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<div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Forces and equilibrium</span> </div> </a> <button aria-controls="toc-Forces_and_equilibrium-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 Forces and equilibrium subsection</span> </button> <ul id="toc-Forces_and_equilibrium-sublist" class="vector-toc-list"> <li id="toc-Simplified_model" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Simplified_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Simplified model</span> </div> </a> <ul id="toc-Simplified_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Static_stability" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Static_stability"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Static stability</span> </div> </a> <ul id="toc-Static_stability-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Fluids_and_objects" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fluids_and_objects"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Fluids and objects</span> </div> </a> <button aria-controls="toc-Fluids_and_objects-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 Fluids and objects subsection</span> </button> <ul id="toc-Fluids_and_objects-sublist" class="vector-toc-list"> <li id="toc-Compressible_objects" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Compressible_objects"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Compressible objects</span> </div> </a> <ul id="toc-Compressible_objects-sublist" class="vector-toc-list"> <li id="toc-Submarines" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Submarines"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Submarines</span> </div> </a> <ul id="toc-Submarines-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Balloons" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Balloons"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2</span> <span>Balloons</span> </div> </a> <ul id="toc-Balloons-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Divers" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Divers"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.3</span> <span>Divers</span> </div> </a> <ul id="toc-Divers-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Density" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Density"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Density</span> </div> </a> <ul id="toc-Density-sublist" class="vector-toc-list"> </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" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Buoyancy</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 62 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-62" 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">62 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/Dryfvermo%C3%AB" title="Dryfvermoë – Afrikaans" lang="af" hreflang="af" data-title="Dryfvermoë" 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%B7%D9%81%D9%88" title="طفو – Arabic" lang="ar" hreflang="ar" data-title="طفو" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Flotabilid%C3%A1" title="Flotabilidá – Asturian" lang="ast" hreflang="ast" data-title="Flotabilidá" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Batmazl%C4%B1q" title="Batmazlıq – Azerbaijani" lang="az" hreflang="az" data-title="Batmazlıq" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A8%D8%A7%D8%AA%D9%85%D8%A7%D8%B2%D9%84%DB%8C%D9%82" title="باتمازلیق – South Azerbaijani" lang="azb" hreflang="azb" data-title="باتمازلیق" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%8D%E0%A6%B2%E0%A6%AC%E0%A6%A4%E0%A6%BE" title="প্লবতা – Bangla" lang="bn" hreflang="bn" data-title="প্লবতা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ph%C3%BB-le%CC%8Dk" title="Phû-le̍k – Minnan" lang="nan" hreflang="nan" data-title="Phû-le̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%BB%D1%8B%D0%B2%D1%83%D1%87%D0%B0%D1%81%D1%86%D1%8C" title="Плывучасць – Belarusian" lang="be" hreflang="be" data-title="Плывучасць" 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%9F%D0%BB%D0%B0%D0%B2%D0%B0%D0%B5%D0%BC%D0%BE%D1%81%D1%82" title="Плаваемост – Bulgarian" lang="bg" hreflang="bg" data-title="Плаваемост" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Potisak" title="Potisak – Bosnian" lang="bs" hreflang="bs" data-title="Potisak" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Flotabilitat" title="Flotabilitat – Catalan" lang="ca" hreflang="ca" data-title="Flotabilitat" 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/Vztlak" title="Vztlak – Czech" lang="cs" hreflang="cs" data-title="Vztlak" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Simudzo" title="Simudzo – Shona" lang="sn" hreflang="sn" data-title="Simudzo" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Opdrift_(statisk)" title="Opdrift (statisk) – Danish" lang="da" hreflang="da" data-title="Opdrift (statisk)" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Statischer_Auftrieb" title="Statischer Auftrieb – German" lang="de" hreflang="de" data-title="Statischer Auftrieb" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/%C3%9Clesl%C3%BCkkej%C3%B5ud" title="Üleslükkejõud – Estonian" lang="et" hreflang="et" data-title="Üleslükkejõud" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%86%CE%BD%CF%89%CF%83%CE%B7" title="Άνωση – Greek" lang="el" hreflang="el" data-title="Άνωση" 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/Flotabilidad" title="Flotabilidad – Spanish" lang="es" hreflang="es" data-title="Flotabilidad" 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/Flotagarritasun" title="Flotagarritasun – Basque" lang="eu" hreflang="eu" data-title="Flotagarritasun" 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%B4%D9%86%D8%A7%D9%88%D8%B1%DB%8C" title="شناوری – Persian" lang="fa" hreflang="fa" data-title="شناوری" 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/Flottabilit%C3%A9" title="Flottabilité – French" lang="fr" hreflang="fr" data-title="Flottabilité" 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/Buacacht" title="Buacacht – Irish" lang="ga" hreflang="ga" data-title="Buacacht" 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/Flotabilidade" title="Flotabilidade – Galician" lang="gl" hreflang="gl" data-title="Flotabilidade" 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%B6%80%EB%A0%A5" title="부력 – Korean" lang="ko" hreflang="ko" data-title="부력" 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%89%E0%A4%A4%E0%A5%8D%E0%A4%AA%E0%A5%8D%E0%A4%B2%E0%A4%BE%E0%A4%B5%E0%A4%A8_%E0%A4%AC%E0%A4%B2" title="उत्प्लावन बल – Hindi" lang="hi" hreflang="hi" data-title="उत्प्लावन बल" 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/Uzgon" title="Uzgon – Croatian" lang="hr" hreflang="hr" data-title="Uzgon" 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/Gaya_apung" title="Gaya apung – Indonesian" lang="id" hreflang="id" data-title="Gaya apung" 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Uppdrif" title="Uppdrif – Icelandic" lang="is" hreflang="is" data-title="Uppdrif" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A6%D7%99%D7%A4%D7%94_(%D7%A4%D7%99%D7%96%D7%99%D7%A7%D7%94)" title="ציפה (פיזיקה) – Hebrew" lang="he" hreflang="he" data-title="ציפה (פיזיקה)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Flotabilite" title="Flotabilite – Haitian Creole" lang="ht" hreflang="ht" data-title="Flotabilite" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%81%E0%BA%B2%E0%BA%99%E0%BA%A5%E0%BA%AD%E0%BA%8D%E0%BA%95%E0%BA%BB%E0%BA%A7" title="ການລອຍຕົວ – Lao" lang="lo" hreflang="lo" data-title="ການລອຍຕົວ" data-language-autonym="ລາວ" data-language-local-name="Lao" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Felhajt%C3%B3er%C5%91_(hidrosztatika)" title="Felhajtóerő (hidrosztatika) – Hungarian" lang="hu" hreflang="hu" data-title="Felhajtóerő (hidrosztatika)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%8D%E0%B4%B2%E0%B4%B5%E0%B4%95%E0%B5%8D%E0%B4%B7%E0%B4%AE%E0%B4%AC%E0%B4%B2%E0%B4%82" title="പ്ലവക്ഷമബലം – Malayalam" lang="ml" hreflang="ml" data-title="പ്ലവക്ഷമബലം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Keapungan" title="Keapungan – Malay" lang="ms" hreflang="ms" data-title="Keapungan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%96%E1%80%B1%E1%80%AC%E1%80%B7%E1%80%82%E1%80%AF%E1%80%8F%E1%80%BA" title="ဖော့ဂုဏ် – Burmese" lang="my" hreflang="my" data-title="ဖော့ဂုဏ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl badge-Q70894304 mw-list-item" title=""><a href="https://nl.wikipedia.org/wiki/Drijfkracht" title="Drijfkracht – Dutch" lang="nl" hreflang="nl" data-title="Drijfkracht" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%89%E0%A4%B0%E0%A5%8D%E0%A4%A7%E0%A5%8D%E0%A4%B5%E0%A4%9A%E0%A4%BE%E0%A4%AA" title="उर्ध्वचाप – Nepali" lang="ne" hreflang="ne" data-title="उर्ध्वचाप" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%B5%AE%E5%8A%9B" title="浮力 – Japanese" lang="ja" hreflang="ja" data-title="浮力" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Oppdrift" title="Oppdrift – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Oppdrift" 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/Oppdrift" title="Oppdrift – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Oppdrift" 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-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%89%E0%A8%A4%E0%A8%AA%E0%A8%B2%E0%A8%BE%E0%A8%B5%E0%A8%A8_%E0%A8%AC%E0%A8%B2" title="ਉਤਪਲਾਵਨ ਬਲ – Punjabi" lang="pa" hreflang="pa" data-title="ਉਤਪਲਾਵਨ ਬਲ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Si%C5%82a_wyporu" title="Siła wyporu – Polish" lang="pl" hreflang="pl" data-title="Siła wyporu" data-language-autonym="Polski" 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data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Pluskueshm%C3%ABria" title="Pluskueshmëria – Albanian" lang="sq" hreflang="sq" data-title="Pluskueshmëria" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%8B%E0%B6%AD%E0%B7%8A%E0%B6%B4%E0%B7%8A%E0%B6%BD%E0%B7%8F%E0%B7%80%E0%B6%9A%E0%B6%AD%E0%B7%8F%E0%B7%80" title="උත්ප්ලාවකතාව – Sinhala" lang="si" hreflang="si" data-title="උත්ප්ලාවකතාව" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Buoyancy" 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title="Uzgon – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Uzgon" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Noste" title="Noste – Finnish" lang="fi" hreflang="fi" data-title="Noste" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Flytkraft" title="Flytkraft – Swedish" lang="sv" hreflang="sv" data-title="Flytkraft" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a 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href="/w/index.php?title=Buoyant&redirect=no" class="mw-redirect" title="Buoyant">Buoyant</a>)</span></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">Upward force that opposes the weight of an object immersed in fluid</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">For the 2019 film, see <a href="/wiki/Buoyancy_(film)" title="Buoyancy (film)">Buoyancy (film)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output 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Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Buoyancy%22">"Buoyancy"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Buoyancy%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Buoyancy%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Buoyancy%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Buoyancy%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Buoyancy%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">July 2014</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Textbook plainlinks metadata ambox ambox-style" 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/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>reads like a <a href="/wiki/Wikipedia:NOTTEXTBOOK" class="mw-redirect" title="Wikipedia:NOTTEXTBOOK">textbook</a></b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Buoyancy&action=edit">improve this article</a> to make it <a href="/wiki/Wikipedia:NPOV" class="mw-redirect" title="Wikipedia:NPOV">neutral</a> in tone and meet Wikipedia's <a href="/wiki/Wikipedia:STYLE" class="mw-redirect" title="Wikipedia:STYLE">quality standards</a>.</span> <span class="date-container"><i>(<span class="date">July 2023</span>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Buoyancy.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Buoyancy.svg/220px-Buoyancy.svg.png" decoding="async" width="220" height="276" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Buoyancy.svg/330px-Buoyancy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/74/Buoyancy.svg/440px-Buoyancy.svg.png 2x" data-file-width="300" data-file-height="376" /></a><figcaption>The forces at work in buoyancy. 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.sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum mechanics</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J=-D{\frac {d\varphi }{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <mo>−</mo> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>φ</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=-D{\frac {d\varphi }{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1856f88def2056f28ed27c7d31180a6240820ea6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.874ex; height:5.509ex;" alt="{\displaystyle J=-D{\frac {d\varphi }{dx}}}"></span><div class="sidebar-caption"><a href="/wiki/Fick%27s_laws_of_diffusion" title="Fick's laws of diffusion">Fick's laws of diffusion</a></div></td></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Laws</div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;"> Conservations</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Conservation_of_mass" title="Conservation of mass">Mass</a></li> <li><a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">Momentum</a></li> <li><a href="/wiki/Conservation_of_energy" title="Conservation of energy">Energy</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;"> Inequalities</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Clausius%E2%80%93Duhem_inequality" title="Clausius–Duhem inequality">Clausius–Duhem (entropy)</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Solid_mechanics" title="Solid mechanics">Solid mechanics</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Deformation_(physics)" title="Deformation (physics)">Deformation</a></li> <li><a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">Elasticity</a> <ul><li><a href="/wiki/Linear_elasticity" title="Linear elasticity">linear</a></li></ul></li> <li><a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">Plasticity</a></li> <li><a href="/wiki/Hooke%27s_law" title="Hooke's law">Hooke's law</a></li> <li><a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">Stress</a></li> <li><a href="/wiki/Strain_(mechanics)" title="Strain (mechanics)">Strain</a> <ul><li><a href="/wiki/Finite_strain_theory" title="Finite strain theory">Finite strain</a></li> <li><a href="/wiki/Infinitesimal_strain_theory" title="Infinitesimal strain theory">Infinitesimal strain</a></li></ul></li> <li><a href="/wiki/Compatibility_(mechanics)" title="Compatibility (mechanics)">Compatibility</a></li> <li><a href="/wiki/Bending" title="Bending">Bending</a></li> <li><a href="/wiki/Contact_mechanics" title="Contact mechanics">Contact mechanics</a> <ul><li><a href="/wiki/Frictional_contact_mechanics" title="Frictional contact mechanics">frictional</a></li></ul></li> <li><a href="/wiki/Material_failure_theory" title="Material failure theory">Material failure theory</a></li> <li><a href="/wiki/Fracture_mechanics" title="Fracture mechanics">Fracture mechanics</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Fluid" title="Fluid">Fluids</a></th></tr><tr><td class="sidebar-content"> <div class="wraplinks"> <ul><li><a href="/wiki/Hydrostatics" title="Hydrostatics">Statics</a> <b>·</b> <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Dynamics</a></li> <li><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a> <b>·</b> <a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a></li> <li><a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equations</a></li> <li><a href="/wiki/Hagen%E2%80%93Poiseuille_equation" title="Hagen–Poiseuille equation">Poiseuille equation</a> <b>·</b> <a href="/wiki/Pascal%27s_law" title="Pascal's law">Pascal's law</a></li> <li><a href="/wiki/Viscosity" title="Viscosity">Viscosity</a> <ul><li>(<a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian</a> <b>·</b> <a href="/wiki/Non-Newtonian_fluid" title="Non-Newtonian fluid">non-Newtonian</a>)</li></ul></li> <li><a class="mw-selflink selflink">Buoyancy</a> <b>·</b> <a href="/wiki/Mixing_(process_engineering)" title="Mixing (process engineering)">Mixing</a> <b>·</b> <a href="/wiki/Pressure" title="Pressure">Pressure</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Liquid" title="Liquid">Liquids</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Adhesion" title="Adhesion">Adhesion</a></li> <li><a href="/wiki/Capillary_action" title="Capillary action">Capillary action</a></li> <li><a href="/wiki/Chromatography" title="Chromatography">Chromatography</a></li> <li><a href="/wiki/Cohesion_(chemistry)" title="Cohesion (chemistry)">Cohesion (chemistry)</a></li> <li><a href="/wiki/Surface_tension" title="Surface tension">Surface tension</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Gas" title="Gas">Gases</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Atmosphere" title="Atmosphere">Atmosphere</a></li> <li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a></li> <li><a href="/wiki/Charles%27s_law" title="Charles's law">Charles's law</a></li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a></li> <li><a href="/wiki/Fick%27s_law" class="mw-redirect" title="Fick's law">Fick's law</a></li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a></li> <li><a href="/wiki/Graham%27s_law" title="Graham's law">Graham's law</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></th></tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Rheology" title="Rheology">Rheology</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Viscoelasticity" title="Viscoelasticity">Viscoelasticity</a></li> <li><a href="/wiki/Rheometry" title="Rheometry">Rheometry</a></li> <li><a href="/wiki/Rheometer" title="Rheometer">Rheometer</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Smart_fluid" title="Smart fluid">Smart fluids</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Electrorheological_fluid" title="Electrorheological fluid">Electrorheological</a></li> <li><a href="/wiki/Magnetorheological_fluid" title="Magnetorheological fluid">Magnetorheological</a></li> <li><a href="/wiki/Ferrofluid" title="Ferrofluid">Ferrofluids</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Robert_Boyle" title="Robert Boyle">Boyle</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li> <li><a href="/wiki/Jacques_Charles" title="Jacques Charles">Charles</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Adolf_Eugen_Fick" title="Adolf Eugen Fick">Fick</a></li> <li><a href="/wiki/Joseph_Louis_Gay-Lussac" title="Joseph Louis Gay-Lussac">Gay-Lussac</a></li> <li><a href="/wiki/Thomas_Graham_(chemist)" title="Thomas Graham (chemist)">Graham</a></li> <li><a href="/wiki/Robert_Hooke" title="Robert Hooke">Hooke</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Claude-Louis_Navier" title="Claude-Louis Navier">Navier</a></li> <li><a href="/wiki/Walter_Noll" title="Walter Noll">Noll</a></li> <li><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascal</a></li> <li><a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">Stokes</a></li> <li><a href="/wiki/Clifford_Truesdell" title="Clifford Truesdell">Truesdell</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Continuum_mechanics" title="Template:Continuum mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Continuum_mechanics" title="Template talk:Continuum mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Continuum_mechanics" title="Special:EditPage/Template:Continuum mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Buoyancy</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'b' in 'buy'">b</span><span title="/ɔɪ/: 'oi' in 'choice'">ɔɪ</span><span title="/ən/: 'on' in 'button'">ən</span><span title="'s' in 'sigh'">s</span><span title="/i/: 'y' in 'happy'">i</span></span>,<span class="wrap"> </span><span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'b' in 'buy'">b</span><span title="/uː/: 'oo' in 'goose'">uː</span><span title="/j/: 'y' in 'yes'">j</span><span title="/ən/: 'on' in 'button'">ən</span><span title="'s' in 'sigh'">s</span><span title="/i/: 'y' in 'happy'">i</span></span>/</a></span></span>),<sup id="cite_ref-lpd_1-0" class="reference"><a href="#cite_note-lpd-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-cepd_2-0" class="reference"><a href="#cite_note-cepd-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> or <b>upthrust</b> is a net upward <a href="/wiki/Force" title="Force">force</a> exerted by a <a href="/wiki/Fluid" title="Fluid">fluid</a> that opposes the <a href="/wiki/Weight" title="Weight">weight</a> of a partially or fully immersed object. In a column of fluid, <a href="/wiki/Pressure" title="Pressure">pressure</a> increases with depth as a result of the weight of the overlying fluid. Thus, the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and (as explained by <a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a>) is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. the <a href="/wiki/Displacement_(fluid)" title="Displacement (fluid)">displaced</a> fluid. </p><p>For this reason, an object whose average <a href="/wiki/Density" title="Density">density</a> is greater than that of the fluid in which it is submerged tends to sink. If the object is less dense than the liquid, the force can keep the object afloat. This can occur only in a <a href="/wiki/Non-inertial_reference_frame" title="Non-inertial reference frame">non-inertial reference frame</a>, which either has a <a href="/wiki/Gravitational_field" title="Gravitational field">gravitational field</a> or is <a href="/wiki/Acceleration" title="Acceleration">accelerating due to a force other than gravity</a> defining a "downward" direction.<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> </p><p>Buoyancy also applies to fluid mixtures, and is the most common driving force of <a href="/wiki/Convection" title="Convection">convection</a> currents. In these cases, the mathematical modelling is altered to apply to <a href="/wiki/Continuum_mechanics" title="Continuum mechanics">continua</a>, but the principles remain the same. Examples of buoyancy driven flows include the spontaneous separation of air and water or oil and water. </p><p>Buoyancy is a function of the force of gravity or other source of acceleration on objects of different densities, and for that reason is considered an apparent force, in the same way that <a href="/wiki/Centrifugal_force" title="Centrifugal force">centrifugal force</a> is an apparent force as a function of inertia. Buoyancy can exist without gravity in the presence of an inertial reference frame, but without an apparent "downward" direction of gravity or other source of acceleration, buoyancy does not exist. </p><p>The <b>center of buoyancy</b> of an object is the <a href="/wiki/Center_of_gravity" class="mw-redirect" title="Center of gravity">center of gravity</a> of the displaced volume of fluid. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Archimedes'_principle"><span id="Archimedes.27_principle"></span>Archimedes' principle</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=1" title="Edit section: Archimedes' principle"><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:Pound-coin-floating-in-mercury.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Pound-coin-floating-in-mercury.jpg/220px-Pound-coin-floating-in-mercury.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Pound-coin-floating-in-mercury.jpg/330px-Pound-coin-floating-in-mercury.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Pound-coin-floating-in-mercury.jpg/440px-Pound-coin-floating-in-mercury.jpg 2x" data-file-width="2448" data-file-height="1836" /></a><figcaption>A metallic coin (an old British <a href="/wiki/British_one_pound_coin" class="mw-redirect" title="British one pound coin">pound coin</a>) floats in <a href="/wiki/Mercury_(element)" title="Mercury (element)">mercury</a> due to the buoyancy force upon it and appears to float higher because of the <a href="/wiki/Surface_tension" title="Surface tension">surface tension</a> of the mercury.</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv/260px--04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="260" height="146" data-durationhint="48" data-mwtitle="04._Галилеево_топче.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/09/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv.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/0/09/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv.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/transcoded/0/09/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/0/09/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv" type="video/ogg; codecs="theora, vorbis"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/09/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/09/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv.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/0/09/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv.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/0/09/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv/04._%D0%93%D0%B0%D0%BB%D0%B8%D0%BB%D0%B5%D0%B5%D0%B2%D0%BE_%D1%82%D0%BE%D0%BF%D1%87%D0%B5.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>The Galileo's Ball experiment, showing the different buoyancy of the same object, depending on its surrounding medium. The ball has certain buoyancy in <a href="/wiki/Water" title="Water">water</a>, but once <a href="/wiki/Ethanol" title="Ethanol">ethanol</a> is added (which is less dense than water), it reduces the density of the medium, thus making the ball sink further down (reducing its buoyancy).</figcaption></figure> <p>Archimedes' principle is named after <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> of <a href="/wiki/Syracuse,_Sicily" title="Syracuse, Sicily">Syracuse</a>, who first discovered this law in 212 BC.<sup id="cite_ref-acottLaw_4-0" class="reference"><a href="#cite_note-acottLaw-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> For objects, floating and sunken, and in gases as well as liquids (i.e. a <a href="/wiki/Fluid" title="Fluid">fluid</a>), Archimedes' principle may be stated thus in terms of forces: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object</p></blockquote> <p>—with the clarifications that for a sunken object the volume of displaced fluid is the volume of the object, and for a floating object on a liquid, the weight of the displaced liquid is the weight of the object.<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> </p><p>More tersely: <b>buoyant force = weight of displaced fluid.</b> </p><p>Archimedes' principle does not consider the <a href="/wiki/Surface_tension" title="Surface tension">surface tension</a> (capillarity) acting on the body,<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> but this additional force modifies only the amount of fluid displaced and <a href="/wiki/Meniscus_(liquid)" title="Meniscus (liquid)">the spatial distribution of the displacement</a>, so the principle that <i>buoyancy = weight of displaced fluid</i> remains valid. </p><p>The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). In simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy. This is also known as upthrust. </p><p>Suppose a rock's weight is measured as 10 <a href="/wiki/Newton_(unit)" title="Newton (unit)">newtons</a> when suspended by a string in a <a href="/wiki/Vacuum" title="Vacuum">vacuum</a> with gravity acting upon it. Suppose that when the rock is lowered into water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyancy force: 10 − 3 = 7 newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the sea floor. It is generally easier to lift an object up through the water than it is to pull it out of the water. </p><p>Assuming Archimedes' principle to be reformulated as follows, </p> <dl><dd><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 {\text{apparent immersed weight}}={\text{weight}}-{\text{weight of displaced fluid}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>apparent immersed weight</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>weight</mtext> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>weight of displaced fluid</mtext> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{apparent immersed weight}}={\text{weight}}-{\text{weight of displaced fluid}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7156b8271fbc964e96c785b25e240c373cd70f6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:63.915ex; height:2.509ex;" alt="{\displaystyle {\text{apparent immersed weight}}={\text{weight}}-{\text{weight of displaced fluid}}\,}"></span></dd></dl> <p>then inserted into the quotient of weights, which has been expanded by the mutual volume </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\text{density of object}}{\text{density of fluid}}}={\frac {\text{weight}}{\text{weight of displaced fluid}}},\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>density of object</mtext> <mtext>density of fluid</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>weight</mtext> <mtext>weight of displaced fluid</mtext> </mfrac> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\text{density of object}}{\text{density of fluid}}}={\frac {\text{weight}}{\text{weight of displaced fluid}}},\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab9131d55f9c02d2854894ae481bdb6d714c1d13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:46.528ex; height:5.843ex;" alt="{\displaystyle {\frac {\text{density of object}}{\text{density of fluid}}}={\frac {\text{weight}}{\text{weight of displaced fluid}}},\,}"></span></dd></dl> <p>yields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volumes: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\text{density of object}}{\text{density of fluid}}}={\frac {\text{weight}}{{\text{weight}}-{\text{apparent immersed weight}}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>density of object</mtext> <mtext>density of fluid</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>weight</mtext> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>weight</mtext> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>apparent immersed weight</mtext> </mrow> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\text{density of object}}{\text{density of fluid}}}={\frac {\text{weight}}{{\text{weight}}-{\text{apparent immersed weight}}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8371d0be919a8507c4378f81a732534e52d7a4d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:57.833ex; height:5.843ex;" alt="{\displaystyle {\frac {\text{density of object}}{\text{density of fluid}}}={\frac {\text{weight}}{{\text{weight}}-{\text{apparent immersed weight}}}}\,}"></span></dd></dl> <p>(This formula is used for example in describing the measuring principle of a <a href="/wiki/Dasymeter" title="Dasymeter">dasymeter</a> and of <a href="/wiki/Hydrostatic_weighing" title="Hydrostatic weighing">hydrostatic weighing</a>.) </p><p>Example: If you drop wood into water, buoyancy will keep it afloat. </p><p>Example: A helium balloon in a moving car. During a period of increasing speed, the air mass inside the car moves in the direction opposite to the car's acceleration (i.e., towards the rear). The balloon is also pulled this way. However, because the balloon is buoyant relative to the air, it ends up being pushed "out of the way", and will actually drift in the same direction as the car's acceleration (i.e., forward). If the car slows down, the same balloon will begin to drift backward. For the same reason, as the car goes round a curve, the balloon will drift towards the inside of the curve. </p> <div class="mw-heading mw-heading2"><h2 id="Forces_and_equilibrium">Forces and equilibrium</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=2" title="Edit section: Forces and equilibrium"><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-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Buoyancy" title="Special:EditPage/Buoyancy">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">January 2016</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Canard_Colvert_02.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Canard_Colvert_02.jpg/280px-Canard_Colvert_02.jpg" decoding="async" width="280" height="419" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Canard_Colvert_02.jpg/420px-Canard_Colvert_02.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Canard_Colvert_02.jpg/560px-Canard_Colvert_02.jpg 2x" data-file-width="2672" data-file-height="4000" /></a><figcaption>A <a href="/wiki/Duck" title="Duck">duck</a> has difficulties to get under water due to its buoyancy. When no swimming forces are implied, the natural equilibrium of forces keeps about half of the duck off water. </figcaption></figure> <p>The equation to calculate the pressure inside a fluid in equilibrium is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {f} +\operatorname {div} \,\sigma =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">f</mi> </mrow> <mo>+</mo> <mi>div</mi> <mspace width="thinmathspace" /> <mi>σ</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {f} +\operatorname {div} \,\sigma =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/704c08e426e6804eb38b58dba374fd1f1df5081c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.425ex; height:2.343ex;" alt="{\displaystyle \mathbf {f} +\operatorname {div} \,\sigma =0}"></span></dd></dl> <p>where <b>f</b> is the force density exerted by some outer field on the fluid, and <i>σ</i> is the <a href="/wiki/Cauchy_stress_tensor" title="Cauchy stress tensor">Cauchy stress tensor</a>. In this case the stress tensor is proportional to the identity tensor: </p> <dl><dd><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 \sigma _{ij}=-p\delta _{ij}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>p</mi> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{ij}=-p\delta _{ij}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4eff92ef09898785388dbecac553ff1aa394214" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.424ex; height:3.009ex;" alt="{\displaystyle \sigma _{ij}=-p\delta _{ij}.\,}"></span></dd></dl> <p>Here <i>δ</i><sub><i>ij</i></sub> is the <a href="/wiki/Kronecker_delta" title="Kronecker delta">Kronecker delta</a>. Using this the above equation becomes: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {f} =\nabla p.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">f</mi> </mrow> <mo>=</mo> <mi mathvariant="normal">∇</mi> <mi>p</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {f} =\nabla p.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42a776f853e91802d869b6170628641af33d999e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.291ex; height:2.509ex;" alt="{\displaystyle \mathbf {f} =\nabla p.\,}"></span></dd></dl> <p>Assuming the outer force field is conservative, that is it can be written as the negative gradient of some scalar valued function: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {f} =-\nabla \Phi .\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">f</mi> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mi mathvariant="normal">Φ</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {f} =-\nabla \Phi .\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c682f918604f924935ebd72445d32fb1195d941d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.608ex; height:2.343ex;" alt="{\displaystyle \mathbf {f} =-\nabla \Phi .\,}"></span></dd></dl> <p>Then: </p> <dl><dd><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 \nabla (p+\Phi )=0\Longrightarrow p+\Phi ={\text{constant}}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>+</mo> <mi mathvariant="normal">Φ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mo stretchy="false">⟹</mo> <mi>p</mi> <mo>+</mo> <mi mathvariant="normal">Φ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>constant</mtext> </mrow> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla (p+\Phi )=0\Longrightarrow p+\Phi ={\text{constant}}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b13796697dd08e1b690c0dc481828d74a7525160" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.278ex; height:2.843ex;" alt="{\displaystyle \nabla (p+\Phi )=0\Longrightarrow p+\Phi ={\text{constant}}.\,}"></span></dd></dl> <p>Therefore, the shape of the open surface of a fluid equals the equipotential plane of the applied outer conservative force field. Let the <i>z</i>-axis point downward. In this case the field is gravity, so Φ = −<i>ρ<sub>f</sub>gz</i> where <i>g</i> is the gravitational acceleration, <i>ρ<sub>f</sub></i> is the mass density of the fluid. Taking the pressure as zero at the surface, where <i>z</i> is zero, the constant will be zero, so the pressure inside the fluid, when it is subject to gravity, is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=\rho _{f}gz.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mi>g</mi> <mi>z</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=\rho _{f}gz.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28057ae2943376ba4076764c7119eae322bcf2f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-left: -0.089ex; width:9.934ex; height:2.343ex;" alt="{\displaystyle p=\rho _{f}gz.\,}"></span></dd></dl> <p>So pressure increases with depth below the surface of a liquid, as <i>z</i> denotes the distance from the surface of the liquid into it. Any object with a non-zero vertical depth will have different pressures on its top and bottom, with the pressure on the bottom being greater. This difference in pressure causes the upward buoyancy force. </p><p>The buoyancy force exerted on a body can now be calculated easily, since the internal pressure of the fluid is known. The force exerted on the body can be calculated by integrating the stress tensor over the surface of the body which is in contact with the fluid: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} =\oint \sigma \,d\mathbf {A} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <mo>∮</mo> <mi>σ</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} =\oint \sigma \,d\mathbf {A} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d53e8b6668b8f0850ba54ec5999a6b04d8256cb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.179ex; height:5.676ex;" alt="{\displaystyle \mathbf {B} =\oint \sigma \,d\mathbf {A} .}"></span></dd></dl> <p>The <a href="/wiki/Surface_integral" title="Surface integral">surface integral</a> can be transformed into a <a href="/wiki/Volume_integral" title="Volume integral">volume integral</a> with the help of the <a href="/wiki/Gauss_theorem" class="mw-redirect" title="Gauss theorem">Gauss theorem</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {B} =\int \operatorname {div} \sigma \,dV=-\int \mathbf {f} \,dV=-\rho _{f}\mathbf {g} \int \,dV=-\rho _{f}\mathbf {g} V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>=</mo> <mo>∫</mo> <mi>div</mi> <mo>⁡</mo> <mi>σ</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>V</mi> <mo>=</mo> <mo>−</mo> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">f</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>V</mi> <mo>=</mo> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">g</mi> </mrow> <mo>∫</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>V</mi> <mo>=</mo> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">g</mi> </mrow> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {B} =\int \operatorname {div} \sigma \,dV=-\int \mathbf {f} \,dV=-\rho _{f}\mathbf {g} \int \,dV=-\rho _{f}\mathbf {g} V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59aa810e63b67d23daabe691fbd06e8879d425b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:53.481ex; height:5.676ex;" alt="{\displaystyle \mathbf {B} =\int \operatorname {div} \sigma \,dV=-\int \mathbf {f} \,dV=-\rho _{f}\mathbf {g} \int \,dV=-\rho _{f}\mathbf {g} V}"></span></dd></dl> <p>where <i>V</i> is the measure of the volume in contact with the fluid, that is the volume of the submerged part of the body, since the fluid does not exert force on the part of the body which is outside of it. </p><p>The magnitude of buoyancy force may be appreciated a bit more from the following argument. Consider any object of arbitrary shape and volume <i>V</i> surrounded by a liquid. The <a href="/wiki/Force" title="Force">force</a> the liquid exerts on an object within the liquid is equal to the weight of the liquid with a volume equal to that of the object. This force is applied in a direction opposite to gravitational force, that is of magnitude: </p> <dl><dd><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 B=\rho _{f}V_{\text{disp}}\,g,\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>disp</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mi>g</mi> <mo>,</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B=\rho _{f}V_{\text{disp}}\,g,\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bfdaf869225d25b36e73474c84673290c69e24b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.258ex; height:2.843ex;" alt="{\displaystyle B=\rho _{f}V_{\text{disp}}\,g,\,}"></span></dd></dl> <p>where <i>ρ<sub>f</sub></i> is the <a href="/wiki/Density" title="Density">density</a> of the fluid, <i>V<sub>disp</sub></i> is the volume of the displaced body of liquid, and <i>g</i> is the <a href="/wiki/Gravitational_acceleration" title="Gravitational acceleration">gravitational acceleration</a> at the location in question. </p><p>If this volume of liquid is replaced by a solid body of exactly the same shape, the force the liquid exerts on it must be exactly the same as above. In other words, the "buoyancy force" on a submerged body is directed in the opposite direction to gravity and is equal in magnitude to </p> <dl><dd><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 B=\rho _{f}Vg.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mi>V</mi> <mi>g</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B=\rho _{f}Vg.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1894cb9c15cec95d8b75d72de800db1da6f04d2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:11.138ex; height:2.843ex;" alt="{\displaystyle B=\rho _{f}Vg.\,}"></span></dd></dl> <p>Though the above derivation of Archimedes principle is correct, a recent paper by the Brazilian physicist Fabio M. S. Lima brings a more general approach for the evaluation of the buoyant force exerted by any fluid (even non-homogeneous) on a body with arbitrary shape.<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> Interestingly, this method leads to the prediction that the buoyant force exerted on a rectangular block touching the bottom of a container points downward! Indeed, this downward buoyant force has been confirmed experimentally.<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> </p><p>The <a href="/wiki/Net_force" title="Net force">net force</a> on the object must be zero if it is to be a situation of fluid statics such that Archimedes principle is applicable, and is thus the sum of the buoyancy force and the object's weight </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\text{net}}=0=mg-\rho _{f}V_{\text{disp}}g\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>net</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>disp</mtext> </mrow> </msub> <mi>g</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\text{net}}=0=mg-\rho _{f}V_{\text{disp}}g\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9acf3dc4f1a54e2227f5ea4404209a086116e9c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:25.729ex; height:2.843ex;" alt="{\displaystyle F_{\text{net}}=0=mg-\rho _{f}V_{\text{disp}}g\,}"></span></dd></dl> <p>If the buoyancy of an (unrestrained and unpowered) object exceeds its weight, it tends to rise. An object whose weight exceeds its buoyancy tends to sink. Calculation of the upwards force on a submerged object during its <a href="/wiki/Acceleration" title="Acceleration">accelerating</a> period cannot be done by the Archimedes principle alone; it is necessary to consider dynamics of an object involving buoyancy. Once it fully sinks to the floor of the fluid or rises to the surface and settles, Archimedes principle can be applied alone. For a floating object, only the submerged volume displaces water. For a sunken object, the entire volume displaces water, and there will be an additional force of reaction from the solid floor. </p><p>In order for Archimedes' principle to be used alone, the object in question must be in equilibrium (the sum of the forces on the object must be zero), therefore; </p> <dl><dd><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 mg=\rho _{f}V_{\text{disp}}g,\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mi>g</mi> <mo>=</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>disp</mtext> </mrow> </msub> <mi>g</mi> <mo>,</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle mg=\rho _{f}V_{\text{disp}}g,\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b3f28e05170a0730fed99e1252a5ac773aaaab8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.264ex; height:2.843ex;" alt="{\displaystyle mg=\rho _{f}V_{\text{disp}}g,\,}"></span></dd></dl> <p>and therefore </p> <dl><dd><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 _{f}V_{\text{disp}}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>disp</mtext> </mrow> </msub> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=\rho _{f}V_{\text{disp}}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1d735720c037f2f02ecef356530e0d1ee3fab1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.032ex; height:2.843ex;" alt="{\displaystyle m=\rho _{f}V_{\text{disp}}.\,}"></span></dd></dl> <p>showing that the depth to which a floating object will sink, and the volume of fluid it will displace, is independent of the <a href="/wiki/Gravitational_field" title="Gravitational field">gravitational field</a> regardless of geographic location. </p> <dl><dd>(<i>Note: If the fluid in question is <a href="/wiki/Seawater" title="Seawater">seawater</a>, it will not have the same <a href="/wiki/Density" title="Density">density</a> (</i>ρ<i>) at every location, since the density depends on temperature and <a href="/wiki/Salinity" title="Salinity">salinity</a>. For this reason, a ship may display a <a href="/wiki/Plimsoll_line" class="mw-redirect" title="Plimsoll line">Plimsoll line</a>.</i>)</dd></dl> <p>It can be the case that forces other than just buoyancy and gravity come into play. This is the case if the object is restrained or if the object sinks to the solid floor. An object which tends to float requires a <a href="/wiki/Tension_(physics)" title="Tension (physics)">tension</a> restraint force T in order to remain fully submerged. An object which tends to sink will eventually have a <a href="/wiki/Normal_force" title="Normal force">normal force</a> of constraint N exerted upon it by the solid floor. The constraint force can be tension in a spring scale measuring its weight in the fluid, and is how apparent weight is defined. </p><p>If the object would otherwise float, the tension to restrain it fully submerged is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T=\rho _{f}Vg-mg.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mi>V</mi> <mi>g</mi> <mo>−</mo> <mi>m</mi> <mi>g</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=\rho _{f}Vg-mg.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12d605c2c69b5c7cfcfaef1801e1b4639b0dfb44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.007ex; height:2.843ex;" alt="{\displaystyle T=\rho _{f}Vg-mg.\,}"></span></dd></dl> <p>When a sinking object settles on the solid floor, it experiences a <a href="/wiki/Normal_force" title="Normal force">normal force</a> of: </p> <dl><dd><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=mg-\rho _{f}Vg.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mi>V</mi> <mi>g</mi> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=mg-\rho _{f}Vg.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8378503ba98abefdebb6fb1641e2840047e0b79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.434ex; height:2.843ex;" alt="{\displaystyle N=mg-\rho _{f}Vg.\,}"></span></dd></dl> <p>Another possible formula for calculating buoyancy of an object is by finding the apparent weight of that particular object in the air (calculated in Newtons), and apparent weight of that object in the water (in Newtons). To find the force of buoyancy acting on the object when in air, using this particular information, this formula applies: </p> <dl><dd><b>Buoyancy force = weight of object in empty space − weight of object immersed in fluid</b></dd></dl> <p>The final result would be measured in Newtons. </p><p>Air's density is very small compared to most solids and liquids. For this reason, the weight of an object in air is approximately the same as its true weight in a vacuum. The buoyancy of air is neglected for most objects during a measurement in air because the error is usually insignificant (typically less than 0.1% except for objects of very low average density such as a balloon or light foam). </p> <div class="mw-heading mw-heading3"><h3 id="Simplified_model">Simplified model</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=3" title="Edit section: Simplified model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Pressure_distribution_on_an_immersed_cube.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Pressure_distribution_on_an_immersed_cube.png/220px-Pressure_distribution_on_an_immersed_cube.png" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Pressure_distribution_on_an_immersed_cube.png/330px-Pressure_distribution_on_an_immersed_cube.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Pressure_distribution_on_an_immersed_cube.png/440px-Pressure_distribution_on_an_immersed_cube.png 2x" data-file-width="1800" data-file-height="1201" /></a><figcaption>Pressure distribution on an immersed cube</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Forces_on_an_immersed_cube.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Forces_on_an_immersed_cube.png/220px-Forces_on_an_immersed_cube.png" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Forces_on_an_immersed_cube.png/330px-Forces_on_an_immersed_cube.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Forces_on_an_immersed_cube.png/440px-Forces_on_an_immersed_cube.png 2x" data-file-width="1800" data-file-height="1201" /></a><figcaption>Forces on an immersed cube</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Approximation_of_an_arbitrary_volume_as_a_group_of_cubes.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Approximation_of_an_arbitrary_volume_as_a_group_of_cubes.png/220px-Approximation_of_an_arbitrary_volume_as_a_group_of_cubes.png" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Approximation_of_an_arbitrary_volume_as_a_group_of_cubes.png/330px-Approximation_of_an_arbitrary_volume_as_a_group_of_cubes.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Approximation_of_an_arbitrary_volume_as_a_group_of_cubes.png/440px-Approximation_of_an_arbitrary_volume_as_a_group_of_cubes.png 2x" data-file-width="1800" data-file-height="1201" /></a><figcaption>Approximation of an arbitrary volume as a group of cubes</figcaption></figure> <p>A simplified explanation for the integration of the pressure over the contact area may be stated as follows: </p><p>Consider a cube immersed in a fluid with the upper surface horizontal. </p><p>The sides are identical in area, and have the same depth distribution, therefore they also have the same pressure distribution, and consequently the same total force resulting from hydrostatic pressure, exerted perpendicular to the plane of the surface of each side. </p><p>There are two pairs of opposing sides, therefore the resultant horizontal forces balance in both orthogonal directions, and the resultant force is zero. </p><p>The upward force on the cube is the pressure on the bottom surface integrated over its area. The surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of the horizontal bottom surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the bottom surface. </p><p>Similarly, the downward force on the cube is the pressure on the top surface integrated over its area. The surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of the horizontal top surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the top surface. </p><p>As this is a cube, the top and bottom surfaces are identical in shape and area, and the pressure difference between the top and bottom of the cube is directly proportional to the depth difference, and the resultant force difference is exactly equal to the weight of the fluid that would occupy the volume of the cube in its absence. </p><p>This means that the resultant upward force on the cube is equal to the weight of the fluid that would fit into the volume of the cube, and the downward force on the cube is its weight, in the absence of external forces. </p><p>This analogy is valid for variations in the size of the cube. </p><p>If two cubes are placed alongside each other with a face of each in contact, the pressures and resultant forces on the sides or parts thereof in contact are balanced and may be disregarded, as the contact surfaces are equal in shape, size and pressure distribution, therefore the buoyancy of two cubes in contact is the sum of the buoyancies of each cube. This analogy can be extended to an arbitrary number of cubes. </p><p>An object of any shape can be approximated as a group of cubes in contact with each other, and as the size of the cube is decreased, the precision of the approximation increases. The limiting case for infinitely small cubes is the exact equivalence. </p><p>Angled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components and each dealt with in the same way. </p> <div class="mw-heading mw-heading3"><h3 id="Static_stability">Static stability</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=4" title="Edit section: Static stability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ship_stability" title="Ship stability">Ship stability</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ship_stability.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Ship_stability.svg/220px-Ship_stability.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Ship_stability.svg/330px-Ship_stability.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Ship_stability.svg/440px-Ship_stability.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>Illustration of the stability of bottom-heavy (left) and top-heavy (right) ships with respect to the positions of their centres of buoyancy (CB) and gravity (CG)</figcaption></figure> <p>A floating object is stable if it tends to restore itself to an equilibrium position after a small displacement. For example, floating objects will generally have vertical stability, as if the object is pushed down slightly, this will create a greater buoyancy force, which, unbalanced by the weight force, will push the object back up. </p><p>Rotational stability is of great importance to floating vessels. Given a small angular displacement, the vessel may return to its original position (stable), move away from its original position (unstable), or remain where it is (neutral). </p><p>Rotational stability depends on the relative lines of action of forces on an object. The upward buoyancy force on an object acts through the center of buoyancy, being the <a href="/wiki/Centroid" title="Centroid">centroid</a> of the displaced volume of fluid. The weight force on the object acts through its <a href="/wiki/Center_of_mass" title="Center of mass">center of gravity</a>. A buoyant object will be stable if the center of gravity is beneath the center of buoyancy because any angular displacement will then produce a 'righting <a href="/wiki/Moment_(physics)" title="Moment (physics)">moment</a>'. </p><p>The stability of a buoyant object at the surface is more complex, and it may remain stable even if the center of gravity is above the center of buoyancy, provided that when disturbed from the equilibrium position, the center of buoyancy moves further to the same side that the center of gravity moves, thus providing a positive righting moment. If this occurs, the floating object is said to have a positive <a href="/wiki/Metacentric_height" title="Metacentric height">metacentric height</a>. This situation is typically valid for a range of heel angles, beyond which the center of buoyancy does not move enough to provide a positive righting moment, and the object becomes unstable. It is possible to shift from positive to negative or vice versa more than once during a heeling disturbance, and many shapes are stable in more than one position. </p> <div class="mw-heading mw-heading2"><h2 id="Fluids_and_objects">Fluids and objects</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=5" title="Edit section: Fluids and objects"><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-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Buoyancy" title="Special:EditPage/Buoyancy">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">January 2016</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>As a <a href="/wiki/Submarine" title="Submarine">submarine</a> expels water from its buoyancy tanks, it rises because its volume is constant (the volume of water it displaces if it is fully submerged) while its mass is decreased. </p> <div class="mw-heading mw-heading3"><h3 id="Compressible_objects">Compressible objects</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=6" title="Edit section: Compressible objects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As a floating object rises or falls, the forces external to it change and, as all objects are compressible to some extent or another, so does the object's volume. Buoyancy depends on volume and so an object's buoyancy reduces if it is compressed and increases if it expands. </p><p>If an object at equilibrium has a <a href="/wiki/Compressibility" title="Compressibility">compressibility</a> less than that of the surrounding fluid, the object's equilibrium is stable and it remains at rest. If, however, its compressibility is greater, its equilibrium is then <a href="/wiki/Unstable" class="mw-redirect" title="Unstable">unstable</a>, and it rises and expands on the slightest upward perturbation, or falls and compresses on the slightest downward perturbation. </p> <div class="mw-heading mw-heading4"><h4 id="Submarines">Submarines</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=7" title="Edit section: Submarines"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Submarine#Submersion_and_trimming" title="Submarine">Submarine § Submersion and trimming</a></div> <p><a href="/wiki/Submarine" title="Submarine">Submarines</a> rise and dive by filling large <a href="/wiki/Ballast" title="Ballast">ballast</a> tanks with seawater. To dive, the tanks are opened to allow air to exhaust out the top of the tanks, while the water flows in from the bottom. Once the weight has been balanced so the overall density of the submarine is equal to the water around it, it has neutral buoyancy and will remain at that depth. Most military submarines operate with a slightly negative buoyancy and maintain depth by using the "lift" of the stabilizers with forward motion.<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. (May 2017)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading4"><h4 id="Balloons">Balloons</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=8" title="Edit section: Balloons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The height to which a <a href="/wiki/Balloon" title="Balloon">balloon</a> rises tends to be stable. As a balloon rises it tends to increase in volume with reducing atmospheric pressure, but the balloon itself does not expand as much as the air on which it rides. The average density of the balloon decreases less than that of the surrounding air. The weight of the displaced air is reduced. A rising balloon stops rising when it and the displaced air are equal in weight. Similarly, a sinking balloon tends to stop sinking. </p> <div class="mw-heading mw-heading4"><h4 id="Divers">Divers</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=9" title="Edit section: Divers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Underwater divers are a common example of the problem of unstable buoyancy due to compressibility. The diver typically wears an exposure suit which relies on gas-filled spaces for insulation, and may also wear a <a href="/wiki/Buoyancy_compensator_(diving)" title="Buoyancy compensator (diving)">buoyancy compensator</a>, which is a variable volume buoyancy bag which is inflated to increase buoyancy and deflated to decrease buoyancy. The desired condition is usually neutral buoyancy when the diver is swimming in mid-water, and this condition is unstable, so the diver is constantly making fine adjustments by control of lung volume, and has to adjust the contents of the buoyancy compensator if the depth varies. </p> <div class="mw-heading mw-heading2"><h2 id="Density">Density</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=10" title="Edit section: Density"><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:Density_column.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Density_column.JPG/170px-Density_column.JPG" decoding="async" width="170" height="427" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Density_column.JPG/255px-Density_column.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Density_column.JPG/340px-Density_column.JPG 2x" data-file-width="1368" data-file-height="3434" /></a><figcaption>Density column of liquids and solids: <a href="/wiki/Baby_oil" title="Baby oil">baby oil</a>, <a href="/wiki/Rubbing_alcohol" title="Rubbing alcohol">rubbing alcohol</a> (with red <a href="/wiki/Food_colouring" class="mw-redirect" title="Food colouring">food colouring</a>), <a href="/wiki/Vegetable_oil" title="Vegetable oil">vegetable oil</a>, <a href="/wiki/Wax" title="Wax">wax</a>, <a href="/wiki/Water" title="Water">water</a> (with blue food colouring) and <a href="/wiki/Aluminium" title="Aluminium">aluminium</a>.</figcaption></figure> <p>If the weight of an object is less than the weight of the displaced fluid when fully submerged, then the object has an average density that is less than the fluid and when fully submerged will experience a buoyancy force greater than its own weight.<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> If the fluid has a surface, such as water in a lake or the sea, the object will float and settle at a level where it displaces the same weight of fluid as the weight of the object. If the object is immersed in the fluid, such as a submerged submarine or air in a balloon, it will tend to rise. If the object has exactly the same density as the fluid, then its buoyancy equals its weight. It will remain submerged in the fluid, but it will neither sink nor float, although a disturbance in either direction will cause it to drift away from its position. An object with a higher average density than the fluid will never experience more buoyancy than weight and it will sink. A ship will float even though it may be made of steel (which is much denser than water), because it encloses a volume of air (which is much less dense than water), and the resulting shape has an average density less than that of the water.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=11" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 35em;"> <ul><li><a href="/wiki/Atmosphere_of_Earth" title="Atmosphere of Earth">Atmosphere of Earth</a>, also known as Air</li> <li><a href="/wiki/Archimedes_paradox" class="mw-redirect" title="Archimedes paradox">Archimedes paradox</a> – Variation in pressure as a function of elevation<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li> <li><a href="/wiki/Buoy" title="Buoy">Buoy</a> – Floating structure or device</li> <li><a href="/wiki/Brunt%E2%80%93V%C3%A4is%C3%A4l%C3%A4_frequency" title="Brunt–Väisälä frequency">Brunt–Väisälä frequency</a> – Measure of fluid stability against vertical displacement</li> <li><a href="/wiki/Buoyancy_compensator_(diving)" title="Buoyancy compensator (diving)">Buoyancy compensator (diving)</a> – Equipment for controlling the buoyancy of a diver</li> <li><a href="/wiki/Buoyancy_compensator_(aviation)" title="Buoyancy compensator (aviation)">Buoyancy compensator (aviation)</a> – Equipment to regulate buoyancy of airships</li> <li><a href="/wiki/Cartesian_diver" title="Cartesian diver">Cartesian diver</a> – Classic science experiment demonstrating the Archimedes' principle and the ideal gas law</li> <li><a href="/wiki/Dasymeter" title="Dasymeter">Dasymeter</a></li> <li><a href="/wiki/Diving_weighting_system" title="Diving weighting system">Diving weighting system</a> – Ballast carried to counteract buoyancy</li> <li><a href="/wiki/Hydrostatics" title="Hydrostatics">Hydrostatics</a> – Branch of fluid mechanics that studies fluids at rest</li> <li><a href="/wiki/Galileo_thermometer" title="Galileo thermometer">Galileo thermometer</a> – Thermometer containing several glass vessels of varying density</li> <li><a href="/wiki/Hull_(ship)" class="mw-redirect" title="Hull (ship)">Hull (ship)</a> – Watertight buoyant body of a watercraft</li> <li><a href="/wiki/Hydrometer" title="Hydrometer">Hydrometer</a> – Device used to measure density of liquids</li> <li><a href="/wiki/Hydrostatic_weighing" title="Hydrostatic weighing">Hydrostatic weighing</a> – Technique for measuring the density of a living person's body</li> <li><a href="/wiki/Lighter_than_air" class="mw-redirect" title="Lighter than air">Lighter than air</a> – Property necessary for a gas to be considered a lifting gas</li> <li><a href="/wiki/Naval_architecture" title="Naval architecture">Naval architecture</a> – Engineering discipline of marine vessels</li> <li><a href="/wiki/Plimsoll_line" class="mw-redirect" title="Plimsoll line">Plimsoll line</a> – Legal limit to which a merchant ship may be loaded</li> <li><a href="/wiki/Pontoon_(boat)" class="mw-redirect" title="Pontoon (boat)">Pontoon</a> – Float used to support a boat</li> <li><a href="/wiki/Quicksand" title="Quicksand">Quicksand</a> – Mixture of sand, silt or clay with water, which creates a liquefied soil when agitated</li> <li><a href="/wiki/Salt_fingering" title="Salt fingering">Salt fingering</a> – Mixing process of warm, salty water with colder, fresher water</li> <li><a href="/wiki/Submarine" title="Submarine">Submarine</a> – Watercraft capable of independent underwater operation</li> <li><a href="/wiki/Swim_bladder" title="Swim bladder">Swim bladder</a> – Gas-filled organ that contributes to the ability of a fish to control its buoyancy</li> <li><a href="/wiki/Thrust" title="Thrust">Thrust</a> – Reaction force</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Buoyancy&action=edit&section=12" 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-lpd-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-lpd_1-0">^</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="CITEREFWells2008" class="citation cs2"><a href="/wiki/John_C._Wells" title="John C. Wells">Wells, John C.</a> (2008), <i>Longman Pronunciation Dictionary</i> (3rd ed.), <a href="/wiki/Longman" title="Longman">Longman</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4058-8118-0" title="Special:BookSources/978-1-4058-8118-0"><bdi>978-1-4058-8118-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Longman+Pronunciation+Dictionary&rft.edition=3rd&rft.pub=Longman&rft.date=2008&rft.isbn=978-1-4058-8118-0&rft.aulast=Wells&rft.aufirst=John+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuoyancy" class="Z3988"></span></span> </li> <li id="cite_note-cepd-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-cepd_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoach2011" class="citation cs2">Roach, Peter (2011), <i>Cambridge <a href="/wiki/English_Pronouncing_Dictionary" title="English Pronouncing Dictionary">English Pronouncing Dictionary</a></i> (18th ed.), Cambridge: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-15253-2" title="Special:BookSources/978-0-521-15253-2"><bdi>978-0-521-15253-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cambridge+English+Pronouncing+Dictionary&rft.place=Cambridge&rft.edition=18th&rft.pub=Cambridge+University+Press&rft.date=2011&rft.isbn=978-0-521-15253-2&rft.aulast=Roach&rft.aufirst=Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuoyancy" 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">Note: In the absence of surface tension, the mass of fluid displaced is equal to the submerged volume multiplied by the fluid density. High repulsive surface tension will cause the body to float higher than expected, though the same total volume will be displaced, but at a greater distance from the object. Where there is doubt about the meaning of "volume of fluid displaced", this should be interpreted as the overflow from a full container when the object is floated in it, or as the volume of the object below the average level of the fluid.</span> </li> <li id="cite_note-acottLaw-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-acottLaw_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAcott,_Chris1999" class="citation journal cs1 cs1-prop-unfit">Acott, Chris (1999). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110402073203/http://archive.rubicon-foundation.org/5990">"The diving "Law-ers": A brief resume of their lives"</a>. <i><a href="/wiki/South_Pacific_Underwater_Medicine_Society_Journal" class="mw-redirect" title="South Pacific Underwater Medicine Society Journal">South Pacific Underwater Medicine Society Journal</a></i>. <b>29</b> (1). <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0813-1988">0813-1988</a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/16986801">16986801</a>. Archived from the original on 2 April 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">13 June</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=South+Pacific+Underwater+Medicine+Society+Journal&rft.atitle=The+diving+%22Law-ers%22%3A+A+brief+resume+of+their+lives.&rft.volume=29&rft.issue=1&rft.date=1999&rft_id=info%3Aoclcnum%2F16986801&rft.issn=0813-1988&rft.au=Acott%2C+Chris&rft_id=http%3A%2F%2Farchive.rubicon-foundation.org%2F5990&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuoyancy" 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="CITEREFPickover2008" class="citation book cs1">Pickover, Clifford A. (2008). <i>Archimedes to Hawking</i>. Oxford University Press US. p. 41. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-533611-5" title="Special:BookSources/978-0-19-533611-5"><bdi>978-0-19-533611-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Archimedes+to+Hawking&rft.pages=41&rft.pub=Oxford+University+Press+US&rft.date=2008&rft.isbn=978-0-19-533611-5&rft.aulast=Pickover&rft.aufirst=Clifford+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuoyancy" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.weizmann.ac.il/home/fnfal/papers/Natfloat.pdf">"Floater clustering in a standing wave: Capillarity effects drive hydrophilic or hydrophobic particles to congregate at specific points on a wave"</a> <span class="cs1-format">(PDF)</span>. 23 June 2005. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110721142904/http://www.weizmann.ac.il/home/fnfal/papers/Natfloat.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 21 July 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Floater+clustering+in+a+standing+wave%3A+Capillarity+effects+drive+hydrophilic+or+hydrophobic+particles+to+congregate+at+specific+points+on+a+wave&rft.date=2005-06-23&rft_id=http%3A%2F%2Fwww.weizmann.ac.il%2Fhome%2Ffnfal%2Fpapers%2FNatfloat.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuoyancy" 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="Lima2012" class="citation journal cs1">Lima, Fábio M. S. (22 January 2012). <a rel="nofollow" class="external text" href="https://iopscience.iop.org/article/10.1088/0143-0807/33/1/009">"Using surface integrals for checking Archimedes' law of buoyancy"</a>. <i>European Journal of Physics</i>. <b>33</b> (1): <span class="nowrap">101–</span>113. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1110.5264">1110.5264</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2012EJPh...33..101L">2012EJPh...33..101L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0143-0807%2F33%2F1%2F009">10.1088/0143-0807/33/1/009</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:54556860">54556860</a><span class="reference-accessdate">. Retrieved <span class="nowrap">8 April</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+of+Physics&rft.atitle=Using+surface+integrals+for+checking+Archimedes%27+law+of+buoyancy&rft.volume=33&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E101-%3C%2Fspan%3E113&rft.date=2012-01-22&rft_id=info%3Aarxiv%2F1110.5264&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A54556860%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0143-0807%2F33%2F1%2F009&rft_id=info%3Abibcode%2F2012EJPh...33..101L&rft.aulast=Lima&rft.aufirst=F%C3%A1bio+M.+S.&rft_id=https%3A%2F%2Fiopscience.iop.org%2Farticle%2F10.1088%2F0143-0807%2F33%2F1%2F009&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuoyancy" 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="Lima2014" class="citation journal cs1">Lima, Fábio M. S. (11 May 2014). <a rel="nofollow" class="external text" href="https://doi.org/10.1590%2FS1806-11172014000200009">"A downward buoyant force experiment"</a>. <i>Revista Brasileira de Ensino de Fisica</i>. <b>36</b> (2): 2309. <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/10.1590%2FS1806-11172014000200009">10.1590/S1806-11172014000200009</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Revista+Brasileira+de+Ensino+de+Fisica&rft.atitle=A+downward+buoyant+force+experiment&rft.volume=36&rft.issue=2&rft.pages=2309&rft.date=2014-05-11&rft_id=info%3Adoi%2F10.1590%2FS1806-11172014000200009&rft.aulast=Lima&rft.aufirst=F%C3%A1bio+M.+S.&rft_id=https%3A%2F%2Fdoi.org%2F10.1590%252FS1806-11172014000200009&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuoyancy" 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 id="CITEREFPickover2008" class="citation book cs1">Pickover, Clifford A. (2008). <i>Archimedes to Hawking</i>. Oxford University Press US. p. 42. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-533611-5" title="Special:BookSources/978-0-19-533611-5"><bdi>978-0-19-533611-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Archimedes+to+Hawking&rft.pages=42&rft.pub=Oxford+University+Press+US&rft.date=2008&rft.isbn=978-0-19-533611-5&rft.aulast=Pickover&rft.aufirst=Clifford+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuoyancy" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStewart2024" class="citation web cs1">Stewart, Ken (15 October 2024). <a rel="nofollow" class="external text" href="https://www.britannica.com/science/buoyancy">"Buoyancy"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Buoyancy&rft.date=2024-10-15&rft.aulast=Stewart&rft.aufirst=Ken&rft_id=https%3A%2F%2Fwww.britannica.com%2Fscience%2Fbuoyancy&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABuoyancy" 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=Buoyancy&action=edit&section=13" 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 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