How do pipes work in series as taught to mechanical engineers in fluid mechanics? What is the difference between pipes in parallel and pipes in series?
Figure below shows a system of pipes in series:
Figure below shows a system of pipes in series:
The difference of water level in the two tanks A and B is given by
![](data:image/png;base64,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)
If a compound pipe is to be replaced by a pipe of uniform diameter (known as equivalent pipe),then the loss of head and discharge of both the pipes should be same. The uniform diameter (d) of the equivalent pipe may be obtained from the following relation:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJoAAAAuCAIAAABfxpcjAAAgAElEQVR4nH1893Nc15Um/sD9YWurtja4dsYzY3vGHltez0hWFk2JWRSpwGQGiUnMQRSzKJEEMwESJCiCBEEioxvd/fqFm+N7vT+c+05fgKqteoXqbnS/cL8Tv3POHfCV85UzTmkrfelcaXxlfKWNE9py62VZmbIyrlSuVPChthxfuFKXPe9K4ytX9cqy5+GE2kptpfXaeVNW3lfOlcZ4xS3jlqlS6lJJL5SXyks4g/Ua/xqn4IWvHP7Xem2ckl5IL5gm0gnbs7pUwnHphak0vF52SC+E47pSqpS6UroK19WVMpXWldKlws+ZJkwT6QV82fTCF+AM3LKcp8xQacNpVSmVl9wy4TjTBK4YLlFKOOCG4wO+ZiotnZBeSMtznsKHzFC8Z26Z9ALv3FQa7g2+oCtle9ZU2pcBPuv1AKw+LBa8rnrOl9qVqqyMMsxX2ldaKAKIAqhSUwDVldqXDn8Lp1JGAACABBzWa+0kMxQeW3mpS2UqbSoN8gQQlj1fVkE+YhGBT1xppBO4fCANsGQAiS5V+NBLWCxcFIQHLg3LpEoJoKpSMk2IzJkmzFD4CXzf9DTCA0sJByyx6Wm4JbgrECyQV1Np+CTcYalszwLYIAqAn+1ZInNdqiDitQTEEgk3ib8SjqOoweKD9A+UPR8W3QdVKHvOeulK5SsNuFov02wRPrReWi+lplwWyjDrlS8d/hYWHYTFOBWU0injlCuNdrL/eKUUjsMTutJIzYViyggUC/gt6qW20nljbJAAbpkuFT45rB2+iHUiXmIABjAAMGzPmp6GA1YK5QA+hIXDIwhNDWSsu31tjr4DZkCXCn4OcMLjw/1TVQBOKA0ggsoH2IJRiR42PEJ9wPpIza3XAU7QCdCDsmcQTuulL7UyzHnlK43aKRThPOM801YAVHD4ypWVj7GEv9Zr67TxyvQ03hmsgu1ZMPKxhUA4QTKcN6i++HMQczjQkAaz6UTfGNYqBf8CdcR1hxWBn8M6grlD+6y8jOGM1/EXYC6Vrv+Ll1t2RVUG44xyiQqHTxHrNMIJr3HR8IClU0YYpwKcsHw1tH04lWHwwnkFHxonjBOUp43G5MSLR920FWuh8wYhRNurjQwvytp1lTKY/p42vWArUAhiOIViadYmLAPX7ktnKyOdUF7anoXzwJIt947RIqIPA/xQmfrGtgySkdIO1xSMJ3whVt9lcKL04Hm4Zb/4BbSxulTSCXC9iFywB7VIBU9ULVkrdEzo1PHApS4r3ze2sJRlz/vKWK9cqXxlINixXhonrZPWSampcaKbNq9cPnno4M65uQkMWLSVTJAYy7LnjVNcUrDGtjK20rqUplK2VKbUttK20nUQpLQFY2tcqa1X1ut2e+HHH848eHCT8gJlgmsiHbelMiCnVTiPLqUtla20qZSplK10/789rbyQjutSSsvhhQnLBFZRNBanb968ON94JTSVhulSCkNjg4zIxUcwnpGDDL4ZACh1sP9eKi9spaVhRGRU5knanHg12mzPGC+1E9IJUFwic6qKZZKKTgTdOfoLU2pTalsZU+oBiDUgaIw9Vhwi1YfUlktNteGt9uz+fdtOndwvJK2FoB8EoSv1VXCr9REiZAiv0Blry+Fz62XZM/AvbYWx6tXEz+vW/e2704cK0q2DXum8gkAMzhMfcbyGFyqrcE48MAjA77tSPXlyb82aD0ZGbnJZwPmlptZL0K3YI6KnXK64PY0BOahL39d46UpV9oxxgouCsG6jMblh3UcP7l/ThklFleUgEMxSZmgcGEO4ZysTXxQi7Tg40JUaiEPH2P+h1iKcmJxITZ+PPdixdePNGxesV2ilw89L50sXSwOexJUabDWEzbD6xgllGIRX4KED2E5yScfGHm756tOh+9et09aF23Clgp8A9nCeGkvpSw2JVnD/TsJriAPCi9fkwFf6yZN7O7Z/9nLisdQ0SJtXxssYP10p2wuG9HULrEppyuA7ICxHOOFmyp7RlgtJuCyeP3/4ztt/mp15phTVhhsf1JF7Hke2IREoJSZUoKzg5uHAwHsgThaXelAIixy+hqWHdR+6d3X7to2vXo66sp8dApCYZqAcYB7pK+PLvpaU9Vs8Lax7ralKaTHy4NbRw99MTo5BwGWcAkfgSgWwLdPLoASVwdcoQLF2/qJC371z5YdLJzrJgrEx/BotHiD3uvdCleWWBcXwxnqN2ukrU/bCYb1UmklNjx/9ZsO6jxjtasMoT7UTulLMskykACEkToXIIBsWhvXjACeoKuLsCLAfWGJgA41Qp6ERNgCntlwZxnl28dyxXTs3Z3nL+n5Yi4qorUSphJPUMmFw0dHQgc0EUNEUg7fmkt6/d+2nK98n3cWCdLmk2khXBuMZIwEHWEi0pf0TlhpPixeFbxontOHKMKnp6VMHrl39ntAE4FSGgTXCkAScaMw8oHZCkKnLsBpl5UFBAVGAs+q5smesk8YKY8VXX6w7dGBHnreM5UISqSi3jKqiky/mPOWWMU0KkaW0k/O0kzUBvwCwoYgl04SqArAfiHMD54112pcOol6wb9rKWi2kccJYkaaLZ04dvHDuqFBEW4F8DYSmrxlYA4oFKm5sfx3hQEaCiVxbjm5VGT439+rMd4cf3L8hFOOCCsWM61vjsmfQaFsvteFCEcpToQiCqgyDtAodLcAJSTNIpzZcadZYmNy1c/Pw8HVEV1uuNFOGQQgdwpxfCpjhQ+BoQnxeLnFeIMdwz9ZLoQiXxVtv/fuN6+cY6ypNlWZSM+E4kXk7a+Y8BSwzluQ8zXmaFC2ANskXC5FRVeQ8JTIHdOFtxpKBfl5ROuMUAJlmbS4ppHqBAbASYhbr5cuJx1u+Wj90/yrnmdJ8GX6YPmJQgAJb9hw4YFhujK1w0dEdGie0FRPjo8eP7ns+NtJozhz+ds/Tpw+EZNbJCHIWPJwT4IO5LFBc4As1GRniLLhuHOzADdy9c+XYka/n5l4ow+7d/XHn3zcNDV1ThinNADNQBYgwYyxBUTAvhBULGlK6SNZ5n1NT9O6dKx988B9zs+OUJi9fPBoZuVmQjvIy52k7awBUSdEC1cx5WoisEFmSL3ayJnzeThsp7QDG8K8lcGLmZ5wiNBWKxYorNYf10pY/eDD48cq3bwyebzanhaJCM+0kULLGKe0UknzxGeoUSEIaYCvtShX8pVeY4FY9B3AaJx/cv7F/346pqWcF6e79ZtuTJ0PaSOP7hzJMO2FrSwvAOK98qZfJTRzrAsDKMGUYKIoy7OqPZ859f7ibNhuNyeHh60ND19at+2h2dlxqCkCCcUNGRvnA0QBtKb0QhmonILyP4wbMC2IJO3hgx5FDu5NuY352fPfOzRs3frx371Yi8kJkrbQB+HVJO2fdjCZJvpjSDljUJF/MeZrSzmJ3frE7n7EkY0lKO0nRYooMhABJE64pUIigoGDZwEi60igTSDip+eTk028P7n7yZIiwrOBZxtJC5oXMAq3sBTOgcOCoNGSuvtS+MtILaghzTJZSljJlCdwAt0wBT1RKYZh0Qjtx4dzRFSvefPBgsCDJsSPfPH58m0sinGCWFroQnnPLZCm549xxZigko5CVc01T0hGaBAdpOUgMl4X1SgPdU2nlhTCUyHz/wb/v3LV56P7Vn3++3+7MUp5+9OF/Pn58m8tC1uQq0Bd9ThVuwFAwzmgnwFWDJcOrC0WEIlJTQhNCk292f3HyxL7L54+l6eLc3IuZmWdr1nzARJ4V7SRbXOzOg11NaSdjSZe0M5aAImYsoaroZM1mMtclbbCxoM2FyAbA5TJDwdMyTagooB4CSgZZKZdUKCY1V0ZwSfMiYYJIzYnIM5YQmTNLmaXhDKrgsgCpRx+pLZeOC8OIzIXj0jIi8pR0qCqSogXeAgRQWs4MZapYbM1MT411u01Ck2NHvh4evl6QDqCO5QtWqw58yC2TlgvD4OGFDmstFFGGUZ6GpKg2niBMOU/37t+2afOq6ekxylPGUqnpl1+sbbVmpQ6ZQPgyBJmOy1KqSgnHhaZKM204F5mxHOwN+A6hCBM5E7lQBOQJbLvUdNUn7/6ff/jv4+MjhCZptrh27YeXLh6nPCU0SfNWl7RT2gEUAU4AEjwokXnGElBTqgpYNEBwAG4OLYlwXFlR5xUOkydlhLZSKEZYBnS5VFxpIS0H6YCfQxokHAd5hCeJglWhLeeykIooTRnrSkWME0m+yAyFiJzIvNGeWWhNp6RNecp5RmjCRH72zKGff75Pecp1COow/cL7h7Wmqih4RkTOFKEiB6kSihDWBUNnXIRNbZmYIkJTqSjlqdR08Pq52ZnnXBRcFsJxzAqoKoCf445zx5gmhKdCEca6SlEhi1gpMT6ApQC04HEI63KeQQLa6cyvWPHmn//8O86zvGgTmsAywsKCtGUsgeCIyByQll6EHMZQXPygnUhj6krZqs+7QlgL9UupeZZ3mCBCMWMx7hXg5EEkmchBPLEmCgoKjk1qqhRRIteSWCuc4VoSJQmhCVXFXHMS1AtqFERkTOSEJoQkTOS3b10aGxsmNAE9g7+wUpSnQlNmKOg9LDrXdGbuxePRO4QkaOjgZkA7ASSmCVOEqoIZqgynPOWyGB8fefF8pCCdTmce4ETxh2CSacJBQUup4NEUWZifGH/2AC+BmbQyjIkczBVhXYCTsVRIYpzgPGMiJyTZuPHjvGhzWTBZMEVA8zD1RNvJLYOIl6oCsxTk8QfQHwDZKL2IS8fGKaVFmrWTTrObLHY6jVZ7Pk3b3bSVF0lBut10sdOZz/N2XrS7aTNNF7nIMLbksmAi5zy7fevSO2+/8cnH72z/cv3h/Tv+vnXjoX3b281pq5mWhIkc7j7naXDhmlBZKM24KChPF1szp07uv37tbDdtGiuUZpSnXBQh8tTMlUpaTlUhDAOcknzx8c/3jhza3WhMass5z6SmkINaLwOfooi0XHkJopDThPNsdPTu6lXv/fWvf1yx4k0wgGA5uGVwb6AKoA1UFkwUUlOl6OmT+y+eOwrayUSOkSOIMljdougQkghJ0OqO/Tx07er3k5NPTp3cD/qQ5q2UdEAoAT8weMpLaTnACUYCOQTMlwbQ8WDRSlkBpW0gAYbuX//ss9W/+9dfv/nmH9es+nDVqg/Wrl3x8cp3d2zf/M3XWzduWPnl5jWfrluxbcuGLzavPnxw58sXjzhPUUGlpkISJvKCdMBPpFmzmzazvAWfM9ZNixakUxlL5ptTU3PPZxuvZucm5mZfzM2+WFh4NT8/8erl6ML8q1ZrdnFxOssWu8lC0pnvdhaM5VIRbTnACdozt/DqxavRa4PnNny68snjO920SUgC2qkt1zXZndGkmcwlRavVXehkzaxoN5pTnWSBsG6WtwhNOM/yvA0hSbvbgEWs4yDBHeeaZnlrbna8tThz6ujePbs+bzanG80pSH8heIalCMaWdQnrMpYS1jVWcFFQ2n348MbE+CNtuVTg4zkROZhZrinYUuTzAGYi82BgNYFsOJB8MT0fcinDIdQOPSJGutKAOnJJ2+2FTqeRdBcpzdqdxvzcRLMxOflydGZ67NXE47Gf73eThSxbRK7HlYrzbGxs+OL5Y4OD5y9dPvHDldNnLxz94afvGq3pnCWFSHOettNGxpJmMrd3/7Y//eVf/+Ov//72e39+773/+8Ybv/3k43fWr1+xdu2HX3y+ZuPGjz/7dOXgtbMH9m7ds+vz0yf353lLG6YMk5aBPVxoTZ+9cHT7rs3rP135zjtvrFnzwa2bF4eGrlGeAr1nvZROCMNm5l5c/uH0uYvHvjt7+Pip/YPXz1398cyxI1+f+/7wuTOHB6+f+/GHUz/9cPryldN3h64+fHR7fnEK3TM1VHohnRgdvbtmzQdrV7//29/86re/+dW6dR+tXvXe6KPbNTYMsmGwMaOjd4fuX338+PaDB4MjIzcfPBh88uTe4LVzYz8PPX06NDn5ZHpq7OHDG49/vvdy6mmzPYtAoo7CWyJzqK6oUobPNWGaDIQSaM/ZyoTqdhW6e4CGrXolkjtI/eBfpZk2jItMGea8NIZbJ7RhkJ8AcaMM76bNlxOjz54/HB65ee/B9XsPbzwYvdMpWoUuuGPCcSAhsRYNK6UMV4ZTnqXZYtJtENptNKaazWljRas1+/TpUDdpAGfmSm1KbbzimlJZSMO5oi8nn54+dbDVmoPzaBs4P+OltFxZsdCcvnn7h8EbFy5eOvHtod0nT+6/dfPiieN7bwyeP33qwNkzhw4d3Hn61IGv9209e+7I+YvHhh8OQnDONRUGDiY1A1Z95/bPjh7aoww3TlqvrFPGSWV4nRDzifFHZ777duuWDbt2fr5t66erPnl33bqP1q37aMWKtz7fvObjle8cP/rNunUf/fNvfvXGX/5t46ZV166fA1+goKhnOaRVcHVmqA39VkI4Dp9H3QhRHRsYDYiGyp4Hmh6r3pDDAKKzs+P37v549cczjeYUpFx1faNP/6IzBuoEQ+i4BI9tNcioKR8kRijGBGEsZ4LkRdJJmnmeKCO0kXAPgUgrXZ0iC6k4VGNu37zSTVuQd0F1HbP7uOslfOKX8PWQp0pNjRUQoMakBLrhwBRavn/ftts3L0F2B2wtVpHxothXBelfTIVyScOqWhXrD96qq9cWEtyoViExFezDGVdzkEMHcg6rLtCTAuulrRSSHT389fvv/+XLL9bOzDwLzA6QBlGJBglMqOVC/h5TZciWSSfAgISCrVPGKam5kIwJQkh6Y/Dijz+cuXH9IhNEabGE5i5dWXmgKrmkXNLm4uyjR3fyIkGmJpRjIz4SyrHwiXESGUFYnYnxR3du/zA8fB1YkbjggxUb6KiyXp45dfDp0yFQgKAYpcPCxrJCxTJO1HqdF8nY2MPpqedp2sbvBAheK2AsK0KgtA3EetlvuatpdxQ0uDlgi7SRQCkURffo4T2bN616/vwhhJeh4GUFlq+hCyl0n5QayvSQDgGXDeCBb4h7amxlkNnXRkrNp6eer/zbO98e3H3vzlUmCOhcuL3SoQ3A+hQwHlJzyLJQ2LGXJRihEmtKGstn1klCky82r9m+beOJ43uR4w1VubpuChVpKKdPTT3tpk2sMCIT3se1ctB8g9Q8vtZW3r51ZdvWz65dOTs/PxmbkEgxQkEXi0U+0lewIgNxY84SlVralgBrBCau2Zj56cr301PPKS9evXxy9syhnX/fND8/AbaornhAXax/5rLnbWWAgQvF2Kg7EpL0fkGxVLoM9QCo7Rirxn5+sG/v9q1bNj57NqJNn+xernDRPWMXYGghi/p4oe4Rq471tZhboS1/8uTe73//Tzu2bszyVmCD6/odvoASJgJc9vogAZCoCX1W3CpUFSxASc1XrnznwN4do4/uUl6E+/QmdlVYq48rfXELtPVyICqXL4cTKCE4fOWMVSDpo6P3V33y/r27V7WVEG1v+uyTx49vg5nqwxlpPLx1PYftcSHZrfoNauA4geiRlksnQL2Gh2/cuf1jmrbzPJmbffXtwd3bt20CihFKQJBWxRDGlip0b0cKgQ4pFlzrtbZCKjo6evfli8ecp7Ozz0+fOvD22396PHILyKzYY2GRbtkByXqsHggJwomvFxamZmcnWu15IdmVy6fPnz125rvDadYO9Si/xDjHrTlQVnq9S2YgluJfRLSsQs+msYqwTCj26NGdLV99Ojf3amrq2dMn96cmn546uX9m5hmqpisVQtg/Sc9DtwsGrlhswhZLbIwTjkvLpeaM5adOHjx+dF+32zJWGauazdnVqz9MuotMEOu1UExbaV0fzr41K52vHAAfopLS+cpZtwTv2HcKRXbv+vz2rUt50W535ihPnzy+s2vnZqS3MPRAx9lXUDhKp63EluNYWZc4S6eVEY3mzFdfbnj06I5QjEs6Pv746OFvxsYe9r1mFTeK9MsyUBh+3ZEP+KV2aRmiqOnW6+bi7OmT3549c2Trlo3HjuwlNF1szY2PP5p8+WR+foLQBOCsS1EGtTNYSxfaX5HXRb3ERtO6+1TpUmkntZGzsxP79m6/feuKUOzWjctXLp++fevK/XvXCE0BTuy/tUs78YObLB06Tqk59ACjvi7TTuPkzMyz9etXPHv2gItiePg6Y+nNGxcuXTyuDceaDDIkkSnqryz0IUThaN+XxwcY/4WFqT/84V8WW3Np1qa86Kat40f3vXgxCn0EfScSKowOyVQ0uSBP6EEHfF1n7l+pntwwlZaW5yTRTra7jT27v7x+7dy9uz+tXvX+vbs/SkWV4VwS6CLAqC88bd2QCBCG6qDlWMQACKkshOMcpzJUIQ1TlhekMzJy87vThzZu+GT16g/Hxh5apxcX52ZnJxY7c1QWoVG90tpJqgrphPNLmmOC34U+9FJJJ5gkROTcMuGEAkbTcm2FddJ5OTH+6OnT+7dunD9z6kC7PUNpcva7w8N3r9+/dy3LW1xToA/BTUBTZ92AL1X9wlYaHNOyWAbwA98BjHdzcXZ25sWe3V+tX7+SS3r92vm1a1dcOHf8yuXTBemCr4FMWhhW5wIwryGU5bYX3krHFaSehjFVDACQsWG0lQlpgxfSiYwmwrCT3x089/3hdntu5MGNtWs/nJt7AW0iLurJi5sEVCmBpsJW5jgnwamjwD36ejDIcmUYIZ0fLp7Yt3drozF98MCunds/bzRnQMWl6je2Q+gEzf+qlGCasJcfwhxdKiJzeJZCZAGPUopS6ErJ0GfK7t6+vHfPl1OTj/d9/fmVS8e73QUusqTdSNqNNG0ZL4GC73fURaMTGApAe3SIM+oavq+bjaFaDMnlxfMnvj24e+832/7x1//z8qVTyohusjg5OdZoznSSpjSBfA5puqYwYQHKAIw0uqS4LkRkXsPZD9YN8Lw4HiUtn5l/8da7b0xNPe0kC+fPHtmw4W/dbjMUbKO2OXQnrlSQe0ATDaIIHpFpktIO00SVkshcekEthQgI8vHJl6Off7Zqfm6i2ZjZsXXTsSN7mSDKCKUFYZmsh6q4ZbZngbdUXi4znqEnplQAAzy2dAL4CmqI8lJZLhQZfXTr0IEd48+G87z59l9/f+PqGc672jCpmNZCGwluPtxhDSGwadiZgJRI7GWWRdeQsl88f2Lrlo0vJ54MXr/wD//4P2ZmX2BMxyVlgkjDseYVbBusnmGQCyB9hqWwUA8A7Vx2YWTuYbkLnp04deDP//lvQpFXE6ObN6365uuvuCygOSr2xlE40J9fwLZ8YBfBMFJVQK0O6nbMMeF4ITKpaZa3Thz95uC+bVrz4fuDq1d/ODx8Q2r+7NnIvbtX06wtTL+gEWZ0nJCWw4MgXQXUFZVFxpJ+e7ETQF4LL7hlVObz8xNbvlq/d8+XadpsLEwc3PfVq4kRpYiQRdJu3L9z1XsDtlR5CWwtjnoht9XviC+VrfsxlRGQHAvFhGLQUzc+/vijD9+6d/cql/TYkb0rV75DaEpYBs5VG6m00E5yyyCdwwgDgwxYRrg02BtcZ2boALY7AymljABZC3XaUqW0c/K7g3/882+PHNq9YsWb69eveOedN27dvAjtyCHvLpfQE8owaJ/RYO7rzBLghLoPVLzhvrnj0omcp9ryxsKrv6148+K5o51k4es9W9599y9D968Tmp46eXDzpjWNxrSuVT8euQLfiZNJhGV5kWgjicixasYMDebdcuGE8pJrOj4+snXLhpuD560TJ499vWfXZ4uLU1rTC2ePrF+7YtXK927duGyrMEaIAmR7FoQemsEQXV0p5J4glMWYCOTszu0f9+z+anr6OeXF1i0bd+38grG8222tWPHX//rf/stnn62Gb8ql04BoV2U092h6ut8aYTmMmQ4gewce1JWm39Dd08JxpkhGkys/nfnh0omJ8Uf37/306OHNLG8xkcd5TzybYOoKFEQr/RapugIM6wLV5kJk3PEkXyQyt162WrObNn784ft/OfLt7tOnvt23d/vg9QvtzsLNwUvHjuztdBootqqU8DxQ8fZ1zQCyF8oLEM2UdjCWZoZyxwuZt4tF5SWV+fj4yM6/b7p25fTVyyf/8Ptf79mx8cWzYc67c7PPBSec5W/86XcavVStFlhVxEYnuB/bs5hlQiwG3VVKC6DSjhz6+ssv1s/OTly/dv6f/vl/P3ky1GhME5p2Oo0s72zetCbpLua0iyePa5nIb8MLINTiogW3rM8Koe8MI6j1KBO03jBVCEmg50VCd0xNScctyJh6YicxvICbIDLvZM122sh5CqINtQLmQosw1EeT9vzwvasL86/m5ydHRm632vNMkOHhGxfOHW93FrB63M9WYbinJtNhNQPtAsLkBPRqYO0+ZYnyUlo2PT225av1b735h5uD5y+cPbT6k7dfvhhRmghZFHkyOnLnzKlDqu6+RN8JRgUKjdjVABhg7gQJMSglvFBGDN8f/OjDtzZs+PjkiQN//ONvP/jgzVZrXluZZu2he9d3bN8Mxjlu+Qyuyku4BJg6uKIwfQkLfbbL4PSVQ3LclBoMFJNEWp7lLS4LaHOSikIbAMS32grrpS8Ncp6QHgR3UhlVN8NRVXRJGxQUNCbnaSFzuBttuTRMKGJDyZcISbWVxsprV8/t37e91Z4H7USXHIq1pdJOmlIbp4Rm2MAdBvCc4JoSmUNMIEtBLQ19YnVnqPPSOg6HL5U2LOk0frp0utWeh1Y01JX+NgDRrLyuR9ttZYxX1mvjFTDJcCgrlBVS83ZnoZu1mCCdbhMUVxlBabZn95e//qf/1WrNSQgOIAMppXRCWgYldzhAL1U9fQyrCq1+v0DBv85O1fmsXHYYJ3CoAb8GqboyApkRLK6ZUkP22Rd2L6UXROZd0u6SNlMF/MuWSrtQeAIz/tOV704c39tqzcrahYAvUPWMXJwIxQd+AUfksQgcqRrXpZShn1QYJ5LOwr6vt4w8uPHq5WhStGDJwvQHGyMAAAUsSURBVI4KPa1xg4V6NwbwUKAotUnoj91jqg0/77d2KqI0IzTJ83ZBOrt2bn41MQq9hkhWoPGLUz6UY/Q4kK4sqXe+TsTj27LncagK6eay6jN5MQMOM/GYQWNG63oOZlr7XYN1jxI0fctoEwDpOGRBMAUw+uj2pYvHW61ZxBJk8/UJvRha+BBmS0Q0jL0EeFQ+w2AprZe3bl5cs+r9bVs/3bplQ5e0pRPBSUcjuksCEyj51fE8hCdLjDN+OTqgVbObNO7euTIx/ujwt7sK0oF7wDJqv33utc0DMGHD/Rx+uXyNb5dS1X0iv64eaFfWFccyaHNZeSZI2AplaRm87HnIlsDNiHpgPXTMKiKd0PVuA6qOmaFvPRh2K2DJEML+dHS0WcFyaxyn/OUSMReGMRXiQwWjP5pCp1aaLbbbc4QmMOIDwC8BI8pP8KiHBm3YdGPpbG+cuelKMVlAIDI0dO3G4Pksb2nLYdAd9bJ/RIT2MtnFiGw5nDGiVa+EfKgGVUfNBrouzWhfl0LjauLrlQ2g4Ps9L0HYNUTYyx5bldJEhQJsMNeW91Uh2uggaEYZwEPfhgO2mNLEuqXqlj4QL+i9w0kHGFSCpItHu5L05yxxjizeMKEK7GZ/wgvz42h7mYCupnChEJHAdDB2O1T9cqaNmAqw27gCcQa8HE7gqLAM4uvJU/SdbukMpSs1Vo9dXIiPeAlf9ySYUmM6hc2G8IR9panNiPESN2SIaW4c40JzhyF0QLdOjWQdPuDuB3H1Jl4FuKiN1i6WpGVaBfagf+bIniNPpOvNSHi0d4aoqWmJQ2f1yAr2AMdsTFn1i6nGiUAa48xab4mLgbe/AOfSokyA09bD9HFCUo+g9GFDOJeVLEINwUkMaENqpWkhMsyc+h0nXkrHwXNY1+/h8LUGQJ6AP8FcWdabDMTJTLBOS9tZ0KtB8GJ71kZznyi42nIZdbTGlhavq6NBT7xKDCG6TySnEE64HFiCwIHH5bZIQSGvhYui4Ymf65fhjMfrIUatwxxZ7yUUvJr1EiJbDHz+PyGVccp4FQsp5FLQkQxUJJQO6mfmONeBkwKu1l34sqxbxVApQ/pRKxMSUrAWr8McQIJW1XqsDMuZYGz7KoX95WWfc8dNpEAj0QDg2A/SDmGmup4401WIQuIHBJGNEUXDa+rdb2TN5aJtxyet4aw8NmNiD5ivHJRVQw5nhdRMKIpduNB96UrtK+MrYxwknca4pa1f/RRIGy+148ZLZbn1UlmubHjULmnDDi19y1YqZbnQVFmundBOqJp/l9HmWoHlgtQ7ghOD50BsuoCiinYRQrXjlnFNqCy4JtIy2PvEVEpG2/0sHxeIYuaYG4LvLKEhHZeGcUXgL1fE1MY8Hj+Fni4L266UCndkqY+gIcYr41XYhKEyS3YuKaN91l6n47GZ0ZUGStDIcdfl/n6vCtZYoDEz9qC1yQ13D804sAEVDADFEybqtd1dlgWEfR9WK2XoR4l5+WiDnjg/wWQjhhO3lkMmL87TMUJG144VMbxPzL6Ul0z1d86DW2L1kAxMlsF4hXFSakpYFyIv3IvFxhvM9WpyracBv2UJ5JJMsnQDca01ZBR1BIRaGOqIVajbQcdQrXMaDAWGgvD2F5NX61VetPOijSIJcTnyZBi84ZZq6BRjb4FwLskZfD8D4/XQaiwBGNCj9uC2H2hIlzm5OEldkjLWChpcV5QawQl5tK8XZDjxpg1oz8GYm3psKxSMI+8Lm9wFOGu/FieTcVbpK/f/AHpaRupOV2j5AAAAAElFTkSuQmCC)
If a compound pipe is to be replaced by a pipe of uniform diameter (known as equivalent pipe),then the loss of head and discharge of both the pipes should be same. The uniform diameter (d) of the equivalent pipe may be obtained from the following relation:
where
l = Length of the equivalent pipe = l1 + l2 + l3
Read more about pipes in parallel to learn the difference between both these techniques.
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