Relative density - Wikipedia

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<ul id="toc-Measurement-sublist" class="vector-toc-list"> <li id="toc-Hydrostatic_weighing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hydrostatic_weighing"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Hydrostatic weighing</span> </div> </a> <ul id="toc-Hydrostatic_weighing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hydrometer" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hydrometer"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Hydrometer</span> </div> </a> <ul id="toc-Hydrometer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pycnometer" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pycnometer"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Pycnometer</span> </div> </a> <ul id="toc-Pycnometer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Digital_density_meters" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Digital_density_meters"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Digital density meters</span> </div> </a> <ul id="toc-Digital_density_meters-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_relative_density_in_soil_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_relative_density_in_soil_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>The relative density in soil mechanics</span> </div> </a> <ul id="toc-The_relative_density_in_soil_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Limitations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Limitations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Limitations</span> </div> </a> <ul id="toc-Limitations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-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">6</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">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-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">9</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 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Available in 30 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-30" 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">30 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%83%D8%AB%D8%A7%D9%81%D8%A9_%D9%86%D8%B3%D8%A8%D9%8A%D8%A9" title="كثافة نسبية – Arabic" lang="ar" hreflang="ar" data-title="كثافة نسبية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%86%E0%A6%AA%E0%A7%87%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%BF%E0%A6%95_%E0%A6%97%E0%A7%81%E0%A6%B0%E0%A7%81%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="আপেক্ষিক গুরুত্ব – Bangla" lang="bn" hreflang="bn" data-title="আপেক্ষিক গুরুত্ব" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Relativna_gusto%C4%87a" title="Relativna gustoća – Bosnian" lang="bs" hreflang="bs" data-title="Relativna gustoća" 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/Densitat_relativa" title="Densitat relativa – Catalan" lang="ca" hreflang="ca" data-title="Densitat relativa" 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/Relativn%C3%AD_hustota" title="Relativní hustota – Czech" lang="cs" hreflang="cs" data-title="Relativní hustota" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Relative_Dichte" title="Relative Dichte – German" lang="de" hreflang="de" data-title="Relative Dichte" 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/Suhteline_tihedus" title="Suhteline tihedus – Estonian" lang="et" hreflang="et" data-title="Suhteline tihedus" 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%95%CE%B9%CE%B4%CE%B9%CE%BA%CF%8C_%CE%B2%CE%AC%CF%81%CE%BF%CF%82" title="Ειδικό βάρος – Greek" lang="el" hreflang="el" data-title="Ειδικό βάρος" 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/Densidad_relativa" title="Densidad relativa – Spanish" lang="es" hreflang="es" data-title="Densidad relativa" 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/Dentsitate_erlatibo" title="Dentsitate erlatibo – Basque" lang="eu" hreflang="eu" data-title="Dentsitate erlatibo" 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/%DA%86%DA%AF%D8%A7%D9%84%DB%8C_%D9%86%D8%B3%D8%A8%DB%8C" title="چگالی نسبی – Persian" lang="fa" hreflang="fa" data-title="چگالی نسبی" 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/Densit%C3%A9" title="Densité – French" lang="fr" hreflang="fr" data-title="Densité" 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/Dl%C3%BAs_coibhneasta" title="Dlús coibhneasta – Irish" lang="ga" hreflang="ga" data-title="Dlús coibhneasta" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B9%84%EC%A4%91" title="비중 – Korean" lang="ko" hreflang="ko" data-title="비중" 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%86%E0%A4%AA%E0%A5%87%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A4%BF%E0%A4%95_%E0%A4%98%E0%A4%A8%E0%A4%A4%E0%A5%8D%E0%A4%B5" title="आपेक्षिक घनत्व – Hindi" lang="hi" hreflang="hi" data-title="आपेक्षिक घनत्व" 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/Relativna_gusto%C4%87a" title="Relativna gustoća – Croatian" lang="hr" hreflang="hr" data-title="Relativna gustoća" 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/Massa_jenis_relatif" title="Massa jenis relatif – Indonesian" lang="id" hreflang="id" data-title="Massa jenis relatif" 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-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%AF%94%E9%87%8D" title="比重 – Japanese" lang="ja" hreflang="ja" data-title="比重" 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Spesifikk_gravitet" title="Spesifikk gravitet – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Spesifikk gravitet" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Densitat" title="Densitat – Occitan" lang="oc" hreflang="oc" data-title="Densitat" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Densit%C3%A0" title="Densità – Piedmontese" lang="pms" hreflang="pms" data-title="Densità" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/G%C4%99sto%C5%9B%C4%87_wzgl%C4%99dna" title="Gęstość względna – Polish" lang="pl" hreflang="pl" data-title="Gęstość względna" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Densidade_relativa" title="Densidade relativa – Portuguese" lang="pt" hreflang="pt" data-title="Densidade relativa" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Densitate_relativ%C4%83" title="Densitate relativă – Romanian" lang="ro" hreflang="ro" data-title="Densitate relativă" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D1%82%D0%BD%D0%BE%D1%81%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%BF%D0%BB%D0%BE%D1%82%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Относительная плотность – Russian" lang="ru" hreflang="ru" data-title="Относительная плотность" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Relative_density" title="Relative density – Simple English" lang="en-simple" hreflang="en-simple" data-title="Relative density" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Specifik_vikt" title="Specifik vikt – Swedish" lang="sv" hreflang="sv" data-title="Specifik vikt" 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 href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AE%BE%E0%AE%B0%E0%AE%9F%E0%AE%B0%E0%AF%8D%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%BF" title="சாரடர்த்தி – Tamil" lang="ta" hreflang="ta" data-title="சாரடர்த்தி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D1%96%D0%B4%D0%BD%D0%BE%D1%81%D0%BD%D0%B0_%D0%B3%D1%83%D1%81%D1%82%D0%B8%D0%BD%D0%B0" title="Відносна густина – Ukrainian" lang="uk" hreflang="uk" data-title="Відносна густина" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%AF%94%E9%87%8D" title="比重 – Chinese" lang="zh" hreflang="zh" data-title="比重" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11027905#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Specific_gravity&redirect=no" class="mw-redirect" title="Specific gravity">Specific gravity</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">Ratio of two densities</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">"Specific gravity" redirects here. Not to be confused with <a href="/wiki/Specific_weight" title="Specific weight">specific weight</a>. For the album by Joe McPhee and Joe Giardullo, see <a href="/wiki/Specific_Gravity_(album)" title="Specific Gravity (album)">Specific Gravity (album)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above">Specific gravity</th></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Common symbols</div></th><td class="infobox-data"><i>SG</i></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/SI_unit" class="mw-redirect" title="SI unit">SI unit</a></th><td class="infobox-data">Unitless</td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Derivations from<br />other quantities</div></th><td class="infobox-data"><span class="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 SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84cfa1728fae21d6e8bc8a77ddc86a645442aff2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:16.795ex; height:5.676ex;" alt="{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}}"></span></td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:US_Navy_111005-N-ZN781-031_Aviation_Boatswain%27s_Mate_(Fuel)_3rd_Class_Rolando_Calilung_tests_for_a_specific_gravity_test_on_JP-5_fuel.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/US_Navy_111005-N-ZN781-031_Aviation_Boatswain%27s_Mate_%28Fuel%29_3rd_Class_Rolando_Calilung_tests_for_a_specific_gravity_test_on_JP-5_fuel.jpg/220px-US_Navy_111005-N-ZN781-031_Aviation_Boatswain%27s_Mate_%28Fuel%29_3rd_Class_Rolando_Calilung_tests_for_a_specific_gravity_test_on_JP-5_fuel.jpg" decoding="async" width="220" height="314" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/US_Navy_111005-N-ZN781-031_Aviation_Boatswain%27s_Mate_%28Fuel%29_3rd_Class_Rolando_Calilung_tests_for_a_specific_gravity_test_on_JP-5_fuel.jpg/330px-US_Navy_111005-N-ZN781-031_Aviation_Boatswain%27s_Mate_%28Fuel%29_3rd_Class_Rolando_Calilung_tests_for_a_specific_gravity_test_on_JP-5_fuel.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/US_Navy_111005-N-ZN781-031_Aviation_Boatswain%27s_Mate_%28Fuel%29_3rd_Class_Rolando_Calilung_tests_for_a_specific_gravity_test_on_JP-5_fuel.jpg/440px-US_Navy_111005-N-ZN781-031_Aviation_Boatswain%27s_Mate_%28Fuel%29_3rd_Class_Rolando_Calilung_tests_for_a_specific_gravity_test_on_JP-5_fuel.jpg 2x" data-file-width="1680" data-file-height="2400" /></a><figcaption>A <a href="/wiki/United_States_Navy" title="United States Navy">United States Navy</a> <a href="/wiki/Aviation_boatswain%27s_mate" title="Aviation boatswain's mate">Aviation boatswain's mate</a> tests the specific gravity of <a href="/wiki/JP-5" class="mw-redirect" title="JP-5">JP-5</a> fuel</figcaption></figure> <p><b>Relative density</b>, also called <b>specific gravity</b>,<sup id="cite_ref-specificgravity1_1-0" class="reference"><a href="#cite_note-specificgravity1-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-specificgravity2_2-0" class="reference"><a href="#cite_note-specificgravity2-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> is a <a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">dimensionless quantity</a> defined as the <a href="/wiki/Ratio" title="Ratio">ratio</a> of the <a href="/wiki/Density" title="Density">density</a> (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for solids and liquids is nearly always measured with respect to <a href="/wiki/Water" title="Water">water</a> at its densest (at 4 °C or 39.2 °F); for gases, the reference is air at <a href="/wiki/Room_temperature" title="Room temperature">room temperature</a> (20 °C or 68 °F). The term "relative density" (abbreviated <b>r.d.</b> or <b>RD</b>) is preferred in <a href="/wiki/SI" class="mw-redirect" title="SI">SI</a>, whereas the term "specific gravity" is gradually being abandoned.<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>If a substance's relative density is less than 1 then it is less dense than the reference; if greater than 1 then it is denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the two substances have the same mass. If the reference material is water, then a substance with a relative density (or specific gravity) less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a relative density greater than 1 will sink. </p><p>Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1 <a href="/wiki/Atmosphere_(unit)" class="mw-redirect" title="Atmosphere (unit)">atm</a> (101.325 <a href="/wiki/Pascal_(unit)" title="Pascal (unit)">kPa</a>). Where it is not, it is more usual to specify the density directly. Temperatures for both sample and reference vary from industry to industry. In British brewing practice, the specific gravity, as specified above, is multiplied by 1000.<sup id="cite_ref-briggs_4-0" class="reference"><a href="#cite_note-briggs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as <a href="/wiki/Brine" title="Brine">brines</a>, <a href="/wiki/Must_weight" title="Must weight">must weight</a> (<a href="/wiki/Syrup" title="Syrup">syrups</a>, juices, honeys, brewers <a href="/wiki/Wort" title="Wort">wort</a>, <a href="/wiki/Must" title="Must">must</a>, etc.) and acids. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Basic_calculation">Basic calculation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=1" title="Edit section: Basic calculation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Relative density (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RD}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f774a0b0f1c80edb4454d3cbdd3165364d6e8d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.688ex; height:2.176ex;" alt="{\displaystyle RD}"></span>) or specific gravity (<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 SG}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SG}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6910f93458a60f1fb5457f21f7054c32fbc347d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.326ex; height:2.176ex;" alt="{\displaystyle SG}"></span>) is a <a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">dimensionless quantity</a>, as it is the ratio of either densities or weights <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {substance} }}{\rho _{\mathrm {reference} }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">R</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {substance} }}{\rho _{\mathrm {reference} }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce089ba2c534a88ac9e199fe126488b7ba0f1200" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.424ex; height:5.343ex;" alt="{\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {substance} }}{\rho _{\mathrm {reference} }}},}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RD}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f774a0b0f1c80edb4454d3cbdd3165364d6e8d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.688ex; height:2.176ex;" alt="{\displaystyle RD}"></span> is relative density, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\mathrm {substance} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\mathrm {substance} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27f743bc29336e906031802c33bbdbdbb6e64750" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.394ex; height:2.176ex;" alt="{\displaystyle \rho _{\mathrm {substance} }}"></span> is the density of the substance being measured, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\mathrm {reference} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\mathrm {reference} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7dad38fe4798f271b3339482b969614ca8647d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.899ex; height:2.176ex;" alt="{\displaystyle \rho _{\mathrm {reference} }}"></span> is the density of the reference. (By convention <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>, the Greek letter <a href="/wiki/Rho" title="Rho">rho</a>, denotes density.) </p><p>The reference material can be indicated using subscripts: <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 RD_{\mathrm {substance/reference} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD_{\mathrm {substance/reference} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aacb5360e8c6fd1c2c9626e9a7bd6e912e5032f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.167ex; height:3.009ex;" alt="{\displaystyle RD_{\mathrm {substance/reference} }}"></span> which means "the relative density of <i>substance</i> with respect to <i>reference</i>". If the reference is not explicitly stated then it is normally assumed to be <a href="/wiki/Water" title="Water">water</a> at 4 °<a href="/wiki/Celsius" title="Celsius">C</a> (or, more precisely, 3.98 °C, which is the temperature at which water reaches its maximum density). In <a href="/wiki/International_System_of_Units" title="International System of Units">SI</a> units, the density of water is (approximately) 1000 <a href="/wiki/Kilogram" title="Kilogram">kg</a>/<a href="/wiki/Cubic_metre" title="Cubic metre">m<sup>3</sup></a> or 1 <a href="/wiki/Gram" title="Gram">g</a>/<a href="/wiki/Cubic_centimetre" title="Cubic centimetre">cm<sup>3</sup></a>, which makes relative density calculations particularly convenient: the density of the object only needs to be divided by 1000 or 1, depending on the units. </p><p>The relative density of gases is often measured with respect to dry <a href="/wiki/Air" class="mw-redirect" title="Air">air</a> at a temperature of 20 °C and a pressure of 101.325 kPa absolute, which has a density of 1.205 kg/m<sup>3</sup>. Relative density with respect to air can be obtained by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {gas} }}{\rho _{\mathrm {air} }}}\approx {\frac {M_{\mathrm {gas} }}{M_{\mathrm {air} }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">R</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {gas} }}{\rho _{\mathrm {air} }}}\approx {\frac {M_{\mathrm {gas} }}{M_{\mathrm {air} }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/885f666a41ff3cdd509521d839160375443c0a51" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.469ex; height:6.009ex;" alt="{\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {gas} }}{\rho _{\mathrm {air} }}}\approx {\frac {M_{\mathrm {gas} }}{M_{\mathrm {air} }}},}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> is the <a href="/wiki/Molar_mass" title="Molar mass">molar mass</a> and the approximately equal sign is used because equality pertains only if 1 <a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a> of the gas and 1 mol of air occupy the same volume at a given temperature and pressure, i.e., they are both <a href="/wiki/Ideal_gas" title="Ideal gas">ideal gases</a>. Ideal behaviour is usually only seen at very low pressure. For example, one mol of an ideal gas occupies 22.414 L at 0 °C and 1 atmosphere whereas <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a> has a molar volume of 22.259 L under those same conditions. </p><p>Those with SG greater than 1 are denser than water and will, disregarding <a href="/wiki/Surface_tension" title="Surface tension">surface tension</a> effects, sink in it. Those with an SG less than 1 are less dense than water and will float on it. In scientific work, the relationship of mass to volume is usually expressed directly in terms of the density (mass per unit volume) of the substance under study. It is in industry where specific gravity finds wide application, often for historical reasons. </p><p>True specific gravity of a liquid can be expressed mathematically as: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0aec7e6083b4b4180b33a0422e01d71002906cf" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.442ex; height:5.676ex;" alt="{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}},}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\mathrm {sample} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\mathrm {sample} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3114e1a74ccf294b74be83704c75e33de35c6691" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.374ex; height:2.343ex;" alt="{\displaystyle \rho _{\mathrm {sample} }}"></span> is the density of the sample and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\mathrm {H_{2}O} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\mathrm {H_{2}O} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7082929be0d2c121f63fa6aa6e6352a71a3dd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.777ex; height:2.343ex;" alt="{\displaystyle \rho _{\mathrm {H_{2}O} }}"></span> is the density of water. </p><p>The apparent specific gravity is simply the ratio of the weights of equal volumes of sample and water in air: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SG_{\mathrm {apparent} }={\frac {W_{\mathrm {A} ,{\text{sample}}}}{W_{\mathrm {A} ,\mathrm {H_{2}O} }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>sample</mtext> </mrow> </mrow> </msub> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SG_{\mathrm {apparent} }={\frac {W_{\mathrm {A} ,{\text{sample}}}}{W_{\mathrm {A} ,\mathrm {H_{2}O} }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ae6874eda96f167e394563d34f915834298473c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:23.596ex; height:6.343ex;" alt="{\displaystyle SG_{\mathrm {apparent} }={\frac {W_{\mathrm {A} ,{\text{sample}}}}{W_{\mathrm {A} ,\mathrm {H_{2}O} }}},}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{A,{\text{sample}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>sample</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{A,{\text{sample}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/523afd04871bc7f70125e1d28c86e0d47bd79e90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.056ex; height:2.843ex;" alt="{\displaystyle W_{A,{\text{sample}}}}"></span> represents the weight of the sample measured in air and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {W_{\mathrm {A} ,\mathrm {H_{2}O} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {W_{\mathrm {A} ,\mathrm {H_{2}O} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3353249c2c35eab76d4b0e8fdcf6317eb496045" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.459ex; height:2.843ex;" alt="{\displaystyle {W_{\mathrm {A} ,\mathrm {H_{2}O} }}}"></span> the weight of an equal volume of water measured in air. </p><p>It can be shown that true specific gravity can be computed from different properties: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}={\frac {\frac {m_{\mathrm {sample} }}{V}}{\frac {m_{\mathrm {H_{2}O} }}{V}}}={\frac {m_{\mathrm {sample} }}{m_{\mathrm {H_{2}O} }}}{\frac {g}{g}}={\frac {W_{\mathrm {V} ,{\text{sample}}}}{W_{\mathrm {V} ,\mathrm {H_{2}O} }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mi>V</mi> </mfrac> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mi>V</mi> </mfrac> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>g</mi> <mi>g</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>sample</mtext> </mrow> </mrow> </msub> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}={\frac {\frac {m_{\mathrm {sample} }}{V}}{\frac {m_{\mathrm {H_{2}O} }}{V}}}={\frac {m_{\mathrm {sample} }}{m_{\mathrm {H_{2}O} }}}{\frac {g}{g}}={\frac {W_{\mathrm {V} ,{\text{sample}}}}{W_{\mathrm {V} ,\mathrm {H_{2}O} }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61c487068bd96ff595df3355149a97dd22843ee7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:53.921ex; height:8.676ex;" alt="{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}={\frac {\frac {m_{\mathrm {sample} }}{V}}{\frac {m_{\mathrm {H_{2}O} }}{V}}}={\frac {m_{\mathrm {sample} }}{m_{\mathrm {H_{2}O} }}}{\frac {g}{g}}={\frac {W_{\mathrm {V} ,{\text{sample}}}}{W_{\mathrm {V} ,\mathrm {H_{2}O} }}},}"></span> </p><p>where <i>g</i> is the local acceleration due to gravity, <i>V</i> is the volume of the sample and of water (the same for both), <i>ρ</i><sub>sample</sub> is the density of the sample, <i>ρ</i><sub>H<sub>2</sub>O</sub> is the density of water, <i>W</i><sub>V</sub> represents a weight obtained in vacuum, <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 {\mathit {m}}_{\mathrm {sample} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">m</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {m}}_{\mathrm {sample} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b65eaa694df1e1cee47c772cdd7b42509778ab0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.073ex; height:2.343ex;" alt="{\displaystyle {\mathit {m}}_{\mathrm {sample} }}"></span> is the mass of the sample and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathit {m}}_{\mathrm {H_{2}O} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">m</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {m}}_{\mathrm {H_{2}O} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5654d28f4903c5d42bec80c32935c1dd3cbda46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.476ex; height:2.343ex;" alt="{\displaystyle {\mathit {m}}_{\mathrm {H_{2}O} }}"></span> is the mass of an equal volume of water. </p><p>The density of water and of the sample varies with temperature and pressure, so it is necessary to specify the temperatures and pressures at which the densities or weights were determined. Measurements are nearly always made at 1 nominal atmosphere (101.325 kPa ± variations from changing weather patterns), but as specific gravity usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products), variations in density caused by pressure are usually neglected at least where apparent specific gravity is being measured. For true (<i>in vacuo</i>) specific gravity calculations, air pressure must be considered (see below). Temperatures are specified by the notation (<i>T</i><sub>s</sub>/<i>T</i><sub>r</sub>), with <i>T</i><sub>s</sub> representing the temperature at which the sample's density was determined and <i>T</i><sub>r</sub> the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, while <i>SG</i><sub>H<sub>2</sub>O</sub> = <span class="nowrap"><span data-sort-value="7000100000000000000♠"></span>1.000<span style="margin-left:.25em;">000</span></span> (20 °C/20 °C), it is also the case that <i>SG</i><sub>H<sub>2</sub>O</sub> = <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num"><span class="nowrap"><span data-sort-value="6999998200800000000♠"></span>0.998<span style="margin-left:.25em;">2008</span></span></span>⁄<span class="den"><span class="nowrap"><span data-sort-value="6999999972000000000♠"></span>0.999<span style="margin-left:.25em;">9720</span></span></span></span> = <span class="nowrap"><span data-sort-value="6999998228800000000♠"></span>0.998<span style="margin-left:.25em;">2288</span></span> (20 °C/4 °C). Here, temperature is being specified using the current <a href="/wiki/ITS-90" class="mw-redirect" title="ITS-90">ITS-90</a> scale and the densities <sup id="cite_ref-PTB-Mitteilungen_5-0" class="reference"><a href="#cite_note-PTB-Mitteilungen-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> used here and in the rest of this article are based on that scale. On the previous IPTS-68 scale, the densities at 20 °C and 4 °C are <span class="nowrap"><span data-sort-value="6999998204100000000♠"></span>0.998<span style="margin-left:.25em;">2041</span></span> and <span class="nowrap"><span data-sort-value="6999999972000000000♠"></span>0.999<span style="margin-left:.25em;">9720</span></span> respectively,<sup id="cite_ref-„kell_6-0" class="reference"><a href="#cite_note-„kell-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> resulting in an SG (20 °C/4 °C) value for water of <span class="nowrap"><span data-sort-value="6999998232000000000♠"></span>0.998<span style="margin-left:.25em;">232</span></span>. </p><p>As the principal use of specific gravity measurements in industry is determination of the concentrations of substances in aqueous solutions and as these are found in tables of SG versus concentration, it is extremely important that the analyst enter the table with the correct form of specific gravity. For example, in the brewing industry, the <a href="/wiki/Plato_scale" class="mw-redirect" title="Plato scale">Plato table</a> lists sucrose concentration by weight against true SG, and was originally (20 °C/4 °C)<sup id="cite_ref-ReferenceA_7-0" class="reference"><a href="#cite_note-ReferenceA-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> i.e. based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density, <i>ρ</i><sub>H<sub>2</sub>O</sub> equal to 999.972 kg/m<sup>3</sup> in SI units (<span class="nowrap"><span data-sort-value="6999999972000000000♠"></span>0.999<span style="margin-left:.25em;">972</span> g/cm<sup>3</sup></span> in <a href="/wiki/CGS_system" class="mw-redirect" title="CGS system">cgs units</a> or 62.43 lb/cu ft in <a href="/wiki/United_States_customary_units" title="United States customary units">United States customary units</a>). The <a href="/wiki/American_Society_of_Brewing_Chemists" title="American Society of Brewing Chemists">ASBC</a> table<sup id="cite_ref-ReferenceB_8-0" class="reference"><a href="#cite_note-ReferenceB-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> in use today in North America for apparent specific gravity measurements at (20 °C/20 °C) is derived from the original Plato table using Plato et al.‘s value for SG(20 °C/4 °C) = <span class="nowrap"><span data-sort-value="6999998234300000000♠"></span>0.998<span style="margin-left:.25em;">2343</span></span>. In the sugar, soft drink, honey, fruit juice and related industries, sucrose concentration by weight is taken from a table prepared by <a href="/wiki/Brix" title="Brix">A. Brix</a>, which uses SG (17.5 °C/17.5 °C). As a final example, the British SG units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/15.56 °C). </p><p>Given the specific gravity of a substance, its actual density can be calculated by rearranging the above formula: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{\mathrm {substance} }=SG\times \rho _{\mathrm {H_{2}O} }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>S</mi> <mi>G</mi> <mo>×</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{\mathrm {substance} }=SG\times \rho _{\mathrm {H_{2}O} }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35859b726ab1d33739fa045ea2f2cead9220adb7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:23.082ex; height:2.843ex;" alt="{\displaystyle \rho _{\mathrm {substance} }=SG\times \rho _{\mathrm {H_{2}O} }.}"></span> </p><p>Occasionally a reference substance other than water is specified (for example, air), in which case specific gravity means density relative to that reference. </p> <div class="mw-heading mw-heading2"><h2 id="Temperature_dependence">Temperature dependence</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=2" title="Edit section: Temperature dependence"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><i>See <a href="/wiki/Density" title="Density">Density</a> for a table of the measured densities of water at various temperatures.</i></dd></dl> <p>The density of substances varies with temperature and pressure so that it is necessary to specify the temperatures and pressures at which the densities or masses were determined. It is nearly always the case that measurements are made at nominally 1 atmosphere (101.325 kPa ignoring the variations caused by changing weather patterns) but as relative density usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products) variations in density caused by pressure are usually neglected at least where apparent relative density is being measured. For true (<i>in vacuo</i>) relative density calculations air pressure must be considered (see below). Temperatures are specified by the notation (<i>T<sub>s</sub></i>/<i>T<sub>r</sub></i>) with <i>T<sub>s</sub></i> representing the temperature at which the sample's density was determined and <i>T<sub>r</sub></i> the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, while SG<sub>H<sub>2</sub>O</sub> = 1.000000 (20 °C/20 °C) it is also the case that RD<sub>H<sub>2</sub>O</sub> = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">0.9982008</span><span class="sr-only">/</span><span class="den">0.9999720</span></span>⁠</span> = 0.9982288 (20 °C/4 °C). Here temperature is being specified using the current <a href="/wiki/ITS-90" class="mw-redirect" title="ITS-90">ITS-90</a> scale and the densities<sup id="cite_ref-PTB-Mitteilungen_5-1" class="reference"><a href="#cite_note-PTB-Mitteilungen-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> used here and in the rest of this article are based on that scale. On the previous IPTS-68 scale the densities<sup id="cite_ref-„kell_6-1" class="reference"><a href="#cite_note-„kell-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> at 20 °C and 4 °C are, respectively, 0.9982041 and 0.9999720 resulting in an RD (20 °C/4 °C) value for water of 0.99823205. </p><p>The temperatures of the two materials may be explicitly stated in the density symbols; for example: </p> <dl><dd>relative density: 8.15<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">20 °C</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4 °C</sub></span></span>; or specific gravity: 2.432<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">15</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">0</sub></span></span></dd></dl> <p>where the superscript indicates the temperature at which the density of the material is measured, and the subscript indicates the temperature of the reference substance to which it is compared. </p> <div class="mw-heading mw-heading2"><h2 id="Uses">Uses</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=3" title="Edit section: Uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Relative density can also help to quantify the <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a> of a substance in a <a href="/wiki/Fluid" title="Fluid">fluid</a> or gas, or determine the density of an unknown substance from the known density of another. Relative density is often used by <a href="/wiki/Geologist" title="Geologist">geologists</a> and <a href="/wiki/Mineralogy" title="Mineralogy">mineralogists</a> to help determine the <a href="/wiki/Mineral" title="Mineral">mineral</a> content of a rock or other sample. <a href="/wiki/Gemology" title="Gemology">Gemologists</a> use it as an aid in the identification of <a href="/wiki/Gemstone" title="Gemstone">gemstones</a>. Water is preferred as the reference because measurements are then easy to carry out in the field (see below for examples of measurement methods). </p><p>As the principal use of relative density measurements in industry is determination of the concentrations of substances in aqueous solutions and these are found in tables of RD vs concentration it is extremely important that the analyst enter the table with the correct form of relative density. For example, in the brewing industry, the <a href="/wiki/Plato_scale" class="mw-redirect" title="Plato scale">Plato table</a>, which lists sucrose concentration by mass against true RD, were originally (20 °C/4 °C)<sup id="cite_ref-ReferenceA_7-1" class="reference"><a href="#cite_note-ReferenceA-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> that is based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density of <i>ρ</i>(<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span>) equal to 0.999972 g/cm<sup>3</sup> (or 62.43 lb·ft<sup>−3</sup>). The <a href="/wiki/American_Society_of_Brewing_Chemists" title="American Society of Brewing Chemists">ASBC</a> table<sup id="cite_ref-ReferenceB_8-1" class="reference"><a href="#cite_note-ReferenceB-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> in use today in North America, while it is derived from the original Plato table is for apparent relative density measurements at (20 °C/20 °C) on the IPTS-68 scale where the density of water is 0.9982071 g/cm<sup>3</sup>. In the sugar, soft drink, honey, fruit juice and related industries sucrose concentration by mass is taken from this work<sup id="cite_ref-briggs_4-1" class="reference"><a href="#cite_note-briggs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> which uses SG (17.5 °C/17.5 °C). As a final example, the British RD units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/15.56 °C).<sup id="cite_ref-briggs_4-2" class="reference"><a href="#cite_note-briggs-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Measurement">Measurement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=4" title="Edit section: Measurement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Relative density can be calculated directly by measuring the density of a sample and dividing it by the (known) density of the reference substance. The density of the sample is simply its mass divided by its volume. Although mass is easy to measure, the volume of an irregularly shaped sample can be more difficult to ascertain. One method is to put the sample in a water-filled <a href="/wiki/Graduated_cylinder" title="Graduated cylinder">graduated cylinder</a> and read off how much water it displaces. Alternatively the container can be filled to the brim, the sample immersed, and the volume of overflow measured. The <a href="/wiki/Surface_tension" title="Surface tension">surface tension</a> of the water may keep a significant amount of water from overflowing, which is especially problematic for small samples. For this reason it is desirable to use a water container with as small a mouth as possible. </p><p>For each substance, the density, <i>ρ</i>, is given by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho ={\frac {\text{Mass}}{\text{Volume}}}={\frac {{\text{Deflection}}\times {\frac {\text{Spring Constant}}{\text{Gravity}}}}{{\text{Displacement}}_{\mathrm {WaterLine} }\times {\text{Area}}_{\mathrm {Cylinder} }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>Mass</mtext> <mtext>Volume</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>Deflection</mtext> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>Spring Constant</mtext> <mtext>Gravity</mtext> </mfrac> </mrow> </mrow> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>Displacement</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">W</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>Area</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">y</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {\text{Mass}}{\text{Volume}}}={\frac {{\text{Deflection}}\times {\frac {\text{Spring Constant}}{\text{Gravity}}}}{{\text{Displacement}}_{\mathrm {WaterLine} }\times {\text{Area}}_{\mathrm {Cylinder} }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49b5a8365b838e631d0266f42845bc012d78db3f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:53.182ex; height:8.009ex;" alt="{\displaystyle \rho ={\frac {\text{Mass}}{\text{Volume}}}={\frac {{\text{Deflection}}\times {\frac {\text{Spring Constant}}{\text{Gravity}}}}{{\text{Displacement}}_{\mathrm {WaterLine} }\times {\text{Area}}_{\mathrm {Cylinder} }}}.}"></span> </p><p>When these densities are divided, references to the spring constant, gravity and cross-sectional area simply cancel, leaving <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RD={\frac {\rho _{\mathrm {object} }}{\rho _{\mathrm {ref} }}}={\frac {\frac {{\text{Deflection}}_{\mathrm {Obj.} }}{{\text{Displacement}}_{\mathrm {Obj.} }}}{\frac {{\text{Deflection}}_{\mathrm {Ref.} }}{{\text{Displacement}}_{\mathrm {Ref.} }}}}={\frac {\frac {3\ \mathrm {in} }{20\ \mathrm {mm} }}{\frac {5\ \mathrm {in} }{34\ \mathrm {mm} }}}={\frac {3\ \mathrm {in} \times 34\ \mathrm {mm} }{5\ \mathrm {in} \times 20\ \mathrm {mm} }}=1.02.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mi>D</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">j</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>Deflection</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">j</mi> <mo>.</mo> </mrow> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>Displacement</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">j</mi> <mo>.</mo> </mrow> </mrow> </msub> </mfrac> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>Deflection</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> <mo>.</mo> </mrow> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>Displacement</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> <mo>.</mo> </mrow> </mrow> </msub> </mfrac> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mfrac> <mrow> <mn>3</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> <mrow> <mn>20</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </mfrac> <mfrac> <mrow> <mn>5</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> <mrow> <mn>34</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </mfrac> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> <mo>×</mo> <mn>34</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow> <mn>5</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> <mo>×</mo> <mn>20</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1.02.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD={\frac {\rho _{\mathrm {object} }}{\rho _{\mathrm {ref} }}}={\frac {\frac {{\text{Deflection}}_{\mathrm {Obj.} }}{{\text{Displacement}}_{\mathrm {Obj.} }}}{\frac {{\text{Deflection}}_{\mathrm {Ref.} }}{{\text{Displacement}}_{\mathrm {Ref.} }}}}={\frac {\frac {3\ \mathrm {in} }{20\ \mathrm {mm} }}{\frac {5\ \mathrm {in} }{34\ \mathrm {mm} }}}={\frac {3\ \mathrm {in} \times 34\ \mathrm {mm} }{5\ \mathrm {in} \times 20\ \mathrm {mm} }}=1.02.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f32bb81eb3a0bacc071f6ea5af93b2df5763e9ee" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:65.405ex; height:10.343ex;" alt="{\displaystyle RD={\frac {\rho _{\mathrm {object} }}{\rho _{\mathrm {ref} }}}={\frac {\frac {{\text{Deflection}}_{\mathrm {Obj.} }}{{\text{Displacement}}_{\mathrm {Obj.} }}}{\frac {{\text{Deflection}}_{\mathrm {Ref.} }}{{\text{Displacement}}_{\mathrm {Ref.} }}}}={\frac {\frac {3\ \mathrm {in} }{20\ \mathrm {mm} }}{\frac {5\ \mathrm {in} }{34\ \mathrm {mm} }}}={\frac {3\ \mathrm {in} \times 34\ \mathrm {mm} }{5\ \mathrm {in} \times 20\ \mathrm {mm} }}=1.02.}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Hydrostatic_weighing">Hydrostatic weighing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=5" title="Edit section: Hydrostatic weighing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Relative density is more easily and perhaps more accurately measured without measuring volume. Using a spring scale, the sample is weighed first in air and then in water. Relative density (with respect to water) can then be calculated using the following formula: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RD={\frac {W_{\mathrm {air} }}{W_{\mathrm {air} }-W_{\mathrm {water} }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mi>D</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD={\frac {W_{\mathrm {air} }}{W_{\mathrm {air} }-W_{\mathrm {water} }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3e7a1685806185c935a6905adc438910b1d775f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.909ex; height:5.676ex;" alt="{\displaystyle RD={\frac {W_{\mathrm {air} }}{W_{\mathrm {air} }-W_{\mathrm {water} }}},}"></span> where </p> <ul><li><i>W</i><sub>air</sub> is the weight of the sample in air (measured in <a href="/wiki/Newton_(unit)" title="Newton (unit)">newtons</a>, <a href="/wiki/Pound-force" class="mw-redirect" title="Pound-force">pounds-force</a> or some other unit of force)</li> <li><i>W</i><sub>water</sub> is the weight of the sample in water (measured in the same units).</li></ul> <p>This technique cannot easily be used to measure relative densities less than one, because the sample will then float. <i>W</i><sub>water</sub> becomes a negative quantity, representing the force needed to keep the sample underwater. </p><p>Another practical method uses three measurements. The sample is weighed dry. Then a container filled to the brim with water is weighed, and weighed again with the sample immersed, after the displaced water has overflowed and been removed. Subtracting the last reading from the sum of the first two readings gives the weight of the displaced water. The relative density result is the dry sample weight divided by that of the displaced water. This method allows the use of scales which cannot handle a suspended sample. A sample less dense than water can also be handled, but it has to be held down, and the error introduced by the fixing material must be considered. </p> <div class="mw-heading mw-heading3"><h3 id="Hydrometer">Hydrometer</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=6" title="Edit section: Hydrometer"><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/Hydrometer" title="Hydrometer">hydrometer</a></div> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/File:Hydro.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/6/67/Hydro.PNG/300px-Hydro.PNG" decoding="async" width="300" height="326" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/6/67/Hydro.PNG 1.5x" data-file-width="353" data-file-height="384" /></a><figcaption></figcaption></figure> <p>The relative density of a liquid can be measured using a hydrometer. This consists of a bulb attached to a stalk of constant cross-sectional area, as shown in the adjacent diagram. </p><p>First the hydrometer is floated in the reference liquid (shown in light blue), and the <a href="/wiki/Displacement_(fluid)" title="Displacement (fluid)">displacement</a> (the level of the liquid on the stalk) is marked (blue line). The reference could be any liquid, but in practice it is usually water. </p><p>The hydrometer is then floated in a liquid of unknown density (shown in green). The change in displacement, Δ<i>x</i>, is noted. In the example depicted, the hydrometer has dropped slightly in the green liquid; hence its density is lower than that of the reference liquid. It is necessary that the hydrometer floats in both liquids. </p><p>The application of simple physical principles allows the relative density of the unknown liquid to be calculated from the change in displacement. (In practice the stalk of the hydrometer is pre-marked with graduations to facilitate this measurement.) </p><p>In the explanation that follows, </p> <ul><li><i>ρ</i><sub>ref</sub> is the known density (<a href="/wiki/Mass" title="Mass">mass</a> per unit <a href="/wiki/Volume" title="Volume">volume</a>) of the reference liquid (typically water).</li> <li><i>ρ</i><sub>new</sub> is the unknown density of the new (green) liquid.</li> <li><i>RD</i><sub>new/ref</sub> is the relative density of the new liquid with respect to the reference.</li> <li><i>V</i> is the volume of reference liquid displaced, i.e. the red volume in the diagram.</li> <li><i>m</i> is the mass of the entire hydrometer.</li> <li><i>g</i> is the <a href="/wiki/Earth%27s_gravity" class="mw-redirect" title="Earth's gravity">local gravitational constant</a>.</li> <li>Δ<i>x</i> is the change in displacement. In accordance with the way in which hydrometers are usually graduated, Δ<i>x</i> is here taken to be negative if the displacement line rises on the stalk of the hydrometer, and positive if it falls. In the example depicted, Δ<i>x</i> is negative.</li> <li><i>A</i> is the cross sectional area of the shaft.</li></ul> <p>Since the floating hydrometer is in <a href="/wiki/Static_equilibrium" class="mw-redirect" title="Static equilibrium">static equilibrium</a>, the downward gravitational force acting upon it must exactly balance the upward buoyancy force. The gravitational force acting on the hydrometer is simply its weight, <i>mg</i>. From the <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a> principle, the buoyancy force acting on the hydrometer is equal to the weight of liquid displaced. This weight is equal to the mass of liquid displaced multiplied by <i>g</i>, which in the case of the reference liquid is <i>ρ</i><sub>ref</sub><i>Vg</i>. Setting these equal, we have <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle mg=\rho _{\mathrm {ref} }Vg}"> <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"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mi>V</mi> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle mg=\rho _{\mathrm {ref} }Vg}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/338ccadfe2ebad88659224838c762f1dd8ca8606" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.579ex; height:2.676ex;" alt="{\displaystyle mg=\rho _{\mathrm {ref} }Vg}"></span> </p><p>or just </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 0em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m=\rho _{\mathrm {ref} }V.}"> <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"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mi>V</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=\rho _{\mathrm {ref} }V.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c091004835ccfbf7e256a9a4e7952308733d1b7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.994ex; height:2.676ex;" alt="{\displaystyle m=\rho _{\mathrm {ref} }V.}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_1" class="reference nourlexpansion" style="font-weight:bold;">1</span>)</b></td></tr></tbody></table> <p>Exactly the same equation applies when the hydrometer is floating in the liquid being measured, except that the new volume is <span class="texhtml"><i>V</i> − <i>A</i>Δ<i>x</i></span> (see note above about the sign of Δ<i>x</i>). Thus, </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 0em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m=\rho _{\mathrm {new} }(V-A\Delta x).}"> <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"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>V</mi> <mo>−</mo> <mi>A</mi> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=\rho _{\mathrm {new} }(V-A\Delta x).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8404d436898f58c0d31b206643d392bb94cc9aa" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.496ex; height:2.843ex;" alt="{\displaystyle m=\rho _{\mathrm {new} }(V-A\Delta x).}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_2" class="reference nourlexpansion" style="font-weight:bold;">2</span>)</b></td></tr></tbody></table> <p>Combining (<b><a href="#math_1">1</a></b>) and (<b><a href="#math_2">2</a></b>) yields </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 0em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RD_{\mathrm {new/ref} }={\frac {\rho _{\mathrm {new} }}{\rho _{\mathrm {ref} }}}={\frac {V}{V-A\Delta x}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">w</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <mrow> <mi>V</mi> <mo>−</mo> <mi>A</mi> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD_{\mathrm {new/ref} }={\frac {\rho _{\mathrm {new} }}{\rho _{\mathrm {ref} }}}={\frac {V}{V-A\Delta x}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3664db833cddcbbc396cdbb38702129bbb0efcb8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:31.976ex; height:5.676ex;" alt="{\displaystyle RD_{\mathrm {new/ref} }={\frac {\rho _{\mathrm {new} }}{\rho _{\mathrm {ref} }}}={\frac {V}{V-A\Delta x}}.}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_3" class="reference nourlexpansion" style="font-weight:bold;">3</span>)</b></td></tr></tbody></table> <p>But from (<b><a href="#math_1">1</a></b>) we have <span class="texhtml"><i>V</i> = <i>m</i>/<i>ρ</i><sub>ref</sub></span>. Substituting into (<b><a href="#math_3">3</a></b>) gives </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 0em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RD_{\mathrm {new/ref} }={\frac {1}{1-{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">w</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> <mi>m</mi> </mfrac> </mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD_{\mathrm {new/ref} }={\frac {1}{1-{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d28bdc1512f67bc7e6bd755ee8b41307efc2853d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:25.942ex; height:6.676ex;" alt="{\displaystyle RD_{\mathrm {new/ref} }={\frac {1}{1-{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }}}.}"></span></td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_4" class="reference nourlexpansion" style="font-weight:bold;">4</span>)</b></td></tr></tbody></table> <p>This equation allows the relative density to be calculated from the change in displacement, the known density of the reference liquid, and the known properties of the hydrometer. If Δ<i>x</i> is small then, as a <a href="/wiki/Orders_of_approximation" class="mw-redirect" title="Orders of approximation">first-order approximation</a> of the <a href="/wiki/Geometric_series" title="Geometric series">geometric series</a> equation (<b><a href="#math_4">4</a></b>) can be written as: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RD_{\mathrm {new/ref} }\approx 1+{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">w</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mo>≈</mo> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> <mi>m</mi> </mfrac> </mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD_{\mathrm {new/ref} }\approx 1+{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/073e794bbbf137e2203c0fa4e3511244d2d7218a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:26.573ex; height:5.343ex;" alt="{\displaystyle RD_{\mathrm {new/ref} }\approx 1+{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }.}"></span> </p><p>This shows that, for small Δ<i>x</i>, changes in displacement are approximately proportional to changes in relative density. </p> <div class="mw-heading mw-heading3"><h3 id="Pycnometer">Pycnometer</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=7" title="Edit section: Pycnometer"><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:PycnometerEmpty.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/PycnometerEmpty.jpg/170px-PycnometerEmpty.jpg" decoding="async" width="170" height="245" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/PycnometerEmpty.jpg/255px-PycnometerEmpty.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/PycnometerEmpty.jpg/340px-PycnometerEmpty.jpg 2x" data-file-width="1232" data-file-height="1777" /></a><figcaption>An empty glass pycnometer and stopper</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Pycnometer_full.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Pycnometer_full.jpg/170px-Pycnometer_full.jpg" decoding="async" width="170" height="357" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Pycnometer_full.jpg/255px-Pycnometer_full.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Pycnometer_full.jpg/340px-Pycnometer_full.jpg 2x" data-file-width="1040" data-file-height="2184" /></a><figcaption>A filled pycnometer</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Gas_pycnometer" title="Gas pycnometer">Gas pycnometer</a></div> <p>A <b>pycnometer</b> (from <a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: <span lang="grc">πυκνός</span>, <small><a href="/wiki/Romanization_of_Ancient_Greek" class="mw-redirect" title="Romanization of Ancient Greek">romanized</a>: </small><span title="Ancient Greek-language romanization"><i lang="grc-Latn">puknos</i></span>, <small><a href="/wiki/Literal_translation" title="Literal translation">lit.</a> </small>'dense'), also called <b>pyknometer</b> or <b>specific gravity bottle</b>, is a device used to determine the <a href="/wiki/Density" title="Density">density</a> of a liquid. A pycnometer is usually made of <a href="/wiki/Glass" title="Glass">glass</a>, with a close-fitting <a href="/wiki/Ground_glass_joint" title="Ground glass joint">ground glass</a> <a href="/wiki/Stopper_(plug)" title="Stopper (plug)">stopper</a> with a <a href="/wiki/Capillary_tube" class="mw-redirect" title="Capillary tube">capillary tube</a> through it, so that air bubbles may escape from the apparatus. This device enables a liquid's density to be measured accurately by reference to an appropriate working fluid, such as <a href="/wiki/Water" title="Water">water</a> or <a href="/wiki/Mercury_(element)" title="Mercury (element)">mercury</a>, using an <a href="/wiki/Analytical_balance" title="Analytical balance">analytical balance</a>.<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 2012)">citation needed</span></a></i>]</sup> </p><p>If the flask is weighed empty, full of water, and full of a liquid whose relative density is desired, the relative density of the liquid can easily be calculated. The <a href="/wiki/Particle_density_(packed_density)" class="mw-redirect" title="Particle density (packed density)">particle density</a> of a powder, to which the usual method of weighing cannot be applied, can also be determined with a pycnometer. The powder is added to the pycnometer, which is then weighed, giving the weight of the powder sample. The pycnometer is then filled with a liquid of known density, in which the powder is completely insoluble. The weight of the displaced liquid can then be determined, and hence the relative density of the powder. </p><p>A <a href="/wiki/Gas_pycnometer" title="Gas pycnometer">gas pycnometer</a>, the gas-based manifestation of a pycnometer, compares the change in pressure caused by a measured change in a closed volume containing a reference (usually a steel sphere of known volume) with the change in pressure caused by the sample under the same conditions. The difference in change of pressure represents the volume of the sample as compared to the reference sphere, and is usually used for solid particulates that may dissolve in the liquid medium of the pycnometer design described above, or for porous materials into which the liquid would not fully penetrate. </p><p>When a pycnometer is filled to a specific, but not necessarily accurately known volume, <i>V</i> and is placed upon a balance, it will exert a force <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {b} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {b} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7892be2b853deda8a90410ff22b20f49fa8e48c9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:24.003ex; height:6.176ex;" alt="{\displaystyle F_{\mathrm {b} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}\right),}"></span> where <i>m</i><sub>b</sub> is the mass of the bottle and <i>g</i> the <a href="/wiki/Gravitational_acceleration" title="Gravitational acceleration">gravitational acceleration</a> at the location at which the measurements are being made. <i>ρ</i><sub>a</sub> is the density of the air at the ambient pressure and <i>ρ</i><sub>b</sub> is the density of the material of which the bottle is made (usually glass) so that the second term is the mass of air displaced by the glass of the bottle whose weight, by <a href="/wiki/Archimedes%27_principle#Archimedes'_principle" title="Archimedes' principle">Archimedes Principle</a> must be subtracted. The bottle is filled with air but as that air displaces an equal amount of air the weight of that air is canceled by the weight of the air displaced. Now we fill the bottle with the reference fluid e.g. pure water. The force exerted on the pan of the balance becomes: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {w} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}+V\rho _{\mathrm {w} }-V\rho _{\mathrm {a} }\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mi>V</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo>−</mo> <mi>V</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {w} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}+V\rho _{\mathrm {w} }-V\rho _{\mathrm {a} }\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ebb3bd3a0dee86ed1ec89f73b4bef6c09dd0589" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:38.408ex; height:6.176ex;" alt="{\displaystyle F_{\mathrm {w} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}+V\rho _{\mathrm {w} }-V\rho _{\mathrm {a} }\right).}"></span> </p><p>If we subtract the force measured on the empty bottle from this (or tare the balance before making the water measurement) we obtain. <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {w,n} }=gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} }),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> <mo>,</mo> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>g</mi> <mi>V</mi> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {w,n} }=gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} }),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09e45f5fc3776bae680b4cd774f825cf24014cfb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.46ex; height:3.009ex;" alt="{\displaystyle F_{\mathrm {w,n} }=gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} }),}"></span> where the subscript <i>n</i> indicated that this force is net of the force of the empty bottle. The bottle is now emptied, thoroughly dried and refilled with the sample. The force, net of the empty bottle, is now: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\mathrm {s,n} }=gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} }),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mo>,</mo> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>g</mi> <mi>V</mi> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\mathrm {s,n} }=gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} }),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ff93a976043cb37a0d7796c1f2ba5c055d52109" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.383ex; height:3.009ex;" alt="{\displaystyle F_{\mathrm {s,n} }=gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} }),}"></span> where <i>ρ</i><sub>s</sub> is the density of the sample. The ratio of the sample and water forces is: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SG_{\mathrm {A} }={\frac {gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} })}{gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} })}}={\frac {\rho _{\mathrm {s} }-\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }-\rho _{\mathrm {a} }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>g</mi> <mi>V</mi> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>g</mi> <mi>V</mi> <mo stretchy="false">(</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> </mrow> <mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SG_{\mathrm {A} }={\frac {gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} })}{gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} })}}={\frac {\rho _{\mathrm {s} }-\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }-\rho _{\mathrm {a} }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9468246f41655c2bc977972d02ae20549a7d57fb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:33.454ex; height:6.509ex;" alt="{\displaystyle SG_{\mathrm {A} }={\frac {gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} })}{gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} })}}={\frac {\rho _{\mathrm {s} }-\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }-\rho _{\mathrm {a} }}}.}"></span> </p><p>This is called the <i>apparent relative density</i>, denoted by subscript A, because it is what we would obtain if we took the ratio of net weighings in air from an analytical balance or used a <a href="/wiki/Hydrometer" title="Hydrometer">hydrometer</a> (the stem displaces air). Note that the result does not depend on the calibration of the balance. The only requirement on it is that it read linearly with force. Nor does <i>RD</i><sub>A</sub> depend on the actual volume of the pycnometer. </p><p>Further manipulation and finally substitution of <i>RD</i><sub>V</sub>, the true relative density (the subscript V is used because this is often referred to as the relative density <span title="Latin-language text"><i lang="la">in vacuo</i></span>), for <i>ρ</i><sub>s</sub>/<i>ρ</i><sub>w</sub> gives the relationship between apparent and true relative density: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RD_{\mathrm {A} }={{\rho _{\mathrm {s} } \over \rho _{\mathrm {w} }}-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}={RD_{\mathrm {V} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> </mrow> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD_{\mathrm {A} }={{\rho _{\mathrm {s} } \over \rho _{\mathrm {w} }}-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}={RD_{\mathrm {V} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cbbea1f764a0175972552456de31f60be6ba740" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:32.944ex; height:8.509ex;" alt="{\displaystyle RD_{\mathrm {A} }={{\rho _{\mathrm {s} } \over \rho _{\mathrm {w} }}-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}={RD_{\mathrm {V} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}.}"></span> </p><p>In the usual case we will have measured weights and want the true relative density. This is found from <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RD_{\mathrm {V} }=RD_{\mathrm {A} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}(RD_{\mathrm {A} }-1).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>R</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>R</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD_{\mathrm {V} }=RD_{\mathrm {A} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}(RD_{\mathrm {A} }-1).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d983b6cc7220ec1fb7bf019ddda59ca846768eb0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:31.314ex; height:5.343ex;" alt="{\displaystyle RD_{\mathrm {V} }=RD_{\mathrm {A} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}(RD_{\mathrm {A} }-1).}"></span> </p><p>Since the density of dry air at 101.325 kPa at 20 °C is<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> 0.001205 g/cm<sup>3</sup> and that of water is 0.998203 g/cm<sup>3</sup> we see that the difference between true and apparent relative densities for a substance with relative density (20 °C/20 °C) of about 1.100 would be 0.000120. Where the relative density of the sample is close to that of water (for example dilute ethanol solutions) the correction is even smaller. </p><p>The pycnometer is used in ISO standard: ISO 1183-1:2004, ISO 1014–1985 and <a href="/wiki/ASTM_International" title="ASTM International">ASTM</a> standard: ASTM D854. </p><p><b>Types</b> </p> <ul><li><a href="/wiki/Gay-Lussac" class="mw-redirect" title="Gay-Lussac">Gay-Lussac</a>, pear shaped, with perforated stopper, adjusted, capacity 1, 2, 5, 10, 25, 50 and 100 mL</li> <li>as above, with ground-in <a href="/wiki/Thermometer" title="Thermometer">thermometer</a>, adjusted, side tube with cap</li> <li>Hubbard, for <a href="/wiki/Bitumen" title="Bitumen">bitumen</a> and <a href="/wiki/Heavy_crude_oil" title="Heavy crude oil">heavy crude oils</a>, cylindrical type, <a href="/wiki/ASTM" class="mw-redirect" title="ASTM">ASTM</a> D 70, 24 mL</li> <li>as above, conical type, ASTM D 115 and D 234, 25 mL</li> <li>Boot, with vacuum jacket and thermometer, capacity 5, 10, 25 and 50 mL</li></ul> <div class="mw-heading mw-heading3"><h3 id="Digital_density_meters">Digital density meters</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=8" title="Edit section: Digital density meters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Hydrostatic Pressure-based Instruments</i>: This technology relies upon Pascal's Principle which states that the pressure difference between two points within a vertical column of fluid is dependent upon the vertical distance between the two points, the density of the fluid and the gravitational force. This technology is often used for tank gauging applications as a convenient means of liquid level and density measure. </p><p><i>Vibrating Element Transducers</i>: This type of instrument requires a vibrating element to be placed in contact with the fluid of interest. The resonant frequency of the element is measured and is related to the density of the fluid by a characterization that is dependent upon the design of the element. In modern laboratories precise measurements of relative density are made using <a href="/wiki/Oscillating_U-tube" title="Oscillating U-tube">oscillating U-tube</a> meters. These are capable of measurement to 5 to 6 places beyond the decimal point and are used in the brewing, distilling, pharmaceutical, petroleum and other industries. The instruments measure the actual mass of fluid contained in a fixed volume at temperatures between 0 and 80 °C but as they are microprocessor based can calculate apparent or true relative density and contain tables relating these to the strengths of common acids, sugar solutions, etc. </p><p><i>Ultrasonic Transducer</i>: Ultrasonic waves are passed from a source, through the fluid of interest, and into a detector which measures the acoustic spectroscopy of the waves. Fluid properties such as density and viscosity can be inferred from the spectrum. </p><p><i>Radiation-based Gauge</i>: Radiation is passed from a source, through the fluid of interest, and into a scintillation detector, or counter. As the fluid density increases, the detected radiation "counts" will decrease. The source is typically the radioactive isotope <a href="/wiki/Caesium-137" title="Caesium-137">caesium-137</a>, with a half-life of about 30 years. A key advantage for this technology is that the instrument is not required to be in contact with the fluid—typically the source and detector are mounted on the outside of tanks or piping.<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><p><i>Buoyant Force Transducer</i>: the buoyancy force produced by a float in a homogeneous liquid is equal to the weight of the liquid that is displaced by the float. Since buoyancy force is linear with respect to the density of the liquid within which the float is submerged, the measure of the buoyancy force yields a measure of the density of the liquid. One commercially available unit claims the instrument is capable of measuring relative density with an accuracy of ± 0.005 RD units. The submersible probe head contains a mathematically characterized spring-float system. When the head is immersed vertically in the liquid, the float moves vertically and the position of the float controls the position of a permanent magnet whose displacement is sensed by a concentric array of Hall-effect linear displacement sensors. The output signals of the sensors are mixed in a dedicated electronics module that provides a single output voltage whose magnitude is a direct linear measure of the quantity to be measured.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="The_relative_density_in_soil_mechanics">The relative density in soil mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=9" title="Edit section: The relative density in soil mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The relative density <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{\mathrm {R} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{\mathrm {R} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77d5f030c8b250b0692bea728a971018fff12372" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.366ex; height:2.509ex;" alt="{\displaystyle D_{\mathrm {R} }}"></span> a measure of the current void ratio in relation to the maximum and minimum void rations, and applied effective stress control the mechanical behavior of cohesionless soil. Relative density is defined by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{\mathrm {R} }={\frac {e_{\mathrm {max} }-e}{e_{\mathrm {max} }-e_{\mathrm {min} }}}\times 100\%}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>−</mo> <mi>e</mi> </mrow> <mrow> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>×</mo> <mn>100</mn> <mi mathvariant="normal">%</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{\mathrm {R} }={\frac {e_{\mathrm {max} }-e}{e_{\mathrm {max} }-e_{\mathrm {min} }}}\times 100\%}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8af547a7da3b362edf4a0d8cd429327e139b8a98" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:26.835ex; height:5.343ex;" alt="{\displaystyle D_{\mathrm {R} }={\frac {e_{\mathrm {max} }-e}{e_{\mathrm {max} }-e_{\mathrm {min} }}}\times 100\%}"></span> in which <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 e_{\mathrm {max} },e_{\mathrm {min} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e_{\mathrm {max} },e_{\mathrm {min} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92a50b57594d8e63b09dd8b658c116ee0611757b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.464ex; height:2.009ex;" alt="{\displaystyle e_{\mathrm {max} },e_{\mathrm {min} }}"></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span> are the maximum, minimum and actual void rations. </p> <div class="mw-heading mw-heading3"><h3 id="Limitations">Limitations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=10" title="Edit section: Limitations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Specific gravity (SG) is a useful concept but has several limitations. One major issue is its sensitivity to temperature since the density of both the substance being measured and the reference changes with temperature, affecting accuracy.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> It also assumes materials are incompressible, which isn't true for gasses or some liquids under varying pressures.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> It doesn't provide detailed information about a material’s composition or properties beyond density.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Errors can also occur due to impurities, incomplete mixing, or air <a href="/wiki/Bubble_(physics)" title="Bubble (physics)">bubbles</a> in liquids, which can skew results.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=11" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable"> <tbody><tr> <th>Material</th> <th>Specific gravity </th></tr> <tr> <td><a href="/wiki/Balsa_wood" class="mw-redirect" title="Balsa wood">Balsa wood</a></td> <td>0.2 </td></tr> <tr> <td><a href="/wiki/Oak" title="Oak">Oak</a> wood</td> <td>0.75 </td></tr> <tr> <td><a href="/wiki/Ethanol" title="Ethanol">Ethanol</a></td> <td>0.78 </td></tr> <tr> <td><a href="/wiki/Olive_oil" title="Olive oil">Olive oil</a></td> <td>0.91 </td></tr> <tr> <td><a href="/wiki/Water" title="Water">Water</a></td> <td>1 </td></tr> <tr> <td><a href="/wiki/Olea_capensis" title="Olea capensis">Ironwood</a></td> <td>1.5 </td></tr> <tr> <td><a href="/wiki/Graphite" title="Graphite">Graphite</a></td> <td>1.9–2.3 </td></tr> <tr> <td><a href="/wiki/Table_salt" class="mw-redirect" title="Table salt">Table salt</a></td> <td>2.17 </td></tr> <tr> <td><a href="/wiki/Aluminium" title="Aluminium">Aluminium</a></td> <td>2.7 </td></tr> <tr> <td><a href="/wiki/Cement" title="Cement">Cement</a></td> <td>3.15 </td></tr> <tr> <td><a href="/wiki/Iron" title="Iron">Iron</a></td> <td>7.87 </td></tr> <tr> <td><a href="/wiki/Copper" title="Copper">Copper</a></td> <td>8.96 </td></tr> <tr> <td><a href="/wiki/Lead" title="Lead">Lead</a></td> <td>11.35 </td></tr> <tr> <td><a href="/wiki/Mercury_(element)" title="Mercury (element)">Mercury</a></td> <td>13.56 </td></tr> <tr> <td><a href="/wiki/Depleted_uranium" title="Depleted uranium">Depleted uranium</a></td> <td>19.1 </td></tr> <tr> <td><a href="/wiki/Gold" title="Gold">Gold</a></td> <td>19.3 </td></tr> <tr> <td><a href="/wiki/Osmium" title="Osmium">Osmium</a></td> <td>22.59 </td></tr></tbody></table> <p>(Samples may vary, and these figures are approximate.) </p><p>Substances with a relative density of 1 are neutrally buoyant, those with RD greater than one are denser than water, and so (ignoring <a href="/wiki/Surface_tension" title="Surface tension">surface tension</a> effects) will sink in it, and those with an RD of less than one are less dense than water, and so will float. </p><p>Example: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RD_{\mathrm {H_{2}O} }={\frac {\rho _{\mathrm {Material} }}{\rho _{\mathrm {H_{2}O} }}}=RD,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mi>R</mi> <mi>D</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RD_{\mathrm {H_{2}O} }={\frac {\rho _{\mathrm {Material} }}{\rho _{\mathrm {H_{2}O} }}}=RD,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0f93ac9dce0ebf588d69bb0b63ea81b7beeceb0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:26.145ex; height:5.509ex;" alt="{\displaystyle RD_{\mathrm {H_{2}O} }={\frac {\rho _{\mathrm {Material} }}{\rho _{\mathrm {H_{2}O} }}}=RD,}"></span> </p><p><a href="/wiki/Helium" title="Helium">Helium</a> gas has a density of 0.164 g/L;<sup id="cite_ref-UCSB_16-0" class="reference"><a href="#cite_note-UCSB-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> it is 0.139 times as dense as <a href="/wiki/Air" class="mw-redirect" title="Air">air</a>, which has a density of 1.18 g/L.<sup id="cite_ref-UCSB_16-1" class="reference"><a href="#cite_note-UCSB-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <ul><li><a href="/wiki/Urine" title="Urine">Urine</a> normally has a specific gravity between 1.003 and 1.030. The Urine Specific Gravity diagnostic test is used to evaluate renal concentration ability for assessment of the urinary system.<sup id="cite_ref-:0_17-0" class="reference"><a href="#cite_note-:0-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Low concentration may indicate <a href="/wiki/Diabetes_insipidus" title="Diabetes insipidus">diabetes insipidus</a>, while high concentration may indicate <a href="/wiki/Albuminuria" title="Albuminuria">albuminuria</a> or <a href="/wiki/Glycosuria" title="Glycosuria">glycosuria</a>.<sup id="cite_ref-:0_17-1" class="reference"><a href="#cite_note-:0-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Blood" title="Blood">Blood</a> normally has a specific gravity of approximately 1.060.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Vodka" title="Vodka">Vodka</a> 80° proof (40% v/v) has a specific gravity of 0.9498.<sup id="cite_ref-Cocktail_Specific_Gravities_19-0" class="reference"><a href="#cite_note-Cocktail_Specific_Gravities-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=12" 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: 20em;"> <ul><li><a href="/wiki/API_gravity" title="API gravity">API gravity</a></li> <li><a href="/wiki/Baum%C3%A9_scale" title="Baumé scale">Baumé scale</a></li> <li><a href="/wiki/Buoyancy" title="Buoyancy">Buoyancy</a></li> <li><a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a></li> <li><a href="/wiki/Gravity_(beer)" class="mw-redirect" title="Gravity (beer)">Gravity (beer)</a></li> <li><a href="/wiki/Hydrometer" title="Hydrometer">Hydrometer</a></li> <li><a href="/wiki/Jolly_balance" title="Jolly balance">Jolly balance</a></li> <li><a href="/wiki/Plato_scale" class="mw-redirect" title="Plato scale">Plato scale</a></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=Relative_density&action=edit&section=13" 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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-specificgravity1-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-specificgravity1_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="CITEREFDana1922" class="citation book cs1">Dana, Edward Salisbury (1922). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rCwaAAAAYAAJ&pg=PA156"><i>A text-book of mineralogy: with an extended treatise on crystallography...</i></a> New York, London(Chapman Hall): John Wiley and Sons. pp. 195–200, 316.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+text-book+of+mineralogy%3A+with+an+extended+treatise+on+crystallography...&rft.place=New+York%2C+London%28Chapman+Hall%29&rft.pages=195-200%2C+316&rft.pub=John+Wiley+and+Sons&rft.date=1922&rft.aulast=Dana&rft.aufirst=Edward+Salisbury&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DrCwaAAAAYAAJ%26pg%3DPA156&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelative+density" class="Z3988"></span></span> </li> <li id="cite_note-specificgravity2-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-specificgravity2_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchetzAllen_E._Fuhs1999" class="citation book cs1">Schetz, Joseph A.; Allen E. Fuhs (1999-02-05). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=YCSSolzuu9IC&pg=PP1"><i>Fundamentals of fluid mechanics</i></a>. 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U.S. Department of the Interior, Bureau of Reclamation. p. 37.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Metric+Manual&rft.pages=37&rft.pub=U.S.+Department+of+the+Interior%2C+Bureau+of+Reclamation&rft.date=1978&rft.au=United+States+Bureau+of+Reclamation&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DE6BLn01jRz8C%26pg%3DPA37&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelative+density" class="Z3988"></span></span> </li> <li id="cite_note-briggs-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-briggs_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-briggs_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-briggs_4-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Hough, J.S., Briggs, D.E., Stevens, R and Young, T.W. Malting and Brewing Science, Vol. II Hopped Wort and Beer, Chapman and Hall, London, 1997, p. 881 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-412-16590-2" title="Special:BookSources/0-412-16590-2">0-412-16590-2</a></span> </li> <li id="cite_note-PTB-Mitteilungen-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-PTB-Mitteilungen_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-PTB-Mitteilungen_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBettinSpieweck1990" class="citation journal cs1 cs1-prop-foreign-lang-source">Bettin, H.; Spieweck, F. (1990). 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Ohmartvega.com. Retrieved on 2011-09-30.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.gardco.com/pages/density/electric_hydrometer.cfm">Process Control Digital Electronic Hydrometer</a>. Gardco. Retrieved on 2011-09-30.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShaw1916" class="citation journal cs1">Shaw, P.E. (1916). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsta.1916.0007">"The newtonian constant of gravitation as affected by temperature"</a>. <i>Philosophical Transactions of the Royal Society of London</i>. <b>216</b> (538–548): 349–392. <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/10.1098%2Frsta.1916.0007">10.1098/rsta.1916.0007</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+of+London&rft.atitle=The+newtonian+constant+of+gravitation+as+affected+by+temperature&rft.volume=216&rft.issue=538%E2%80%93548&rft.pages=349-392&rft.date=1916&rft_id=info%3Adoi%2F10.1098%2Frsta.1916.0007&rft.aulast=Shaw&rft.aufirst=P.E.&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frsta.1916.0007&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelative+density" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=2gVTWYmMuZwC&dq=Specific+gravity+sensitive+to+temperature&pg=RA2-SA3-PA38">"Chapter 3-Specific Gravity"</a>. <i>Engineering Design Handbook:Hydraulic Fluids</i>. 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St. Louis, Missouri. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-323-10089-2" title="Special:BookSources/978-0-323-10089-2"><bdi>978-0-323-10089-2</bdi></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/228373703">228373703</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Medical-surgical+nursing+%3A+assessment+and+management+of+clinical+problems&rft.place=St.+Louis%2C+Missouri&rft.edition=9th&rft.date=2013-12-05&rft_id=info%3Aoclcnum%2F228373703&rft.isbn=978-0-323-10089-2&rft.aulast=Lewis&rft.aufirst=Sharon+Mantik&rft.au=Dirksen%2C+Shannon+Ruff&rft.au=Heitkemper%2C+Margaret+M.&rft.au=Bucher%2C+Linda&rft.au=Harding%2C+Mariann&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelative+density" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShmukler2004" class="citation web cs1">Shmukler, Michael (2004). Elert, Glenn (ed.). <a rel="nofollow" class="external text" href="https://hypertextbook.com/facts/2004/MichaelShmukler.shtml">"Density of blood"</a>. <i>The Physics Factbook</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-01-23</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Physics+Factbook&rft.atitle=Density+of+blood&rft.date=2004&rft.aulast=Shmukler&rft.aufirst=Michael&rft_id=https%3A%2F%2Fhypertextbook.com%2Ffacts%2F2004%2FMichaelShmukler.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelative+density" class="Z3988"></span></span> </li> <li id="cite_note-Cocktail_Specific_Gravities-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cocktail_Specific_Gravities_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.goodcocktails.com/bartending/specific_gravity.php">"Specific Gravity of Liqueurs"</a>. <i>Good Cocktails.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Good+Cocktails.com&rft.atitle=Specific+Gravity+of+Liqueurs&rft_id=http%3A%2F%2Fwww.goodcocktails.com%2Fbartending%2Fspecific_gravity.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelative+density" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relative_density&action=edit&section=14" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Fundamentals of Fluid Mechanics</i> Wiley, B.R. Munson, D.F. Young & T.H. Okishi</li> <li><i>Introduction to Fluid Mechanics</i> Fourth Edition, Wiley, SI Version, R.W. Fox & A.T. McDonald</li> <li><i>Thermodynamics: An Engineering Approach</i> Second Edition, McGraw-Hill, International Edition, Y.A. Cengel & M.A. Boles</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMunsonD._F._YoungT._H._Okishi2001" class="citation book cs1">Munson, B. R.; D. F. Young; T. H. Okishi (2001). <i>Fundamentals of Fluid Mechanics</i> (4th ed.). Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-44250-9" title="Special:BookSources/978-0-471-44250-9"><bdi>978-0-471-44250-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Fluid+Mechanics&rft.edition=4th&rft.pub=Wiley&rft.date=2001&rft.isbn=978-0-471-44250-9&rft.aulast=Munson&rft.aufirst=B.+R.&rft.au=D.+F.+Young&rft.au=T.+H.+Okishi&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelative+density" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFoxMcDonald,_A._T.2003" class="citation book cs1">Fox, R. W.; McDonald, A. T. (2003). <i>Introduction to Fluid Mechanics</i> (4th ed.). Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-20231-2" title="Special:BookSources/0-471-20231-2"><bdi>0-471-20231-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Fluid+Mechanics&rft.edition=4th&rft.pub=Wiley&rft.date=2003&rft.isbn=0-471-20231-2&rft.aulast=Fox&rft.aufirst=R.+W.&rft.au=McDonald%2C+A.+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARelative+density" class="Z3988"></span></li></ul> <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=Relative_density&action=edit&section=15" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060522133528/http://www.reade.com/particle_briefings/spec_gra2.html">Specific Gravity Weights Of Materials</a> (archived 22 May 2006)</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist 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.navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Laboratory_equipment" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><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 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id="Laboratory_equipment" style="font-size:114%;margin:0 4em"><a href="/wiki/Laboratory#Laboratory_equipment" title="Laboratory">Laboratory equipment</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="General" style="font-size:114%;margin:0 4em">General</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist"><ul><li>Heaters</li><li>Dryers</li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alcohol_burner" title="Alcohol burner">Alcohol burner</a></li> <li><a href="/wiki/Bunsen_burner" title="Bunsen burner">Bunsen burner</a></li> <li><a href="/wiki/Desiccator" title="Desiccator">Desiccator</a></li> <li><a href="/wiki/Heating_mantle" title="Heating mantle">Heating mantle</a></li> <li><a href="/wiki/Hot_plate" title="Hot plate">Hot plate</a></li> <li><a href="/wiki/Hot_air_oven" title="Hot air oven">Lab oven</a></li> <li><a href="/wiki/Kiln" title="Kiln">Kiln</a></li> <li><a href="/wiki/Meker%E2%80%93Fisher_burner" title="Meker–Fisher burner">Meker–Fisher burner</a></li> <li>Striker</li> <li><a href="/wiki/Teclu_burner" title="Teclu burner">Teclu burner</a></li> <li><a href="/wiki/Laboratory_water_bath" title="Laboratory water bath">Water bath</a></li> <li><a href="/wiki/Vacuum_dry_box" title="Vacuum dry box">Vacuum dry box</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist"><ul><li>Mixers</li><li>Shakers</li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chemostat" title="Chemostat">Chemostat</a></li> <li><a href="/wiki/Homogenizer" title="Homogenizer">Homogenizer</a></li> <li><a href="/wiki/Liquid_whistle" title="Liquid whistle">Liquid whistle</a></li> <li><a href="/wiki/Magnetic_stirrer" title="Magnetic stirrer">Magnetic stirrer</a></li> <li><a href="/wiki/Mortar_and_pestle" title="Mortar and pestle">Mortar and pestle</a></li> <li><a href="/wiki/Shaker_(laboratory)" title="Shaker (laboratory)">Shaker</a></li> <li><a href="/wiki/Sonication" title="Sonication">Sonicator</a></li> <li><a href="/wiki/Static_mixer" title="Static mixer">Static mixer</a></li> <li><a href="/wiki/Glass_rod" title="Glass rod">Stirring rod</a></li> <li><a href="/wiki/Vortex_mixer" title="Vortex mixer">Vortex mixer</a></li> <li><a href="/wiki/Wash_bottle" title="Wash bottle">Wash bottle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist"><ul><li>Stands</li><li><a href="/wiki/Clamp_(tool)" title="Clamp (tool)">Clamps</a> <br /></li><li>Holders</li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Beaker clamp</li> <li><a href="/wiki/Clamp_holder" title="Clamp holder">Clamp holder</a></li> <li><a href="/wiki/Tripod_(laboratory)" title="Tripod (laboratory)">Tripod</a></li> <li><a href="/wiki/Burette_clamp" title="Burette clamp">Burette clamp</a></li> <li>Extension clamp</li> <li>Flask clamp</li> <li>Funnel support</li> <li><a href="/wiki/Iron_ring_(laboratory)" title="Iron ring (laboratory)">Iron ring</a></li> <li>Pinch clamp</li> <li><a href="/wiki/Retort_stand" title="Retort stand">Retort stand</a></li> <li>Screw clamp</li> <li><a href="/wiki/Test_tube_holder" title="Test tube holder">Test tube holder</a></li> <li><a href="/wiki/Test_tube_rack" title="Test tube rack">Test tube rack</a></li> <li><a href="/wiki/Wire_gauze" title="Wire gauze">Wire gauze</a></li> <li><a href="/wiki/Laboratory_drying_rack" title="Laboratory drying rack">Lab drying rack</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist"><ul><li>Containers <br /></li><li>Storage</li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Agar_plate" title="Agar plate">Agar plate</a></li> <li><a href="/wiki/Cryogenic_storage_dewar" title="Cryogenic storage dewar">Cryogenic storage dewar</a></li> <li><a href="/wiki/Incubator_(culture)" title="Incubator (culture)">Incubator</a></li> <li><a href="/wiki/Laminar_flow_cabinet" title="Laminar flow cabinet">Laminar flow cabinet</a></li> <li><a href="/wiki/Microplate" title="Microplate">Microtiter plate</a></li> <li><a href="/wiki/Petri_dish" title="Petri dish">Petri dish</a></li> <li><a href="/wiki/Picotiter_plate" title="Picotiter plate">Picotiter plate</a></li> <li><a href="/wiki/Refrigerator" title="Refrigerator">Refrigerator</a></li> <li>Weighing boat</li> <li>Weighing dish</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other items</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aspirator_(pump)" class="mw-redirect" title="Aspirator (pump)">Aspirator</a></li> <li><a href="/wiki/Autoclave" title="Autoclave">Autoclave</a></li> <li>Balance brush</li> <li><a href="/wiki/Cork_borer" title="Cork borer">Cork borer</a></li> <li><a href="/wiki/Crucible" title="Crucible">Crucible</a></li> <li><a href="/wiki/Filter_paper" title="Filter paper">Filter paper</a></li> <li><a href="/wiki/File_(tool)" title="File (tool)">File</a></li> <li><a href="/wiki/Forceps" title="Forceps">Forceps</a></li> <li><a href="/wiki/Laboratory_centrifuge" title="Laboratory centrifuge">Centrifuge</a></li> <li><a href="/wiki/Microscope" title="Microscope">Microscope</a></li> <li><a href="/wiki/Pipeclay_triangle" title="Pipeclay triangle">Pipeclay triangle</a></li> <li><a href="/wiki/Spectrophotometry" title="Spectrophotometry">Spectrophotometer</a></li> <li><a href="/wiki/Splint_(laboratory_equipment)" title="Splint (laboratory equipment)">Splint</a></li> <li><a href="/wiki/Laboratory_rubber_stopper" title="Laboratory rubber stopper">Stopper</a></li> <li><a href="/wiki/Scoopula" title="Scoopula">Scoopula</a></li> <li><a href="/wiki/Spatula" title="Spatula">Spatula</a></li> <li><a href="/wiki/Test_tube_brush" title="Test tube brush">Test tube brush</a></li> <li><a href="/wiki/Wire_brush" title="Wire brush">Wire brush</a></li> <li><a href="/wiki/Inoculation_needle" title="Inoculation needle">Inoculation needle</a></li> <li><a href="/wiki/Inoculation_loop" title="Inoculation loop">Inoculation loop</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Glassware" style="font-size:114%;margin:0 4em"><a href="/wiki/Laboratory_glassware" title="Laboratory glassware">Glassware</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Apparatus</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dean%E2%80%93Stark_apparatus" title="Dean–Stark apparatus">Dean–Stark</a></li> <li><a href="/wiki/Soxhlet_extractor" title="Soxhlet extractor">Soxhlet extractor</a></li> <li><a href="/wiki/Kipp%27s_apparatus" title="Kipp's apparatus">Kipp's</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Bottles</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boston_round_(bottle)" title="Boston round (bottle)">Boston round</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Condenser_(laboratory)" title="Condenser (laboratory)">Condensers</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cold_finger" title="Cold finger">Cold finger</a></li> <li><a href="/wiki/Liebig_condenser" title="Liebig condenser">Liebig</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Dishes</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Evaporating_dish" title="Evaporating dish">Evaporating</a></li> <li><a href="/wiki/Petri_dish" title="Petri dish">Petri</a></li> <li><a href="/wiki/Syracuse_dish" title="Syracuse dish">Syracuse</a></li> <li><a href="/wiki/Watch_glass" title="Watch glass">Watch glass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Laboratory_flask" title="Laboratory flask">Flasks</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/B%C3%BCchner_flask" title="Büchner flask">Büchner</a></li> <li><a href="/wiki/Vacuum_flask" title="Vacuum flask">Vacuum (Dewar)</a></li> <li><a href="/wiki/Erlenmeyer_flask" title="Erlenmeyer flask">Erlenmeyer</a></li> <li><a href="/wiki/Fernbach_flask" title="Fernbach flask">Fernbach</a></li> <li><a href="/wiki/Fleaker" title="Fleaker">Fleaker</a></li> <li><a href="/wiki/Florence_flask" title="Florence flask">Florence</a></li> <li><a href="/wiki/Retort" title="Retort">Retort</a></li> <li><a href="/wiki/Round-bottom_flask" title="Round-bottom flask">Round-bottom</a></li> <li><a href="/wiki/Schlenk_flask" title="Schlenk flask">Schlenk</a></li> <li><a href="/wiki/Volumetric_flask" title="Volumetric flask">Volumetric</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Funnels</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/B%C3%BCchner_funnel" title="Büchner funnel">Büchner</a></li> <li><a href="/wiki/B%C3%BCchner_funnel" title="Büchner funnel">Hirsch</a></li> <li><a href="/wiki/Dropping_funnel" title="Dropping funnel">Dropping</a></li> <li><a href="/wiki/Separatory_funnel" title="Separatory funnel">Separatory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Measuring devices</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Burette" title="Burette">Burette</a></li> <li><a href="/wiki/Conical_measure" title="Conical measure">Conical measure</a></li> <li><a href="/wiki/Cuvette" title="Cuvette">Cuvette</a></li> <li><a href="/wiki/Eye_dropper" title="Eye dropper">Eye dropper</a></li> <li><a href="/wiki/Eudiometer" title="Eudiometer">Eudiometer</a></li> <li><a href="/wiki/Graduated_cylinder" title="Graduated cylinder">Graduated cylinder</a></li> <li><a href="/wiki/Ostwald_viscometer" class="mw-redirect" title="Ostwald viscometer">Ostwald viscometer</a></li> <li><a href="/wiki/Pipette" title="Pipette">Pipette</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Glass_tube" title="Glass tube">Tubes</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Drying_tube" title="Drying tube">Drying</a></li> <li><a href="/wiki/Cragie_tube" title="Cragie tube">Cragie</a></li> <li><a href="/wiki/NMR_tube" title="NMR tube">Nuclear magnetic resonance (NMR)</a></li> <li><a href="/wiki/Test_tube" title="Test tube">Test</a></li> <li><a href="/wiki/Thiele_tube" title="Thiele tube">Thiele</a></li> <li><a href="/wiki/Thistle_tube" title="Thistle tube">Thistle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other items</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Beaker_(glassware)" class="mw-redirect" title="Beaker (glassware)">Beaker</a></li> <li><a href="/wiki/Bell_jar" title="Bell jar">Bell jar</a></li> <li><a href="/wiki/Gas_syringe" title="Gas syringe">Gas syringe</a></li> <li><a href="/wiki/Vial" title="Vial">Vial</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Analytical_chemistry" style="font-size:114%;margin:0 4em"><a href="/wiki/Analytical_chemistry" title="Analytical chemistry">Analytical chemistry</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Compositional</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AutoAnalyzer" title="AutoAnalyzer">AutoAnalyzer</a></li> <li><a href="/wiki/CHN_analyzer" class="mw-redirect" title="CHN analyzer">CHN analyzer</a></li> <li><a href="/wiki/Colorimeter_(chemistry)" title="Colorimeter (chemistry)">Colorimeter</a></li> <li><a href="/wiki/Inductively_coupled_plasma" title="Inductively coupled plasma">Inductively coupled plasma (ICP) device</a></li> <li><a href="/wiki/Gas_chromatography" title="Gas chromatography">Gas chromatograph (GC)</a></li> <li><a href="/wiki/High-performance_liquid_chromatography" title="High-performance liquid chromatography">Liquid chromatograph (LC)</a></li> <li><a href="/wiki/Mass_spectrometry" title="Mass spectrometry">Mass spectrometer (MS)</a></li> <li><a href="/wiki/PH_indicator" title="PH indicator">pH indicator</a></li> <li><a href="/wiki/PH_meter" title="PH meter">pH meter</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Microscopy" title="Microscopy">Microscopy</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Scanning_electron_microscope" title="Scanning electron microscope">Scanning electron microscope (SEM)</a></li> <li><a href="/wiki/Transmission_electron_microscopy" title="Transmission electron microscopy">Transmission electron microscope (TEM)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Thermochemistry" title="Thermochemistry">Thermochemistry</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Calorimeter" title="Calorimeter">Calorimeter</a> <ul><li><a href="/wiki/Differential_scanning_calorimetry" title="Differential scanning calorimetry">differential scanning</a></li></ul></li> <li><a href="/wiki/Melting-point_apparatus" title="Melting-point apparatus">Melting-point apparatus</a></li> <li><a href="/wiki/Thermometer" title="Thermometer">Thermometer</a></li> <li><a href="/wiki/Thermogravimetric_analysis" title="Thermogravimetric analysis">Thermogravimetric analyzer (TGA)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other items</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Analytical_balance" title="Analytical balance">Analytical balance</a></li> <li><a href="/wiki/Colony_counter" class="mw-redirect" title="Colony counter">Colony counter</a></li> <li><a href="/wiki/Spiral_plater" title="Spiral plater">Spiral plater</a></li> <li><a href="/wiki/Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">Nuclear magnetic resonance (NMR) instrument</a></li> <li><a href="/wiki/Plate_reader" title="Plate reader">Plate reader</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Electronics" style="font-size:114%;margin:0 4em"><a href="/wiki/Electronics" title="Electronics">Electronics</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Control devices</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bench_power_supply" class="mw-redirect" title="Bench power supply">Bench power supply</a> <ul><li><a href="/wiki/Current_source" title="Current source">Current source</a></li> <li><a href="/wiki/Voltage_source" title="Voltage source">Voltage source</a></li></ul></li> <li><a href="/wiki/Function_generator" title="Function generator">Function generator</a></li> <li><a href="/wiki/Galvanostat" title="Galvanostat">Galvanostat</a></li> <li><a href="/wiki/Pulse_generator" title="Pulse generator">Pulse generator</a></li> <li><a href="/wiki/Potentiostat" title="Potentiostat">Potentiostat</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Measurement</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ammeter" title="Ammeter">Ammeter</a></li> <li><a href="/wiki/Logic_analyzer" title="Logic analyzer">Logic analyzer</a></li> <li><a href="/wiki/Multimeter" title="Multimeter">Multimeter</a></li> <li><a href="/wiki/Network_analyzer_(electrical)" title="Network analyzer (electrical)">Network analyzer</a></li> <li><a href="/wiki/Oscilloscope" title="Oscilloscope">Oscilloscope</a></li> <li><a href="/wiki/Spectrum_analyzer" title="Spectrum analyzer">Spectrum analyzer</a></li> <li><a href="/wiki/Time-domain_reflectometer" title="Time-domain reflectometer">Time-domain reflectometer</a></li> <li><a href="/wiki/Transistor_tester" title="Transistor tester">Transistor tester</a></li> <li><a href="/wiki/Voltmeter" title="Voltmeter">Voltmeter</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Tools</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Heat_gun" title="Heat gun">Heat gun</a></li> <li><a href="/wiki/Soldering_iron" title="Soldering iron">Soldering iron</a></li> <li><a href="/wiki/Tweezers" title="Tweezers">Tweezers</a></li> <li><a href="/wiki/Wire_stripper" title="Wire stripper">Wire stripper</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alligator_clip" class="mw-redirect" title="Alligator clip">Alligator clip</a></li> <li><a href="/wiki/Test_probe" title="Test probe">Test probe</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Safety" style="font-size:114%;margin:0 4em">Safety</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Personal_protective_equipment" title="Personal protective equipment">Personal protective<br />equipment (PPE)</a></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/White_coat" title="White coat">Lab coat</a></li> <li><a href="/wiki/Face_shield" title="Face shield">Face shield</a></li> <li><a href="/wiki/Respirator" title="Respirator">Respirator</a></li> <li><a href="/wiki/Apron" title="Apron">Rubber apron</a></li> <li><a href="/wiki/Emergency_eyewash_and_safety_shower_station" title="Emergency eyewash and safety shower station">Safety shower</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Eye and hand</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Glove" title="Glove">Acid-resistant gloves</a></li> <li><a href="/wiki/Emergency_eyewash_and_safety_shower_station" title="Emergency eyewash and safety shower station">Eyewash station</a></li> <li><a href="/wiki/Glovebox" title="Glovebox">Glove box</a></li> <li><a href="/wiki/Medical_glove" title="Medical glove">Medical gloves</a></li> <li><a href="/wiki/Nitrile_rubber" title="Nitrile rubber">Nitrile gloves</a></li> <li><a href="/wiki/Glasses" title="Glasses">Safety glasses</a></li> <li><a href="/wiki/Goggles" title="Goggles">Safety goggles</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other items</th><td 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Relative density - Wikipedia