{"id":3039,"date":"2024-08-23T12:42:55","date_gmt":"2024-08-23T07:12:55","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=3039"},"modified":"2025-07-16T15:08:04","modified_gmt":"2025-07-16T09:38:04","slug":"various-connections-pipelines","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ce\/fluid-mechanics\/various-connections-pipelines","title":{"rendered":"Various Connections in Pipelines"},"content":{"rendered":"<h2>Series Connections<\/h2>\n<p style=\"text-align: justify;\">If a pipe line connecting two reservoirs is made up of several pipes of different diameter D<sub>1<\/sub>, D<sub>2<\/sub>, D<sub>3<\/sub> ,&#8230; etc, and length L<sub>1<\/sub>, L<sub>2<\/sub>, L<sub>3<\/sub>,&#8230; etc. all connected in series (i.e. end to end) the flow rate through the entire system remains constant regardless of the diameters of individual pipes in the system and total head loss in this case in equal to sum of the head loss in individual pipes in the system.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3040 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/series-connections.jpg\" alt=\"Series Connections\" width=\"280\" height=\"83\" \/><\/p>\n<p>From Equations (i) and (ii) we can solve problems of pipelines in series. There are two types of problems as given:<\/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\/ce\/fluid-mechanics\/various-connections-pipelines\/#Given-discharge-Q-to-determine-hL\" >Given discharge Q ; to determine hL<\/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\/ce\/fluid-mechanics\/various-connections-pipelines\/#Given-hL-to-determine-discharge-Q\" >Given hL; to determine discharge Q<\/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\/ce\/fluid-mechanics\/various-connections-pipelines\/#Equivalent-Pipe\" >Equivalent Pipe<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/fluid-mechanics\/various-connections-pipelines\/#Parallel-Connections\" >Parallel Connections<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/fluid-mechanics\/various-connections-pipelines\/#FLOW-THROUGH-A-BY-PASS\" >FLOW THROUGH A BY-PASS<\/a><\/li><\/ul><\/nav><\/div>\n<h3><span class=\"ez-toc-section\" id=\"Given-discharge-Q-to-determine-hL\"><\/span><strong>Given discharge Q ; to determine h<sub>L <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3041 alignright\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/series-connection.jpg\" alt=\"Series Connection\" width=\"272\" height=\"152\" \/><\/sub><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"text-align: justify;\">Since discharge, diameter and length of the pipes are known, the Reynolds number can be computed and values of f<sub>1<\/sub>, f<sub>2<\/sub>, f<sub>3<\/sub> etc. can be found from Moody\u2019s chart.<\/li>\n<li style=\"text-align: justify;\">These values can be substituted in Equations (i) and (ii) to get discharge.<\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Given-hL-to-determine-discharge-Q\"><\/span><strong>Given h<sub>L<\/sub>; to determine discharge Q<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"text-align: justify;\">Assume f1, f2 and f3 (These can be assumed equal for simplicity).<\/li>\n<li style=\"text-align: justify;\">Compute V, Re, \u2208\/D (relative roughness) and then calculate \u2018f \u2019 (Moody\u2019s chart can be used).<\/li>\n<li style=\"text-align: justify;\">Repeat the process to get accurate results.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Equivalent-Pipe\"><\/span>Equivalent Pipe<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"text-align: justify;\">When a compound pipeline consisting of several pipes of varying diameters and lengths, is replaced by a pipe of uniform diameter having same material, it is called equivalent pipeline.<\/li>\n<li style=\"text-align: justify;\">The uniform diameter of equivalent pipe is known as equivalent diameter of the compound pipe.<\/li>\n<li style=\"text-align: justify;\">If L<sub>1<\/sub>, L<sub>2<\/sub>, L<sub>3<\/sub>, etc be the length and D<sub>1<\/sub>, D<sub>2<\/sub>, D<sub>3<\/sub>&#8230; etc be the diameter of the different pipes of a compound pipe line, and if D is the diameter and Le is the length of the equivalent pipe, then<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3044 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/equivalent-pipe.jpg\" alt=\"Equivalent Pipe \" width=\"205\" height=\"41\" \/><br \/>\nThe above Equation is called Dupuit\u2019s Equation.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Parallel-Connections\"><\/span>Parallel Connections<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"text-align: justify;\">When a main pipeline divides into two or more parallel pipes which again join together downstream and continue as a main pipeline, the pipes are said to be in parallel connection.<\/li>\n<li style=\"text-align: justify;\">If pipe divides into two parallel pipes then rate of discharge in the main line is equal to the sum of discharges in each parallel pipe;<br \/>\nQ = Q<sub>1<\/sub> + Q<sub>2<\/sub> &#8230;(iii)<\/li>\n<li style=\"text-align: justify;\">Since end condition of parallel pipes are same hence loss of energy through each pipe will be the same<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3045 size-full aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/parallel-connections.jpg\" alt=\"Parallel Connections\" width=\"164\" height=\"43\" \/><\/li>\n<li>Using Equations (iii) and (iv) we can solve problems of pipes in parallel.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"FLOW-THROUGH-A-BY-PASS\"><\/span>FLOW THROUGH A BY-PASS<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"text-align: justify;\">A by-pass is a diversion provided for main pipeline in which mainline is tapped at some point by a smaller pipe which later returns to the main at another point as shown.\u00a0 Head loss in mainline between sections (1) and (2)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3046 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/parallel-connections-1.jpg\" alt=\"Parallel Connections\" width=\"594\" height=\"260\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/parallel-connections-1.jpg 594w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/parallel-connections-1-300x131.jpg 300w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3047 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/by-pass.jpg\" alt=\"\" width=\"595\" height=\"361\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/by-pass.jpg 595w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/by-pass-300x182.jpg 300w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><\/p>\n<p style=\"text-align: justify;\">A by-pass may be used for measuring the discharge passing through the city water supply mains which are usually of very big size and for these other discharge measuring devices are not available.<\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/fluid-mechanics\/thicknesses-boundary-layer\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/fluid-mechanics\/types-of-pressure\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/ce\/what-is-fluid-mechanics\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Fluid Mechanics?<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Series Connections If a pipe line connecting two reservoirs is made up of several pipes of different diameter D1, D2,<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[814,2],"tags":[840,841,839],"class_list":["post-3039","post","type-post","status-publish","format-standard","hentry","category-fluid-mechanics","category-ce","tag-equivalent-pipe","tag-parallel-connections","tag-series-connections"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/3039","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=3039"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/3039\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=3039"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=3039"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=3039"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}