens_Herschel" title="Clemens Herschel">Clemens Herschel</a> who used them to measure small and large flows of water and wastewater beginning at the end of the 19th century.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> While working for the <a href="/wiki/Holyoke_Water_Power_Company" class="mw-redirect" title="Holyoke Water Power Company">Holyoke Water Power Company</a>, Herschel would develop the means for measuring these flows to determine the water power consumption of different mills on the <a href="/wiki/Holyoke_Canal_System" title="Holyoke Canal System">Holyoke Canal System</a>, first beginning development of the device in 1886, two years later he would describe his invention of the Venturi meter to <a href="/wiki/William_Unwin" title="William Unwin">William Unwin</a> in a letter dated June 5, 1888.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Compensation_for_temperature,_pressure,_and_mass"><span id="Compensation_for_temperature.2C_pressure.2C_and_mass"></span>Compensation for temperature, pressure, and mass</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=10" title="Edit section: Compensation for temperature, pressure, and mass"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Fundamentally, pressure-based meters measure <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> density. <a href="/wiki/Bernoulli%27s_equation" class="mw-redirect" title="Bernoulli's equation">Bernoulli's equation</a> (used above) relates this to <a href="/wiki/Mass_density" class="mw-redirect" title="Mass density">mass density</a> and volumetric flow: </p><p><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 \Delta P={\frac {1}{2}}\rho (v_{2}^{2}-v_{1}^{2})={\frac {1}{2}}\rho \left(\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1\right)v_{1}^{2}={\frac {1}{2}}\rho \left({\frac {1}{A_{2}^{2}}}-{\frac {1}{A_{1}^{2}}}\right)Q^{2}=k\,\rho \,Q^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ρ</mi> <mo stretchy="false">(</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ρ</mi> <mrow> <mo>(</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ρ</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msup> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>k</mi> <mspace width="thinmathspace" /> <mi>ρ</mi> <mspace width="thinmathspace" /> <msup> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta P={\frac {1}{2}}\rho (v_{2}^{2}-v_{1}^{2})={\frac {1}{2}}\rho \left(\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1\right)v_{1}^{2}={\frac {1}{2}}\rho \left({\frac {1}{A_{2}^{2}}}-{\frac {1}{A_{1}^{2}}}\right)Q^{2}=k\,\rho \,Q^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f25bc630308d34d104b8e0356c8157a907a4d2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:76.975ex; height:7.509ex;" alt="{\displaystyle \Delta P={\frac {1}{2}}\rho (v_{2}^{2}-v_{1}^{2})={\frac {1}{2}}\rho \left(\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1\right)v_{1}^{2}={\frac {1}{2}}\rho \left({\frac {1}{A_{2}^{2}}}-{\frac {1}{A_{1}^{2}}}\right)Q^{2}=k\,\rho \,Q^{2}}"></span> </p><p>where constant terms are absorbed into <i>k</i>. Using the definitions of 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 m=\rho V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mi>ρ</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=\rho V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b240d52d06cda51976790d64665c0c9311a837ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.128ex; height:2.676ex;" alt="{\displaystyle m=\rho V}"></span>), <a href="/wiki/Molar_concentration" title="Molar concentration">molar concentration</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=CV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>C</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=CV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f602152d892b2b0e9eb6a3c49cac592f99dbf5a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.047ex; height:2.176ex;" alt="{\displaystyle n=CV}"></span>), and <a href="/wiki/Molar_mass" title="Molar mass">molar mass</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 m=Mn}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mi>M</mi> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=Mn}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/416edcbe5962b795764587d5941f9573d8312aaa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.976ex; height:2.176ex;" alt="{\displaystyle m=Mn}"></span>), one can also derive mass flow or molar flow (i.e. standard volume flow): </p><p><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 {\begin{aligned}\Delta P&=k\,\rho \,Q^{2}\\&=k{\frac {1}{\rho }}\,{\dot {m}}^{2}\\&=k{\frac {\rho }{C^{2}}}\,{\dot {n}}^{2}=k{\frac {M}{C}}\,{\dot {n}}^{2}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <mi>P</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>k</mi> <mspace width="thinmathspace" /> <mi>ρ</mi> <mspace width="thinmathspace" /> <msup> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>ρ</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <mi>C</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\Delta P&=k\,\rho \,Q^{2}\\&=k{\frac {1}{\rho }}\,{\dot {m}}^{2}\\&=k{\frac {\rho }{C^{2}}}\,{\dot {n}}^{2}=k{\frac {M}{C}}\,{\dot {n}}^{2}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5869971eae21d1b1b6a9e7a8145a6ac296e71908" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.518ex; margin-bottom: -0.32ex; width:26.338ex; height:14.843ex;" alt="{\displaystyle {\begin{aligned}\Delta P&=k\,\rho \,Q^{2}\\&=k{\frac {1}{\rho }}\,{\dot {m}}^{2}\\&=k{\frac {\rho }{C^{2}}}\,{\dot {n}}^{2}=k{\frac {M}{C}}\,{\dot {n}}^{2}.\end{aligned}}}"></span> </p><p>However, measurements outside the design point must compensate for the effects of temperature, pressure, and molar mass on density and concentration. The <a href="/wiki/Ideal_gas_law" title="Ideal gas law">ideal gas law</a> is used to relate actual values to <a href="/wiki/Standard_state" title="Standard state">design values</a>: </p><p><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={\frac {P}{RT}}={\frac {\left({\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}C^{\ominus }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>T</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mfrac> </mrow> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\frac {P}{RT}}={\frac {\left({\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}C^{\ominus }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c86be03ee8fdf6b11ea67bec1fe944ecf5b42c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:22.446ex; height:10.176ex;" alt="{\displaystyle C={\frac {P}{RT}}={\frac {\left({\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}C^{\ominus }}"></span> <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 ={\frac {MP}{RT}}={\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>M</mi> <mi>P</mi> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>T</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mfrac> </mrow> <msup> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {MP}{RT}}={\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3424950922a4c143b00e92403e7308a2b9429c00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:26.526ex; height:10.176ex;" alt="{\displaystyle \rho ={\frac {MP}{RT}}={\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }.}"></span> </p><p>Substituting these two relations into the pressure-flow equations above yields the fully compensated flows: </p><p><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 {\begin{aligned}\Delta P&=k{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }\,Q^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\left({\frac {Q}{Q_{\max }}}\right)^{2}\\&=k{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)\rho ^{\ominus }}}{\dot {m}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {m}}{{\dot {m}}_{\max }}}\right)^{2}\\&=k{\frac {M\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)C^{\ominus }}}{\dot {n}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {n}}{{\dot {n}}_{\max }}}\right)^{2}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <mi>P</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>T</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mfrac> </mrow> <msup> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> <mspace width="thinmathspace" /> <msup> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>T</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>T</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msup> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>T</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙</mo> </mover> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>M</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>T</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>T</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo>˙</mo> </mover> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\Delta P&=k{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }\,Q^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\left({\frac {Q}{Q_{\max }}}\right)^{2}\\&=k{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)\rho ^{\ominus }}}{\dot {m}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {m}}{{\dot {m}}_{\max }}}\right)^{2}\\&=k{\frac {M\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)C^{\ominus }}}{\dot {n}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {n}}{{\dot {n}}_{\max }}}\right)^{2}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/965b3a2cdde3396d59b84ed7d5afb4312e2ac27a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -14.838ex; width:60.884ex; height:30.843ex;" alt="{\displaystyle {\begin{aligned}\Delta P&=k{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }\,Q^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\left({\frac {Q}{Q_{\max }}}\right)^{2}\\&=k{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)\rho ^{\ominus }}}{\dot {m}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {m}}{{\dot {m}}_{\max }}}\right)^{2}\\&=k{\frac {M\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)C^{\ominus }}}{\dot {n}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {n}}{{\dot {n}}_{\max }}}\right)^{2}.\end{aligned}}}"></span> </p><p><i>Q</i>, <i>m</i>, or <i>n</i> are easily isolated by dividing and taking the <a href="/wiki/Square_root" title="Square root">square root</a>. Note that pressure-, temperature-, and mass-compensation is required for every flow, regardless of the end units or dimensions. Also we see the relations: </p><p><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 {\begin{aligned}{\frac {k}{\Delta P_{\max }}}&={\frac {1}{\rho ^{\ominus }Q_{\max }^{2}}}\\&={\frac {\rho ^{\ominus }}{{\dot {m}}_{\max }^{2}}}\\&={\frac {{C^{\ominus }}^{2}}{\rho ^{\ominus }{\dot {n}}_{\max }^{2}}}={\frac {C^{\ominus }}{M^{\ominus }{\dot {n}}_{\max }^{2}}}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>k</mi> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msup> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> <msubsup> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <msup> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> <mrow> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\frac {k}{\Delta P_{\max }}}&={\frac {1}{\rho ^{\ominus }Q_{\max }^{2}}}\\&={\frac {\rho ^{\ominus }}{{\dot {m}}_{\max }^{2}}}\\&={\frac {{C^{\ominus }}^{2}}{\rho ^{\ominus }{\dot {n}}_{\max }^{2}}}={\frac {C^{\ominus }}{M^{\ominus }{\dot {n}}_{\max }^{2}}}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f93640564b45b66f68a16c9107428f108bc6236" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.27ex; margin-bottom: -0.234ex; width:32.917ex; height:20.176ex;" alt="{\displaystyle {\begin{aligned}{\frac {k}{\Delta P_{\max }}}&={\frac {1}{\rho ^{\ominus }Q_{\max }^{2}}}\\&={\frac {\rho ^{\ominus }}{{\dot {m}}_{\max }^{2}}}\\&={\frac {{C^{\ominus }}^{2}}{\rho ^{\ominus }{\dot {n}}_{\max }^{2}}}={\frac {C^{\ominus }}{M^{\ominus }{\dot {n}}_{\max }^{2}}}.\end{aligned}}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=11" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Example_farm plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>may contain <a href="/wiki/Wikipedia:Manual_of_Style/Lists#List_size" title="Wikipedia:Manual of Style/Lists">excessive</a> or <a href="/wiki/Wikipedia:Neutral_point_of_view#Due_and_undue_weight" title="Wikipedia:Neutral point of view">irrelevant</a> examples</b>.<span class="hide-when-compact"> Please help <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Venturi_effect&action=edit">improve the article</a> by adding descriptive text and removing <a href="/wiki/Wikipedia:Example_cruft" title="Wikipedia:Example cruft">less pertinent examples</a>.</span> <span class="date-container"><i>(<span class="date">February 2024</span>)</i></span></div></td></tr></tbody></table> <p>The Venturi effect may be observed or used in the following: </p> <div class="mw-heading mw-heading3"><h3 id="Machines">Machines</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=12" title="Edit section: Machines"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>During <a href="/wiki/Underway_replenishment" title="Underway replenishment">Underway replenishment</a> the helmsman of each ship must constantly steer away from the other ship due to the Venturi effect, otherwise they will collide.</li> <li>Cargo <a href="/wiki/Eductor-jet_pump" class="mw-redirect" title="Eductor-jet pump">eductors</a> on oil product and chemical ship tankers</li> <li><a href="/wiki/Inspirator" title="Inspirator">Inspirators</a> mix air and flammable gas in <a href="/wiki/Grill_(cooking)" class="mw-redirect" title="Grill (cooking)">grills</a>, <a href="/wiki/Gas_stove" title="Gas stove">gas stoves</a> and <a href="/wiki/Bunsen_burner" title="Bunsen burner">Bunsen burners</a></li> <li><a href="/wiki/Water_aspirators" class="mw-redirect" title="Water aspirators">Water aspirators</a> produce a partial vacuum using the kinetic energy from the faucet water pressure</li> <li><a href="/wiki/Steam_injector#Vacuum_ejectors" class="mw-redirect" title="Steam injector">Steam siphons</a> use the kinetic energy from the steam pressure to create a partial vacuum</li> <li><a href="/wiki/Atomizer_nozzle" class="mw-redirect" title="Atomizer nozzle">Atomizers</a> disperse perfume or spray paint (i.e. from a spray gun or <a href="/wiki/Airbrush" title="Airbrush">airbrush</a>)</li> <li><a href="/wiki/Carburetor" title="Carburetor">Carburetors</a> use the effect to suck <a href="/wiki/Gasoline" title="Gasoline">gasoline</a> into an engine's intake air stream</li> <li><a href="/wiki/Cylinder_head" title="Cylinder head">Cylinder heads</a> in piston engines have multiple Venturi areas like the valve seat and the port entrance, although these are not part of the design intent, merely a byproduct and any venturi effect is without specific function.</li> <li><a href="/wiki/Wine_aerator" class="mw-redirect" title="Wine aerator">Wine aerators</a> infuse air into wine as it is poured into a glass</li> <li><a href="/wiki/Protein_skimmer" title="Protein skimmer">Protein skimmers</a> filter saltwater <a href="/wiki/Aquarium" title="Aquarium">aquaria</a></li> <li><a href="/wiki/Automated_pool_cleaner" title="Automated pool cleaner">Automated pool cleaners</a> use pressure-side water flow to collect sediment and debris</li> <li><a href="/wiki/Clarinet" title="Clarinet">Clarinets</a> use a reverse taper to speed the air down the tube, enabling better tone, response and intonation<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li> <li>The <a href="/wiki/Leadpipe" title="Leadpipe">leadpipe</a> of a <a href="/wiki/Trombone" title="Trombone">trombone</a>, affecting the <a href="/wiki/Timbre" title="Timbre">timbre</a></li> <li>Industrial <a href="/wiki/Vacuum_cleaner" title="Vacuum cleaner">vacuum cleaners</a> use compressed air</li> <li><a href="/wiki/Venturi_scrubber" title="Venturi scrubber">Venturi scrubbers</a> are used to clean <a href="/wiki/Flue_gas" title="Flue gas">flue gas</a> emissions</li> <li>Injectors (also called ejectors) are used to add chlorine gas to <a href="/wiki/Water_treatment" title="Water treatment">water treatment</a> <a href="/wiki/Water_chlorination" title="Water chlorination">chlorination</a> systems</li> <li><a href="/wiki/Injector" title="Injector">Steam injectors</a> use the Venturi effect and the <a href="/wiki/Latent_heat" title="Latent heat">latent heat</a> of evaporation to deliver feed water to a <a href="/wiki/Steam_locomotive" title="Steam locomotive">steam locomotive</a> <a href="/wiki/Boiler" title="Boiler">boiler</a>.</li> <li>Sandblasting nozzles accelerate and air and media mixture</li> <li><a href="/wiki/Bilge" title="Bilge">Bilge</a> water can be emptied from a moving boat through a small waste gate in the hull. The air pressure inside the moving boat is greater than the water sliding by beneath.</li> <li>A <a href="/wiki/Diving_regulator" title="Diving regulator">scuba diving regulator</a> uses the Venturi effect to assist maintaining the flow of gas once it starts flowing</li> <li>In <a href="/wiki/Recoilless_rifle" title="Recoilless rifle">recoilless rifles</a> to decrease the recoil of firing</li> <li>The <a href="/wiki/Diffuser_(automotive)" title="Diffuser (automotive)">diffuser</a> on an automobile</li> <li>Race cars utilising <a href="/wiki/Ground_effect_(cars)" title="Ground effect (cars)">ground effect</a> to increase <a href="/wiki/Downforce" title="Downforce">downforce</a> and thus become capable of higher cornering speeds</li> <li>Foam proportioners used to induct <a href="/wiki/Fire_fighting_foam" class="mw-redirect" title="Fire fighting foam">fire fighting foam</a> concentrate into fire protection systems</li> <li><a href="/wiki/Trompe" title="Trompe">Trompe</a> air compressors entrain air into a falling column of water</li> <li>The bolts in some brands of paintball markers</li> <li>Low-speed <a href="/wiki/Wind_tunnel" title="Wind tunnel">wind tunnels</a> can be considered very large Venturi because they take advantage of the Venturi effect to increase velocity and decrease pressure to simulate expected flight conditions.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Architecture">Architecture</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=13" title="Edit section: Architecture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Hawa_Mahal" title="Hawa Mahal">Hawa Mahal</a> of Jaipur, also utilizes the Venturi effect, by allowing cool air to pass through, thus making the whole area more pleasant during the high temperatures in summer.</li> <li>Large cities where wind is forced between buildings - the gap between the Twin Towers of the original <a href="/wiki/World_Trade_Center_(1973%E2%80%932001)" title="World Trade Center (1973–2001)">World Trade Center</a> was an extreme example of the phenomenon, which made the ground level plaza notoriously windswept.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> In fact, some gusts were so high that pedestrian travel had to be aided by ropes.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></li> <li>In the south of Iraq, near the modern town of <a href="/wiki/Nasiriyah" title="Nasiriyah">Nasiriyah</a>, a 4000-year-old flume structure has been discovered at the ancient site of <a href="/wiki/Girsu" title="Girsu">Girsu</a>. This construction by the ancient <a href="/wiki/Sumerians" class="mw-redirect" title="Sumerians">Sumerians</a> forced the contents of a nineteen kilometre canal through a constriction to enable the side-channeling of water off to agricultural lands from a higher origin than would have been the case without the flume. A recent dig by archaeologists from the British museum confirmed the finding.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Nature">Nature</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Venturi_effect&action=edit&section=14" title="Edit section: Nature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>In windy mountain passes, resulting in erroneous <a href="/wiki/Pressure_altimeter" title="Pressure altimeter">pressure altimeter</a> readings<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li>The <a href="/wiki/Mistral_wind" class="mw-redirect" title="Mistral wind">mistral wind</a> in southern France increases in speed through the <a href="/wiki/Rhone_valley" class="mw-redirect" title="Rhone valley">Rhone valley</a>.</li></ul> <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=Venturi_effect&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Joule%E2%80%93Thomson_effect" title="Joule–Thomson effect">Joule–Thomson effect</a></li> <li><a href="/wiki/Venturi_flume" title="Venturi flume">Venturi flume</a></li> <li><a href="/wiki/Parshall_flume" title="Parshall flume">Parshall flume</a></li></ul> <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=Venturi_effect&action=edit&section=16" title="Edit section: References"><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"> <div class="mw-references-wrap"><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="CITEREFNasrConnor2014" class="citation book cs1">Nasr, G. G.; Connor, N. E. (2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=C-01BAAAQBAJ&pg=PA183">"5.3 Gas Flow Measurement"</a>. <i>Natural Gas Engineering and Safety Challenges: Downstream Process, Analysis, Utilization and Safety</i>. Springer. p. 183. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783319089485" title="Special:BookSources/9783319089485"><bdi>9783319089485</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=5.3+Gas+Flow+Measurement&rft.btitle=Natural+Gas+Engineering+and+Safety+Challenges%3A+Downstream+Process%2C+Analysis%2C+Utilization+and+Safety&rft.pages=183&rft.pub=Springer&rft.date=2014&rft.isbn=9783319089485&rft.aulast=Nasr&rft.aufirst=G.+G.&rft.au=Connor%2C+N.+E.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DC-01BAAAQBAJ%26pg%3DPA183&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVenturi+effect" class="Z3988"></span></span> </li> <li id="cite_note-wolfram-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-wolfram_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://demonstrations.wolfram.com/TheVenturiEffect/">"The Venturi effect"</a>. Wolfram Demonstrations Project<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-11-03</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Venturi+effect&rft.pub=Wolfram+Demonstrations+Project&rft_id=http%3A%2F%2Fdemonstrations.wolfram.com%2FTheVenturiEffect%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVenturi+effect" 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">Herschel, Clemens. (1898). <i>Measuring Water.</i> Providence, RI:Builders Iron Foundry.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F136254a0">"Invention of the Venturi Meter"</a>. <i>Nature</i>. <b>136</b> (3433): 254. August 17, 1935. <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/1935Natur.136Q.254.">1935Natur.136Q.254.</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F136254a0">10.1038/136254a0</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Invention+of+the+Venturi+Meter&rft.volume=136&rft.issue=3433&rft.pages=254&rft.date=1935-08-17&rft_id=info%3Adoi%2F10.1038%2F136254a0&rft_id=info%3Abibcode%2F1935Natur.136Q.254.&rft_id=https%3A%2F%2Fdoi.org%2F10.1038%252F136254a0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVenturi+effect" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlasco" class="citation web cs1 cs1-prop-foreign-lang-source">Blasco, Daniel Cortés. <a rel="nofollow" class="external text" href="https://www.face2fire.com/venturi-or-air-circulation-thats-the-question/">"Venturi or air circulation?, that's the question"</a>. <i>face2fire</i> (in Spanish)<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-07-14</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=face2fire&rft.atitle=Venturi+or+air+circulation%3F%2C+that%27s+the+question.&rft.aulast=Blasco&rft.aufirst=Daniel+Cort%C3%A9s&rft_id=https%3A%2F%2Fwww.face2fire.com%2Fventuri-or-air-circulation-thats-the-question%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVenturi+effect" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAnderson2017" class="citation book cs1">Anderson, John (2017). <i>Fundamentals of Aerodynamics</i> (6th ed.). New York, NY: McGraw-Hill Education. p. 218. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-259-12991-9" title="Special:BookSources/978-1-259-12991-9"><bdi>978-1-259-12991-9</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+Aerodynamics&rft.place=New+York%2C+NY&rft.pages=218&rft.edition=6th&rft.pub=McGraw-Hill+Education&rft.date=2017&rft.isbn=978-1-259-12991-9&rft.aulast=Anderson&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVenturi+effect" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDunlap,_David_W2006" class="citation news cs1">Dunlap, David W (December 7, 2006). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2006/12/07/nyregion/07blocks.html?fta=y">"At New Trade Center, Seeking Lively (but Secure) Streets"</a>. <i>The New York Times</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=At+New+Trade+Center%2C+Seeking+Lively+%28but+Secure%29+Streets&rft.date=2006-12-07&rft.au=Dunlap%2C+David+W&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2006%2F12%2F07%2Fnyregion%2F07blocks.html%3Ffta%3Dy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVenturi+effect" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDunlap,_David_W2004" class="citation news cs1">Dunlap, David W (March 25, 2004). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2004/03/25/nyregion/25blocks.html">"Girding Against Return of the Windy City in Manhattan"</a>. <i>The New York Times</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Girding+Against+Return+of+the+Windy+City+in+Manhattan&rft.date=2004-03-25&rft.au=Dunlap%2C+David+W&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2004%2F03%2F25%2Fnyregion%2F25blocks.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVenturi+effect" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation audio-visual cs1"><a rel="nofollow" class="external text" href="https://archive.org/details/gov.ntis.ava20333vnb1"><i>Dusk to Dawn</i></a> (educational film). Federal Aviation Administration. 1971. 17 minutes in. AVA20333VNB1.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Dusk+to+Dawn&rft.pub=Federal+Aviation+Administration&rft.date=1971&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgov.ntis.ava20333vnb1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVenturi+effect" class="Z3988"></span></span> </li> </ol></div></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=Venturi_effect&action=edit&section=17" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Venturi_effect" class="extiw" title="commons:Category:Venturi effect">Venturi effect</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=oUd4WxjoHKY">3D animation of the Differential Pressure Flow Measuring Principle (Venturi meter)</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUT_Austin" class="citation web cs1">UT Austin. <a rel="nofollow" class="external text" href="http://www.ce.utexas.edu/prof/KINNAS/319LAB/Applets/Venturi/venturi.html">"Venturi Tube Simulation"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2009-11-03</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Venturi+Tube+Simulation&rft.au=UT+Austin&rft_id=http%3A%2F%2Fwww.ce.utexas.edu%2Fprof%2FKINNAS%2F319LAB%2FApplets%2FVenturi%2Fventuri.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVenturi+effect" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=fT2KhJ8W-Kg">Use of the Venturi effect for gas pumps to know when to turn off (video)</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Venturi_effect&oldid=1247073958">https://en.wikipedia.org/w/index.php?title=Venturi_effect&oldid=1247073958</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Fluid_dynamics" title="Category:Fluid dynamics">Fluid dynamics</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_Spanish-language_sources_(es)" title="Category:CS1 Spanish-language sources (es)">CS1 Spanish-language sources (es)</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Wikipedia_introduction_cleanup_from_February_2024" title="Category:Wikipedia introduction cleanup from February 2024">Wikipedia introduction cleanup from February 2024</a></li><li><a href="/wiki/Category:All_pages_needing_cleanup" title="Category:All pages needing cleanup">All pages needing cleanup</a></li><li><a href="/wiki/Category:Articles_covered_by_WikiProject_Wikify_from_February_2024" title="Category:Articles covered by WikiProject Wikify from February 2024">Articles covered by WikiProject Wikify from February 2024</a></li><li><a href="/wiki/Category:All_articles_covered_by_WikiProject_Wikify" title="Category:All articles covered by WikiProject Wikify">All articles covered by WikiProject Wikify</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_April_2016" title="Category:Articles with unsourced statements from April 2016">Articles with unsourced statements from April 2016</a></li><li><a href="/wiki/Category:Articles_with_too_many_examples_from_February_2024" title="Category:Articles with too many examples from February 2024">Articles with too many examples from February 2024</a></li><li><a href="/wiki/Category:All_articles_with_too_many_examples" title="Category:All articles with too many examples">All articles with too many examples</a></li><li><a href="/wiki/Category:Wikipedia_articles_with_style_issues_from_February_2024" title="Category:Wikipedia articles with style issues from February 2024">Wikipedia articles with style issues from February 2024</a></li><li><a href="/wiki/Category:Commons_category_link_from_Wikidata" title="Category:Commons category link from Wikidata">Commons category link from Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 22 September 2024, at 17:50<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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Venturi effect - Wikipedia