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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">nascondi</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigazione </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Pagina_principale" title="Visita la pagina principale [z]" accesskey="z"><span>Pagina principale</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Speciale:UltimeModifiche" title="Elenco delle ultime modifiche del sito [r]" accesskey="r"><span>Ultime modifiche</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Speciale:PaginaCasuale" title="Mostra una pagina a caso [x]" accesskey="x"><span>Una voce a caso</span></a></li><li id="n-nearby-pages-title" class="mw-list-item"><a href="/wiki/Speciale:NelleVicinanze"><span>Nelle vicinanze</span></a></li><li id="n-vetrina" class="mw-list-item"><a href="/wiki/Wikipedia:Vetrina"><span>Vetrina</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Aiuto:Aiuto" title="Pagine di aiuto"><span>Aiuto</span></a></li><li id="n-Sportello-informazioni" class="mw-list-item"><a href="/wiki/Aiuto:Sportello_informazioni"><span>Sportello informazioni</span></a></li> </ul> </div> </div> <div id="p-Comunità" class="vector-menu mw-portlet mw-portlet-Comunità" > <div class="vector-menu-heading"> Comunità </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-portal" class="mw-list-item"><a href="/wiki/Portale:Comunit%C3%A0" title="Descrizione del progetto, cosa puoi fare, dove trovare le cose"><span>Portale Comunità</span></a></li><li id="n-villagepump" class="mw-list-item"><a href="/wiki/Wikipedia:Bar"><span>Bar</span></a></li><li id="n-wikipediano" class="mw-list-item"><a href="/wiki/Wikipedia:Wikipediano"><span>Il Wikipediano</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="/wiki/Wikipedia:Contatti"><span>Contatti</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Pagina_principale" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="L'enciclopedia libera" src="/static/images/mobile/copyright/wikipedia-tagline-it.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" 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<div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_it.wikipedia.org&uselang=it" class=""><span>Fai una donazione</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speciale:CreaUtenza&returnto=Portata" title="Si consiglia di registrarsi e di effettuare l'accesso, anche se non è obbligatorio" class=""><span>registrati</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speciale:Entra&returnto=Portata" title="Si consiglia di effettuare l'accesso, anche se non è obbligatorio [o]" accesskey="o" class=""><span>entra</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Altre opzioni" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Strumenti personali" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Strumenti personali</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" 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accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>entra</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pagine per utenti anonimi <a href="/wiki/Aiuto:Benvenuto" aria-label="Ulteriori informazioni sulla contribuzione"><span>ulteriori informazioni</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Speciale:MieiContributi" title="Un elenco delle modifiche fatte da questo indirizzo IP [y]" accesskey="y"><span>contributi</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speciale:MieDiscussioni" title="Discussioni sulle modifiche fatte da questo indirizzo IP [n]" accesskey="n"><span>discussioni</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sito"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Indice" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Indice</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">nascondi</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inizio</div> </a> </li> <li id="toc-Storia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Storia"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Storia</span> </div> </a> <ul id="toc-Storia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Definizione" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definizione"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Definizione</span> </div> </a> <ul id="toc-Definizione-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Esempi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Esempi"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Esempi</span> </div> </a> <button aria-controls="toc-Esempi-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Attiva/disattiva la sottosezione Esempi</span> </button> <ul id="toc-Esempi-sublist" class="vector-toc-list"> <li id="toc-Portata_volumetrica" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Portata_volumetrica"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Portata volumetrica</span> </div> </a> <ul id="toc-Portata_volumetrica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Portata_molare" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Portata_molare"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Portata molare</span> </div> </a> <ul id="toc-Portata_molare-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Portata_massica" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Portata_massica"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Portata massica</span> </div> </a> <ul id="toc-Portata_massica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Portata_ponderale" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Portata_ponderale"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Portata ponderale</span> </div> </a> <ul id="toc-Portata_ponderale-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Nell'idraulica" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Nell'idraulica"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Nell'idraulica</span> </div> </a> <ul id="toc-Nell'idraulica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nella_cultura_di_massa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Nella_cultura_di_massa"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Nella cultura di massa</span> </div> </a> <ul id="toc-Nella_cultura_di_massa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voci_correlate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voci_correlate"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Voci correlate</span> </div> </a> <ul id="toc-Voci_correlate-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Indice" 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="Mostra/Nascondi l'indice" > <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">Mostra/Nascondi l'indice</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">Portata</span></h1> <div 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mw-list-item"><a href="/w/index.php?title=Portata&action=history" title="Versioni precedenti di questa pagina [h]" accesskey="h"><span>Cronologia</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Strumenti pagine"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Strumenti" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Strumenti</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div 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class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciale:PuntanoQui/Portata" title="Elenco di tutte le pagine che sono collegate a questa [j]" accesskey="j"><span>Puntano qui</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciale:ModificheCorrelate/Portata" rel="nofollow" title="Elenco delle ultime modifiche alle pagine collegate a questa [k]" accesskey="k"><span>Modifiche correlate</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speciale:PagineSpeciali" title="Elenco di tutte le pagine speciali [q]" accesskey="q"><span>Pagine speciali</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Portata&oldid=141363122" title="Collegamento permanente a questa versione di questa pagina"><span>Link permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Portata&action=info" title="Ulteriori informazioni su questa 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href="/w/index.php?title=Speciale:Libro&bookcmd=book_creator&referer=Portata"><span>Crea un libro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciale:DownloadAsPdf&page=Portata&action=show-download-screen"><span>Scarica come PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Portata&printable=yes" title="Versione stampabile di questa pagina [p]" accesskey="p"><span>Versione stampabile</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In altri progetti </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q109342160" title="Collegamento all'elemento connesso dell'archivio dati [g]" accesskey="g"><span>Elemento Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Strumenti pagine"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspetto"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspetto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">nascondi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Da Wikipedia, l'enciclopedia libera.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Reindirizzamento da <strong><a href="/w/index.php?title=Portata_volumetrica&redirect=no" class="mw-redirect" title="Portata volumetrica">Portata volumetrica</a></strong>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="it" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r130658281">body:not(.skin-minerva) .mw-parser-output .hatnote.nota-disambigua{clear:both;margin-top:0;padding:.05em .5em}</style> <style data-mw-deduplicate="TemplateStyles:r139142988">.mw-parser-output .hatnote-content{align-items:center;display:flex}.mw-parser-output .hatnote-icon{flex-shrink:0}.mw-parser-output .hatnote-icon img{display:flex}.mw-parser-output .hatnote-text{font-style:italic}body:not(.skin-minerva) .mw-parser-output .hatnote{border:1px solid #CCC;display:flex;margin:.5em 0;padding:.2em .5em}body:not(.skin-minerva) .mw-parser-output .hatnote-text{padding-left:.5em}body.skin-minerva .mw-parser-output .hatnote-icon{padding-right:8px}body.skin-minerva .mw-parser-output .hatnote-icon img{height:auto;width:16px}body.skin--responsive .mw-parser-output .hatnote a.new{color:#d73333}body.skin--responsive .mw-parser-output .hatnote a.new:visited{color:#a55858}</style> <div class="hatnote noprint nota-disambigua"> <div class="hatnote-content"><span class="noviewer hatnote-icon" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/18px-Nota_disambigua.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/27px-Nota_disambigua.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nota_disambigua.svg/36px-Nota_disambigua.svg.png 2x" data-file-width="200" data-file-height="200" /></span></span> <span class="hatnote-text"><a href="/wiki/Aiuto:Disambiguazione" title="Aiuto:Disambiguazione">Disambiguazione</a> – Se stai cercando altri significati, vedi <b><a href="/wiki/Portata_(disambigua)" class="mw-disambig" title="Portata (disambigua)">Portata (disambigua)</a></b>.</span></div> </div> <p>La <b>portata</b>, nella <a href="/wiki/Fluidodinamica" title="Fluidodinamica">fluidodinamica</a>, è una misura della quantità di un <a href="/wiki/Fluido" title="Fluido">fluido</a> che attraversa nell'unità di <a href="/wiki/Tempo" title="Tempo">tempo</a> una sezione di <a href="/wiki/Area" title="Area">area</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>. </p><p>La nozione corrisponde a una classe di <a href="/wiki/Grandezza_fisica" title="Grandezza fisica">grandezze fisiche</a>. In effetti, la quantità estensiva considerata può essere una <a href="/wiki/Numero" title="Numero">quantità numerica</a>, una <a href="/wiki/Quantit%C3%A0_di_sostanza" title="Quantità di sostanza">quantità chimica</a>, una <a href="/wiki/Massa_(fisica)" title="Massa (fisica)">massa</a>, un <a href="/wiki/Volume" title="Volume">volume</a>. Il concetto è stato spesso utilizzato anche nella descrizione di <a href="/wiki/Fenomeni_fisici" class="mw-redirect" title="Fenomeni fisici">fenomeni fisici</a> non direttamente collegati alla fluidodinamica classica, in cui il <a href="/wiki/Modello_fisico" class="mw-redirect" title="Modello fisico">modello fisico</a> può essere assimilato a quello di un fluido. Esempi notevoli si riscontrano nell'ambito dell'elettromagnetismo, dove l'<a href="/wiki/Intensit%C3%A0_di_corrente" title="Intensità di corrente">intensità di corrente elettrica</a> e il <a href="/wiki/Flusso_magnetico" title="Flusso magnetico">flusso magnetico</a> sono assimilati a portate, e nel caso del <a href="/wiki/Teorema_di_Liouville_(meccanica_hamiltoniana)" title="Teorema di Liouville (meccanica hamiltoniana)">teorema di Liouville</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Storia">Storia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=1" title="Modifica la sezione Storia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=1" title="Edit section's source code: Storia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Divenne molto importante nella storia dell'<a href="/wiki/Idraulica" title="Idraulica">idraulica</a> e si forma all'inizio del <a href="/wiki/XVII_secolo" title="XVII secolo">Seicento</a> nella scuola di <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a>, dove maturano metodi esatti di misura delle acque. La critica ai sistemi tradizionali di misura delle acque è anticipata già da <a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo Da Vinci</a>, ma sarà <a href="/wiki/Benedetto_Castelli" title="Benedetto Castelli">Benedetto Castelli</a> a sviluppare per primo misure sistematiche di portata nel suo trattato <i>Della misura dell'acque correnti</i>. </p><p>In precedenza le quantità d'acqua erano misurate semplicemente con le sezioni d'efflusso dalle luci o di deflusso nei corsi d'acqua, senza considerare il volume totale che le attraversava, cosa che poteva esser fatta tenendo conto della velocità con cui il fluido attraversava la sezione. Per evidenziare il concetto di portata, Castelli introdusse in modo efficace la velocità come terza dimensione, accanto alle due della sezione trasversale. Castelli usò l'espressione “quantità dell'acqua” per indicare la portata, un'espressione che rimase a lungo e lasciò tracce nel simbolo ancor oggi universalmente usato per indicare la portata, ossia la lettera Q, che rappresenta appunto l'iniziale di “quantità”.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Definizione">Definizione</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=2" title="Modifica la sezione Definizione" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=2" title="Edit section's source code: Definizione"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In generale, data una <a href="/wiki/Funzione_scalare" title="Funzione scalare">funzione scalare</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 q(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b1f8079f76d0e8a89cf19db8fc43f34ec569d25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.718ex; height:2.843ex;" alt="{\displaystyle q(t)}"></span>, in grado di descrivere una quantità di fluido, si può definire la portata di quest'ultimo come: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {q}}={\frac {\mathrm {d} q}{\mathrm {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>q</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>q</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {q}}={\frac {\mathrm {d} q}{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/963336ed59e788f6502b289c4c7a736b91dfc474" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.674ex; height:5.509ex;" alt="{\displaystyle {\dot {q}}={\frac {\mathrm {d} q}{\mathrm {d} t}}}"></span></dd></dl> <p>Nel caso di una funzione con anche altre variabili, ad esempio <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(r_{i},t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q(r_{i},t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3781b7ab7a4e83b7379d1107528a0f69b874db36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.601ex; height:2.843ex;" alt="{\displaystyle q(r_{i},t)}"></span> si generalizza al caso di <a href="/wiki/Derivata_totale" title="Derivata totale">derivata totale</a>, includendo un <a href="/wiki/Gradiente" title="Gradiente">gradiente</a> spaziale: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {q}}={\frac {\partial q}{\partial t}}+\sum _{i}{\frac {\partial r_{i}}{\partial t}}{\frac {\partial q}{\partial r_{i}}}={\frac {\partial q}{\partial t}}+\mathbf {v} \cdot \nabla q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>q</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>q</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>q</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>⋅</mo> <mi mathvariant="normal">∇</mi> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {q}}={\frac {\partial q}{\partial t}}+\sum _{i}{\frac {\partial r_{i}}{\partial t}}{\frac {\partial q}{\partial r_{i}}}={\frac {\partial q}{\partial t}}+\mathbf {v} \cdot \nabla q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29072277d5afc0e37aad9241f4c5523c6e60d640" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:37.545ex; height:6.509ex;" alt="{\displaystyle {\dot {q}}={\frac {\partial q}{\partial t}}+\sum _{i}{\frac {\partial r_{i}}{\partial t}}{\frac {\partial q}{\partial r_{i}}}={\frac {\partial q}{\partial t}}+\mathbf {v} \cdot \nabla q}"></span> </p><p>In questo caso si è impiegata prima per semplicità la <a href="/wiki/Notazione_tensoriale" class="mw-redirect" title="Notazione tensoriale">notazione tensoriale</a> (contratta) e poi la definizione di <a href="/wiki/Velocit%C3%A0" title="Velocità">velocità</a> e si è indicato con <a href="/wiki/Nabla" class="mw-redirect" title="Nabla">nabla</a> il gradiente spaziale. </p><p>In alternativa, essa può essere definita come il <a href="/wiki/Flusso" title="Flusso">flusso</a> della <a href="/wiki/Densit%C3%A0_di_corrente" class="mw-redirect" title="Densità di corrente">densità di corrente</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {j} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {j} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca5d874dbb32b8b33e83ca521f592808387a486e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.164ex; width:0.98ex; height:2.509ex;" alt="{\displaystyle \mathbf {j} }"></span> di <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(\mathbf {r} ,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q(\mathbf {r} ,t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd04583487d60335fda80e9a9614ca0320dce0b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.854ex; height:2.843ex;" alt="{\displaystyle q(\mathbf {r} ,t)}"></span> attraverso la sezione <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {q}}=\int _{A}\mathbf {j} \cdot \mathrm {d} \mathbf {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {q}}=\int _{A}\mathbf {j} \cdot \mathrm {d} \mathbf {S} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b52b0c4892b7bc19277beab1f2b5e89c8adfd395" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.893ex; height:5.676ex;" alt="{\displaystyle {\dot {q}}=\int _{A}\mathbf {j} \cdot \mathrm {d} \mathbf {S} }"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Esempi">Esempi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=3" title="Modifica la sezione Esempi" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=3" title="Edit section's source code: Esempi"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Più nello specifico, data una sezione si può definire: </p> <ul><li>portata molare, se riferita alla <a href="/wiki/Quantit%C3%A0_di_sostanza" title="Quantità di sostanza">quantità di sostanza</a>;</li> <li>portata massica, se riferita alla <a href="/wiki/Massa_(fisica)" title="Massa (fisica)">massa</a>;</li> <li>portata ponderale, se riferita al <a href="/wiki/Forza_peso" title="Forza peso">peso</a>;</li> <li>portata volumetrica, se riferita al <a href="/wiki/Volume" title="Volume">volume</a>, che si conserva per i <a href="/wiki/Liquidi" class="mw-redirect" title="Liquidi">liquidi</a> ma non sempre per i gas in generale.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Portata_volumetrica">Portata volumetrica</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=4" title="Modifica la sezione Portata volumetrica" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=4" title="Edit section's source code: Portata volumetrica"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Per un fluido comprimibile ha spesso poca importanza parlare della portata volumetrica, perché solitamente questa grandezza non si conserva. La portata volumetrica di liquido che scorre nell'unità di tempo attraverso una sezione di area <i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span></i> è pari a: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {V}}={\frac {\mathrm {d} V}{\mathrm {d} t}}=\int _{A}\mathbf {v} \cdot \mathrm {d} \mathbf {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>V</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {V}}={\frac {\mathrm {d} V}{\mathrm {d} t}}=\int _{A}\mathbf {v} \cdot \mathrm {d} \mathbf {S} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4878d3bfadfa6199ee7f73cd3ef41ded988a6e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.912ex; height:5.843ex;" alt="{\displaystyle {\dot {V}}={\frac {\mathrm {d} V}{\mathrm {d} t}}=\int _{A}\mathbf {v} \cdot \mathrm {d} \mathbf {S} }"></span></dd></dl> <p>pertanto, la <a href="/wiki/Velocit%C3%A0" title="Velocità">velocità</a> del liquido <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {v} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35c1866e359fbfd2e0f606c725ba5cc37a5195d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;" alt="{\displaystyle \mathbf {v} }"></span> può essere interpretata come la densità di flusso del volume <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> attraverso la sezione <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>. </p><p>Nella maggior parte delle applicazioni pratiche, il flusso di un fluido attraverso un condotto, se riferito ai valori medi delle proprietà nella generica sezione perpendicolare alla direzione del flusso, si può approssimare ad un flusso unidimensionale, ovverosia si trascurano le variazioni delle proprietà del fluido in ogni direzione tranne la direzione del flusso. Questa approssimazione se influisce poco sulla maggior parte delle proprietà del fluido, quali temperatura, pressione, densità, ha invece un effetto rilevante sulla velocità, il cui valore varia da zero in prossimità delle pareti ad un massimo in corrispondenza dell'asse, a causa degli effetti viscosi. </p><p>Considerando <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 \langle v\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mi>v</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle v\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61604fdde22cb90ecdbdd2813be95b938722f54c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.937ex; height:2.843ex;" alt="{\displaystyle \langle v\rangle }"></span> la velocità media del fluido uniforme su tutto <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> e inclinata con un certo angolo <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>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/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> rispetto alla normale unitaria associata alla sezione, si ha che: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {V}}=\langle v\rangle \cdot A=\langle v\rangle A\cos \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>V</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo fence="false" stretchy="false">⟨</mo> <mi>v</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>⋅</mo> <mi>A</mi> <mo>=</mo> <mo fence="false" stretchy="false">⟨</mo> <mi>v</mi> <mo fence="false" stretchy="false">⟩</mo> <mi>A</mi> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {V}}=\langle v\rangle \cdot A=\langle v\rangle A\cos \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03df1fa73b9cd813344243ccccb422a2afddc108" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.999ex; height:3.176ex;" alt="{\displaystyle {\dot {V}}=\langle v\rangle \cdot A=\langle v\rangle A\cos \theta }"></span></dd></dl> <p>inoltre, nel caso particolare in cui <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {v} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35c1866e359fbfd2e0f606c725ba5cc37a5195d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;" alt="{\displaystyle \mathbf {v} }"></span> risulti ortogonale all'area, si avrà che: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {V}}=\langle v\rangle \,A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>V</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo fence="false" stretchy="false">⟨</mo> <mi>v</mi> <mo fence="false" stretchy="false">⟩</mo> <mspace width="thinmathspace" /> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {V}}=\langle v\rangle \,A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4141090e591554850e1c82c144cf9468aaad4be1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.953ex; height:3.176ex;" alt="{\displaystyle {\dot {V}}=\langle v\rangle \,A}"></span></dd></dl> <p>Nel <a href="/wiki/Sistema_internazionale_di_unit%C3%A0_di_misura" title="Sistema internazionale di unità di misura">Sistema Internazionale</a> la portata volumetrica si misura in <a href="/wiki/Metri_cubi" class="mw-redirect" title="Metri cubi">metri cubi</a> al <a href="/wiki/Secondo" title="Secondo">secondo</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [m^{3}/s]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>s</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [m^{3}/s]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/100b9c847f4b2cfb4aecb434403c18826cd0665b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.641ex; height:3.176ex;" alt="{\displaystyle [m^{3}/s]}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Portata_molare">Portata molare</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=5" title="Modifica la sezione Portata molare" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=5" title="Edit section's source code: Portata molare"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La portata molare di un fluido che scorre nell'unità di tempo attraverso una sezione di area <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> è pari a: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {n}}={\frac {\mathrm {d} n}{\mathrm {d} t}}=\int _{A}\mathbf {J} _{n}\cdot \mathrm {d} \mathbf {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>n</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {n}}={\frac {\mathrm {d} n}{\mathrm {d} t}}=\int _{A}\mathbf {J} _{n}\cdot \mathrm {d} \mathbf {S} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/114580d86d0247db2c964cf632bb18b92e718556" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.316ex; height:5.843ex;" alt="{\displaystyle {\dot {n}}={\frac {\mathrm {d} n}{\mathrm {d} t}}=\int _{A}\mathbf {J} _{n}\cdot \mathrm {d} \mathbf {S} }"></span></dd></dl> <p>Nel Sistema Internazionale la portata molare si misura in <a href="/wiki/Mole" title="Mole">moli</a> al secondo <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 [mol/s]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>s</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [mol/s]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/857b400b749668df82fd0f34ddc09b23b5d60bcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.408ex; height:2.843ex;" alt="{\displaystyle [mol/s]}"></span>. </p><p>Nell'ipotesi di flusso unidimensionale, assumendo la velocità costante sull'intera sezione trasversale e pari ad un valore medio equivalente, è possibile passare dalla portata volumetrica alla portata molare attraverso la relazione: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {n}}={\frac {1}{M}}{\dot {(\rho V)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mo stretchy="false">(</mo> <mi>ρ</mi> <mi>V</mi> <mo stretchy="false">)</mo> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {n}}={\frac {1}{M}}{\dot {(\rho V)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20e2e0b6dc0a572bf76245b90b79d3cee3e58c52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.57ex; height:5.176ex;" alt="{\displaystyle {\dot {n}}={\frac {1}{M}}{\dot {(\rho V)}}}"></span></dd></dl> <p>dove <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> è la <a href="/wiki/Densit%C3%A0" title="Densità">densità</a> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> la <a href="/wiki/Massa_molare" title="Massa molare">massa molare</a>. Supponendo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> costante su tutta la sezione si può riscrivere la relazione come: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {n}}={\frac {\rho }{M}}{\dot {V}}={\frac {\rho }{M}}\langle v\rangle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <mi>M</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>V</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <mi>M</mi> </mfrac> </mrow> <mo fence="false" stretchy="false">⟨</mo> <mi>v</mi> <mo fence="false" stretchy="false">⟩</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {n}}={\frac {\rho }{M}}{\dot {V}}={\frac {\rho }{M}}\langle v\rangle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63b6b6960a4adbe5f69a30a5de3d10c44abef9d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.616ex; height:4.843ex;" alt="{\displaystyle {\dot {n}}={\frac {\rho }{M}}{\dot {V}}={\frac {\rho }{M}}\langle v\rangle A}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Portata_massica">Portata massica</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=6" title="Modifica la sezione Portata massica" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=6" title="Edit section's source code: Portata massica"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La portata massica<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> di un fluido che scorre nell'unità di tempo attraverso una sezione di area <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> è pari a: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {m}}={\frac {\mathrm {d} m}{\mathrm {d} t}}=\int _{A}\mathbf {J} _{m}\cdot \mathrm {d} \mathbf {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>m</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {m}}={\frac {\mathrm {d} m}{\mathrm {d} t}}=\int _{A}\mathbf {J} _{m}\cdot \mathrm {d} \mathbf {S} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f14f19c0a82198309e7530c1d7583a63e7e6f52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.064ex; height:5.843ex;" alt="{\displaystyle {\dot {m}}={\frac {\mathrm {d} m}{\mathrm {d} t}}=\int _{A}\mathbf {J} _{m}\cdot \mathrm {d} \mathbf {S} }"></span></dd></dl> <p>Nel Sistema Internazionale la portata massica si misura in <a href="/wiki/Chilogrammo" title="Chilogrammo">chilogrammi</a> al secondo <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 [kg/s]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>k</mi> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>s</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [kg/s]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4570107ac04d8bb1f6162c736aaf05887ba1641" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.874ex; height:2.843ex;" alt="{\displaystyle [kg/s]}"></span>. </p><p>Nell'ipotesi di flusso unidimensionale, assumendo la velocità costante sull'intera sezione trasversale e pari ad un valore medio equivalente, è possibile passare dalla portata volumetrica alla portata massica attraverso la relazione: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {m}}={\dot {(\rho V)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mo stretchy="false">(</mo> <mi>ρ</mi> <mi>V</mi> <mo stretchy="false">)</mo> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {m}}={\dot {(\rho V)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbbfbd7a00986b654f6355e1cfd72ff9f17d2220" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.937ex; height:3.343ex;" alt="{\displaystyle {\dot {m}}={\dot {(\rho V)}}}"></span></dd></dl> <p>Supponendo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> costante su tutta la sezione si può riscrivere la relazione come: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {m}}=\rho {\dot {V}}=\rho \langle v\rangle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>V</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>ρ</mi> <mo fence="false" stretchy="false">⟨</mo> <mi>v</mi> <mo fence="false" stretchy="false">⟩</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {m}}=\rho {\dot {V}}=\rho \langle v\rangle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/769cf7ecce0c62093f74607a394cef3891c7cf30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.108ex; height:3.176ex;" alt="{\displaystyle {\dot {m}}=\rho {\dot {V}}=\rho \langle v\rangle A}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Portata_ponderale">Portata ponderale</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=7" title="Modifica la sezione Portata ponderale" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=7" title="Edit section's source code: Portata ponderale"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La portata ponderale di un fluido che scorre nell'unità di tempo attraverso una sezione di area <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> è pari a: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\mathbf {N} }}={\dot {m}}\mathbf {g} =\mathbf {g} {\frac {\mathrm {d} m}{\mathrm {d} t}}=\mathbf {g} \int _{A}\mathbf {J} _{m}\cdot \mathrm {d} \mathbf {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">g</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">g</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>m</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">g</mi> </mrow> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\mathbf {N} }}={\dot {m}}\mathbf {g} =\mathbf {g} {\frac {\mathrm {d} m}{\mathrm {d} t}}=\mathbf {g} \int _{A}\mathbf {J} _{m}\cdot \mathrm {d} \mathbf {S} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef8e53e0287423abe142abc6829f90c42c49ba02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.651ex; height:5.843ex;" alt="{\displaystyle {\dot {\mathbf {N} }}={\dot {m}}\mathbf {g} =\mathbf {g} {\frac {\mathrm {d} m}{\mathrm {d} t}}=\mathbf {g} \int _{A}\mathbf {J} _{m}\cdot \mathrm {d} \mathbf {S} }"></span></dd></dl> <p>dove <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {g} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">g</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {g} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cdf843789e9564a867aee3ff184453b72ecbafe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.337ex; height:2.009ex;" alt="{\displaystyle \mathbf {g} }"></span> è l'<a href="/wiki/Accelerazione_di_gravit%C3%A0" title="Accelerazione di gravità">accelerazione di gravità</a>. Nel Sistema Internazionale la portata ponderale si misura in <a href="/wiki/Newton_(unit%C3%A0_di_misura)" title="Newton (unità di misura)">newton</a> al secondo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [N/s]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>s</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [N/s]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87b147cd968baf9e5ee6ae70673a149fb555d44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.61ex; height:2.843ex;" alt="{\displaystyle [N/s]}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Nell'idraulica"><span id="Nell.27idraulica"></span>Nell'idraulica</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=8" title="Modifica la sezione Nell'idraulica" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=8" title="Edit section's source code: Nell'idraulica"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Idraulica" title="Idraulica">idraulica</a> il termine è di rilevanza per indicare la portata di liquido che attraversa nell'unità di tempo la sezione di un <a href="/wiki/Fiume" title="Fiume">corso d'acqua</a>, un <a href="/wiki/Canale_artificiale" title="Canale artificiale">canale</a> o un condotto, e la capacità idraulica di un'opera o di un dispositivo per la captazione o l'erogazione dell'acqua. </p><p>La portata di un corso d'acqua è qualificata da <a href="/wiki/Aggettivo" title="Aggettivo">aggettivi</a> (per esempio portata "minima", "media" od "ordinaria", "massima" o "di punta"), corrispondenti a specifiche elaborazioni <a href="/wiki/Statistica" title="Statistica">statistiche</a> <a href="/wiki/Idrologia" title="Idrologia">idrologiche</a>. La <a href="/wiki/Trasporto_solido" title="Trasporto solido">portata solida</a>, invece, è la massa di sedimenti che attraversano nell'unità di tempo la sezione di un corso d'acqua naturale. </p> <div class="mw-heading mw-heading2"><h2 id="Nella_cultura_di_massa">Nella cultura di massa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=9" title="Modifica la sezione Nella cultura di massa" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=9" title="Edit section's source code: Nella cultura di massa"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Franco_Battiato" title="Franco Battiato">Franco Battiato</a> citò la formula della portata nel suo album "<a href="/wiki/Pollution" title="Pollution">Pollution</a>" nel 1973, più precisamente nell'ultima canzone.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=10" title="Modifica la sezione Note" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=10" title="Edit section's source code: Note"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1"><b>^</b></a> <span class="reference-text"><cite class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="http://idraulica.beic.it/glossario-it/portata/"><span style="font-style:italic;">Biblioteca Idraulica Italiana</span></a>, su <span style="font-style:italic;">idraulica.beic.it</span>.</cite></span> </li> <li id="cite_note-2"><a href="#cite_ref-2"><b>^</b></a> <span class="reference-text"><cite class="citation web" style="font-style:normal"> The International Union of Pure and Applied Chemistry (IUPAC), <a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/M03720"><span style="font-style:italic;">IUPAC - mass flow rate (M03720)</span></a>, su <span style="font-style:italic;">goldbook.iupac.org</span>.</cite></span> </li> <li id="cite_note-3"><a href="#cite_ref-3"><b>^</b></a> <span class="reference-text"><cite class="citation pubblicazione" style="font-style:normal"> Franco Battiato - Topic, <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=jhKNmWyhI74"><span style="font-style:italic;">Pollution / Ti sei mai chiesto quale funzione hai?</span></a>, 31 agosto 2023. <small>URL consultato il 1º ottobre 2024</small>.</cite></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=11" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=11" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="http://idraulica.beic.it/glossario-it/portata/"><span style="font-style:italic;">Biblioteca Idraulica Italiana</span></a>, su <span style="font-style:italic;">idraulica.beic.it</span>. <small>URL consultato il 31 agosto 2015</small>.</cite></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Portata&veaction=edit&section=12" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Portata&action=edit&section=12" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Flusso" title="Flusso">Flusso</a></li> <li><a href="/wiki/Legge_di_Leonardo" title="Legge di Leonardo">Legge di Leonardo</a></li> <li><a href="/wiki/Effetto_Venturi" title="Effetto Venturi">Effetto Venturi</a></li> <li><a href="/wiki/Equazione_di_Bernoulli" title="Equazione di Bernoulli">Equazione di Bernoulli</a></li> <li><a href="/wiki/Fluidodinamica" title="Fluidodinamica">Fluidodinamica</a></li> <li><a href="/wiki/Flusso_quasi-unidimensionale" title="Flusso quasi-unidimensionale">Flusso quasi-unidimensionale</a></li> <li><a href="/wiki/Misure_di_portata" title="Misure di portata">Misure di portata</a></li></ul> <style data-mw-deduplicate="TemplateStyles:r140554510">.mw-parser-output .CdA{border:1px solid #aaa;width:100%;margin:auto;font-size:90%;padding:2px}.mw-parser-output .CdA th{background-color:#f2f2f2;font-weight:bold;width:20%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .CdA{border-color:#54595D}html.skin-theme-clientpref-night .mw-parser-output .CdA th{background-color:#202122}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .CdA{border-color:#54595D}html.skin-theme-clientpref-os .mw-parser-output .CdA th{background-color:#202122}}</style><table class="CdA"><tbody><tr><th><a href="/wiki/Aiuto:Controllo_di_autorit%C3%A0" title="Aiuto:Controllo di autorità">Controllo di autorità</a></th><td><a href="/wiki/Nuovo_soggettario" title="Nuovo soggettario">Thesaurus BNCF</a> <span class="uid"><a rel="nofollow" class="external text" href="https://thes.bncf.firenze.sbn.it/termine.php?id=53404">53404</a></span></td></tr></tbody></table> <div class="noprint" style="width:100%; padding: 3px 0; display: flex; flex-wrap: wrap; row-gap: 4px; column-gap: 8px; box-sizing: border-box;"><div style="flex-basis: calc( 100% / 2 - 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