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aria-label="Sadržaj" 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">Sadržaj</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</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">Početak</div> </a> </li> <li id="toc-Maseni_protok" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Maseni_protok"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Maseni protok</span> </div> </a> <ul id="toc-Maseni_protok-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Izvori" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Izvori"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Izvori</span> </div> </a> <ul id="toc-Izvori-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="Sadržaj" 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="Prikaz sadržaja stranice" > <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">Prikaz sadržaja stranice</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">Volumni protok</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="Idi na druge jezične varijante članka. Dostupan je na 30 jezika" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-30" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">30 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%AF%D9%81%D9%82_%D8%AD%D8%AC%D9%85%D9%8A" title="تدفق حجمي – arapski" lang="ar" hreflang="ar" data-title="تدفق حجمي" data-language-autonym="العربية" data-language-local-name="arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/H%C9%99cmli_ax%C4%B1n%C4%B1_%C3%B6l%C3%A7%C9%99n" title="Həcmli axını ölçən – azerbajdžanski" lang="az" hreflang="az" data-title="Həcmli axını ölçən" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžanski" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D0%B1%D0%B5%D0%BC%D0%B5%D0%BD_%D1%80%D0%B0%D0%B7%D1%85%D0%BE%D0%B4" title="Обемен разход – bugarski" lang="bg" hreflang="bg" data-title="Обемен разход" data-language-autonym="Български" data-language-local-name="bugarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Zapreminski_protok" title="Zapreminski protok – bosanski" lang="bs" hreflang="bs" data-title="Zapreminski protok" data-language-autonym="Bosanski" data-language-local-name="bosanski" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Objemov%C3%BD_pr%C5%AFtok" title="Objemový průtok – češki" lang="cs" hreflang="cs" data-title="Objemový průtok" data-language-autonym="Čeština" data-language-local-name="češki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Volumenstrom" title="Volumenstrom – njemački" lang="de" hreflang="de" data-title="Volumenstrom" data-language-autonym="Deutsch" data-language-local-name="njemački" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%B1%CF%81%CE%BF%CF%87%CE%AE" title="Παροχή – grčki" lang="el" hreflang="el" data-title="Παροχή" data-language-autonym="Ελληνικά" data-language-local-name="grčki" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Volumetric_flow_rate" title="Volumetric flow rate – engleski" lang="en" hreflang="en" data-title="Volumetric flow rate" data-language-autonym="English" data-language-local-name="engleski" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Caudal_volum%C3%A9trico" title="Caudal volumétrico – španjolski" lang="es" hreflang="es" data-title="Caudal volumétrico" data-language-autonym="Español" data-language-local-name="španjolski" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D8%A8%DB%8C_%D8%AD%D8%AC%D9%85%DB%8C" title="دبی حجمی – perzijski" lang="fa" hreflang="fa" data-title="دبی حجمی" data-language-autonym="فارسی" data-language-local-name="perzijski" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Virtaama" title="Virtaama – finski" lang="fi" hreflang="fi" data-title="Virtaama" data-language-autonym="Suomi" data-language-local-name="finski" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr badge-Q70894304 mw-list-item" title=""><a href="https://fr.wikipedia.org/wiki/D%C3%A9bit_volumique" title="Débit volumique – francuski" lang="fr" hreflang="fr" data-title="Débit volumique" data-language-autonym="Français" data-language-local-name="francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%A4%D7%99%D7%A7%D7%94" title="ספיקה – hebrejski" lang="he" hreflang="he" data-title="ספיקה" data-language-autonym="עברית" data-language-local-name="hebrejski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/T%C3%A9rfogat%C3%A1ram" title="Térfogatáram – mađarski" lang="hu" hreflang="hu" data-title="Térfogatáram" data-language-autonym="Magyar" data-language-local-name="mađarski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Laju_alir_volumetrik" title="Laju alir volumetrik – indonezijski" lang="id" hreflang="id" data-title="Laju alir volumetrik" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it badge-Q70894304 mw-list-item" title=""><a href="https://it.wikipedia.org/wiki/Portata_volumetrica" title="Portata volumetrica – talijanski" lang="it" hreflang="it" data-title="Portata volumetrica" data-language-autonym="Italiano" data-language-local-name="talijanski" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%B5%81%E9%87%8F" title="流量 – japanski" lang="ja" hreflang="ja" data-title="流量" data-language-autonym="日本語" data-language-local-name="japanski" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Debiet" title="Debiet – nizozemski" lang="nl" hreflang="nl" data-title="Debiet" data-language-autonym="Nederlands" data-language-local-name="nizozemski" 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/Strumie%C5%84_obj%C4%99to%C5%9Bci" title="Strumień objętości – poljski" lang="pl" hreflang="pl" data-title="Strumień objętości" data-language-autonym="Polski" data-language-local-name="poljski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fluxo_volum%C3%A9trico" title="Fluxo volumétrico – portugalski" lang="pt" hreflang="pt" data-title="Fluxo volumétrico" data-language-autonym="Português" data-language-local-name="portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Debit_volumic_de_curgere" title="Debit volumic de curgere – rumunjski" lang="ro" hreflang="ro" data-title="Debit volumic de curgere" data-language-autonym="Română" data-language-local-name="rumunjski" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D0%B1%D1%8A%D1%91%D0%BC%D0%BD%D1%8B%D0%B9_%D1%80%D0%B0%D1%81%D1%85%D0%BE%D0%B4" title="Объёмный расход – ruski" lang="ru" hreflang="ru" data-title="Объёмный расход" data-language-autonym="Русский" data-language-local-name="ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Volumni_protok" title="Volumni protok – srpsko-hrvatski" lang="sh" hreflang="sh" data-title="Volumni protok" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpsko-hrvatski" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Objemov%C3%BD_prietok" title="Objemový prietok – slovački" lang="sk" hreflang="sk" data-title="Objemový prietok" data-language-autonym="Slovenčina" data-language-local-name="slovački" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Prostorninski_pretok" title="Prostorninski pretok – slovenski" lang="sl" hreflang="sl" data-title="Prostorninski pretok" data-language-autonym="Slovenščina" data-language-local-name="slovenski" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Volymfl%C3%B6de" title="Volymflöde – švedski" lang="sv" hreflang="sv" data-title="Volymflöde" data-language-autonym="Svenska" data-language-local-name="švedski" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Debi" title="Debi – turski" lang="tr" hreflang="tr" data-title="Debi" data-language-autonym="Türkçe" data-language-local-name="turski" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D0%B1%27%D1%94%D0%BC%D0%BD%D0%B0_%D0%B2%D0%B8%D1%82%D1%80%D0%B0%D1%82%D0%B0" title="Об'ємна витрата – ukrajinski" lang="uk" hreflang="uk" data-title="Об'ємна витрата" data-language-autonym="Українська" data-language-local-name="ukrajinski" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%C6%B0u_l%C6%B0%E1%BB%A3ng_d%C3%B2ng_ch%E1%BA%A3y" title="Lưu lượng dòng chảy – vijetnamski" lang="vi" hreflang="vi" data-title="Lưu lượng dòng chảy" data-language-autonym="Tiếng Việt" data-language-local-name="vijetnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%AB%94%E7%A9%8D%E6%B5%81%E7%8E%87" title="體積流率 – kineski" lang="zh" hreflang="zh" data-title="體積流率" data-language-autonym="中文" data-language-local-name="kineski" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1134348#sitelinks-wikipedia" title="Poveznice na druge jezike" class="wbc-editpage">Uredi poveznice</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Volumni_protok" title="Pogledaj sadržaj [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Razgovor:Volumni_protok&action=edit&redlink=1" rel="discussion" class="new" title="Razgovorna stranica (stranica ne postoji) [t]" accesskey="t"><span>Razgovor</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Promijeni jezičnu varijantu" > <label id="vector-variants-dropdown-label" for="vector-variants-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">hrvatski</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Pogledi"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Volumni_protok"><span>Čitaj</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Volumni_protok&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Volumni_protok&action=edit" title="Uredite izvorni kôd ove stranice [e]" accesskey="e"><span>Uredi kôd</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Volumni_protok&action=history" title="Ranije izmjene na ovoj stranici [h]" accesskey="h"><span>Vidi povijest</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <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="Pomagala" > <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">Pomagala</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" 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data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</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">Izvor: Wikipedija</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hr" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Mjerna_prigusnica_1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/d/de/Mjerna_prigusnica_1.png/300px-Mjerna_prigusnica_1.png" decoding="async" width="300" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/d/de/Mjerna_prigusnica_1.png/450px-Mjerna_prigusnica_1.png 1.5x, //upload.wikimedia.org/wikipedia/hr/d/de/Mjerna_prigusnica_1.png 2x" data-file-width="485" data-file-height="406" /></a><figcaption><a href="/wiki/Mjerna_prigu%C5%A1nica" title="Mjerna prigušnica">Mjerna prigušnica</a> prema <a href="/wiki/Standard" title="Standard">standardu</a> ISO 5167.</figcaption></figure> <p><b>Volumni protok</b> ili <b>volumetrijski protok</b> je <a href="/wiki/Fizikalna_veli%C4%8Dina" class="mw-redirect" title="Fizikalna veličina">fizikalna veličina</a> koja određuje <a href="/wiki/Obujam" title="Obujam">obujam</a> (volumen) <a href="/wiki/Fluid" title="Fluid">fluida</a> koji prolazi neku točku u jedinici <a href="/wiki/Vrijeme_(fizika)" title="Vrijeme (fizika)">vremena</a> (<a href="/wiki/Kubni_metar_u_sekundi" title="Kubni metar u sekundi">m<sup>3</sup>/s</a>). Protok je jedna od osnovnih fizikalnih veličina koja se mjeri u industrijskom pogonu. <a href="/wiki/Mjerenje_protoka" title="Mjerenje protoka">Mjerenjem protoka</a> određuju se <a href="/wiki/Energetika" title="Energetika">energetske</a> i materijalne bilance na osnovu kojih se određuje produktivnost procesa <a href="/wiki/Proizvodnja" title="Proizvodnja">proizvodnje</a>. Istovremeno protok je najčešće i osnovna veličina čijom se promjenom upravlja procesom proizvodnje. Mjerenje protoka <a href="/wiki/Teku%C4%87ine" title="Tekućine">kapljevina</a>, <a href="/wiki/Plin" title="Plin">plinova</a>, višefaznih tekućina i <a href="/wiki/Suspenzija_(kemija)" title="Suspenzija (kemija)">suspenzija</a> je složeno, podložno je brojnim pogreškama, i zato je razvijen je veliki broj različitih <a href="/wiki/Mjerni_instrument" title="Mjerni instrument">mjernih postupka</a> u svrhu preciznog i pouzdanog <a href="/wiki/Mjerenje" title="Mjerenje">mjerenja</a>.<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><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><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Volumni protok se određuje kao: </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 Q={\frac {\Delta V}{\Delta t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q={\frac {\Delta V}{\Delta t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0bd02687ca9647fa7af126b03b69137fb81bfe5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.496ex; height:5.509ex;" alt="{\displaystyle Q={\frac {\Delta V}{\Delta t}}}"></span> .</dd></dl> <p>gdje je: </p> <ul><li><i>Q</i> - volumni protok (<a href="/wiki/Kubni_metar_u_sekundi" title="Kubni metar u sekundi">m<sup>3</sup>/s</a>),</li> <li>Δ<i>V</i> - promjena obujma fluida (<a href="/wiki/Kubi%C4%8Dni_metar" title="Kubični metar">m<sup>3</sup></a>), koji teče kroz neki presjek (npr. <a href="/wiki/Cijev" title="Cijev">cijevi</a>), ,</li> <li>Δ<i>t</i> - vrijeme trajanja toka fluida koji teče kroz neki presjek (<a href="/wiki/Sekunda" title="Sekunda">s</a>).</li></ul> <p>Volumni protok u cijevi je određen <a href="/wiki/Limes_(matematika)" title="Limes (matematika)">limesom</a> omjera <a href="/wiki/Volumen" class="mw-redirect" title="Volumen">volumena</a> tekućine koja protječe kroz presjek <a href="/wiki/Cijev" title="Cijev">cijevi</a> u intervalu vremena kada interval postaje beskonačno mali: </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 Q={\frac {{\rm {d}}V}{{\rm {d}}t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mi>V</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q={\frac {{\rm {d}}V}{{\rm {d}}t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d52cb72c8a468b158a82d00b8d44bfc3fa394ce1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.853ex; height:5.509ex;" alt="{\displaystyle Q={\frac {{\rm {d}}V}{{\rm {d}}t}}}"></span></dd></dl> <p><a href="/wiki/Kubni_metar_u_sekundi" title="Kubni metar u sekundi">Kubni metar u sekundi</a> je <a href="/wiki/Mjerna_jedinica" title="Mjerna jedinica">mjerna jedinica</a> za volumni protok. Najčešće se koristi za mjerenje volumnog protoka vode. Također može poslužiti i za mjerenje količine eksploatacije raznih materijala poput <a href="/wiki/Kamen" title="Kamen">kamena</a>, <a href="/wiki/Pijesak" title="Pijesak">pijeska</a> i sl. </p> <ul><li>1 m<sup>3</sup>/s je 1000 <a href="/wiki/Litra" title="Litra">litara</a> u <a href="/wiki/Sekunda" title="Sekunda">sekundi</a>.</li></ul> <p>Volumni protok u cijevi se može odrediti i kao: </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 Q=\mathbf {v} \cdot \mathbf {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=\mathbf {v} \cdot \mathbf {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42dc971056f36be78e18446cdd7112256cfb3707" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.046ex; height:2.509ex;" alt="{\displaystyle Q=\mathbf {v} \cdot \mathbf {A} }"></span></dd></dl> <p>gdje je: </p> <ul><li><b>v</b> – <a href="/wiki/Brzina" title="Brzina">brzina</a> <a href="/wiki/Fluid" title="Fluid">fluida</a> u cijevi (<a href="/wiki/Metar_u_sekundi" title="Metar u sekundi">m/s</a>),</li> <li><b>A</b> – presjek cijevi (<a href="/wiki/%C4%8Cetvorni_metar" title="Četvorni metar">m<sup>2</sup></a>).</li></ul> <p>Brzina tekućine u cijevi mijenja se položajem i vremenom. Bitno se razlikuje <a href="/wiki/Laminarno_strujanje" title="Laminarno strujanje">laminarno</a> od <a href="/wiki/Turbulencija" title="Turbulencija">turbulentnog</a> protjecanja.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Maseni_protok">Maseni protok</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volumni_protok&veaction=edit&section=1" title="Uredi odlomak: Maseni protok" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Volumni_protok&action=edit&section=1" title="Uredi kôd odjeljka Maseni protok"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Maseni_protok" title="Maseni protok">Maseni protok</a> je <a href="/wiki/Masa" title="Masa">masa</a> fluida koja prolazi neku točku u jedinici vremena (<a href="/wiki/Kilogram" title="Kilogram">kg</a>/<a href="/wiki/Sekunda" title="Sekunda">s</a>). Maseni protok se može odrediti kao: </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 \cdot \mathbf {v} \cdot \mathbf {A} =\rho \cdot Q=\mathbf {j} _{\rm {m}}\cdot \mathbf {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> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> <mo>=</mo> <mi>ρ</mi> <mo>⋅</mo> <mi>Q</mi> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {m}}=\rho \cdot \mathbf {v} \cdot \mathbf {A} =\rho \cdot Q=\mathbf {j} _{\rm {m}}\cdot \mathbf {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44f76cc8be7f446d2f226dbce82340b057901eab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.162ex; height:2.676ex;" alt="{\displaystyle {\dot {m}}=\rho \cdot \mathbf {v} \cdot \mathbf {A} =\rho \cdot Q=\mathbf {j} _{\rm {m}}\cdot \mathbf {A} }"></span></dd></dl> <p>gdje je: </p> <ul><li><i>ρ</i> - <a href="/wiki/Gusto%C4%87a" title="Gustoća">gustoća</a> fluida (kg/m<sup>3</sup>),</li> <li><b>v</b> – <a href="/wiki/Brzina" title="Brzina">brzina</a> <a href="/wiki/Fluid" title="Fluid">fluida</a> u cijevi (<a href="/wiki/Metar_u_sekundi" title="Metar u sekundi">m/s</a>),</li> <li><b>A</b> – presjek cijevi (<a href="/wiki/%C4%8Cetvorni_metar" title="Četvorni metar">m<sup>2</sup></a>),</li> <li><i>Q</i> - volumni protok (<a href="/wiki/Kubni_metar_u_sekundi" title="Kubni metar u sekundi">m<sup>3</sup>/s</a>),</li> <li><b>j</b><sub>m</sub> - maseni fluks.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Izvori">Izvori</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volumni_protok&veaction=edit&section=2" title="Uredi odlomak: Izvori" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Volumni_protok&action=edit&section=2" title="Uredi kôd odjeljka Izvori"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r6541845">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="http://www.fer.unizg.hr/_download/repository/PREDAVANJE-4.pdf">[1]</a>  <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131211085344/http://www.fer.unizg.hr/_download/repository/PREDAVANJE-4.pdf">Arhivirana inačica izvorne stranice</a> od 11. prosinca 2013. (<a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>) "Mjerenje protoka", www.fer.unizg.hr, 2011.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="http://www.fer.unizg.hr/_download/repository/Mjerenje-Protoka.pdf">[2]</a>  <a rel="nofollow" class="external text" href="https://web.archive.org/web/20111215235642/http://www.fer.unizg.hr/_download/repository/Mjerenje-Protoka.pdf">Arhivirana inačica izvorne stranice</a> od 15. prosinca 2011. (<a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>) "Mjerenje brzine i protoka fluida", www.fer.unizg.hr, 2011.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="http://www.unidu.hr/datoteke/majelic/ABP-6.pdf">[3]</a>  <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304225901/http://www.unidu.hr/datoteke/majelic/ABP-6.pdf">Arhivirana inačica izvorne stranice</a> od 4. ožujka 2016. (<a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>) "Mjerenje protoka", www.unidu.hr, 2011.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="http://www.vuka.hr/fileadmin/_temp_/PiH_skripta.pdf">[4]</a>  <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130718022643/http://www.vuka.hr/fileadmin/_temp_/PiH_skripta.pdf">Arhivirana inačica izvorne stranice</a> od 18. srpnja 2013. (<a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>) "Pneumatika i hidraulika" Radoslav Korbar, Veleučilište u Karlovcu, www.vuka.hr, 2007.</span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Dobavljeno iz "<a dir="ltr" href="https://hr.wikipedia.org/w/index.php?title=Volumni_protok&oldid=6209553">https://hr.wikipedia.org/w/index.php?title=Volumni_protok&oldid=6209553</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Posebno:Kategorije" title="Posebno:Kategorije">Kategorije</a>: <ul><li><a href="/wiki/Kategorija:Mehanika_fluida" title="Kategorija:Mehanika fluida">Mehanika fluida</a></li><li><a href="/wiki/Kategorija:Hidraulika" title="Kategorija:Hidraulika">Hidraulika</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Ova stranica posljednji je put uređivana 30. prosinca 2021. u 02:22.</li> <li id="footer-info-copyright">Tekst je dostupan pod licencijom <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.hr">Creative Commons: Imenuj autora/Dijeli pod istim uvjetima</a>; mogu se primjenjivati i dodatni uvjeti. 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