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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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假定的流量。那么,对于一个环路而言76010/QHNKL必须再次强调的是方程76的分子和分母都是采用了适当的计算符号确定的。方程76中的负号表明,当顺时针方向的环路上有过量的水头损失时,Q必须从顺时针方向的Q0中减去,并增加到逆时针方向上去。如果顺时针方向的环路上水头损失不足时,情况正好相反。5在每条环路都给予了一个最初的修正值后,由于环路之间的相互影响,损失仍不平衡(一些两条环路共有的管道就有两个单独的修正值,每个值对应一条环路)。重复这样的程序,获得第二个修正值,乃至第三、第四个等等,直到修正值可以忽略不计。方程76的两种形式都可以用来找出Q。由于K值同时出现在第一种形式的分子和分母上,相应实际的K值就可以用来确定分配量。结合水管的管道摩擦力图表,第二种方程形式使用起来最简便。近似法最吸引人的一个特点就是计算上的误差与判断误差有相同的效果,而最终它们会在过程中被加以改正。管网问题非常适合于采用计算机来解决。编制程序需花费大量的时间和精力,但是一旦完成,就有很大的机动灵活性,许多耗人费时的劳动就可省去。更高压力下塑料管道的前景美国煤气协会AGA的一个针对塑料管道的专案小组的成员讨论了在较高压力下使用聚乙烯输气管的的可能性。讨论的主题包括有设计方程(其中包括国际科学组织ISO在更新版本上完成的工作),以及对PE管树脂上裂缝快速扩展的评估。这一点非常重要,因为当管道在较高压力下使用、而管径更大的情况下,钢筋混凝土管的可能性增加了。若干年以前,AGA的塑料管道设计任务小组检查了设计方程,以确定是否能在塑料管道系统中使用更高的工作压力。小组成员认为管道树脂的性能并没有通过设计方程反映出来。一般认为新的树脂塑管在耐用性上远远胜过过去的树脂塑管,因此主要考虑的问题是新方程的发展以及合适的设计要素的选择。改良的管道性能许多设备用来监测塑料管道树脂的性能。在这里讲述一下一些针对典型的输气管道树脂进行过的耐久性测试,以及几种性能上的变化。温升爆裂测试他们使用像温升爆裂测试之类的测试。在这一测试中管系的耐久性能通过高温和高压下管壁形成脆裂所需的时间来校核(通常是80摄氏度和45MPA的环压下)。在供应燃气时我们希望老的树脂塑管在80摄氏度、3MPA的环压下至少可以坚持使用170个小时。推断表明通过了这些极限的树脂预期其寿命应该能超过50年。装运时对这些树脂塑管质量检测,有时会由于没有达到这一标准而对该产品拒绝使用。在相同温度条件下,今天的树脂塑管在46MPA环压下可持续使用数千小时。测试表明用新树脂制造的管道可使用超过5700小时而没有任何损坏。这些结果是在临测试前检出的(树脂)抽样得出的。这种压力从未在早期的测试中使用过。根据工作条件推断,测试性能上的区别与数百年的寿命增长是相等的(某些情况下甚至是数千年)。环压下的防裂测试也有些公司进行了环压下的防裂测试,用来测量管道中脆裂的形成,并加大了压力来减短测试的时间。这个试验表明了在防止脆裂上的惊人的改进。例如,在我的公司里对于我们的早期树脂塑管进行试验需要20小时以上的时间和50摄氏度的温度。而现在的树脂塑管能够良好地持续1000小时以上而没有损坏。槽口测试可以快速进行的槽口测试,用来测量带有槽口的管道或专门浇铸的试验管中脆裂的形成。这对新的树脂塑管非常重要,因为其他的试验需要很长的时间才能使管道发生损

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