LAMINARANDTURBULENTFLOWOBSERVATIONSHOWSTHATTWOENTIRELYDIFFERENTTYPESOFFLUIDFLOWEXISTTHISWASDEMONSTRATEDBYOSBORNEREYNOLDSIN1883THROUGHANEXPERIMENTINWHICHWATERWASDISCHARGEDFROMATANKTHROUGHAGLASSTUBETHERATEOFFLOWCOULDBECONTROLLEDBYAVALVEATTHEOUTLET,ANDAFINEFILAMENTOFDYEINJECTEDATTHEENTRANCETOTHETUBEATLOWVELOCITIES,ITWASFOUNDTHATTHEDYEFILAMENTREMAINEDINTACTTHROUGHOUTTHELENGTHOFTHETUBE,SHOWINGTHATTHEPARTICLESOFWATERMOVEDINPARALLELLINESTHISTYPEOFFLOWISKNOWNASLAMINAR,VISCOUSORSTREAMLINE,THEPARTICLESOFFLUIDMOVINGINANORDERLYMANNERANDRETAININGTHESAMERELATIVEPOSITIONSINSUCCESSIVECROSSSECTIONSASTHEVELOCITYINTHETUBEWASINCREASEDBYOPENINGTHEOUTLETVALVE,APOINTWASEVENTUALLYREACHEDATWHICHTHEDYEFILAMENTATFIRSTBEGANTOOSCILLATEANDTHENBROKEUPSOTHATTHECOLOURWASDIFFUSEDOVERTHEWHOLECROSSSECTION,SHOWINGTHATTHEPARTICLESOFFLUIDNOLONGERMOVEDINANORDERLYMANNERBUTOCCUPIEDDIFFERENTRELATIVEPOSITIONINSUCCESSIVECROSSSECTIONSTHISTYPEOFFLOWISKNOWNASTURBULENTANDISCHARACTERIZEDBYCONTINUOUSSMALLFLUCTUATIONSINTHEMAGNITUDEANDDIRECTIONOFTHEVELOCITYOFTHEFLUIDPARTICLES,WHICHAREACCOMPANIEDBYCORRESPONDINGSMALLFLUCTUATIONSOFPRESSUREWHENTHEMOTIONOFAFLUIDPARTICLEINASTREAMISDISTURBED,ITSINERTIAWILLTENDTOCARRYITONINTHENEWDIRECTION,BUTTHEVISCOUSFORCESDUETOTHESURROUNDINGFLUIDWILLTENDTOMAKEITCONFORMTOTHEMOTIONOFTHERESTOFTHESTREAMINVISCOUSFLOW,THEVISCOUSSHEARSTRESSESARESUFFICIENTTOELIMINATETHEEFFECTSOFANYDEVIATION,BUTINTURBULENTFLOWTHEYAREINADEQUATETHECRITERIONWHICHDETERMINESWHETHERFLOWWILLBEVISCOUSOFTURBULENTISTHEREFORETHERATIOOFTHEINERTIALFORCETOTHEVISCOUSFORCEACTINGONTHEPARTICLETHERATIOVLCONSTFREVISCOUINTALTHUS,THECRITERIONWHICHDETERMINESWHETHERFLOWISVISCOUSORTURBULENTISTHEQUANTITYVL/,KNOWNASTHEREYNOLDSNUMBERITISARATIOOFFORCESAND,THEREFORE,APURENUMBERANDMAYALSOBEWRITTENASUL/VWHEREISTHEKINEMATICVISCOSITYV/EXPERIMENTSCARRIEDOUTWITHANUMBEROFDIFFERENTFLUIDSINSTRAIGHTPIPESOFDIFFERENTDIAMETERSHAVEESTABLISHEDTHATIFTHEREYNOLDSNUMBERISCALCULATEDBYMAKING1EQUALTOTHEPIPEDIAMETERANDUSINGTHEMEANVELOCITYV,THEN,BELOWACRITICALVALUEOFVD/2000,FLOWWILLNORMALLYBELAMINARVISCOUS,ANYTENDENCYTOTURBULENCEBEINGDAMPEDOUTBYVISCOUSFRICTIONTHISVALUEOFTHEREYNOLDSNUMBERAPPLIESONLYTOFLOWINPIPES,BUTCRITICALVALUESOFTHEREYNOLDSNUMBERCANBEESTABLISHEDFOROTHERTYPESOFFLOW,CHOOSINGASUITABLECHARACTERISTICLENGTHSUCHASTHECHORDOFANAEROFOILINPLACEOFTHEPIPEDIAMETERFORAGIVENFLUIDFLOWINGINAPIPEOFAGIVENDIAMETER,THEREWILLBEACRITICALVELOCITYOFFLOWCORRESPONDINGTOTHECRITICALVALUEOFTHEREYNOLDSNUMBER,BELOWWHICHFLOWWILLBEVISCOUSINPIPES,ATVALUESOFTHEREYNOLDSNUMBER2000,FLOWWILLNOTNECESSARILYBETURBULENTLAMINARFLOWHASBEENMAINTAINEDUPTORE50,000,BUTCONDITIONSAREUNSTABLEANDANYDISTURBANCEWILLCAUSEREVERSIONTONORMALTURBULENTFLOWINSTRAIGHTPIPESOFCONSTANTDIAMETER,FLOWCANBEASSUMEDTOBETURBULENTIFTHEREYNOLDSNUMBEREXCEEDS4000PIPENETWORKSANEXTENSIONOFCOMPOUNDPIPESINPARALLELISACASEFREQUENTLYENCOUNTEREDINMUNICIPALDISTRIBUTIONSYSTEM,INWHICHTHEPIPESAREINTERCONNECTEDSOTHATTHEFLOWTOAGIVENOUTLETMAYCOMEBYSEVERALDIFFERENTPATHSINDEED,ITISFREQUENTLYIMPOSSIBLETOTELLBYINSPECTIONWHICHWAYTHEFLOWTRAVELSNEVERTHELESS,THEFLOWINANYNETWORKS,HOWEVERCOMPLICATED,MUSTSATISFYTHEBASICRELATIONSOFCONTINUITYANDENERGYASFOLLOWS1THEFLOWINTOANYJUNCTIONMUSTEQUALTHEFLOWOUTOFIT2THEFLOWINEACHPIPEMUSTSATISFYTHEPIPEFRICTIONLAWSFORFLOWINASINGLEPIPE3THEALGEBRAICSUMOFTHEHEADLOSSESAROUNDANYCLOSEDCIRCUITMUSTBEZEROPIPENETWORKSAREGENERALLYTOOCOMPLICATEDTOSOLVEANALYTICALLY,ASWASPOSSIBLEINTHESIMPLERCASESOFPARALLELPIPESAPRACTICALPROCEDUREISTHEMETHODOFSUCCESSIVEAPPROXIMATIONS,INTRODUCEDBYCROSSITCONSISTSOFTHEFOLLOWINGELEMENTS,INORDER1BYCAREFULINSPECTIONASSUMETHEMOSTREASONABLEDISTRIBUTIONOFFLOWSTHATSATISFIESCONDITION12WRITECONDITION2FOREACHPIPEINTHEFORMHLKQN75WHEREKISACONSTANTFOREACHPIPEFOREXAMPLE,THESTANDARDPIPEFRICTIONEQUATIONWOULDYIELDK1/C2ANDN2FORCONSTANTFMINORLOSSESWITHINANYCIRCUITMAYBEINCLUDED,BUTMINORLOSSESATTHEJUNCTIONPOINTSARENEGLECTED3TOINVESTIGATECONDITION3,COMPUTETHEALGEBRAICSUMOFTHEHEADLOSSESAROUNDEACHELEMENTARYCIRCUITHLKQNCONSIDERLOSSESFROMCLOCKWISEFLOWSASPOSITIVE,COUNTERCLOCKWISENEGATIVEONLYBYGOODLUCKWILLTHESEADDTOZEROONTHEFIRSTTRIAL4ADJUSTTHEFLOWINEACHCIRCUITBYACORRECTION,Q,TOBALANCETHEHEADINTHATCIRCUITANDGIVEKQN0THEHEARTOFTHISMETHODLIESINTHEDETERMINATIONOFQFORANYPIPEWEMAYWRITEQQ0QWHEREQISTHECORRECTDISCHARGEANDQ0ISTHEASSUMEDDISCHARGETHEN,FORACIRCUIT76010/HNKLITMUSTBEEMPHASIZEDAGAINTHATTHENUMERATOROFEQ76ISTOBESUMMEDALGEBRAICALLY,WITHDUEACCOUNTOFSIGN,WHILETHEDENOMINATORISSUMMEDARITHMETICALLYTHENEGATIVESIGNINEQ76INDICATESTHATWHENTHEREISANEXCESSOFHEADLOSSAROUNDALOOPINTHECLOCKWISEDIRECTION,THEQMUSTBESUBTRACTEDFROMCLOCKWISEQ0SANDADDEDTOCOUNTERCLOCKWISEONESTHEREVERSEISTRUEIFTHEREISADEFICIENCYOFHEADLOSSAROUNDALOOPINTHECLOCKWISEDIRECTION5AFTEREACHCIRCUITISGIVENAFIRSTCORRECTION,THELOSSESWILLSTILLNOTBALANCEBECAUSEOFTHEINTERACTIONOFONECIRCUITUPONANOTHERPIPESWHICHARECOMMONTOTWOCIRCUITSRECEIVETWOINDEPENDENTCORRECTIONS,ONEFOREACHCIRCUITTHEPROCEDUREISREPEATED,ARRIVINGATASECONDCORRECTION,ANDSOON,UNTILTHECORRECTIONSBECOMENEGLIGIBLEEITHERFORMOFEQ76MAYBEUSEDTOFINDQASVALUESOFKAPPEARINBOTHNU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STRAIGHTPIPESOFSAMELENGTHBUTDIFFERENTDIAMETERS,RIGIDLYHELDATBOTHENDSANDWITHTEMPERATURERAISEDBYSAY100C,TOTALMAGNITUDEOFLINEARFORCESAGAINSTFIXEDPOINTSWOULDBENEARENOUGHPROPORTIONATETOTHERESPECTIVEDIAMETERSITISTHEREFOREESSENTIALTHATDESIGNOFANYPIPINGLAYOUTMAKESADEQUATECOMPENSATORYPROVISIONFORSUCHTHERMALINFLUENCEBYRELIEVINGTHESYSTEMOFLINEARSTRESSESWHICHWOULDBEDIRECTLYRELATEDTOLENGTHOFPIPEWORKBETWEENFIXEDPOINTSANDTHERANGEOFOPERATIONALTEMPERATURESCOMPENSATIONFORFORCESDUETOTHERMALEXPANSIONTHEIDEALPIPEWORKASFARASEXPANSIONISCONCERNED,ISONEWHEREMAXIMUMFREEMOVEMENTWITHTHEMINIMUMOFRESTRAINTISPOSSIBLEHENCETHESIMPLESTANDMOSTECONOMICALWAYTOENSURECOMPENSATIONANDRELIEFOFFORCESISTOTAKEADVANTAGEOFCHANGESINDIRECTION,ORWHERETHISISNOTPARTOFTHELAYOUTANDLONGSTRAIGHTRUNSAREINVOLVEDITMAYBEFEASIBLETOINTRODUCEDELIBERATEDOGLEGOFFSETCHANGESINDIRECTIONATSUITABLEINTERVALSASANALTERNATIVE,ATCALCULATEDINTERVALSINASTRAIGHTPIPERUNSPECIALLYDESIGNEDEXPANSIONLOOPSOR“U”BENDSSHOULDBEINSERTEDDEPENDINGUPONDESIGNANDSPACEAVAILABILITY,EXPANSIONBENDSWITHINASTRAIGHTPIPERUNCANFEATURETHESOCALLEDDOUBLEOFFSET“U”BANDORTHEHORSESHOETYPEOR“LYRE”LOOPTHELASTNAMEDARESELDOMUSEDFORLARGEHEATINGNETWORKSTHEYCANBESUPPLIEDINMANUFACTURERSSTANDARDUNITSBUTREQUIREELABORATECONSTRUCTIONALWORKSFORUNDERGROUNDINSTALLATIONANCHOREDTHERMALMOVEMENTINUNDERGROUNDPIPINGWOULDNORMALLYBEABSORBEDBYTHREEBASICTYPESOFEXPANSIONBENDSANDTHESEINCLUDETHE“U”BEND,THE“L”BENDANDTHE“Z”BENDINCASESOF90CHANGESINDIRECTIONTHE“L”AND“Z”BENDSAREUSEDPRINCIPLESINVOLVEDINTHEDESIGNOFPROVISIONFOREXPANSIONBETWEENANCHORPOINTSAREVIRTUALLYTHESAMEFORALLTHREETYPESOFCOMPENSATORTHEOFFSET“U”BENDISUSUALLYMADEUPFROMFOUR90ELBOWSANDSTRAIGHTPIPESITPERMITSGOODTHERMALDISPLACEMENTANDIMPOSESSMALLERANCHORLOADSTHANTHEOTHERTYPEOFLOOPTHISSHAPEOFEXPANSIONBENDISTHESTANDARDISEDPATTERNFORPREFABRICATEDPIPEINPIPESYSTEMSALLTHERMALCOMPENSATORSAREINSTALLEDTOACCOMMODATEANEQUALAMOUNTOFEXPANSIONORCONTRACTIONTHEREFORETOOBTAINFULLADVANTAGEOFTHELENGTHOFTHERMALMOVEMENTITISNECESSARYTOEXTENDTHEUNITDURINGINSTALLATIONTHUSOPENINGUPTHELOOPBYANEXTENTROUGHLYEQUALTHEHALFTHEOVERALLCALCULATEDTHERMALMOVEMENTTHISISDONEBY“COLDPULL”OROTHERMECHANICALMEANSTHETOTALAMOUNTOFEXTENSIONBETWEENTWOFIXEDPOINTSHASTOBECALCULATEDONBASISOFAMBIENTTEMPERATUREPREVAILINGANDOPERATIONALDESIGNTEMPERATURESSOTHATDISTRIBUTIONOFSTRESSESANDREACTIONSATLOWERANDHIGHERTEMPERATURESARECONTROLLEDWITHINPERMISSIBLELIMITSPRESTRESSINGDOESNOTAFFECTTHEFATIGUELIFEOFPIPINGTHEREFOREITDOESNOTFEATUREINCALCULATIONOFPIPEWORKSTRESSESTHEREARENUMEROUSSPECIALISTPUBLICATIONDEALINGWITHDESIGNANDSTRESSINGCALCULATIONSFORPIPINGANDESPECIALLYFORPROPRIETARYPIPINGANDEXPANSIONUNITSCOMPREHENSIVEEXPERIENCEBACKDESIGNDATAASWELLASCHARTSANDGRAPHSMAYBEOBTAINEDINMANUFACTURERSPUBLICATIONS,OFFERINGSOLUTIONSFOREVERYKINDOFPIPESTRESSINGPROBLEMASANALTERNATIVETOABOVEMENTIONEDMETHODSOFCOMPENSATIONFORTHERMALEXPANSIONANDUSEABLEINPLACESWHERESPACEISRESTRICTED,ISTHEMOREEXPENSIVEBELLOWSORTELESCOPICTYPEMECHANICALCOMPENSATORTHEREAREMANYPROPRIETARYTYPESANDMODELSONTHEMARKETANDTHEFOLLOWINGTYPESOFCOMPENSATORSAREGENERALLYUSEDTHEBELLOWSTYPEEXPANSIONUNITINFORMOFANAXIALCOMPENSATORPROVIDESFOREXPANSIONMOVEMENTINAPIPEALONGITSAXISMOTIONINTHISBELLOWSISDUETOTENSIONORCOMPRESSIONONLYTHEREAREALSOARTICULATEDBELLOWSUNITSRESTRAINEDWHICHCOMBINEANGULARANDLATERALMOVEMENTTHEYCONSISTOFDOUBLECOMPENSATORUNITSRESTRAINEDBYSTRAPSPINNEDOVERTHECENTEROFEACHBELLOWSORDOUBLETIEDTHUSBEINGRESTRAINEDOVERITSLENGTHSUCHCOMPENSATORSARESUITABLEFORACCOMMODATINGVERYPIPELINEEXPANSIONANDALSOFORCOMBINATIONSOFANGULARANDLATERALMOVEMENTS層流與紊流有兩種完全不同的流體流動形式存在，這一點在1883年就由OSBORNEREYNOLDS用試驗演示證明。在試驗里，水通過玻璃管從水箱里放出。流量由出口處的閥門來控制，一股很細的染色流束由入口注入玻璃管內。在較低的流速時，可以看到染色流束在玻璃管中保持著一條完整的遷流。這表明流體粒子以平行的層狀流動。這種粘性流體的流動就是我們所知的層流，流體各層的質點以有序的方式移動，并在連續的截面上保持著相同的相對位置。打開出口閥門，管子里的速度就提高。隨著速度提高，最后會達到這樣的程度，即染色流束起初開始擺動然后破碎，這樣顏色就擴散在整個截面上，這表明流體粒子已不再有次序流動卻在連續的截面上占有相對不同的位置。這種流體的流動形式就是紊流，它的特點就是不斷產生無數大小不等的渦團，質點摻混使得空間各點的速度隨時間無規則地變化。與之相關聯，壓強也隨之無規則地變化。當一條流束中的某個流體粒子的運動被擾亂，則它的慣性會使它移向新的方向，但周圍流體的粘滯力會使它與其余流束的運動保持一致。在粘性流體中，粘性切應力足以抵消任何偏差的影響，但在紊流中是不夠的。因此，確定流動是粘滯性的還是紊流性的標準就是作用在粒子上的慣性力和粘性力之比VLCONSTFREVISCOUINTAL這樣，用來判斷流動是粘滯性的還是紊流性的標準就是VL/，也就是雷諾數。這是力之間的比，因此理論上也可以寫成UL/V（V/，流體的運動粘滯系數）。在不同管徑的直管里用許多不同流體所進行的試驗已經證實，如雷諾數是通過使L等于管徑并且使用平均速度V來計算，那么在低于臨界值VD/2000的條件下流動一般是層流（粘滯流動），任何紊流的傾向都會由于粘滯摩擦而受到抑制。這個雷諾數的值僅適用于管道中的流體，但雷諾數的臨界值可以用來確定其他形式的流動，例如選擇合適的弦桿翼剖面來代替管道直徑。對于已知直徑的管道中的流體而言，會有一個臨界流速VC，以及對應的雷諾數，如果低于這個數，則表明流體是粘滯流動。在管道中，雷諾數值大于2000的情況下，流體不一定就變為紊流。層流可以維持到RE50,000,但是條件并不穩定，任何干擾都會使其它又變為一般的紊流。在直徑一定的直管中，如果雷諾數超過4000那么流體就有可能變為紊流。管網平行復合管道的延伸是市政分配系統中常見的一種情況，在這種情況下管道相互連接，使得通向某一出口的流體可以來自不同的路徑。的確，通過觀察往往很難說清楚流體將流經哪一個管路。但是，不管管網有多復雜，其中的流體都必須確保連續性與能量的基礎關系。如下所述1流入接合處的流體必須與流出的等量；2在每根管中的流體都必須滿足流體在單管中的管道摩擦定律；3在任何閉合回路中，水頭損失的代數和必須為0。管網一般來講由于太過復雜而難以分析解決，但在簡單一些的情況下是可以的，例如平行管。CROSS介紹了一種實用的程序，采用的是連續性近似法。它由以下的原理組成，包括1通過仔細的觀察采取最合理的流體分配方案以滿足條件1；2對每根管道以方程HLKQN來判斷是否滿足條件2，式中K是每根管的特性常數。例如，標準管道摩擦方程中的K1/C2以及N2。任何環路中較小的沿程水頭損失可能是包括的，但局部水頭損失可以忽略不計。3為了研究條件3，計算每個基本環路中水頭損失的代數和。HLKQN。假設順時針方向流動的損失為正，逆時針的則為負，那么在第一次試驗中，它們的和只有在非常幸運的情況下才會為零。4通過一個修正值Q來調整每條環路中的流體，使該管路中的水頭平衡，并給出KQN0。這個方法的核心取決于Q的確定。對于任何管道我們有QQ0Q式中Q是準確的流量而Q0是假定的流量。那么，對于一個環路而言76010/QHNKL必須再次強調的是方程76的分子和分母都是采用了適當的計算符號確定的。方程76中的負號表明，當順時針方向的環路上有過量的水頭損失時，Q必須從順時針方向的Q0中減去，并增加到逆時針方向上去。如果順時針方向的環路上水頭損失不足時，情況正好相反。5在每條環路都給予了一個最初的修正值后，由于環路之間的相互影響，損失仍不平衡（一些兩條環路共有的管道就有兩個單獨的修正值，每個值對應一條環路）。重復這樣的程序，獲得第二個修正值，乃至第三、第四個等等，直到修正值可以忽略不計。方程76的兩種形式都可以用來找出Q。由于K值同時出現在第一種形式的分子和分母上，相應實際的K值就可以用來確定分配量。結合水管的管道摩擦力圖表，第二種方程形式使用起來最簡便。近似法最吸引人的一個特點就是計算上的誤差與判斷誤差有相同的效果，而最終它們會在過程中被加以改正。管網問題非常適合于采用計算機來解決。編制程序需花費大量的時間和精力，但是一旦完成，就有很大的機動靈活性，許多耗人費時的勞動就可省去。更高壓力下塑料管道的前景美國煤氣協會AGA的一個針對塑料管道的專案小組的成員討論了在較高壓力下使用聚乙烯輸氣管的的可能性。討論的主題包括有設計方程（其中包括國際科學組織ISO在更新版本上完成的工作），以及對PE管樹脂上裂縫快速擴展的評估。這一點非常重要，因為當管道在較高壓力下使用、而管徑更大的情況下，鋼筋混凝土管的可能性增加了。若干年以前，AGA的塑料管道設計任務小組檢查了設計方程，以確定是否能在塑料管道系統中使用更高的工作壓力。小組成員認為管道樹脂的性能并沒有通過設計方程反映出來。一般認為新的樹脂塑管在耐用性上遠遠勝過過去的樹脂塑管，因此主要考慮的問題是新方程的發展以及合適的設計要素的選擇。改良的管道性能許多設備用來監測塑料管道樹脂的性能。在這里講述一下一些針對典型的輸氣管道樹脂進行過的耐久性測試，以及幾種性能上的變化。溫升爆裂測試他們使用像溫升爆裂測試之類的測試。在這一測試中管系的耐久性能通過高溫和高壓下管壁形成脆裂所需的時間來校核（通常是80攝氏度和45MPA的環壓下）。在供應燃氣時我們希望老的樹脂塑管在80攝氏度、3MPA的環壓下至少可以堅持使用170個小時。推斷表明通過了這些極限的樹脂預期其壽命應該能超過50年。裝運時對這些樹脂塑管質量檢測，有時會由于沒有達到這一標準而對該產品拒絕使用。在相同溫度條件下，今天的樹脂塑管在46MPA環壓下可持續使用數千小時。測試表明用新樹脂制造的管道可使用超過5700小時而沒有任何損壞。這些結果是在臨測試前檢出的（樹脂）抽樣得出的。這種壓力從未在早期的測試中使用過。根據工作條件推斷，測試性能上的區別與數百年的壽命增長是相等的（某些情況下甚至是數千年）。環壓下的防裂測試也有些公司進行了環壓下的防裂測試，用來測量管道中脆裂的形成，并加大了壓力來減短測試的時間。這個試驗表明了在防止脆裂上的驚人的改進。例如，在我的公司里對于我們的早期樹脂塑管進行試驗需要20小時以上的時間和50攝氏度的溫度。而現在的樹脂塑管能夠良好地持續1000小時以上而沒有損壞。槽口測試可以快速進行的槽口測試，用來測量帶有槽口的管道或專門澆鑄的試驗管中脆裂的形成。這對新的樹脂塑管非常重要，因為其他的試驗需要很長的時間才能使管道發生損