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<div class="vector-toc-text"> <span class="vector-toc-numb">5</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">6</span> <span>References</span> </div> </a> <ul id="toc-References-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" 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src="//upload.wikimedia.org/wikipedia/commons/2/2e/Hydraulic_vena_contracta_275px.png" decoding="async" width="275" height="206" class="mw-file-element" data-file-width="275" data-file-height="206" /></a><figcaption>Vena contracta</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Flow_separation_in_a_river.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Flow_separation_in_a_river.JPG/220px-Flow_separation_in_a_river.JPG" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Flow_separation_in_a_river.JPG/330px-Flow_separation_in_a_river.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Flow_separation_in_a_river.JPG/440px-Flow_separation_in_a_river.JPG 2x" data-file-width="3648" data-file-height="2736" /></a><figcaption>Just beyond the <a href="/wiki/Swartswood_Lake" title="Swartswood Lake">Swartswood Lake</a> Dam, the river is forced to narrow by a concrete bridge support. Flow separation is evident at the sharp bend, just above the vena contracta</figcaption></figure> <p><b>Vena contracta</b> is the point in a fluid stream where the diameter of the stream is the least, and the fluid velocity is at its maximum, such as in the case of a stream issuing out of a <a href="/wiki/Nozzle" title="Nozzle">nozzle</a> (<a href="https://en.wiktionary.org/wiki/orifice" class="extiw" title="wikt:orifice">orifice</a>). (<a href="/wiki/Evangelista_Torricelli" title="Evangelista Torricelli">Evangelista Torricelli</a>, 1643). It is a place where the cross section area is minimal. The maximum contraction takes place at a section slightly downstream of the orifice, where the jet is more or less horizontal. </p><p>The effect is also observed in flow from a tank into a pipe, or a sudden contraction in pipe diameter. Streamlines will converge just downstream of the diameter change, and a region of <a href="/wiki/Separated_flow" class="mw-redirect" title="Separated flow">separated flow</a> occurs at the sharp corner of the diameter change and extends past the vena contracta. </p><p>The formation of the vena contracta can be seen in the <a href="/wiki/Flow_measurement#Venturi_meter" title="Flow measurement">venturimeter</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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Explanation">Explanation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vena_contracta&action=edit&section=1" title="Edit section: Explanation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The reason for this phenomenon is that fluid streamlines cannot abruptly change direction. In the case of both the free jet and the sudden pipe diameter change, the streamlines are unable to closely follow the sharp angle in the pipe/tank wall. The converging streamlines follow a smooth path, which results in the narrowing of the jet (or primary pipe flow). </p> <div class="mw-heading mw-heading2"><h2 id="Echocardiography">Echocardiography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vena_contracta&action=edit&section=2" title="Edit section: Echocardiography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Measurement of the vena contracta is useful in <a href="/wiki/Echocardiography" title="Echocardiography">echocardiography</a>, where it describes the smallest area of the blood flow jet as it exits a heart valve. This corresponds to the <a href="/wiki/Artificial_heart_valve#Fluid_mechanics" title="Artificial heart valve">effective orifice area (EOA)</a> calculated for heart valves using the continuity equation. </p> <div class="mw-heading mw-heading2"><h2 id="Shotguns">Shotguns</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vena_contracta&action=edit&section=3" title="Edit section: Shotguns"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Vena Contracta was a term used by several English <a href="/wiki/Shotgun" title="Shotgun">shotgun</a> builders of the 19th and 20th Century. The <a href="/wiki/Gun_barrel" title="Gun barrel">gun barrels</a> of sporting shotguns tapered very heavily from the breech to the muzzle. Thus a gun with a 12 bore breech would have a 20 bore muzzle. The idea was to retain the advantages of a heavy-hitting large bore shotgun while retaining the lesser recoil and easy maneuverability of a small bore. Several leading firms built this type of gun but it proved unpopular and most were returned to the manufacturers for large bore barrels. To most shooters perhaps the idea of placing a 12 bore cartridge into a 20 bore barrel was too "explosive". Complete functioning examples are now rare, though they are still not highly sought after.<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 2018)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Coefficient_of_contraction">Coefficient of contraction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vena_contracta&action=edit&section=4" title="Edit section: Coefficient of contraction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The coefficient of contraction is defined as the ratio between the area of the jet at the vena contracta and the area of the orifice. </p><p>C<sub>c</sub> = Area at vena contracta/Area of orifice. </p><p>The typical value may be taken as 0.611 for a sharp orifice (concentric with the flow channel).<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> The smaller the value, the greater the effect the vena contracta has. </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=Vena_contracta&action=edit&section=5" title="Edit section: See also"><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 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Vena_contracta" class="extiw" title="commons:Category:Vena contracta">Vena contracta</a></span>.</div></div> </div> <ul><li><a href="/wiki/Borda-Carnot_equation" class="mw-redirect" title="Borda-Carnot equation">Borda-Carnot equation</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=Vena_contracta&action=edit&section=6" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><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 id="CITEREFEligoprojects2018" class="citation web cs1">Eligoprojects (2018-10-30). <a rel="nofollow" class="external text" href="https://eligoprojects.com/what-is-venturimeter-construction-and-working-equation/">"What is Venturimeter ? Construction and Working"</a>. <i>Eligoprojects</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-12-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Eligoprojects&rft.atitle=What+is+Venturimeter+%3F+Construction+and+Working&rft.date=2018-10-30&rft.au=Eligoprojects&rft_id=https%3A%2F%2Feligoprojects.com%2Fwhat-is-venturimeter-construction-and-working-equation%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVena+contracta" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLienhard1984" class="citation journal cs1">Lienhard, J. H. (1984-03-01). <a rel="nofollow" class="external text" href="https://www.uh.edu/engines/VelocityCoefficients.pdf">"Velocity Coefficients For Free Jets From Sharp-Edged Orifices"</a> <span class="cs1-format">(PDF)</span>. <i>Journal of Fluids Engineering</i>. <b>106</b> (1): 13–17. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1984ATJFE.106...13L">1984ATJFE.106...13L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1115%2F1.3242391">10.1115/1.3242391</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0098-2202">0098-2202</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Fluids+Engineering&rft.atitle=Velocity+Coefficients+For+Free+Jets+From+Sharp-Edged+Orifices&rft.volume=106&rft.issue=1&rft.pages=13-17&rft.date=1984-03-01&rft.issn=0098-2202&rft_id=info%3Adoi%2F10.1115%2F1.3242391&rft_id=info%3Abibcode%2F1984ATJFE.106...13L&rft.aulast=Lienhard&rft.aufirst=J.+H.&rft_id=https%3A%2F%2Fwww.uh.edu%2Fengines%2FVelocityCoefficients.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVena+contracta" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKatopodes,_Nikolaos_D.2018" class="citation book cs1">Katopodes, Nikolaos D. (21 August 2018). <i>Free-surface flow. Environmental fluid mechanics</i>. Kidlington, Oxford: Butterworth-Heinemann. p. 512. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-816251-4" title="Special:BookSources/978-0-12-816251-4"><bdi>978-0-12-816251-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1049568159">1049568159</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Free-surface+flow.+Environmental+fluid+mechanics&rft.place=Kidlington%2C+Oxford&rft.pages=512&rft.pub=Butterworth-Heinemann&rft.date=2018-08-21&rft_id=info%3Aoclcnum%2F1049568159&rft.isbn=978-0-12-816251-4&rft.au=Katopodes%2C+Nikolaos+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVena+contracta" class="Z3988"></span></span> </li> </ol></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFalkovich2011" class="citation book cs1">Falkovich, G. (2011). <i>Fluid Mechanics, a short course for physicists</i>. Cambridge University Press. p. 11 and Exercise 1.3. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-00575-4" title="Special:BookSources/978-1-107-00575-4"><bdi>978-1-107-00575-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fluid+Mechanics%2C+a+short+course+for+physicists&rft.pages=11+and+Exercise+1.3&rft.pub=Cambridge+University+Press&rft.date=2011&rft.isbn=978-1-107-00575-4&rft.aulast=Falkovich&rft.aufirst=G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVena+contracta" class="Z3988"></span></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Vena_contracta&oldid=1224766982">https://en.wikipedia.org/w/index.php?title=Vena_contracta&oldid=1224766982</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Fluid_mechanics" title="Category:Fluid mechanics">Fluid mechanics</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_October_2018" title="Category:Articles with unsourced statements from October 2018">Articles with unsourced statements from October 2018</a></li><li><a href="/wiki/Category:Commons_category_link_from_Wikidata" title="Category:Commons category link from Wikidata">Commons category link from Wikidata</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"> This page was last edited on 20 May 2024, at 10:01<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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