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<span>Turbine physics and derivation</span> </div> </a> <button aria-controls="toc-Turbine_physics_and_derivation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Turbine physics and derivation subsection</span> </button> <ul id="toc-Turbine_physics_and_derivation-sublist" class="vector-toc-list"> <li id="toc-Energy_and_initial_jet_velocity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Energy_and_initial_jet_velocity"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Energy and initial jet velocity</span> </div> </a> <ul id="toc-Energy_and_initial_jet_velocity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Final_jet_velocity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Final_jet_velocity"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Final jet velocity</span> </div> </a> <ul id="toc-Final_jet_velocity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Optimal_wheel_speed" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Optimal_wheel_speed"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Optimal wheel speed</span> </div> </a> <ul id="toc-Optimal_wheel_speed-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Torque" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Torque"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Torque</span> </div> </a> <ul id="toc-Torque-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Power" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Power"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Power</span> </div> </a> <ul id="toc-Power-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Efficiency" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Efficiency"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Efficiency</span> </div> </a> <ul id="toc-Efficiency-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-System_components" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#System_components"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>System components</span> </div> </a> <ul id="toc-System_components-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown 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="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Pelton wheel</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 35 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-35" 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">35 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AC%D9%84%D8%A9_%D8%A8%D9%8A%D9%84%D8%AA%D9%88%D9%86" title="عجلة بيلتون – Arabic" lang="ar" hreflang="ar" data-title="عجلة بيلتون" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%B5%D0%BB%D1%82%D0%BE%D0%BD%D0%BE%D0%B2%D0%B0_%D1%82%D1%83%D1%80%D0%B1%D0%B8%D0%BD%D0%B0" title="Пелтонова турбина – Bulgarian" lang="bg" hreflang="bg" data-title="Пелтонова турбина" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Turbina_Pelton" title="Turbina Pelton – Catalan" lang="ca" hreflang="ca" data-title="Turbina Pelton" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Peltonova_turb%C3%ADna" title="Peltonova turbína – Czech" lang="cs" hreflang="cs" data-title="Peltonova turbína" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Pelton-Turbine" title="Pelton-Turbine – German" lang="de" hreflang="de" data-title="Pelton-Turbine" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Peltoni_turbiin" title="Peltoni turbiin – Estonian" lang="et" hreflang="et" data-title="Peltoni turbiin" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Turbina_Pelton" title="Turbina Pelton – Spanish" lang="es" hreflang="es" data-title="Turbina Pelton" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Pelton-turbino" title="Pelton-turbino – Esperanto" lang="eo" hreflang="eo" data-title="Pelton-turbino" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Pelton_turbina" title="Pelton turbina – Basque" lang="eu" hreflang="eu" data-title="Pelton turbina" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D9%88%D8%B1%D8%A8%DB%8C%D9%86_%D9%BE%D9%84%D8%AA%D9%88%D9%86" title="توربین پلتون – Persian" lang="fa" hreflang="fa" data-title="توربین پلتون" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Turbine_Pelton" title="Turbine Pelton – French" lang="fr" hreflang="fr" data-title="Turbine Pelton" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8E%A0%ED%86%A4%EC%88%98%EC%B0%A8" title="펠톤수차 – Korean" lang="ko" hreflang="ko" data-title="펠톤수차" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%87%D5%A5%D6%80%D5%A5%D6%83%D5%A1%D5%BE%D5%B8%D6%80_%D5%B0%D5%AB%D5%A4%D6%80%D5%B8%D5%BF%D5%B8%D6%82%D6%80%D5%A2%D5%AB%D5%B6" title="Շերեփավոր հիդրոտուրբին – Armenian" lang="hy" hreflang="hy" data-title="Շերեփավոր հիդրոտուրբին" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%87%E0%A4%B2%E0%A5%8D%E0%A4%9F%E0%A4%A8_%E0%A4%9F%E0%A4%B0%E0%A4%AC%E0%A4%BE%E0%A4%87%E0%A4%A8" title="पेल्टन टरबाइन – Hindi" lang="hi" hreflang="hi" data-title="पेल्टन टरबाइन" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Peltonova_turbina" title="Peltonova turbina – Croatian" lang="hr" hreflang="hr" data-title="Peltonova turbina" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Turbina_Pelton" title="Turbina Pelton – Italian" lang="it" hreflang="it" data-title="Turbina Pelton" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Pelton-turbina" title="Pelton-turbina – Hungarian" lang="hu" hreflang="hu" data-title="Pelton-turbina" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%B5%D0%BB%D1%82%D0%BE%D0%BD%D0%BE%D0%B2%D0%B0_%D1%82%D1%83%D1%80%D0%B1%D0%B8%D0%BD%D0%B0" title="Пелтонова турбина – Macedonian" lang="mk" hreflang="mk" data-title="Пелтонова турбина" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Peltonturbine" title="Peltonturbine – Dutch" lang="nl" hreflang="nl" data-title="Peltonturbine" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9A%E3%83%AB%E3%83%88%E3%83%B3%E6%B0%B4%E8%BB%8A" title="ペルトン水車 – Japanese" lang="ja" hreflang="ja" data-title="ペルトン水車" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://no.wikipedia.org/wiki/Peltonturbin" title="Peltonturbin – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Peltonturbin" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Peltonturbin" title="Peltonturbin – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Peltonturbin" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A9%88%E0%A8%B2%E0%A8%9F%E0%A8%A8_%E0%A8%9A%E0%A9%B1%E0%A8%95%E0%A8%B0_%E0%A8%9F%E0%A8%B0%E0%A8%AC%E0%A8%BE%E0%A8%88%E0%A8%A8" title="ਪੈਲਟਨ ਚੱਕਰ ਟਰਬਾਈਨ – Punjabi" lang="pa" hreflang="pa" data-title="ਪੈਲਟਨ ਚੱਕਰ ਟਰਬਾਈਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Turbina_Peltona" title="Turbina Peltona – Polish" lang="pl" hreflang="pl" data-title="Turbina Peltona" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Turbina_Pelton" title="Turbina Pelton – Portuguese" lang="pt" hreflang="pt" data-title="Turbina Pelton" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Turbin%C4%83_Pelton" title="Turbină Pelton – Romanian" lang="ro" hreflang="ro" data-title="Turbină Pelton" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9F%D0%B5%D0%BB%D1%82%D0%BE%D0%BD%D0%BE%D0%B2%D0%B0_%D1%82%D1%83%D1%80%D0%B1%D0%B8%D0%BD%D0%B0" title="Пелтонова турбина – Rusyn" lang="rue" hreflang="rue" data-title="Пелтонова турбина" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D1%88%D0%BE%D0%B2%D0%B0%D1%8F_%D1%82%D1%83%D1%80%D0%B1%D0%B8%D0%BD%D0%B0" title="Ковшовая турбина – Russian" lang="ru" hreflang="ru" data-title="Ковшовая турбина" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Pelton_wheel" title="Pelton wheel – Simple English" lang="en-simple" hreflang="en-simple" data-title="Pelton wheel" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Peltonova_turb%C3%ADna" title="Peltonova turbína – Slovak" lang="sk" hreflang="sk" data-title="Peltonova turbína" data-language-autonym="Slovenčina" data-language-local-name="Slovak" 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/Peltonova_turbina" title="Peltonova turbina – Slovenian" lang="sl" hreflang="sl" data-title="Peltonova turbina" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Pelton-turbiini" title="Pelton-turbiini – Finnish" lang="fi" hreflang="fi" data-title="Pelton-turbiini" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Peltonturbin" title="Peltonturbin – Swedish" lang="sv" hreflang="sv" data-title="Peltonturbin" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/B%C3%A1nh_xe_Pelton" title="Bánh xe Pelton – Vietnamese" lang="vi" hreflang="vi" data-title="Bánh xe Pelton" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" 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/%E4%BD%A9%E7%88%BE%E9%A0%93%E5%BC%8F%E6%B0%B4%E8%BC%AA%E6%A9%9F" title="佩爾頓式水輪機 – Chinese" lang="zh" hreflang="zh" data-title="佩爾頓式水輪機" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q745900#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a 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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Type of turbine</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Peltonturbine-1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Peltonturbine-1.jpg/220px-Peltonturbine-1.jpg" decoding="async" width="220" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Peltonturbine-1.jpg/330px-Peltonturbine-1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Peltonturbine-1.jpg/440px-Peltonturbine-1.jpg 2x" data-file-width="587" data-file-height="800" /></a><figcaption>Old Pelton wheel from <a href="/wiki/Walchensee_Hydroelectric_Power_Station" title="Walchensee Hydroelectric Power Station">Walchensee Hydroelectric Power Station</a>, Germany.</figcaption></figure> <p>The <b>Pelton wheel</b> or <b>Pelton Turbine</b> is an <a href="/wiki/Impulse_(physics)" title="Impulse (physics)">impulse</a>-type <a href="/wiki/Water_turbine" title="Water turbine">water turbine</a> invented by American inventor <a href="/wiki/Lester_Allan_Pelton" title="Lester Allan Pelton">Lester Allan Pelton</a> in the 1870s.<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> The Pelton wheel extracts <a href="/wiki/Energy" title="Energy">energy</a> from the impulse of moving water, as opposed to water's dead weight like the traditional overshot <a href="/wiki/Water_wheel" title="Water wheel">water wheel</a>. Many earlier variations of impulse turbines existed, but they were less <a href="/wiki/Energy_conversion_efficiency" title="Energy conversion efficiency">efficient</a> than Pelton's design. Water leaving those wheels typically still had high speed, carrying away much of the dynamic energy brought to the wheels. Pelton's paddle geometry was designed so that when the rim ran at half the speed of the water jet, the water left the wheel with very little speed; thus his design extracted almost all of the water's impulse energy—which made for a very efficient turbine. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Pelton_wheel_(patent).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pelton_wheel_%28patent%29.png/220px-Pelton_wheel_%28patent%29.png" decoding="async" width="220" height="264" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pelton_wheel_%28patent%29.png/330px-Pelton_wheel_%28patent%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pelton_wheel_%28patent%29.png/440px-Pelton_wheel_%28patent%29.png 2x" data-file-width="1685" data-file-height="2022" /></a><figcaption>Figure from <a href="/wiki/Lester_Allan_Pelton" title="Lester Allan Pelton">Lester Allan Pelton</a>'s original October 1880 patent</figcaption></figure> <p>Lester Allan Pelton was born in <a href="/wiki/Vermillion,_Ohio" class="mw-redirect" title="Vermillion, Ohio">Vermillion, Ohio</a> in 1829. In 1850, he traveled overland to take part in the <a href="/wiki/California_Gold_Rush" class="mw-redirect" title="California Gold Rush">California Gold Rush</a>. Pelton worked by selling fish he caught in the <a href="/wiki/Sacramento_River" title="Sacramento River">Sacramento River</a>.<sup id="cite_ref-rpl_3-0" class="reference"><a href="#cite_note-rpl-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In 1860, he moved to <a href="/wiki/Camptonville" class="mw-redirect" title="Camptonville">Camptonville</a>, a center of <a href="/wiki/Placer_mining" title="Placer mining">placer mining</a> activity. At this time many mining operations were powered by <a href="/wiki/Steam_engine" title="Steam engine">steam engines</a> which consumed vast amounts of wood as their fuel. Some water wheels were used in the larger rivers, but they were ineffective in the smaller streams that were found near the mines. Pelton worked on a design for a water wheel that would work with the relatively small flow found in these streams.<sup id="cite_ref-asme_4-0" class="reference"><a href="#cite_note-asme-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>By the mid 1870s, Pelton had developed a wooden prototype of his new wheel. In 1876, he approached the <a href="/wiki/Miners_Foundry" title="Miners Foundry">Miners Foundry</a> in <a href="/wiki/Nevada_City,_California" title="Nevada City, California">Nevada City, California</a> to build the first commercial models in iron. The first Pelton Wheel was installed at the Mayflower Mine in Nevada City in 1878.<sup id="cite_ref-asme_4-1" class="reference"><a href="#cite_note-asme-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The efficiency advantages of Pelton's invention were quickly recognized and his product was soon in high demand. He patented his invention on 26 October 1880.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> By the mid-1880s, the Miners Foundry could not meet the demand, and in 1888, Pelton sold the rights to his name and the patents to his invention to the Pelton Water Wheel Company in San Francisco. The company established a factory at 121/123 Main Street in <a href="/wiki/San_Francisco" title="San Francisco">San Francisco</a>.<sup id="cite_ref-sfpd_6-0" class="reference"><a href="#cite_note-sfpd-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>The Pelton Water Wheel Company manufactured a large number of Pelton Wheels in San Francisco which were shipped around the world. In 1892, the Company added a branch on the east coast at 143 Liberty Street in <a href="/wiki/New_York_City" title="New York City">New York City</a>. By 1900, over 11,000 turbines were in use. In 1914, the company moved manufacturing to new, larger premises at 612 Alabama Street in San Francisco. In 1956, the company was acquired by the <a href="/wiki/Baldwin_Locomotive_Works" title="Baldwin Locomotive Works">Baldwin-Lima-Hamilton Company</a>, which company ended manufacture of Pelton Wheels.<sup id="cite_ref-sfpd_6-1" class="reference"><a href="#cite_note-sfpd-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>In New Zealand, <a href="/wiki/A_%26_G_Price" title="A & G Price">A & G Price</a> in <a href="/wiki/Thames,_New_Zealand" title="Thames, New Zealand">Thames, New Zealand</a> produced Pelton waterwheels for the local market. One of these is on outdoor display at the Thames Goldmine Experience. </p> <div class="mw-heading mw-heading2"><h2 id="Design">Design</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=2" title="Edit section: Design"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nozzles direct forceful, high-speed streams of water against a series of spoon-shaped buckets, also known as impulse blades, which are mounted around the outer rim of a drive wheel (also called a <i>runner</i>). As the water jet hits the blades, the direction of water velocity is changed to follow the contours of the blades. The impulse energy of the water jet exerts torque on the bucket-and-wheel system, spinning the wheel; the water jet does a "u-turn" and exits at the outer sides of the bucket, decelerated to a low velocity. In the process, the water jet's momentum is transferred to the wheel and hence to a turbine. Thus, "<a href="/wiki/Impulse_(physics)" title="Impulse (physics)">impulse</a>" energy does <a href="/wiki/Work_(physics)" title="Work (physics)">work</a> on the turbine. </p><p>Maximum power and efficiency are achieved when the velocity of the water jet is twice the velocity of the rotating buckets, which, assuming that water jet collides elastically with the bucket, would mean the water leaves the bucket with zero velocity, thus imparting all kinetic energy to the wheel. In practice, a very small percentage of the water jet's original <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> will remain in the water, which causes the bucket to be emptied at the same rate it is filled, and thereby allows the high-pressure input flow to continue uninterrupted and without waste of energy. </p><p>Typically two buckets are mounted side-by-side on the wheel, with the water jet split into two equal streams; this balances the side-load forces on the wheel and helps to ensure smooth, efficient transfer of momentum from the water jet to the turbine wheel. </p><p>Because water is nearly incompressible, almost all of the available energy is extracted in the first stage of the hydraulic turbine. "Therefore, Pelton wheels have only one turbine stage, unlike gas turbines that operate with compressible fluid."<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=3" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Walchenseewerk_Pelton_120.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Walchenseewerk_Pelton_120.jpg/220px-Walchenseewerk_Pelton_120.jpg" decoding="async" width="220" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Walchenseewerk_Pelton_120.jpg/330px-Walchenseewerk_Pelton_120.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Walchenseewerk_Pelton_120.jpg/440px-Walchenseewerk_Pelton_120.jpg 2x" data-file-width="1434" data-file-height="1248" /></a><figcaption>Assembly of a Pelton wheel at <a href="/wiki/Walchensee_Hydroelectric_Power_Station" title="Walchensee Hydroelectric Power Station">Walchensee Hydroelectric Power Station</a>, Germany.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Pelton-wheel.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/a/a8/Pelton-wheel.jpg/220px-Pelton-wheel.jpg" decoding="async" width="220" height="232" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/a/a8/Pelton-wheel.jpg/330px-Pelton-wheel.jpg 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/a/a8/Pelton-wheel.jpg/440px-Pelton-wheel.jpg 2x" data-file-width="600" data-file-height="633" /></a><figcaption>Bucket detail on a small turbine.</figcaption></figure> <p>Pelton wheels are the preferred turbine for hydro-power where the available water source has relatively high <a href="/wiki/Hydraulic_head" title="Hydraulic head">hydraulic head</a> at low flow rates. Pelton wheels are made in all sizes. There exist multi-ton Pelton wheels mounted on vertical oil pad <a href="/wiki/Bearing_(mechanical)" title="Bearing (mechanical)">bearings</a> in <a href="/wiki/Hydroelectricity" title="Hydroelectricity">hydroelectric plants</a>. The largest units – the <a href="/wiki/Bieudron_Hydroelectric_Power_Station" title="Bieudron Hydroelectric Power Station">Bieudron Hydroelectric Power Station</a> at the <a href="/wiki/Grande_Dixence_Dam" title="Grande Dixence Dam">Grande Dixence Dam</a> complex in Switzerland – are over 400 <a href="/wiki/Watt" title="Watt">megawatts</a>.<sup id="cite_ref-GD_8-0" class="reference"><a href="#cite_note-GD-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>The smallest Pelton wheels are only a few inches across, and can be used to tap power from mountain streams having flows of a few gallons per minute. Some of these systems use household <a href="/wiki/Plumbing" title="Plumbing">plumbing</a> fixtures for water delivery. These small units are recommended for use with 30 metres (100 ft) or more of head, in order to generate significant power levels. Depending on water flow and design, Pelton wheels operate best with heads from 15–1,800 metres (50–5,910 ft), although there is no theoretical limit.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2024)">citation needed</span></a></i>]</sup> Such "peltric sets", consisting of a Pelton wheel, an induction generator and a control mechanism, are used in Nepal.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Design_rules">Design rules</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=4" title="Edit section: Design rules"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:S_vs_pelton_schnitt_1_zoom.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/S_vs_pelton_schnitt_1_zoom.png/220px-S_vs_pelton_schnitt_1_zoom.png" decoding="async" width="220" height="186" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/S_vs_pelton_schnitt_1_zoom.png/330px-S_vs_pelton_schnitt_1_zoom.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/S_vs_pelton_schnitt_1_zoom.png/440px-S_vs_pelton_schnitt_1_zoom.png 2x" data-file-width="500" data-file-height="423" /></a><figcaption>Sectional view of a Pelton turbine installation.</figcaption></figure> <p>The <a href="/wiki/Specific_speed" title="Specific speed">specific speed</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 \eta _{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta _{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6755933b9e4f2b35cd6822c6baa536f923831ae8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.159ex; height:2.176ex;" alt="{\displaystyle \eta _{s}}"></span> parameter is independent of a particular turbine's size. </p><p>Compared to other turbine designs, the relatively low <a href="/wiki/Specific_speed" title="Specific speed">specific speed</a> of the Pelton wheel implies that the geometry is inherently a "<a href="/wiki/Low_gear" class="mw-redirect" title="Low gear">low gear</a>" design. Thus it is most suitable to being fed by a hydro source with a low ratio of flow to pressure (meaning relatively low flow and/or relatively high pressure). </p><p>The specific speed is the main criterion for matching a specific hydro-electric site with the optimal turbine type. It also allows a new turbine design to be scaled from an existing design of known performance. </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 \eta _{s}=n{\sqrt {P}}/{\sqrt {\rho }}(gH)^{5/4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>P</mi> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>ρ</mi> </msqrt> </mrow> <mo stretchy="false">(</mo> <mi>g</mi> <mi>H</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta _{s}=n{\sqrt {P}}/{\sqrt {\rho }}(gH)^{5/4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b123c36db28228550b5954722f862341ee3f7dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:22.321ex; height:3.676ex;" alt="{\displaystyle \eta _{s}=n{\sqrt {P}}/{\sqrt {\rho }}(gH)^{5/4}}"></span> (dimensionless parameter), <sup id="cite_ref-Sayers1990_10-0" class="reference"><a href="#cite_note-Sayers1990-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>where: </p> <ul><li><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> = Frequency of rotation (rpm)</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> = Power (W)</li> <li><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 H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle H}"></span> = Water head (m)</li> <li><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> = Density (kg/m<sup>3</sup>)</li></ul> <p>The formula implies that the Pelton turbine is <i>geared</i> most suitably for applications with relatively high hydraulic head <i>H</i>, due to the 5/4 exponent being greater than unity, and given the characteristically low specific speed of the Pelton.<sup id="cite_ref-jcalvert_11-0" class="reference"><a href="#cite_note-jcalvert-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Turbine_physics_and_derivation">Turbine physics and derivation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=5" title="Edit section: Turbine physics and derivation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Energy_and_initial_jet_velocity">Energy and initial jet velocity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=6" title="Edit section: Energy and initial jet velocity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the ideal (<a href="/wiki/Friction" title="Friction">frictionless</a>) case, all of the hydraulic <a href="/wiki/Potential_energy" title="Potential energy">potential energy</a> (<i>E</i><sub><i>p</i></sub> = <i>mgh</i>) is converted into <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> (<i>E</i><sub><i>k</i></sub> = <i>mv</i><sup>2</sup>/2) (see <a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a>). Equating these two equations and solving for the initial jet velocity (<i>V</i><sub><i>i</i></sub>) indicates that the theoretical (maximum) jet velocity is <i>V</i><sub><i>i</i></sub> = <span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2<i>gh</i></span></span>. For simplicity, assume that all of the velocity vectors are parallel to each other. Defining the velocity of the wheel runner as: (<i>u</i>), then as the jet approaches the runner, the initial jet velocity relative to the runner is: (<i>V</i><sub><i>i</i></sub> − <i>u</i>).<sup id="cite_ref-jcalvert_11-1" class="reference"><a href="#cite_note-jcalvert-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The initial velocity of jet is <i>V</i><sub><i>i</i></sub> </p> <div class="mw-heading mw-heading3"><h3 id="Final_jet_velocity">Final jet velocity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=7" title="Edit section: Final jet velocity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Assuming that the jet velocity is higher than the runner velocity, if the water is not to become backed-up in runner, then due to conservation of mass, the mass entering the runner must equal the mass leaving the runner. The fluid is assumed to be incompressible (an accurate assumption for most liquids). Also, it is assumed that the cross-sectional area of the jet is constant. The jet <i><a href="/wiki/Speed" title="Speed">speed</a></i> remains constant relative to the runner. So as the jet recedes from the runner, the jet velocity relative to the runner is: − (<i>V</i><sub><i>i</i></sub> − <i>u</i>) = −<i>V</i><sub><i>i</i></sub> + <i>u</i>. In the standard reference frame (relative to the earth), the final velocity is then: <i>V</i><sub><i>f</i></sub> = (−<i>V</i><sub><i>i</i></sub> + u) + <i>u</i> = −<i>V</i><sub><i>i</i></sub> + 2<i>u</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Optimal_wheel_speed">Optimal wheel speed</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=8" title="Edit section: Optimal wheel speed"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The ideal runner speed will cause all of the kinetic energy in the jet to be transferred to the wheel. In this case the final jet velocity must be zero. If −<i>V</i><sub><i>i</i></sub> + 2<i>u</i> = 0, then the optimal runner speed will be <i>u</i> = <i>V</i><sub><i>i</i></sub> /2, or half the initial jet velocity. </p> <div class="mw-heading mw-heading3"><h3 id="Torque">Torque</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=9" title="Edit section: Torque"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>By <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's second and third laws</a>, the force <i>F</i> imposed by the jet on the runner is equal but opposite to the rate of momentum change of the fluid, so </p> <dl><dd><i>F</i> = −<i>m</i>(<i>V</i><sub>f</sub> − <i>V</i><sub>i</sub>)/<i>t</i> = −<i>ρQ</i>[(−<i>V</i><sub>i</sub> + 2<i>u</i>) − <i>V</i><sub>i</sub>] = −<i>ρQ</i>(−2<i>V</i><sub>i</sub> + 2<i>u</i>) = 2<i>ρQ</i>(<i>V</i><sub>i</sub> − <i>u</i>),</dd></dl> <p>where <i>ρ</i> is the density, and <i>Q</i> is the volume rate of flow of fluid. If <i>D</i> is the wheel diameter, the torque on the runner is. </p> <dl><dd><i>T</i> = <i>F</i>(<i>D</i>/2) = <i>ρQD</i>(<i>V</i><sub>i</sub> − <i>u</i>).</dd></dl> <p>The torque is maximal when the runner is stopped (i.e. when <i>u</i> = 0, <i>T</i> = <i>ρQDV</i><sub>i</sub>). When the speed of the runner is equal to the initial jet velocity, the torque is zero (i.e., when <i>u</i> = <i>V</i><sub>i</sub>, then <i>T</i> = 0). On a plot of torque versus runner speed, the torque curve is straight between these two points: (0, <i>pQDV</i><sub>i</sub>) and (<i>V</i><sub>i</sub>, 0).<sup id="cite_ref-jcalvert_11-2" class="reference"><a href="#cite_note-jcalvert-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Nozzle efficiency is the ratio of the jet power to the waterpower at the base of the nozzle. </p> <div class="mw-heading mw-heading3"><h3 id="Power">Power</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=10" title="Edit section: Power"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The power <i>P</i> = <i>Fu</i> = <i>Tω</i>, where <i>ω</i> is the angular velocity of the wheel. Substituting for <i>F</i>, we have <i>P</i> = 2<i>ρQ</i>(<i>V</i><sub><i>i</i></sub> − <i>u</i>)<i>u</i>. To find the runner speed at maximum power, take the derivative of <i>P</i> with respect to <i>u</i> and set it equal to zero, [<i>dP</i>/<i>du</i> = 2<i>ρQ</i>(<i>V</i><sub><i>i</i></sub> − 2<i>u</i>)]. Maximum power occurs when <i>u</i> = <i>V</i><sub><i>i</i></sub> /2. <i>P</i><sub>max</sub> = <i>ρQV</i><sub><i>i</i></sub><sup>2</sup>/2. Substituting the initial jet power <i>V</i><sub><i>i</i></sub> = <span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2<i>gh</i></span></span>, this simplifies to <i>P</i><sub>max</sub> = <i>ρghQ</i>. This quantity exactly equals the kinetic power of the jet, so in this ideal case, the efficiency is 100%, since all the energy in the jet is converted to shaft output.<sup id="cite_ref-jcalvert_11-3" class="reference"><a href="#cite_note-jcalvert-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Efficiency">Efficiency</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=11" title="Edit section: Efficiency"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A wheel power divided by the initial jet power, is the turbine efficiency, <i>η</i> = 4<i>u</i>(<i>V</i><sub><i>i</i></sub> − <i>u</i>)/<i>V</i><sub><i>i</i></sub><sup>2</sup>. It is zero for <i>u</i> = 0 and for <i>u</i> = <i>V</i><sub><i>i</i></sub>. As the equations indicate, when a real Pelton wheel is working close to maximum efficiency, the fluid flows off the wheel with very little residual velocity.<sup id="cite_ref-jcalvert_11-4" class="reference"><a href="#cite_note-jcalvert-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> In theory, the <a href="/wiki/Efficient_energy_use" title="Efficient energy use">energy efficiency</a> varies only with the efficiency of the nozzle and wheel, and does not vary with hydraulic head.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The term "efficiency" can refer to: Hydraulic, Mechanical, Volumetric, Wheel, or overall efficiency. </p> <div class="mw-heading mw-heading2"><h2 id="System_components">System components</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=12" title="Edit section: System components"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The conduit bringing high-pressure water to the impulse wheel is called the <a href="/wiki/Penstock" title="Penstock">penstock</a>. Originally the penstock was the name of the valve, but the term has been extended to include all of the fluid supply hydraulics. Penstock is now used as a general term for a water passage and control that is under pressure, whether it supplies an impulse turbine or not.<sup id="cite_ref-jcalvert_11-5" class="reference"><a href="#cite_note-jcalvert-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=13" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Peltric_set" class="mw-redirect" title="Peltric set">Peltric set</a></li> <li><a href="/wiki/Centrifugal_pump" title="Centrifugal pump">Centrifugal pump</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://nla.gov.au/nla.news-article200979544">"COW THAT ASSISTED SCIENCE"</a>. <i><a href="/wiki/The_South_Eastern_Times" class="mw-redirect" title="The South Eastern Times">The South Eastern Times</a></i>. 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Tasmania, Australia. 22 August 1885. p. 3<span class="reference-accessdate">. Retrieved <span class="nowrap">10 March</span> 2017</span> – via National Library of Australia.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Launceston+Examiner&rft.atitle=MINING+INTELLIGENCE.&rft.volume=XLV&rft.issue=210&rft.pages=3&rft.date=1885-08-22&rft_id=http%3A%2F%2Fnla.gov.au%2Fnla.news-article38303792&rfr_id=info%3Asid%2Fen.wikipedia.org%3APelton+wheel" class="Z3988"></span></span> </li> <li id="cite_note-rpl-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-rpl_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLescohier2011" class="citation book cs1">Lescohier, Roger P. (2011). <i>Lester Pelton and the Pelton Water Wheel</i>. Nevada County Historical Society. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-915641-15-4" title="Special:BookSources/978-0-915641-15-4"><bdi>978-0-915641-15-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lester+Pelton+and+the+Pelton+Water+Wheel&rft.pub=Nevada+County+Historical+Society&rft.date=2011&rft.isbn=978-0-915641-15-4&rft.aulast=Lescohier&rft.aufirst=Roger+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APelton+wheel" class="Z3988"></span></span> </li> <li id="cite_note-asme-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-asme_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-asme_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.asme.org/engineering-topics/articles/energy/lester-allan-pelton">"Lester Allan Pelton"</a>. 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Pelton, "Water Wheel", issued Oct. 26,1880</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=233692&rft.cc=US&rft.title=Water+Wheel&rft.inventor=L.+A.+Pelton&rft.date=Oct. 26,1880"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-sfpd-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-sfpd_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-sfpd_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://commissions.sfplanning.org/hpcpackets/2010.0485Uc2.pdf">"Showplace Square Historic Resource Survey Findings"</a> <span class="cs1-format">(PDF)</span>. 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Berlin, Heidelberg: Springer Berlin Heidelberg. p. 86. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-20709-9">10.1007/978-3-642-20709-9</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-20708-2" title="Special:BookSources/978-3-642-20708-2"><bdi>978-3-642-20708-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Hydro+Energy+Systems&rft.place=Berlin%2C+Heidelberg&rft.series=Green+Energy+and+Technology&rft.pages=86&rft.pub=Springer+Berlin+Heidelberg&rft.date=2011&rft_id=info%3Adoi%2F10.1007%2F978-3-642-20709-9&rft.isbn=978-3-642-20708-2&rft.aulast=Wagner&rft.aufirst=Hermann-Josef&rft.au=Mathur%2C+Jyotirmay&rft_id=http%3A%2F%2Flink.springer.com%2F10.1007%2F978-3-642-20709-9&rfr_id=info%3Asid%2Fen.wikipedia.org%3APelton+wheel" class="Z3988"></span></span> </li> <li id="cite_note-GD-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-GD_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.grande-dixence.ch/en#bieudron">"Renewable Energy in the Heart of the Alps"</a>. <i>Grande Dixence</i><span class="reference-accessdate">. Retrieved <span class="nowrap">13 August</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Grande+Dixence&rft.atitle=Renewable+Energy+in+the+Heart+of+the+Alps&rft_id=http%3A%2F%2Fwww.grande-dixence.ch%2Fen%23bieudron&rfr_id=info%3Asid%2Fen.wikipedia.org%3APelton+wheel" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.aepc.gov.np/pages/minimicro-hydro">"Mini/Micro Hydro"</a>. <i>www.aepc.gov.np</i><span class="reference-accessdate">. Retrieved <span class="nowrap">24 October</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.aepc.gov.np&rft.atitle=Mini%2FMicro+Hydro&rft_id=https%3A%2F%2Fwww.aepc.gov.np%2Fpages%2Fminimicro-hydro&rfr_id=info%3Asid%2Fen.wikipedia.org%3APelton+wheel" class="Z3988"></span></span> </li> <li id="cite_note-Sayers1990-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Sayers1990_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSayers1990" class="citation book cs1">Sayers, A. T. (1990). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=YNpSAAAAMAAJ"><i>Hydraulic and Compressible Flow Turbomachines</i></a>. McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-707219-3" title="Special:BookSources/978-0-07-707219-3"><bdi>978-0-07-707219-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hydraulic+and+Compressible+Flow+Turbomachines&rft.pub=McGraw-Hill&rft.date=1990&rft.isbn=978-0-07-707219-3&rft.aulast=Sayers&rft.aufirst=A.+T.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DYNpSAAAAMAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APelton+wheel" class="Z3988"></span></span> </li> <li id="cite_note-jcalvert-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-jcalvert_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-jcalvert_11-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-jcalvert_11-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-jcalvert_11-3"><sup><i><b>d</b></i></sup></a> <a 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class="external text" href="http://people.rit.edu/rfaite/courses/tflab/Cussons/pelton/pelton.htm">Pelton Wheel Water Turbine</a>, Ron Amberger's Pages</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pelton_wheel&action=edit&section=15" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 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