{"id":484,"date":"2024-07-02T10:32:50","date_gmt":"2024-07-02T10:32:50","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=484"},"modified":"2025-07-16T14:50:46","modified_gmt":"2025-07-16T09:20:46","slug":"velocity-distribution","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ce\/open-channel-flow\/velocity-distribution","title":{"rendered":"Velocity Distribution"},"content":{"rendered":"\r\n<ul>\r\n<li>In an open channel, velocity across any section is not constant. It is zero at the channel boundary and maximum at certain depth below the surface due to the production of secondary current which is a function of aspect ratio (d\/B).<\/li>\r\n<li>The contours of equal velocity are called <strong> Isovels<\/strong>.<\/li>\r\n<li>The dip of the maximum velocity point depends on aspect ratio (depth to width) of the channel.<\/li>\r\n<li>For a deep narrow channel, the location of maximum velocity point will be much lower than the wider channel with the same depth.<\/li>\r\n<li>For rivers and canals, average velocity attains at a depth of 0.6 <em>y<\/em><sub>0<\/sub> below the free surface, where, <em>y<\/em><sub>0 <\/sub>is the depth of flow.<\/li>\r\n<li>Also, average velocity can be represented as (two-point problem)<\/li>\r\n<\/ul>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-307 aligncenter\" src=\"http:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/natural-channel.jpg\" alt=\"Natural Channel\" width=\"548\" height=\"304\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-308 aligncenter\" src=\"http:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/particular-channel.jpg\" alt=\" Rectangular Channel\" width=\"634\" height=\"518\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-309 aligncenter\" src=\"http:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/velocity.jpg\" alt=\"velocity\" width=\"648\" height=\"268\" \/> <strong>NOTE:<\/strong> The presence of corners and boundaries in open channel causes the velocity vectors of flow to have components not only in longitudinal and lateral direction but also in normal direction of flow.<\/p>\r\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-4'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/open-channel-flow\/velocity-distribution\/#For-Steady-Flow\" >For Steady Flow<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/open-channel-flow\/velocity-distribution\/#For-Spatially-varied-Steady-Flow\" >For Spatially varied Steady Flow<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/open-channel-flow\/velocity-distribution\/#Rectangular-Channel-Section\" >Rectangular Channel Section<\/a><\/li><\/ul><\/nav><\/div>\n<h4><span class=\"ez-toc-section\" id=\"For-Steady-Flow\"><\/span>For Steady Flow<span class=\"ez-toc-section-end\"><\/span><\/h4>\r\n<p>The continuity equation for steady flow can be expressed as<\/p>\r\n<p style=\"text-align: center;\"><em>Q <\/em>= <em>A<\/em><sub>1<\/sub><em>V<\/em><sub>1<\/sub> = <em>A<\/em><sub>2<\/sub><em>V<\/em><sub>2<\/sub><\/p>\r\n<h4><span class=\"ez-toc-section\" id=\"For-Spatially-varied-Steady-Flow\"><\/span>For Spatially varied Steady Flow<span class=\"ez-toc-section-end\"><\/span><\/h4>\r\n<ul>\r\n<li>In a steady spatially-varied flow, the discharge at various section will not be the same. A budgeting of inflows and outflows of a reach is necessary.<\/li>\r\n<li>Consider an SVF with linearly increasing discharge at the rate of <em>q<\/em>\u00a2 per unit length.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center;\"><em>Q <\/em>= <em>Q<\/em><sub>1<\/sub> + <em>q<\/em>\u00b4 <em>x<\/em><br \/><em>Q<\/em>2 = <em>Q<\/em>1 + <em>q<\/em>\u00b4 <em>L<br \/><\/em><em>Q<\/em><sub>2<\/sub> = <em>Q <\/em>+ <em>q<\/em>\u00b4 (<em>L <\/em>\u2013 <em>x<\/em>)<\/p>\r\n<p><br \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-310\" src=\"http:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/spatially-varied-.jpg\" alt=\"Spatially varied \" width=\"345\" height=\"92\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-312 aligncenter\" src=\"http:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/spatially-varied-flow.jpg\" alt=\"Spatially varied flow\" width=\"374\" height=\"234\" \/><\/p>\r\n<h4><span class=\"ez-toc-section\" id=\"Rectangular-Channel-Section\"><\/span><strong>Rectangular<\/strong> <strong>Channel<\/strong> <strong>Section<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\r\n<p>Consider a rectangular channel section of width (<em>B<\/em>) and depth of flow (<em>y<\/em>) , thus<\/p>\r\n<p style=\"text-align: center;\">Wetted Perimeter,\u00a0 \u00a0 \u00a0<em>P <\/em>= <em>B <\/em>+ 2<em>y <\/em>Area of the flow,\u00a0 \u00a0 \u00a0 \u00a0 <em>A <\/em>= <em>By<\/em><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-313 aligncenter\" src=\"http:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/rectangular-channel-section.jpg\" alt=\"Rectangular Channel section\" width=\"724\" height=\"420\" \/> \u00a0 For most economical rectangular channel, <br \/><strong>(a) <\/strong><em>A <\/em>= 2<em>y<\/em><sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>(b) <\/strong><em>T <\/em>= 2<em>y<\/em><em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><strong>(c) <\/strong><em>P <\/em>= 4<em>y\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/em><strong>(d) <\/strong><em>R <\/em>= <em>y<\/em>\/2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>(e) <\/strong><em>D <\/em>= <em>y<\/em><\/p>\r\n\r\n\r\n\r\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-open-channel-flow\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/open-channel-flow\/specific-force\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a> <br \/><strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-open-channel-flow\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Open Channel Flow?<\/strong><\/a><\/p>\r\n<p>&nbsp;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>In an open channel, velocity across any section is not constant. It is zero at the channel boundary and maximum<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[173,2],"tags":[170,171,172],"class_list":["post-484","post","type-post","status-publish","format-standard","hentry","category-open-channel-flow","category-ce","tag-natural-channel","tag-rectangular-channel-section","tag-spatially-varied-steady-flow"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/484","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=484"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/484\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=484"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=484"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}