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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,UNTILTHECORRECTIONSBECOMENEGLIGIBLEEITHERFORMOFEQ76MAYBEUSEDTOFINDQASVALUESOFKAPPEARINBOTHNUMERATORANDDENOMINATOROFTHEFIRSTFORM,VALUESPROPORTIONALTOTHEACTUALKMAYBEUSEDTOFINDTHEDISTRIBUTIONTHESECONDFORMWILLBEFOUNDMOSTCONVENIENTFORUSEWITHPIPEFRICTIONDIAGRAMSFORWATERPIPESANATTRACTIVEFEATUREOFTHEAPPROXIMATIONMETHODISTHATERRORSINCOMPUTATIONHAVETHESAMEEFFECTASERRORSINJUDGMENTANDWILLEVENTUALLYBECORRECTEDBYTHEPROCESSTHEPIPENETWORKSPROBLEMLENDSITSELFWELLTOSOLUTIONBYUSEOFADIGITALCOMPUTERPROGRAMMINGTAKESTIMEANDCARE,BUTONCESETUP,THEREISGREATFLEXIBILITYANDMANYMANHOURSOFLABORCANBESAVEDTHEFUTUREOFPLASTICPIPEATHIGHERPRESSURESPARTICIPANTSINANAGAMEETINGPANELONPLASTICPIPEDISCUSSEDTHEPOSSIBILITYOFUSINGPOLYETHYLENEGASPIPEATHIGHERPRESSURESTOPICSINCLUDEDTHEDESIGNEQUATION,INCLUDINGWORKBEINGDONEBYISOONANUPDATEDVERSION,ANDTHEEVALUATIONOFRAPIDCRACKPROPAGATIONINAPEPIPERESINTHISISOFCRITICALIMPORTANCEBECAUSEASPIPEISUSEDATHIGHERPRESSUREANDINLARGERDIAMETERS,THEPOSSIBILITYOFRCPINCREASESSEVERALYEARSAGO,AGASPLASTICPIPEDESIGNEQUATIONTASKGROUPREVIEWEDTHEDESIGNEQUATIONTODETERMINEIFHIGHEROPERATINGPRESSURESCOULDBEUSEDINPLASTICPIPINGSYSTEMSMEMBERSFELTTHEPERFORMANCEOFOURPIPERESINSWASNOTTRULYREFLECTEDBYTHEDESIGNEQUATIONITWASGENERALLYACCEPTEDTHATTHELONGTERMPROPERTIESOFMODERNRESINSFARSURPASSEDTHOSEOFOLDERRESINSMAJORCONSIDERATIONSWERENEWEQUATIONSBEINGDEVELOPEDANDSELECTIONOFANAPPROPRIATEDESIGNFACTORIMPROVEDPIPEPERFORMANCEMANYUTILITIESMONITOREDTHEPERFORMANCEOFPLASTICPIPERESINSHEREARESOMEOFTHELONGTERMTESTSUSEDANDTHEKINDSOFPERFORMANCECHANGETHEYHAVESHOWNFORTYPICALGASPIPERESINSELEVATEDTEMPERATUREBURSTTESTTHEYUSEDTESTSLIKETHEELEVATEDTEMPERATUREBURSTTEST,INWHICHTHELONGTERMPERFORMANCEOFTHEPIPEISCHECKEDBYMEASURINGTHETIMEREQUIREDFORFORMATIONOFBRITTLECRACKSINTHEPIPEWALLUNDERHIGHTEMPERATURESANDPRESSURESOFTEN80DEGREESCANDAROUND4TO5MPAHOOPSTRESSATCONSUMERSGASWEEXPECTEDEARLYRESINSTOLASTATLEAST170HRSAT80DEGREESCANDAHOOPSTRESSOF3MPAEXTRAPOLATIONSHOWEDTHATRESINSPASSINGTHESELIMITSSHOULDHAVEALIFEEXPECTANCYOFMORETHAN50YRSQUALITYCONTROLTESTINGONSHIPMENTSOFPIPEMADEFROMTHESERESINSSOMETIMESRESULTEDINPRODUCTREJECTIONFORFAILURETOMEETTHISCRITERIONATTHESAMETEMPERATURE,TODAYSRESINSLASTTHOUSANDSOFHOURSATHOOPSTRESSESOF46MPATESTSPERFORMEDONPIPEMADEFROMNEWRESINSHAVEBEENTERMINATEDWITHNOFAILUREATTIMESEXCEEDING5,700HRSTHESERESULTSWEREPERFORMEDONSAMPLESTHATWERESQUEEZEDOFFBEFORETESTINGSUCHSTRESSESWERENEVERAPPLIEDINEARLYTESTINGWHENEXTRAPOLATEDTOOPERATINGCONDITIONS,THISDIFFERENCEINTESTPERFORMANCEISEQUIVALENTTOANINCREASEINLIFETIMEOFHUNDREDSANDINSOMECASESEVENTHOUSANDSOFYEARSENVIRONMENTALSTRESSCRACKRESISTANCETESTSOMECOMPANIESALSOUSEDTHEENVIRONMENTALSTRESSCRACKRESISTANCETESTWHICHMEASUREDBRITTLECRACKFORMATIONINPIPESBUTWHICHUSEDSTRESSCRACKINGAGENTSTOSHORTENTESTTIMESTHISTESTHASALSOSHOWNDRAMATICIMPROVEMENTINRESISTANCEBRITTLEFAILUREFOREXAMPLE,ATMYCOMPANYATESTTIMEOFMORETHAN20HRSAT50DEGREESCWASREQUIREDONOUREARLYRESINSTODAYSRESINSLASTWELLABOVE1,000HRSWITHNOFAILURENOTCHTESTSNOTCHTESTS,WHICHAREQUICKLYRUN,MEASUREBRITTLECRACKFORMATIONINNOTCHEDPIPEORMOLDEDCOUPONSAMPLESTHISISIMPORTANTFORTHENEWERRESINSSINCESOMEOTHERTESTSTOFAILURECANTAKEVERYLONGTIMESNOTCHTESTRESULTSSHOWTHATWHILEEARLYRESINSLASTEDFORTESTTIMESRANGINGBETWEEN1,000TO10,000MIN,CURRENTRESINSUSUALLYLASTFORLONGERTHAN200,000MINALLOFOURTESTSDEMONSTRATEDTHESAMETHINGNEWERRESINSAREMUCHMORERESISTANTTOTHEGROWTHOFBRITTLECRACKTHANTHEIRPREDECESSORSSINCEBRITTLEFAILUREISCONSIDEREDTOBETHEULTIMATEFAILUREMECHANISMINPOLYETHYLENEPIPES,WEKNOWTHATNEWMATERIALSWILLLASTMUCHLONGERTHANTHEOLDTHISISESPECIALLYREASSURINGTOTHEGASINDUSTRYSINCEMANYOFTHESEOLDERRESINSHAVEPERFORMEDVERYWELLINTHEFIELDFORTHEPAST25YRSWITHMINIMALDETECTABLECHANGEINPROPERTIESWHILETHETESTSSHOWEDGREATLYIMPROVEDPERFORMANCE,THEEQUATIONUSEDTOESTABLISHTHEPRESSURERATINGOFTHEPIPEISSTILLIDENTICALTOTHEORIGINALEXCEPTFORACHANGEIN1978TOASINGLEDESIGNFACTORFORALLCLASSLOCATIONSTOMANYITSEEMEDTHATTHEMETHODSUSEDTOPRESSURERATEOURPIPEWERENOWUNDULYCONSERVATIVEANDTHATANEWDESIGNEQUATIONWASNEEDEDATTHISTIMEWEBECAMEAWAREOFANEWEQUATIONBEINGBALLOTEDATISOTHEMETHODOLOGYBEINGUSEDSEEMEDTOBEAMORETECHNICALLYCORRECTMETHODOFANALYZINGTHEDATAANDOFFEREDANUMBEROFADVANTAGESTHERMALEXPANSIONOFPIPINGANDITSCOMPENSATIONAVERYRELEVANTCONSIDERATIONREQUIRINGCAREFULATTENTIONISTHEFACTTHATWITHTEMPERATUREOFALENGTHOFPIPERAISEDORLOWERED,THEREISACORRESPONDINGINCREASEORDECREASEINITSLENGTHANDCROSSSECTIONALAREABECAUSEOFTHEINHERENTCOEFFICIENTOFTHERMALEXPANSIONFORTHEPARTICULARPIPEMATERIALTHECOEFFICIENTOFEXPANSIONFORCARBONSTEELIS0012MM/MCANDFORCOPPER00168MM/MCRESPECTIVEMODULEOFELASTICITYAREFORSTEELE207106KN/M2ANDFORCOPPERE103106KN/M2ASANEXAMPLE,ASSUMINGABASETEMPERATUREFORWATERCONDUCTINGPIPINGAT0C,ASTEELPIPEOFANYDIAMETERIFHEATEDTO120CWOULDEXPERIENCEALINEAREXTENSIONOF14MMANDASIMILARLYIFHEATEDTOCOPPERPIPEWOULDEXTENDBY2016MMFOREACHMETEROFTHEIRRESPECTIVELENGTHSTHEUNITAXIALFORCEINTHESTEELPIPEHOWEVERWOULDBE39GREATERTHANFORCOPPERTHECHANGEINPIPEDIAMETERISOFNOPRACTICALCONSEQUENCETOLINEAREXTENSIONBUTTHEAXIALFORCESCREATEDBYEXPANSIONORCONTRACTIONARECONSIDERABLEANDCAPABLEOFFRACTURINGANYFITMENTSWHICHMAYTENDTOIMPOSEARESTRAINTTHEMAGNITUDEOFSUCHFORCESISRELATEDTOPIPESIZEASANEXAMPLE,IN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方程中的K1/C2以及N2。任何環(huán)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(huán)路中水頭損失的代數(shù)和。HLKQN。假設(shè)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(diào)整每條環(huán)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(huán)路而言76010/QHNKL必須再次強調(diào)的是方程76的分子和分母都是采用了適當?shù)挠嬎惴柎_定的。方程76中的負號表明,當順時針方向的環(huán)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(huán)路上水頭損失不足時,情況正好相反。5在每條環(huán)路都給予了一個最初的修正值后,由于環(huán)路之間的相互影響,損失仍不平衡(一些兩條環(huán)路共有的管道就有兩個單獨的修正值,每個值對應(yīng)一條環(huán)路)。重復(fù)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(xiàn)在第一種形式的分子和分母上,相應(yīng)實際的K值就可以用來確定分配量。結(jié)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(wǎng)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(xié)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(shè)計方程(其中包括國際科學(xué)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(shè)計任務(wù)小組檢查了設(shè)計方程,以確定是否能在塑料管道系統(tǒng)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(shè)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(fā)展以及合適的設(shè)計要素的選擇。改良的管道性能許多設(shè)備用來監(jiān)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(huán)壓下)。在供應(yīng)燃氣時我們希望老的樹脂塑管在80攝氏度、3MPA的環(huán)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(yù)期其壽命應(yīng)該能超過50年。裝運時對這些樹脂塑管質(zhì)量檢測,有時會由于沒有達到這一標準而對該產(chǎn)品拒絕使用。在相同溫度條件下,今天的樹脂塑管在46MPA環(huán)壓下可持續(xù)使用數(shù)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(jié)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(jù)工作條件推斷,測試性能上的區(qū)別與數(shù)百年的壽命增長是相等的(某些情況下甚至是數(shù)千年)。環(huán)壓下的防裂測試也有些公司進行了環(huán)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(xiàn)在的樹脂塑管能夠良好地持續(xù)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?qū)iT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(fā)生損
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