{"id":4788,"date":"2025-05-05T15:20:37","date_gmt":"2025-05-05T09:50:37","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=4788"},"modified":"2025-07-22T13:25:44","modified_gmt":"2025-07-22T07:55:44","slug":"bernoullis-equation-and-its-application","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/me\/fluid-mechanics-me\/bernoullis-equation-and-its-application","title":{"rendered":"BERNOULLI\u2019S EQUATION AND ITS APPLICATION"},"content":{"rendered":"<h2 style=\"text-align: justify;\">Assumptions in Bernoulli\u2019s equation:<\/h2>\n<ul style=\"text-align: justify;\">\n<li>fluid is ideal<\/li>\n<li>flow is steady<\/li>\n<li>flow is continuous<\/li>\n<li>fluid is incompressible<\/li>\n<li>flow is irrotational<\/li>\n<li>applicable along a streamline.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">This equation is obtained by integrating <a href=\"https:\/\/study.madeeasy.in\/ce\/euler-equation\/\" target=\"_blank\" rel=\"noopener\">Euler\u2019s equation<\/a>.<\/p>\n<p style=\"text-align: justify;\">p\/w + z + V2\/2g = C<\/p>\n<p style=\"text-align: justify;\">Here, p\/w + z<\/p>\n<p style=\"text-align: justify;\">= Pressure head + gravitational head<\/p>\n<p style=\"text-align: justify;\">= Piezometric head<\/p>\n<p style=\"text-align: justify;\"><strong>Remember:<\/strong><\/p>\n<p style=\"text-align: justify;\">Bernoulli\u2019s equation is applicable across the streamlines if flow is irrotational.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_1 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.madeeasy.in\/study\/me\/fluid-mechanics-me\/bernoullis-equation-and-its-application\/#Venturimeter\" >Venturimeter<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.madeeasy.in\/study\/me\/fluid-mechanics-me\/bernoullis-equation-and-its-application\/#Orifice-Meter\" >Orifice Meter<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.madeeasy.in\/study\/me\/fluid-mechanics-me\/bernoullis-equation-and-its-application\/#Pitot-Tube\" >Pitot Tube<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Venturimeter\"><\/span>Venturimeter<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4789 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/05\/Venturimeter.jpg\" alt=\"Venturimeter\" width=\"664\" height=\"639\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/05\/Venturimeter.jpg 664w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/05\/Venturimeter-300x289.jpg 300w\" sizes=\"auto, (max-width: 664px) 100vw, 664px\" \/><\/p>\n<p style=\"text-align: justify;\">Here, x = Manometric deflection, Sm = Relative density of manometric fluid, S = Relative density of flowing<br \/>\nfluid<\/p>\n<p style=\"text-align: justify;\">Qactual =Cd Qideal<\/p>\n<p style=\"text-align: justify;\">For venturimeter, Cd = 0.97 \u2013 0.99<\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Orifice-Meter\"><\/span>Orifice Meter<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">It is cheaper arrangement but has more energy loss.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4790 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/05\/orifice-meter.jpg\" alt=\" Orifice Meter \" width=\"263\" height=\"303\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/05\/orifice-meter.jpg 263w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/05\/orifice-meter-260x300.jpg 260w\" sizes=\"auto, (max-width: 263px) 100vw, 263px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Pitot-Tube\"><\/span>Pitot Tube<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">It is based on the principle of conversion of kinetic head into pressure head. The point at which <a href=\"https:\/\/study.madeeasy.in\/me\/fluid-mechanics-me\/velocity-potential-function\/\" target=\"_blank\" rel=\"noopener\">velocity<\/a> reduces to zero is called the stagnation point.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4791 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/05\/pitot-tube.jpg\" alt=\"Pitot Tube\" width=\"642\" height=\"391\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/05\/pitot-tube.jpg 642w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/05\/pitot-tube-300x183.jpg 300w\" sizes=\"auto, (max-width: 642px) 100vw, 642px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Assumptions in Bernoulli\u2019s equation: fluid is ideal flow is steady flow is continuous fluid is incompressible flow is irrotational applicable<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1413,10],"tags":[1503,1504],"class_list":["post-4788","post","type-post","status-publish","format-standard","hentry","category-fluid-mechanics-me","category-me","tag-eulers-equation","tag-stagnation-point"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4788","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=4788"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4788\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=4788"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=4788"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=4788"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}