{"id":3719,"date":"2024-09-10T15:35:20","date_gmt":"2024-09-10T10:05:20","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=3719"},"modified":"2025-08-11T16:33:23","modified_gmt":"2025-08-11T11:03:23","slug":"analysis-pipe-network","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ce\/environmental-engineering\/analysis-pipe-network","title":{"rendered":"Analysis of Pipe Network"},"content":{"rendered":"<p style=\"text-align: justify;\">Analysis of pipe network includes determination of quantities of flow and head loss in various pipelines and the resulting residual water head.<br \/>\nThe Hazen-Williams formula is mostly used for computation of flow through pipes, and following two methods are used for analysis.<\/p>\n<h2 style=\"text-align: justify;\">Methods are used for Analysis<\/h2>\n<p style=\"text-align: justify;\">(i) Equivalent pipe method<br \/>\n(ii) Hardy cross method<\/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\/environmental-engineering\/analysis-pipe-network\/#Equivalent-Pipe-Method\" >Equivalent Pipe Method<\/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\/environmental-engineering\/analysis-pipe-network\/#Hardy-Cross-Method\" >Hardy Cross Method<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/environmental-engineering\/analysis-pipe-network\/#Steps-for-computation-of-discharge-through-each-pipe\" >Steps for computation of discharge through each pipe:<\/a><\/li><\/ul><\/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\/environmental-engineering\/analysis-pipe-network\/#Water-Meter\" >Water Meter<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/environmental-engineering\/analysis-pipe-network\/#i-Velocity-or-inferential-meters\" >(i) Velocity or inferential meters<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/environmental-engineering\/analysis-pipe-network\/#ii-Positive-or-Displacement-Meters\" >(ii) Positive or Displacement Meters<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/environmental-engineering\/analysis-pipe-network\/#Metal-Pipes\" >Metal Pipes<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Equivalent-Pipe-Method\"><\/span>Equivalent Pipe Method<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul style=\"text-align: justify;\">\n<li>In equivalent pipe method, different small loops are replaced by an imaginary single equivalent pipes having same discharge capacity and causing same head loss.<\/li>\n<li>The equivalent pipe method is used in solving large <a href=\"https:\/\/study.madeeasy.in\/ce\/environmental-engineering\/analysis-pipe-network\/\" target=\"_blank\" rel=\"noopener\">networks of pipes<\/a>.<\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Hardy-Cross-Method\"><\/span>Hardy Cross Method<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">In Hardy Cross method of analysis, a distribution of flow in the network is assumed and resulting head losses are balanced. Formula of the pipe flow are used to evaluate losses and successive connections are made in the flow until the network is hydraulically balanced. In pipe network, following two conditions are to be satisfied:<\/p>\n<p style=\"text-align: justify;\">(i) The algebraic sum of the pressure drops around a closed loop must be equal to zero. i.e. In each loop loss of head due to flow in clockwise direction must be equal to loss of head due to flow in anticlockwise direction.<\/p>\n<p style=\"text-align: justify;\">(ii) The flow entering a junction must be equal to the flow leaving the same junction.<\/p>\n<p style=\"text-align: justify;\">Here, loss of head is h<sub>L<\/sub> = rQ<sup>n<\/sup><\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Steps-for-computation-of-discharge-through-each-pipe\"><\/span>Steps for computation of discharge through each pipe:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\">Assume flow in each pipe satisfying continuity equation.<br \/>\nTake clockwise flow as positive, anticlockwise flow as negative.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3720 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/hardy-cross-method.jpg\" alt=\"Hardy Cross Method\" width=\"324\" height=\"127\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/hardy-cross-method.jpg 324w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/hardy-cross-method-300x118.jpg 300w\" sizes=\"auto, (max-width: 324px) 100vw, 324px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Water-Meter\"><\/span>Water Meter<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul style=\"text-align: justify;\">\n<li>Water meters are connected after the stopcock to measure the quantity of water supplied to a building.<\/li>\n<li>Water meters are classified according to the method of measuring flux. Mainly, there are two types of meters.<\/li>\n<\/ul>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"i-Velocity-or-inferential-meters\"><\/span>(i) Velocity or inferential meters<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul style=\"text-align: justify;\">\n<li>Such types of meters measure the horizontal velocity of water flowing through them.<\/li>\n<li>They measure large flow and are often used by industries for measuring large supply.<\/li>\n<li>They have an additional advantage of measuring water containing suspended particles.<\/li>\n<\/ul>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"ii-Positive-or-Displacement-Meters\"><\/span>(ii) Positive or Displacement Meters<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul style=\"text-align: justify;\">\n<li>They work by the flow of water causing a piston to reciprocate within a cylinder or communicating the movement finally to a system of dials, which register the quantity of flow.<\/li>\n<li>Such type of meters are very bulky and heavy, hence, an improvement has been done and the improved ones are known as semi-positive meters. semi-positive meters.<\/li>\n<li>They are widely used for domestic supplies.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">The two most common type of semi-positive meters are<\/p>\n<p style=\"text-align: justify;\">(a) Rotary piston meters<br \/>\n(b) Rotating disc meters<\/p>\n<p style=\"text-align: justify;\">In selecting a type of meter for a particular use, the following points should be considered.<\/p>\n<p style=\"text-align: justify;\">(a) Quantity of flow to be measured<br \/>\n(b) Nature of flow (whether continuous or intermittent)<br \/>\n(c) Permissible head loss (should not be more than 3 m)<br \/>\n(d) Cost (the inferential meters being less costly)<\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Metal-Pipes\"><\/span>Metal Pipes<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">The following types of metal pipe are used<\/p>\n<p style=\"text-align: justify;\">(i) Cast-iron pipes<br \/>\n(ii) Steel pipes<br \/>\n(iii) Wrought iron pipes<br \/>\n(iv) Copper, lead and brass pipes<\/p>\n<p style=\"text-align: justify;\"><strong>(i) Cast Iron Pipes:<\/strong><br \/>\nCast iron pipes are most widely used in water supply for trunk as well as distributary mains due to their durability, strength, resistance to corrosion, ease in laying and simplicity in repairs and maintenance. There are two general processes for manufacture of cast iron water pipes :<\/p>\n<ul style=\"text-align: justify;\">\n<li>Foundry method<\/li>\n<li>The centrifugal process<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>(a) Foundry Method:<\/strong> Foundry method of casting is done in fire sand moulds or more popularly brown pit-cast pipe. Pipes are cast in vertical moulds with hub end down for pipes greater than 45 cm diameter and horizontally casted pipes are called Mc. Wane Pipes.<\/p>\n<p style=\"text-align: justify;\"><strong>(b) The Centrifugal Process:<\/strong> The <a href=\"https:\/\/study.madeeasy.in\/ce\/fluid-mechanics\/efficiencies-centrifugal-pump\/\" target=\"_blank\" rel=\"noopener\">Centrifugal<\/a> Process: this process, the core is omitted and the mould placed horizontally is rotated while the iron is pored so that by centrifugal force the molten iron is evenly distributed<br \/>\naround the mould. Pipes made by centrifugal process have less variation in thickness, are stronger and more uniform as well as lighter. They are popularly known as spuniran.<\/p>\n<p style=\"text-align: justify;\"><strong>Disadvantages of cast iron pipes are:<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>Water carrying capacity decrease with the time, as the valve friction factor increases due to tuberculation in certain waters.<\/li>\n<li>They cannot be used for high pressure. Generally, not used for pressure above 700 kN\/m<sup>2<\/sup><\/li>\n<li>When large, they are very heavy and uneconomical.<\/li>\n<li>They are likely to break during transportation or while making connection.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>(ii) Steel Pipes:<\/strong> Steel Pipes of larger sizes made from steel plate made to circular form<\/p>\n<ul>\n<li style=\"text-align: justify;\">Used as water mains passing over bridges and culverts of longer span.<\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/study.madeeasy.in\/me\/strength-of-materials\/stress-strain-graph\/\" target=\"_blank\" rel=\"noopener\">Steel<\/a> pipes are frequently used for raw water trunk mains, inverted syphons, or pumping mains, where pressure is high and sizes are larger.<\/li>\n<li style=\"text-align: justify;\">Life is generally taken around 40 years under ordinary conditions.<\/li>\n<li style=\"text-align: justify;\">Steel pipes are not adapted to withstand external loads of backfill, traffic etc. while a partial vacuum caused by emptying of the pipe may cause collapse or distortions if not designed properly.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/environmental-engineering\/water-distribution\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/environmental-engineering\/corrosion-in-pipes\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-environmental-engineering\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Environmental Engineering?<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Analysis of pipe network includes determination of quantities of flow and head loss in various pipelines and the resulting residual<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1012,2],"tags":[1063,1062,1061],"class_list":["post-3719","post","type-post","status-publish","format-standard","hentry","category-environmental-engineering","category-ce","tag-equivalent-pipe-method","tag-hardy-cross-method","tag-water-meter"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/3719","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=3719"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/3719\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=3719"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=3719"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=3719"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}