Dimension (physique)

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vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dimension_et_nature_d'une_grandeur"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Dimension et nature d'une grandeur</span> </div> </a> <ul id="toc-Dimension_et_nature_d'une_grandeur-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Grandeurs_de_base" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Grandeurs_de_base"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Grandeurs de base</span> </div> </a> <ul id="toc-Grandeurs_de_base-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Grandeurs_dérivées" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Grandeurs_dérivées"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Grandeurs dérivées</span> </div> </a> <ul id="toc-Grandeurs_dérivées-sublist" 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class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sommaire" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Basculer la table des matières" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Basculer la table des matières</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Dimension (physique)</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Aller à un article dans une autre langue. Disponible en 14 langues." > <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-14" 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">14 langues</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%D0%BD%D0%B0%D1%81%D1%86%D1%8C_%D1%84%D1%96%D0%B7%D1%96%D1%87%D0%BD%D0%B0%D0%B9_%D0%B2%D0%B5%D0%BB%D1%96%D1%87%D1%8B%D0%BD%D1%96" title="Размернасць фізічнай велічыні – biélorusse" lang="be" hreflang="be" data-title="Размернасць фізічнай велічыні" data-language-autonym="Беларуская" data-language-local-name="biélorusse" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Fyzik%C3%A1ln%C3%AD_rozm%C4%9Br_veli%C4%8Diny" title="Fyzikální rozměr veličiny – tchèque" lang="cs" hreflang="cs" data-title="Fyzikální rozměr veličiny" data-language-autonym="Čeština" data-language-local-name="tchèque" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A4%D0%B8%D0%B7%D0%B8%D0%BA%C4%83%D0%BB%D0%BB%D0%B0_%D0%BA%D0%B0%D0%BF%C4%83%D0%BD_%D1%85%D0%B0%D0%BF%D0%B8" title="Физикăлла капăн хапи – tchouvache" lang="cv" hreflang="cv" data-title="Физикăлла капăн хапи" data-language-autonym="Чӑвашла" data-language-local-name="tchouvache" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Dimension_(Gr%C3%B6%C3%9Fensystem)" title="Dimension (Größensystem) – allemand" lang="de" hreflang="de" data-title="Dimension (Größensystem)" data-language-autonym="Deutsch" data-language-local-name="allemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Dimension_(physics)" title="Dimension (physics) – anglais" lang="en" hreflang="en" data-title="Dimension (physics)" data-language-autonym="English" data-language-local-name="anglais" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Dimensioon" title="Dimensioon – estonien" lang="et" hreflang="et" data-title="Dimensioon" data-language-autonym="Eesti" data-language-local-name="estonien" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%9E%D7%93_(%D7%A4%D7%99%D7%96%D7%99%D7%A7%D7%94)" title="ממד (פיזיקה) – hébreu" lang="he" hreflang="he" data-title="ממד (פיזיקה)" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D3%A8%D0%BB%D1%88%D0%B5%D0%BC%D0%B4%D1%96%D0%BB%D1%96%D0%BA" title="Өлшемділік – kazakh" lang="kk" hreflang="kk" data-title="Өлшемділік" data-language-autonym="Қазақша" data-language-local-name="kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Dimensie_van_een_grootheid" title="Dimensie van een grootheid – néerlandais" lang="nl" hreflang="nl" data-title="Dimensie van een grootheid" data-language-autonym="Nederlands" data-language-local-name="néerlandais" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wymiar_wielko%C5%9Bci_fizycznej" title="Wymiar wielkości fizycznej – polonais" lang="pl" hreflang="pl" data-title="Wymiar wielkości fizycznej" data-language-autonym="Polski" data-language-local-name="polonais" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%D0%BD%D0%BE%D1%81%D1%82%D1%8C_%D1%84%D0%B8%D0%B7%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD%D1%8B" title="Размерность физической величины – russe" lang="ru" hreflang="ru" data-title="Размерность физической величины" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%BD%D0%B4%D0%BE%D0%B7%D0%B0%D0%BD%D0%BE%D0%BA%D0%B8%D0%B8_%D0%B1%D1%83%D0%B7%D1%83%D1%80%D0%B3%D0%B8%D0%B8_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D3%A3" title="Андозанокии бузургии физикӣ – tadjik" lang="tg" hreflang="tg" data-title="Андозанокии бузургии физикӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="tadjik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%BE%D0%B7%D0%BC%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_%D1%84%D1%96%D0%B7%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD%D0%B8" title="Розмірність фізичної величини – ukrainien" lang="uk" hreflang="uk" data-title="Розмірність фізичної величини" data-language-autonym="Українська" data-language-local-name="ukrainien" 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class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/30px-Logo_disambig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/40px-Logo_disambig.svg.png 2x" data-file-width="512" data-file-height="375" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p>Pour les articles homonymes, voir <a href="/wiki/Dimension" class="mw-disambig" title="Dimension">Dimension</a>. </p> </div></div> <p>En <a href="/wiki/Physique" title="Physique">physique</a>, la <b>dimension</b> d'une <a href="/wiki/Grandeur_physique" title="Grandeur physique">grandeur physique</a> est une propriété qui la relie aux grandeurs de base d'un <a href="/wiki/Syst%C3%A8me_de_grandeurs" title="Système de grandeurs">système de grandeurs</a> choisi. Dans un système de grandeurs donné, une grandeur physique peut être mesurée à l'aide de multiples <a href="/wiki/Unit%C3%A9_de_mesure" title="Unité de mesure">unités</a>, mais sa dimension est unique. Certaines grandeurs sont de <a href="/wiki/Grandeur_sans_dimension" title="Grandeur sans dimension">dimension 1</a>, comme l'<a href="/wiki/Indice_de_r%C3%A9fraction" title="Indice de réfraction">indice de réfraction</a>, l'<a href="/wiki/Indice_adiabatique" title="Indice adiabatique">indice adiabatique</a> d'un gaz ou la <a href="/wiki/Constante_de_structure_fine" title="Constante de structure fine">constante de structure fine</a>. Elles sont dites <i>sans dimension</i> ou <i>adimensionelles</i>. </p><p>La manipulation des dimensions au moyen de l'<a href="/wiki/Analyse_dimensionnelle" title="Analyse dimensionnelle">analyse dimensionnelle</a> permet de contrôler la cohérence des formules physiques, en vérifiant le principe d'<a href="/wiki/Homog%C3%A9n%C3%A9it%C3%A9_(physique)" title="Homogénéité (physique)">homogénéité</a>. Elle permet aussi, notamment en <a href="/wiki/Dynamique_des_fluides" title="Dynamique des fluides">dynamique des fluides</a>, de rassembler les différentes grandeurs influençant un <a href="/wiki/Syst%C3%A8me_physique" title="Système physique">système physique</a> en nombres sans dimension qui caractérisent fondamentalement son comportement. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Définition"><span id="D.C3.A9finition"></span>Définition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dimension_(physique)&veaction=edit&section=1" title="Modifier la section : Définition" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dimension_(physique)&action=edit&section=1" title="Modifier le code source de la section : Définition"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Le <i>Vocabulaire international de métrologie</i> (VIM) définit comme suit la dimension d'une grandeur<sup id="cite_ref-JCGM_200:2012JCGM_200:20124,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_1-0" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20124,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup> : </p> <blockquote> <p>« Expression de la dépendance d'une grandeur par rapport aux grandeurs de base d'un système de grandeurs sous la forme d'un <a href="/wiki/Produit_(math%C3%A9matiques)" title="Produit (mathématiques)">produit</a> de <a href="/wiki/Puissance_d%27un_nombre" title="Puissance d'un nombre">puissances</a> de <a href="/wiki/Facteur_(math%C3%A9matiques)" title="Facteur (mathématiques)">facteurs</a> correspondant aux grandeurs de base, en omettant tout facteur numérique. » </p> </blockquote> <p>La dimension d'une grandeur ne tient pas compte de son caractère <a href="/wiki/Scalaire_(physique)" title="Scalaire (physique)">scalaire</a>, <a href="/wiki/Vecteur" title="Vecteur">vectoriel</a> ou <a href="/wiki/Tenseur" title="Tenseur">tensoriel</a><sup id="cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;3</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_2-0" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;3</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-2"><span class="cite_crochet">[</span>2<span class="cite_crochet">]</span></a></sup>. Elle consiste en un produit dit <span class="citation">« produit de dimensions »</span><sup id="cite_ref-CourtierGiacomo2003R113-4,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.5</span>_:_dimension_d'une_grandeur_3-0" class="reference"><a href="#cite_note-CourtierGiacomo2003R113-4,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.5</span>_:_dimension_d'une_grandeur-3"><span class="cite_crochet">[</span>3<span class="cite_crochet">]</span></a></sup>, dans lequel chaque facteur est la dimension d'une grandeur de base<sup id="cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_4-0" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-4"><span class="cite_crochet">[</span>4<span class="cite_crochet">]</span></a></sup> mise à une <a href="/wiki/Puissance_d%27un_nombre" title="Puissance d'un nombre">puissance</a> <a href="/wiki/Nombre_rationnel" title="Nombre rationnel">rationnelle</a><sup id="cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_4-1" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-4"><span class="cite_crochet">[</span>4<span class="cite_crochet">]</span></a></sup> appelée <span class="citation">« exposant dimensionnel »</span><sup id="cite_ref-CourtierGiacomo2003R113-4,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.5</span>_:_dimension_d'une_grandeur_3-1" class="reference"><a href="#cite_note-CourtierGiacomo2003R113-4,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.5</span>_:_dimension_d'une_grandeur-3"><span class="cite_crochet">[</span>3<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-JCGM_200:2012JCGM_200:20126,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;5</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_5-0" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20126,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;5</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-5"><span class="cite_crochet">[</span>5<span class="cite_crochet">]</span></a></sup>. Par exemple, la dimension d'une force dans le système international est : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{dim}}(F)={\mathsf {L}}{\mathsf {M}}{\mathsf {T}}^{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dim</mtext> </mrow> <mo stretchy="false">(</mo> <mi>F</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">T</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{dim}}(F)={\mathsf {L}}{\mathsf {M}}{\mathsf {T}}^{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d140244c20606f8ab9d112c97a31ae951b901a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.733ex; height:3.176ex;" alt="{\displaystyle {\text{dim}}(F)={\mathsf {L}}{\mathsf {M}}{\mathsf {T}}^{-2}}"></span>, où les trois symboles de droite désignent respectivement la dimension de la <a href="/wiki/Longueur" title="Longueur">longueur</a>, de la <a href="/wiki/Masse" title="Masse">masse</a> et du <a href="/wiki/Temps_(physique)" title="Temps (physique)">temps</a>. </p><p>Tout <a href="/wiki/Syst%C3%A8me_de_grandeurs" title="Système de grandeurs">système de grandeurs</a> se fonde sur des grandeurs dites <span class="citation">« de base »</span><sup id="cite_ref-Deplace_2004Delaplace_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_200417_6-0" class="reference"><a href="#cite_note-Deplace_2004Delaplace_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_200417-6"><span class="cite_crochet">[</span>6<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite_crochet">[</span>N 1<span class="cite_crochet">]</span></a></sup>. Par exemple, le système de grandeurs sur lequel s'appuie le <a href="/wiki/Syst%C3%A8me_international_d%27unit%C3%A9s" title="Système international d'unités">Système international</a> (SI) se fonde sur sept grandeurs de base, indépendantes entre elles au sens où aucune équation physique ne permet d'exprimer une de ces grandeurs en fonction des autres. Leurs dimensions sont les dimensions de base du système. Les autres grandeurs sont dites « grandeurs dérivées », leurs dimensions pouvant toujours s'exprimer par combinaison des dimensions de base. </p> <div class="mw-heading mw-heading2"><h2 id="Dimension_et_nature_d'une_grandeur"><span id="Dimension_et_nature_d.27une_grandeur"></span>Dimension et nature d'une grandeur</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dimension_(physique)&veaction=edit&section=2" title="Modifier la section : Dimension et nature d'une grandeur" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dimension_(physique)&action=edit&section=2" title="Modifier le code source de la section : Dimension et nature d'une grandeur"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La dimension d'une grandeur est reliée à sa nature : dans un système de grandeurs donné, d'une part, les grandeurs de même nature ont toujours la même dimension<sup id="cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;4</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_9-0" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;4</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-9"><span class="cite_crochet">[</span>8<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur_10-0" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur-10"><span class="cite_crochet">[</span>9<span class="cite_crochet">]</span></a></sup> et, par contraposée, des grandeurs de dimensions différentes sont toujours de nature différente<sup id="cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;4</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_9-1" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;4</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-9"><span class="cite_crochet">[</span>8<span class="cite_crochet">]</span></a></sup> ; mais des grandeurs de même dimension ne sont pas nécessairement de même nature<sup id="cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;4</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_9-2" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;4</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-9"><span class="cite_crochet">[</span>8<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur_10-1" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur-10"><span class="cite_crochet">[</span>9<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite_crochet">[</span>N 2<span class="cite_crochet">]</span></a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Grandeurs_de_base">Grandeurs de base</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dimension_(physique)&veaction=edit&section=3" title="Modifier la section : Grandeurs de base" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dimension_(physique)&action=edit&section=3" title="Modifier le code source de la section : Grandeurs de base"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Le <a href="/wiki/Bureau_international_des_poids_et_mesures" title="Bureau international des poids et mesures">Bureau international des poids et mesures</a> a choisi comme grandeurs de base pour le <a href="/wiki/Syst%C3%A8me_international_d%27unit%C3%A9s" title="Système international d'unités">Système international d'unités</a> (SI) : </p> <ul><li>la <a href="/wiki/Longueur" title="Longueur">longueur</a>, dont la dimension est de symbole <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d25704a85c37e68d78dd9f549587912bf314b3c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.26ex; height:2.176ex;" alt="{\displaystyle {\mathsf {L}}}"></span> ;</li> <li>la <a href="/wiki/Masse" title="Masse">masse</a>, dont la dimension est de symbole <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d2825874b1ad46c9fab585139f2f5e6e6b3b200" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.033ex; height:2.176ex;" alt="{\displaystyle {\mathsf {M}}}"></span> ;</li> <li>le <a href="/wiki/Temps_(physique)" title="Temps (physique)">temps</a>, dont la dimension est de symbole <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">T</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7860e4d66c67ce669b88f07a796b143537193daf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle {\mathsf {T}}}"></span> ;</li> <li>le <a href="/wiki/Courant_%C3%A9lectrique#Intensité_du_courant" title="Courant électrique">courant électrique</a>, dont la dimension est de symbole <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {I}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">I</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {I}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/878f98bf0bd7d51626d3e31ac531de48f5092654" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.647ex; height:2.176ex;" alt="{\displaystyle {\mathsf {I}}}"></span> ;</li> <li>la <a href="/wiki/Temp%C3%A9rature_thermodynamique" title="Température thermodynamique">température thermodynamique</a>, dont la dimension est de symbole <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 \Theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc927b19f46d005b4720db7a0f96cd5b6f1a0d9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \Theta }"></span> ;</li> <li>la <a href="/wiki/Quantit%C3%A9_de_mati%C3%A8re" title="Quantité de matière">quantité de matière</a>, dont la dimension est de symbole <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">N</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffa685ddb7886a1992609db0700aebc0990e611" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.646ex; height:2.176ex;" alt="{\displaystyle {\mathsf {N}}}"></span> ;</li> <li>l'<a href="/wiki/Intensit%C3%A9_lumineuse" title="Intensité lumineuse">intensité lumineuse</a>, dont la dimension est de symbole <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {J}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">J</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {J}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3921f53f831b8865be77debe5b3f1f55a9bd06a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.097ex; height:2.176ex;" alt="{\displaystyle {\mathsf {J}}}"></span>.</li></ul> <p>Le choix de ces grandeurs de base est arbitraire. L'<a href="/wiki/Union_internationale_de_chimie_pure_et_appliqu%C3%A9e" title="Union internationale de chimie pure et appliquée">union internationale de chimie pure et appliquée</a> écrit dans la <abbr class="abbr" title="Troisième">3<sup>e</sup></abbr> édition de <span class="lang-en" lang="en"><i>Quantities, Units and Symbols in Physical Chemistry</i></span> : </p> <blockquote> <p>« Le nombre et le choix des grandeurs de base est purement arbitraire. D'autres quantités pourraient être considérées plus fondamentales, comme la charge électrique <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 Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> au lieu du courant électrique <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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> <sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite_crochet">[</span>11<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite_crochet">[</span>N 3<span class="cite_crochet">]</span></a></sup>. » </p> </blockquote> <p>D'autres systèmes de grandeurs, historiques ou actuels, ont fait d'autres choix. Par exemple dans les <a href="/wiki/Syst%C3%A8me_CGS" title="Système CGS">systèmes CGS</a>, il n'y a pas de grandeur de base associée aux phénomènes électromagnétiques. La dimension du courant électrique est <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{dim}}(I)={\mathsf {M}}^{1/2}{\mathsf {L}}^{1/2}{\mathsf {T}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dim</mtext> </mrow> <mo stretchy="false">(</mo> <mi>I</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">T</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{dim}}(I)={\mathsf {M}}^{1/2}{\mathsf {L}}^{1/2}{\mathsf {T}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8acde8cdfe32e0b4a4bb7f7e40e8423da27baca5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.56ex; height:3.343ex;" alt="{\displaystyle {\text{dim}}(I)={\mathsf {M}}^{1/2}{\mathsf {L}}^{1/2}{\mathsf {T}}^{-1}}"></span> dans le système CGS électromagnétique, ou encore <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{dim}}(I)={\mathsf {M}}^{1/2}{\mathsf {L}}^{3/2}{\mathsf {T}}^{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dim</mtext> </mrow> <mo stretchy="false">(</mo> <mi>I</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">T</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{dim}}(I)={\mathsf {M}}^{1/2}{\mathsf {L}}^{3/2}{\mathsf {T}}^{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33d6a30f7ab1460a8a279b3677c1a79111b9a384" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.56ex; height:3.343ex;" alt="{\displaystyle {\text{dim}}(I)={\mathsf {M}}^{1/2}{\mathsf {L}}^{3/2}{\mathsf {T}}^{-2}}"></span> dans le système CGS électrostatique. Autre exemple, l'ancien système <a href="/w/index.php?title=English_Engineering_Units&action=edit&redlink=1" class="new" title="English Engineering Units (page inexistante)">English Engineering Units</a> <a href="https://en.wikipedia.org/wiki/English_Engineering_Units" class="extiw" title="en:English Engineering Units"><span class="indicateur-langue" title="Article en anglais : « English Engineering Units »">(en)</span></a> compte parmi ses grandeurs de base à la fois la durée, la longueur, la masse et la force. </p> <div class="mw-heading mw-heading2"><h2 id="Grandeurs_dérivées"><span id="Grandeurs_d.C3.A9riv.C3.A9es"></span>Grandeurs dérivées</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dimension_(physique)&veaction=edit&section=4" title="Modifier la section : Grandeurs dérivées" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dimension_(physique)&action=edit&section=4" title="Modifier le code source de la section : Grandeurs dérivées"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>On obtient la dimension d'une grandeur dérivée à partir d'une relation entre cette grandeur et d'autres grandeurs dont les dimensions sont connues. Par exemple, dans le cas d'une vitesse, on peut exploiter <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=d/t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=d/t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9462f1a9f13208cd6e95c53a0174ef5c53f7809b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.444ex; height:2.843ex;" alt="{\displaystyle v=d/t}"></span> avec <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span> une distance et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> une durée : on en déduit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{dim}}(v)={\mathsf {LT^{-1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dim</mtext> </mrow> <mo stretchy="false">(</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> <msup> <mi mathvariant="sans-serif">T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="sans-serif">−</mo> <mn mathvariant="sans-serif">1</mn> </mrow> </msup> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{dim}}(v)={\mathsf {LT^{-1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a864d7b586d3b0b6ca17c5e8aa0ce72da5470db5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.086ex; height:3.176ex;" alt="{\displaystyle {\text{dim}}(v)={\mathsf {LT^{-1}}}}"></span>. En connaissant la dimension d'une vitesse, on peut utiliser pour une force la seconde loi de Newton <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 {\vec {F}}=m{\operatorname {d} \!{\vec {v}} \over \operatorname {d} \!t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}=m{\operatorname {d} \!{\vec {v}} \over \operatorname {d} \!t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0842b74e552fb2c074afd2ada6fb8bd31cce1ff0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.214ex; height:5.509ex;" alt="{\displaystyle {\vec {F}}=m{\operatorname {d} \!{\vec {v}} \over \operatorname {d} \!t}}"></span>, et obtenir <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{dim}}({\vec {F}})={\mathsf {MLT^{-2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dim</mtext> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> <mi mathvariant="sans-serif">L</mi> <msup> <mi mathvariant="sans-serif">T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="sans-serif">−</mo> <mn mathvariant="sans-serif">2</mn> </mrow> </msup> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{dim}}({\vec {F}})={\mathsf {MLT^{-2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/115f4f7004a3e8ea11d222ed28fa023dbcc45da9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.763ex; height:3.343ex;" alt="{\displaystyle {\text{dim}}({\vec {F}})={\mathsf {MLT^{-2}}}}"></span>. </p><p>Par exemple, les dimensions de quelques grandeurs dérivées sont : </p> <ul><li><a href="/wiki/Acc%C3%A9l%C3%A9ration" title="Accélération">Accélération</a> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{dim}}({\vec {a}})={\mathsf {LT^{-2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dim</mtext> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> <msup> <mi mathvariant="sans-serif">T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="sans-serif">−</mo> <mn mathvariant="sans-serif">2</mn> </mrow> </msup> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{dim}}({\vec {a}})={\mathsf {LT^{-2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17b1702fadb155417dc43d0a2e52fc3ad076af8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.188ex; height:3.176ex;" alt="{\displaystyle {\text{dim}}({\vec {a}})={\mathsf {LT^{-2}}}}"></span> ;</li> <li><a href="/wiki/%C3%89nergie_(physique)" title="Énergie (physique)">Énergie</a> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{dim}}(E)={\mathsf {ML^{2}T^{-2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dim</mtext> </mrow> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> <msup> <mi mathvariant="sans-serif">L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="sans-serif">2</mn> </mrow> </msup> <msup> <mi mathvariant="sans-serif">T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="sans-serif">−</mo> <mn mathvariant="sans-serif">2</mn> </mrow> </msup> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{dim}}(E)={\mathsf {ML^{2}T^{-2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd89252b57e0893640eb4bcfa30773c04e7712a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.822ex; height:3.176ex;" alt="{\displaystyle {\text{dim}}(E)={\mathsf {ML^{2}T^{-2}}}}"></span> ;</li> <li><a href="/wiki/Capacit%C3%A9_thermique" title="Capacité thermique">Capacité thermique</a> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{dim}}(C)={\mathsf {MLT^{-2}\Theta ^{-1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dim</mtext> </mrow> <mo stretchy="false">(</mo> <mi>C</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> <mi mathvariant="sans-serif">L</mi> <msup> <mi mathvariant="sans-serif">T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="sans-serif">−</mo> <mn mathvariant="sans-serif">2</mn> </mrow> </msup> <msup> <mi mathvariant="sans-serif">Θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="sans-serif">−</mo> <mn mathvariant="sans-serif">1</mn> </mrow> </msup> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{dim}}(C)={\mathsf {MLT^{-2}\Theta ^{-1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ab652bf38fe27641e127e4b5aa84c6c375710e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.899ex; height:3.176ex;" alt="{\displaystyle {\text{dim}}(C)={\mathsf {MLT^{-2}\Theta ^{-1}}}}"></span> ;</li> <li><a href="/wiki/Champ_magn%C3%A9tique" title="Champ magnétique">Champ magnétique</a> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{dim}}({\vec {B}})={\mathsf {MT^{-2}I^{-1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dim</mtext> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> <msup> <mi mathvariant="sans-serif">T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="sans-serif">−</mo> <mn mathvariant="sans-serif">2</mn> </mrow> </msup> <msup> <mi mathvariant="sans-serif">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="sans-serif">−</mo> <mn mathvariant="sans-serif">1</mn> </mrow> </msup> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{dim}}({\vec {B}})={\mathsf {MT^{-2}I^{-1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8174f9bdd5efa2bfcd38e29aee3c447906dd3601" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.476ex; height:3.343ex;" alt="{\displaystyle {\text{dim}}({\vec {B}})={\mathsf {MT^{-2}I^{-1}}}}"></span> ;</li> <li><a href="/wiki/Champ_%C3%A9lectrique" title="Champ électrique">Champ électrique</a> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{dim}}({\vec {E}})={\mathsf {MLT^{-3}I^{-1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dim</mtext> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> <mi mathvariant="sans-serif">L</mi> <msup> <mi mathvariant="sans-serif">T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="sans-serif">−</mo> <mn mathvariant="sans-serif">3</mn> </mrow> </msup> <msup> <mi mathvariant="sans-serif">I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="sans-serif">−</mo> <mn mathvariant="sans-serif">1</mn> </mrow> </msup> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{dim}}({\vec {E}})={\mathsf {MLT^{-3}I^{-1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54e823c92b4d820afe90e9a91d957095d6a5e89e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.747ex; height:3.343ex;" alt="{\displaystyle {\text{dim}}({\vec {E}})={\mathsf {MLT^{-3}I^{-1}}}}"></span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Histoire">Histoire</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dimension_(physique)&veaction=edit&section=5" title="Modifier la section : Histoire" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dimension_(physique)&action=edit&section=5" title="Modifier le code source de la section : Histoire"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La notion moderne de dimension d'une grandeur apparaît avec le mathématicien et physicien français <a href="/wiki/Joseph_Fourier" title="Joseph Fourier">Joseph Fourier</a><sup id="cite_ref-Melzani2022352_15-0" class="reference"><a href="#cite_note-Melzani2022352-15"><span class="cite_crochet">[</span>12<span class="cite_crochet">]</span></a></sup> et sa <span class="ouvrage"><cite class="italique">Théorie analytique de la chaleur</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Th%C3%A9orie+analytique+de+la+chaleur&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADimension+%28physique%29"></span></span><sup id="cite_ref-Worstell201416_16-0" class="reference"><a href="#cite_note-Worstell201416-16"><span class="cite_crochet">[</span>13<span class="cite_crochet">]</span></a></sup> parue en 1822<sup id="cite_ref-Melzani2022352_15-1" class="reference"><a href="#cite_note-Melzani2022352-15"><span class="cite_crochet">[</span>12<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-Worstell201416_16-1" class="reference"><a href="#cite_note-Worstell201416-16"><span class="cite_crochet">[</span>13<span class="cite_crochet">]</span></a></sup>. Il assimile à l'origine les dimensions aux valeurs numériques que prennent les exposants dimensionnels. Pour lui, par exemple, l'<a href="/wiki/Acc%C3%A9l%C3%A9ration" title="Accélération">accélération</a> est donc de dimension 1 en longueur, et de dimension -2 en temps. </p><p>Pour <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a>, la dimension de l'accélération est toute l'expression <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {L}}{\mathsf {T}}^{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">T</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {L}}{\mathsf {T}}^{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2639355e0e107e11e7d06c0f772f155c24a0ed1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.176ex; height:2.676ex;" alt="{\displaystyle {\mathsf {L}}{\mathsf {T}}^{-2}}"></span>, et non la série des exposants<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite_crochet">[</span>14<span class="cite_crochet">]</span></a></sup> : c'est cette terminologie qui est utilisée aujourd'hui. </p> <div class="mw-heading mw-heading2"><h2 id="Notes_et_références"><span id="Notes_et_r.C3.A9f.C3.A9rences"></span>Notes et références</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dimension_(physique)&veaction=edit&section=6" title="Modifier la section : Notes et références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dimension_(physique)&action=edit&section=6" title="Modifier le code source de la section : Notes et références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dimension_(physique)&veaction=edit&section=7" title="Modifier la section : Notes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dimension_(physique)&action=edit&section=7" title="Modifier le code source de la section : Notes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-8"><span class="mw-cite-backlink noprint"><a href="#cite_ref-8">↑</a> </span><span class="reference-text">On les nomme parfois <span class="citation">« primaires »</span><sup id="cite_ref-ÇengelCimbala201715_7-0" class="reference"><a href="#cite_note-ÇengelCimbala201715-7"><span class="cite_crochet">[</span>7<span class="cite_crochet">]</span></a></sup> ou <span class="citation">« fondamentales »</span><sup id="cite_ref-ÇengelCimbala201715_7-1" class="reference"><a href="#cite_note-ÇengelCimbala201715-7"><span class="cite_crochet">[</span>7<span class="cite_crochet">]</span></a></sup><sup id="cite_ref-Deplace_2004Delaplace_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_200417_6-1" class="reference"><a href="#cite_note-Deplace_2004Delaplace_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_200417-6"><span class="cite_crochet">[</span>6<span class="cite_crochet">]</span></a></sup>. Le vocabulaire retenu par le <a href="/wiki/Bureau_international_des_poids_et_mesures" title="Bureau international des poids et mesures">Bureau international des poids et mesures</a> est <span class="citation">« de base »</span><sup id="cite_ref-JCGM_200:2012JCGM_200:20124,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_1-1" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20124,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup>.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink noprint"><a href="#cite_ref-12">↑</a> </span><span class="reference-text">Par exemple, les grandeurs <a href="/wiki/Moment_d%27une_force" title="Moment d'une force">moment d'une force</a> et <a href="/wiki/%C3%89nergie_(physique)" title="Énergie (physique)">énergie</a> ne sont pas considérées, par convention, comme étant de même nature, bien qu'elles aient la même dimension<sup id="cite_ref-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="Exemple"_>ex._:</abbr><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur_11-0" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="Exemple"_>ex._:</abbr><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur-11"><span class="cite_crochet">[</span>10<span class="cite_crochet">]</span></a></sup> ; il en est de même, pour la <a href="/wiki/Capacit%C3%A9_thermique" title="Capacité thermique">capacité thermique</a> et l'<a href="/wiki/Entropie_(thermodynamique)" title="Entropie (thermodynamique)">entropie</a><sup id="cite_ref-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="Exemple"_>ex._:</abbr><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur_11-1" class="reference"><a href="#cite_note-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="Exemple"_>ex._:</abbr><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur-11"><span class="cite_crochet">[</span>10<span class="cite_crochet">]</span></a></sup>.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink noprint"><a href="#cite_ref-14">↑</a> </span><span class="reference-text">Citation originale : <span class="citation not_fr_quote" lang="en">« <span class="italique">The number and choice of base quantities is pure convention. Other quantities could be considered to be more fundamental, such as electric charge Q instead of electric current I</span> »</span>.</span> </li> </ol></div> </div> <div class="mw-heading mw-heading3"><h3 id="Références"><span id="R.C3.A9f.C3.A9rences"></span>Références</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dimension_(physique)&veaction=edit&section=8" title="Modifier la section : Références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dimension_(physique)&action=edit&section=8" title="Modifier le code source de la section : Références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""><div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-JCGM_200:2012JCGM_200:20124,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-1"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-JCGM_200:2012JCGM_200:20124,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_1-0">a</a> et <a href="#cite_ref-JCGM_200:2012JCGM_200:20124,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_1-1">b</a></sup> </span><span class="reference-text"><a href="#JCGM_200:2012">JCGM 200:2012</a>, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 1.7</span> : dimension, <abbr class="abbr" title="page(s)">p.</abbr> 4, <span class="nowrap"><abbr class="abbr" title="colonne(s)">col.</abbr> 2</span>. </span> </li> <li id="cite_note-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;3</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-2"><span class="mw-cite-backlink noprint"><a href="#cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;3</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_2-0">↑</a> </span><span class="reference-text"><a href="#JCGM_200:2012">JCGM 200:2012</a>, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 1.7</span> : dimension, <abbr class="abbr" title="page(s)">p.</abbr> 5, <span class="nowrap"><abbr class="abbr" title="colonne(s)">col.</abbr> 2</span>, <span class="nowrap"><abbr class="abbr" title="note(s)">n.</abbr> 3</span>. </span> </li> <li id="cite_note-CourtierGiacomo2003R113-4,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.5</span>_:_dimension_d'une_grandeur-3"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-CourtierGiacomo2003R113-4,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.5</span>_:_dimension_d'une_grandeur_3-0">a</a> et <a href="#cite_ref-CourtierGiacomo2003R113-4,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.5</span>_:_dimension_d'une_grandeur_3-1">b</a></sup> </span><span class="reference-text"><a href="#CourtierGiacomo2003">Courtier et Giacomo 2003</a>, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 1.5</span> : dimension d'une grandeur, <abbr class="abbr" title="page(s)">p.</abbr> R113-4, <span class="nowrap"><abbr class="abbr" title="colonne(s)">col.</abbr> 1</span>. </span> </li> <li id="cite_note-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-4"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_4-0">a</a> et <a href="#cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;1</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_4-1">b</a></sup> </span><span class="reference-text"><a href="#JCGM_200:2012">JCGM 200:2012</a>, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 1.7</span> : dimension, <abbr class="abbr" title="page(s)">p.</abbr> 5, <span class="nowrap"><abbr class="abbr" title="colonne(s)">col.</abbr> 2</span>, <span class="nowrap"><abbr class="abbr" title="note(s)">n.</abbr> 1</span>. </span> </li> <li id="cite_note-JCGM_200:2012JCGM_200:20126,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;5</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-5"><span class="mw-cite-backlink noprint"><a href="#cite_ref-JCGM_200:2012JCGM_200:20126,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;5</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_5-0">↑</a> </span><span class="reference-text"><a href="#JCGM_200:2012">JCGM 200:2012</a>, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 1.7</span> : dimension, <abbr class="abbr" title="page(s)">p.</abbr> 6, <span class="nowrap"><abbr class="abbr" title="colonne(s)">col.</abbr> 2</span>,<span class="nowrap"><abbr class="abbr" title="note(s)">n.</abbr> 5</span>. </span> </li> <li id="cite_note-Deplace_2004Delaplace_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_200417-6"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-Deplace_2004Delaplace_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_200417_6-0">a</a> et <a href="#cite_ref-Deplace_2004Delaplace_''<abbr_class="abbr_"_title="et_alii_(«_et_d’autres_»)"_lang="la">et_al.</abbr>''_200417_6-1">b</a></sup> </span><span class="reference-text"><a href="#Deplace_2004">Delaplace <i><abbr class="abbr" title="et alii (« et d’autres »)" lang="la">et al.</abbr></i> 2004</a>, <abbr class="abbr" title="page(s)">p.</abbr> 17. </span> </li> <li id="cite_note-ÇengelCimbala201715-7"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-ÇengelCimbala201715_7-0">a</a> et <a href="#cite_ref-ÇengelCimbala201715_7-1">b</a></sup> </span><span class="reference-text"><a href="#ÇengelCimbala2017">Çengel et Cimbala 2017</a>, <abbr class="abbr" title="page(s)">p.</abbr> 15. </span> </li> <li id="cite_note-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;4</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension-9"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;4</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_9-0">a</a> <a href="#cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;4</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_9-1">b</a> et <a href="#cite_ref-JCGM_200:2012JCGM_200:20125,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;4</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.7</span>_:_dimension_9-2">c</a></sup> </span><span class="reference-text"><a href="#JCGM_200:2012">JCGM 200:2012</a>, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 1.7</span> : dimension, <abbr class="abbr" title="page(s)">p.</abbr> 5, <span class="nowrap"><abbr class="abbr" title="colonne(s)">col.</abbr> 2</span>, <span class="nowrap"><abbr class="abbr" title="note(s)">n.</abbr> 4</span>. </span> </li> <li id="cite_note-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur-10"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur_10-0">a</a> et <a href="#cite_ref-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur_10-1">b</a></sup> </span><span class="reference-text"><a href="#JCGM_200:2012">JCGM 200:2012</a>, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 1.2</span> : nature de grandeur, <abbr class="abbr" title="page(s)">p.</abbr> 3, <span class="nowrap"><abbr class="abbr" title="colonne(s)">col.</abbr> 2</span>, <span class="nowrap"><abbr class="abbr" title="note(s)">n.</abbr> 2</span>. </span> </li> <li id="cite_note-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="Exemple"_>ex._:</abbr><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur-11"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="Exemple"_>ex._:</abbr><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur_11-0">a</a> et <a href="#cite_ref-JCGM_200:2012JCGM_200:20123,_<span_class="nowrap"><abbr_class="abbr_"_title="colonne(s)"_>col.</abbr>&nbsp;2</span>,_<span_class="nowrap"><abbr_class="abbr_"_title="note(s)"_>n.</abbr>&nbsp;2</span>,_<abbr_class="abbr_"_title="Exemple"_>ex._:</abbr><span_class="nowrap"><abbr_class="abbr_"_title="paragraphe(s)"_>§</abbr>&nbsp;1.2</span>_:_nature_de_grandeur_11-1">b</a></sup> </span><span class="reference-text"><a href="#JCGM_200:2012">JCGM 200:2012</a>, <span class="nowrap"><abbr class="abbr" title="paragraphe(s)">§</abbr> 1.2</span> : nature de grandeur, <abbr class="abbr" title="page(s)">p.</abbr> 3, <span class="nowrap"><abbr class="abbr" title="colonne(s)">col.</abbr> 2</span>, <span class="nowrap"><abbr class="abbr" title="note(s)">n.</abbr> 2</span>, <abbr class="abbr" title="Exemple">ex. :</abbr>. </span> </li> <li id="cite_note-13"><span class="mw-cite-backlink noprint"><a href="#cite_ref-13">↑</a> </span><span class="reference-text"><span class="ouvrage" id="IUPAC">IUPAC, <cite class="italique">Quantities, Units and Symbols in Physical Chemistry, <abbr class="abbr" title="Troisième">3<sup>e</sup></abbr> édition</cite>, <abbr class="abbr" title="page">p.</abbr> 4<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantities%2C+Units+and+Symbols+in+Physical+Chemistry%2C+3e+%C3%A9dition&rft.au=IUPAC&rft.pages=4&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADimension+%28physique%29"></span></span>.</span> </li> <li id="cite_note-Melzani2022352-15"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-Melzani2022352_15-0">a</a> et <a href="#cite_ref-Melzani2022352_15-1">b</a></sup> </span><span class="reference-text"><a href="#Melzani2022">Melzani 2022</a>, <abbr class="abbr" title="page(s)">p.</abbr> 352. </span> </li> <li id="cite_note-Worstell201416-16"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-Worstell201416_16-0">a</a> et <a href="#cite_ref-Worstell201416_16-1">b</a></sup> </span><span class="reference-text"><a href="#Worstell2014">Worstell 2014</a>, <abbr class="abbr" title="page(s)">p.</abbr> 16. </span> </li> <li id="cite_note-17"><span class="mw-cite-backlink noprint"><a href="#cite_ref-17">↑</a> </span><span class="reference-text"><span class="ouvrage" id="Clerk_Maxwell1873"><span class="ouvrage" id="James_Clerk_Maxwell1873"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a>, <cite class="italique" lang="en">A Treatise on Electricity and Magnetism, volume 1</cite>, <time>1873</time> <small style="line-height:1em;">(<a rel="nofollow" class="external text" href="https://archive.org/stream/electricandmagne01maxwrich#page/n41/mode/2up">lire en ligne</a>)</small>, <abbr class="abbr" title="page">p.</abbr> 5<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Treatise+on+Electricity+and+Magnetism%2C+volume+1&rft.au=James+Clerk+Maxwell&rft.date=1873&rft.pages=5&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADimension+%28physique%29"></span></span></span>.</span> </li> </ol></div> </div> <div class="mw-heading mw-heading2"><h2 id="Bibliographie">Bibliographie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dimension_(physique)&veaction=edit&section=9" title="Modifier la section : Bibliographie" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dimension_(physique)&action=edit&section=9" title="Modifier le code source de la section : Bibliographie"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span title="Document utilisé pour la rédaction de l’article"><span typeof="mw:File"><span><img alt="Document utilisé pour la rédaction de l’article" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/20px-Icon_flat_design_plume.svg.png" decoding="async" width="20" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/30px-Icon_flat_design_plume.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/40px-Icon_flat_design_plume.svg.png 2x" data-file-width="330" data-file-height="158" /></span></span></span> : document utilisé comme source pour la rédaction de cet article. </p> <ul><li><span class="ouvrage" id="JCGM_200:2012"><small>[JCGM 200:2012]</small> <abbr class="abbr indicateur-langue" title="Langues : anglais et français">(en + fr)</abbr> Comité commun pour les guides en métrologie (JCGM), <cite class="italique" lang="en">Vocabulaire international de métrologie (VIM) : concepts fondamentaux et généraux et termes associés <i>(JCGM 200:2012)</i></cite>, Sèvres, <a href="/wiki/Bureau_international_des_poids_et_mesures" title="Bureau international des poids et mesures">Bureau international des poids et mesures</a>, <time>2012</time>, <abbr class="abbr" title="troisième">3<sup>e</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="15"><span class="romain" style="text-transform:uppercase">XV</span></abbr>-[1]-91 <small style="line-height:1em;">(<a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/812030900">812030900</a></span>, <a rel="nofollow" class="external text" href="https://www.bipm.org/documents/20126/2071204/JCGM_200_2012.pdf/f0e1ad45-d337-bbeb-53a6-15fe649d0ff1">lire en ligne</a> <span typeof="mw:File"><span title="Accès libre au document"><img alt="Accès libre" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span> <abbr class="abbr indicateur-format format-pdf" title="Document au format Portable Document Format (PDF) d'Adobe">[PDF]</abbr>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vocabulaire+international+de+m%C3%A9trologie+%28VIM%29&rft.place=S%C3%A8vres&rft.pub=Bureau+international+des+poids+et+mesures&rft.edition=3&rft.stitle=concepts+fondamentaux+et+g%C3%A9n%C3%A9raux+et+termes+associ%C3%A9s+%27%27%28JCGM+200%3A2012%29%27%27&rft.au=Comit%C3%A9+commun+pour+les+guides+en+m%C3%A9trologie+%28JCGM%29&rft.date=2012&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%2215%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EXV%3C%2Fspan%3E%3C%2Fabbr%3E-%5B1%5D-91&rft_id=info%3Aoclcnum%2F812030900&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADimension+%28physique%29"></span></span>.<span class="nowrap" title="Ouvrage utilisé pour la rédaction de l'article"> <span typeof="mw:File"><span><img alt="Ouvrage utilisé pour la rédaction de l'article" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/20px-Icon_flat_design_plume.svg.png" decoding="async" width="20" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/30px-Icon_flat_design_plume.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/40px-Icon_flat_design_plume.svg.png 2x" data-file-width="330" data-file-height="158" /></span></span></span></li> <li><span class="ouvrage" id="ÇengelCimbala2017"><span class="ouvrage" id="Yunus_A._ÇengelJohn_M._Cimbala2017"><small>[Çengel et Cimbala 2017]</small> Yunus A. <span class="nom_auteur">Çengel</span> et John M. <span class="nom_auteur">Cimbala</span> (<abbr class="abbr" title="traduction">trad.</abbr> de l'anglais par Alexandre Chagnes, Sophie Griveau, Virginie Lair et Armelle Ringuedé), <cite class="italique">Mécanique des fluides : fondements et applications</cite> [« <span class="lang-en" lang="en">Fluid mechanics : fundamentals and applications</span> »], Louvain-la-Neuve, <a href="/wiki/Groupe_De_Boeck" title="Groupe De Boeck">De Boeck Supérieur</a>, <abbr class="abbr" title="collection">coll.</abbr> « Sciences de l'ingénieur », <time class="nowrap" datetime="2017-09" data-sort-value="2017-09">septembre 2017</time>, <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="21"><span class="romain" style="text-transform:uppercase">XXI</span></abbr>-972 <abbr class="abbr" title="pages">p.</abbr>, 21,5 × 27,5 <abbr class="abbr" title="centimètre">cm</abbr> <small style="line-height:1em;">(<a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9782804164836" title="Spécial:Ouvrages de référence/9782804164836"><span class="nowrap">9782804164836</span></a>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb457976864.public">45797686</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/20434316X">20434316X</a></span>, <a rel="nofollow" class="external text" href="https://www.deboecksuperieur.com/ouvrage/9782804164836-mecanique-des-fluides">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=dig2DwAAQBAJ">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=M%C3%A9canique+des+fluides&rft.place=Louvain-la-Neuve&rft.pub=De+Boeck+Sup%C3%A9rieur&rft.edition=1&rft.stitle=fondements+et+applications&rft.aulast=%C3%87engel&rft.aufirst=Yunus+A.&rft.au=Cimbala%2C+John+M.&rft.date=2017-09&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%2221%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EXXI%3C%2Fspan%3E%3C%2Fabbr%3E-972&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADimension+%28physique%29"></span></span></span>.<span class="nowrap" title="Ouvrage utilisé pour la rédaction de l'article"> <span typeof="mw:File"><span><img alt="Ouvrage utilisé pour la rédaction de l'article" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/20px-Icon_flat_design_plume.svg.png" decoding="async" width="20" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/30px-Icon_flat_design_plume.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/40px-Icon_flat_design_plume.svg.png 2x" data-file-width="330" data-file-height="158" /></span></span></span></li> <li><span class="ouvrage" id="CourtierGiacomo2003"><span class="ouvrage" id="Jean-Claude_CourtierPierre_Giacomo2003"><small>[Courtier et Giacomo 2003]</small> Jean-Claude <span class="nom_auteur">Courtier</span> et Pierre <span class="nom_auteur">Giacomo</span>, <cite class="italique">Vocabulaire de la mesure</cite>, Saint-Denis, <a href="/wiki/%C3%89ditions_techniques_de_l%27ing%C3%A9nieur" title="Éditions techniques de l'ingénieur">TI</a>, <abbr class="abbr" title="collection">coll.</abbr> « Techniques de l'ingénieur / instrumentation et méthodes de mesure » (<abbr class="abbr" title="numéro">n<sup>o</sup></abbr> R113), <time class="nowrap" datetime="2003-09" data-sort-value="2003-09">septembre 2003</time>, <abbr class="abbr" title="troisième">3<sup>e</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr> (<abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr> octobre 1988) <small style="line-height:1em;">(<a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/9709555237">9709555237</a></span>, <a href="/wiki/Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.51257/a-v1-r113">10.51257/a-v1-r113</a></span>, <a rel="nofollow" class="external text" href="https://www.techniques-ingenieur.fr/base-documentaire/archives-th12/archives-instrumentation-et-methodes-de-mesure-tiarb/archive-1/vocabulaire-de-la-mesure-r113/">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=9qUuX69x8EwC">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vocabulaire+de+la+mesure&rft.place=Saint-Denis&rft.pub=TI&rft.edition=3&rft.aulast=Courtier&rft.aufirst=Jean-Claude&rft.au=Giacomo%2C+Pierre&rft.date=2003-09&rft_id=info%3Adoi%2F10.51257%2Fa-v1-r113&rft_id=info%3Aoclcnum%2F9709555237&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADimension+%28physique%29"></span></span></span>.<span class="nowrap" title="Ouvrage utilisé pour la rédaction de l'article"> <span typeof="mw:File"><span><img alt="Ouvrage utilisé pour la rédaction de l'article" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/20px-Icon_flat_design_plume.svg.png" decoding="async" width="20" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/30px-Icon_flat_design_plume.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/40px-Icon_flat_design_plume.svg.png 2x" data-file-width="330" data-file-height="158" /></span></span></span></li> <li><span class="ouvrage" id="Deplace_2004"><small>[Delaplace <i><abbr class="abbr" title="et alii (« et d’autres »)" lang="la">et al.</abbr></i> 2004]</small> Guillaume <span class="nom_auteur">Delaplace</span>, Karine <span class="nom_auteur">Loubière</span>, Fabrice <span class="nom_auteur">Ducept</span> et Romain <span class="nom_auteur">Jeantet</span>, <cite class="italique">Modélisation en génie des procédés par analyse dimensionnelle : méthode et exemples résolus</cite>, Paris, <a href="/wiki/%C3%89ditions_Lavoisier" title="Éditions Lavoisier">Lavoisier</a>, <abbr class="abbr" title="collection">coll.</abbr> « Tec & Doc », <time class="nowrap" datetime="2014-05" data-sort-value="2014-05">mai 2014</time>, <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="14"><span class="romain" style="text-transform:uppercase">XIV</span></abbr>-443 <abbr class="abbr" title="pages">p.</abbr>, 15,5 × 23,5 <abbr class="abbr" title="centimètre">cm</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-7430-1570-1" title="Spécial:Ouvrages de référence/978-2-7430-1570-1"><span class="nowrap">978-2-7430-1570-1</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9782743015701" title="Spécial:Ouvrages de référence/9782743015701"><span class="nowrap">9782743015701</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/880405874">880405874</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb43863617m.public">43863617</a></span>, <a href="/wiki/HAL_(archive_ouverte)" title="HAL (archive ouverte)">HAL</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://hal.science/hal-01173099">hal-01173099</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/178433454">178433454</a></span>, <a rel="nofollow" class="external text" href="https://www.lavoisier.fr/livre/industries-chimiques/modelisation-en-genie-des-procedes-par-analyse-dimensionnelle/delaplace/descriptif-9782743015701">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=DybJAwAAQBAJ">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mod%C3%A9lisation+en+g%C3%A9nie+des+proc%C3%A9d%C3%A9s+par+analyse+dimensionnelle&rft.place=Paris&rft.pub=Lavoisier&rft.edition=1&rft.stitle=m%C3%A9thode+et+exemples+r%C3%A9solus&rft.aulast=Delaplace&rft.aufirst=Guillaume&rft.au=Loubi%C3%A8re%2C+Karine&rft.au=Ducept%2C+Fabrice&rft.au=Jeantet%2C+Romain&rft.date=2014&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%2214%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EXIV%3C%2Fspan%3E%3C%2Fabbr%3E-443&rft.isbn=978-2-7430-1570-1&rft_id=info%3Aoclcnum%2F880405874&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADimension+%28physique%29"></span></span>.<span class="nowrap" title="Ouvrage utilisé pour la rédaction de l'article"> <span typeof="mw:File"><span><img alt="Ouvrage utilisé pour la rédaction de l'article" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/20px-Icon_flat_design_plume.svg.png" decoding="async" width="20" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/30px-Icon_flat_design_plume.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/40px-Icon_flat_design_plume.svg.png 2x" data-file-width="330" data-file-height="158" /></span></span></span></li> <li><span class="ouvrage" id="Melzani2022"><span class="ouvrage" id="Mickaël_Melzani2022"><small>[Melzani 2022]</small> Mickaël <span class="nom_auteur">Melzani</span>, <cite class="italique">Physique et mesure : histoire et fonctionnement de la physique à travers la mesure et les unités</cite>, Paris, <a href="/wiki/%C3%89ditions_Ellipses" title="Éditions Ellipses">Ellipses</a>, hors <abbr class="abbr" title="collection">coll.</abbr>, <time class="nowrap" datetime="2022-06" data-sort-value="2022-06">juin 2022</time>, <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="16"><span class="romain" style="text-transform:uppercase">XVI</span></abbr>-395 <abbr class="abbr" title="pages">p.</abbr>, 16,5 × 24 <abbr class="abbr" title="centimètre">cm</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-340-06866-7" title="Spécial:Ouvrages de référence/978-2-340-06866-7"><span class="nowrap">978-2-340-06866-7</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9782340068667" title="Spécial:Ouvrages de référence/9782340068667"><span class="nowrap">9782340068667</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/1331669648">1331669648</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb47059018q.public">47059018</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/263154351">263154351</a></span>, <a rel="nofollow" class="external text" href="https://www.editions-ellipses.fr/accueil/14291-physique-et-mesure-histoire-et-fonctionnement-de-la-physique-a-travers-la-mesure-et-les-unites-9782340068667.html">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=KcF0EAAAQBAJ">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physique+et+mesure&rft.place=Paris&rft.pub=Ellipses&rft.edition=1&rft.stitle=histoire+et+fonctionnement+de+la+physique+%C3%A0+travers+la+mesure+et+les+unit%C3%A9s&rft.aulast=Melzani&rft.aufirst=Micka%C3%ABl&rft.date=2022-06&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%2216%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EXVI%3C%2Fspan%3E%3C%2Fabbr%3E-395&rft.isbn=978-2-340-06866-7&rft_id=info%3Aoclcnum%2F1331669648&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADimension+%28physique%29"></span></span></span>.<span class="nowrap" title="Ouvrage utilisé pour la rédaction de l'article"> <span typeof="mw:File"><span><img alt="Ouvrage utilisé pour la rédaction de l'article" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/20px-Icon_flat_design_plume.svg.png" decoding="async" width="20" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/30px-Icon_flat_design_plume.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/40px-Icon_flat_design_plume.svg.png 2x" data-file-width="330" data-file-height="158" /></span></span></span></li> <li><span class="ouvrage" id="Worstell2014"><span class="ouvrage" id="Jonathan_Worstell2014"><small>[Worstell 2014]</small> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Jonathan <span class="nom_auteur">Worstell</span>, <cite class="italique" lang="en">Dimensional analysis</cite> [« Analyse dimensionnelle »], Oxford et Waltham, <a href="/w/index.php?title=Butterworth-Heinemann&action=edit&redlink=1" class="new" title="Butterworth-Heinemann (page inexistante)">BH</a> <a href="https://en.wikipedia.org/wiki/Butterworth-Heinemann" class="extiw" title="en:Butterworth-Heinemann"><span class="indicateur-langue" title="Article en anglais : « Butterworth-Heinemann »">(en)</span></a> – <a href="/wiki/Elsevier" title="Elsevier">Elsevier</a>, <abbr class="abbr" title="collection">coll.</abbr> « <a href="/w/index.php?title=Institution_of_Chemical_Engineers&action=edit&redlink=1" class="new" title="Institution of Chemical Engineers (page inexistante)">IChemE</a> <a href="https://en.wikipedia.org/wiki/Institution_of_Chemical_Engineers" class="extiw" title="en:Institution of Chemical Engineers"><span class="indicateur-langue" title="Article en anglais : « Institution of Chemical Engineers »">(en)</span></a> / Practical guides in chemical engineering », <time class="nowrap" datetime="2014-03" data-sort-value="2014-03">mars 2014</time>, <abbr class="abbr" title="première">1<sup>re</sup></abbr> <abbr class="abbr" title="édition">éd.</abbr>, <abbr class="abbr" title="9"><span class="romain" style="text-transform:uppercase">IX</span></abbr>-149 <abbr class="abbr" title="pages">p.</abbr>, 15,2 × 22,8 <abbr class="abbr" title="centimètre">cm</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-0-12-801236-9" title="Spécial:Ouvrages de référence/978-0-12-801236-9"><span class="nowrap">978-0-12-801236-9</span></a>, <a href="/wiki/EAN_13" title="EAN 13">EAN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9780128012369" title="Spécial:Ouvrages de référence/9780128012369"><span class="nowrap">9780128012369</span></a>, <a href="/wiki/Online_Computer_Library_Center" title="Online Computer Library Center">OCLC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://worldcat.org/fr/title/871305380">871305380</a></span>, <a href="/wiki/Biblioth%C3%A8que_nationale_de_France" title="Bibliothèque nationale de France">BNF</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb446399548.public">44639954</a></span>, <a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://www.sudoc.fr/200740288">200740288</a></span>, <a rel="nofollow" class="external text" href="https://www.elsevier.com/books/dimensional-analysis/worstell/978-0-12-801236-9">présentation en ligne</a>, <a rel="nofollow" class="external text" href="//books.google.com/books?id=EfXJAgAAQBAJ">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dimensional+analysis&rft.place=Oxford+et+Waltham&rft.pub=BH&rft.edition=1&rft.aulast=Worstell&rft.aufirst=Jonathan&rft.date=2014-03&rft.tpages=%3Cabbr+class%3D%22abbr+%22+title%3D%229%22+%3E%3Cspan+class%3D%22romain%22+style%3D%22text-transform%3Auppercase%22%3EIX%3C%2Fspan%3E%3C%2Fabbr%3E-149&rft.isbn=978-0-12-801236-9&rft_id=info%3Aoclcnum%2F871305380&rfr_id=info%3Asid%2Ffr.wikipedia.org%3ADimension+%28physique%29"></span></span></span>.<span class="nowrap" title="Ouvrage utilisé pour la rédaction de l'article"> <span typeof="mw:File"><span><img alt="Ouvrage utilisé pour la rédaction de l'article" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Icon_flat_design_plume.svg/20px-Icon_flat_design_plume.svg.png" decoding="async" width="20" height="10" class="mw-file-element" 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