UnitOperationsofChemicalEngineering化工单元操作.docx

UnitOperationsofChemicalEngineering化工单元操作.docx

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UnitOperationsofChemicalEngineering化工单元操作

1.1Whatwillbethe（a）thegaugepressureand（b）theabsolutepressureofwateratdepth12mbelowthesurface?

ρwater=1000kg/m3,andPatmosphere=101kN/m2.

Solution:

Rearrangingtheequation1.1-4

Setthepressureofatmospheretobezero,thenthegaugepressureatdepth12mbelowthesurfaceis

Absolutepressureofwateratdepth12m

1.3AdifferentialmanometerasshowninFig.issometimesusedtomeasuresmallpressuredifference.Whenthereadingiszero,thelevelsintworeservoirsareequal.AssumethatfluidBismethane（甲烷）,thatliquidCinthereservoirsiskerosene（specificgravity=0.815）,andthatliquidAintheUtubeiswater.TheinsidediametersofthereservoirsandUtubeare51mmand6.5mm,respectively.Ifthereadingofthemanometeris145mm.,whatisthepressuredifferenceovertheinstrumentInmetersofwater,（a）whenthechangeinthelevelinthereservoirsisneglected,（b）whenthechangeinthelevelsinthereservoirsistakenintoaccount?

Whatisthepercenterrorintheanswertothepart（a）?

Solution：

pa=1000kg/m3pc=815kg/m3pb=0.77kg/m3D/d=8R=0.145m

Whenthepressuredifferencebetweentworeservoirsisincreased,thevolumetricchangesinthereservoirsandUtubes

（1）

so

（2）

andhydrostaticequilibriumgivesfollowingrelationship

（3）

so

（4）

substitutingtheequation

（2）forxintoequation（4）gives

（5）

（a）whenthechangeinthelevelinthereservoirsisneglected,

（b）whenthechangeinthelevelsinthereservoirsistakenintoaccount

error=

1.4TherearetwoU-tubemanometersfixedonthefluidbedreactor,asshowninthefigure.ThereadingsoftwoU-tubemanometersareR1=400mm，R2=50mm,respectively.Theindicatingliquidismercury.Thetopofthemanometerisfilledwiththewatertopreventfromthemercuryvapordiffusingintotheair,andtheheightR3=50mm.TrytocalculatethepressureatpointAandB.

Figureforproblem1.4

Solution:

ThereisagaseousmixtureintheU-tubemanometermeter.Thedensitiesoffluidsaredenotedby,respectively.ThepressureatpointAisgivenbyhydrostaticequilibrium

issmallandnegligibleincomparisonwithandρH2O,equationabovecanbesimplified

=

=1000×9.81×0.05+13600×9.81×0.05

=7161N/m²

=7161+13600×9.81×0.4=60527N/m

1.5Waterdischargesfromthereservoirthroughthedrainpipe,whichthethroatdiameterisd.TheratioofDtodequals1.25.TheverticaldistancehbetweenthetankAandaxisofthedrainpipeis2m.WhatheightHfromthecenterlineofthedrainpipetothewaterlevelinreservoirisrequiredfordrawingthewaterfromthetankAtothethroatofthepipe?

Assumethatfluidflowisapotentialflow.Thereservoir,tankAandtheexitofdrainpipeareallopentoair.

Solution:

Bernoulliequationiswrittenbetweenstations1-1and2-2,withstation2-2beingreferenceplane:

Wherep1=0,p2=0,andu1=0,simplificationoftheequation

1

Therelationshipbetweenthevelocityatoutletandvelocityuoatthroatcanbederivedbythecontinuityequation:

2

Bernoulliequationiswrittenbetweenthethroatandthestation2-2

3

Combiningequation1,2,and3gives

SolvingforH

H=1.39m

1.6Aliquidwithaconstantdensityρkg/m3isflowingatanunknownvelocityV1m/sthroughahorizontalpipeofcross-sectionalareaA1m2atapressurep1N/m2,andthenitpassestoasectionofthepipeinwhichtheareaisreducedgraduallytoA2m2andthepressureisp2.Assumingnofrictionlosses,calculatethevelocitiesV1andV2ifthepressuredifference（p1-p2）ismeasured.

Solution:

InFig1.6,theflowdiagramisshownwithpressuretapstomeasurep1andp2.Fromthemass-balancecontinuityequation,forconstantρwhereρ1=ρ2=ρ,

FortheitemsintheBernoulliequation,forahorizontalpipe,

z1=z2=0

ThenBernoulliequationbecomes,aftersubstitutingforV2,

Rearranging,

PerformingthesamederivationbutintermsofV2,

1.7AliquidwhosecoefficientofviscosityisµflowsbelowthecriticalvelocityforlaminarflowinacircularpipeofdiameterdandwithmeanvelocityV.Showthatthepressurelossinalengthofpipeis.

Oilofviscosity0.05Pasflowsthroughapipeofdiameter0.1mwithaaveragevelocityof0.6m/s.Calculatethelossofpressureinalengthof120m.

Solution:

TheaveragevelocityVforacrosssectionisfoundbysummingupallthevelocitiesoverthecrosssectionanddividingbythecross-sectionalarea

1

Fromvelocityprofileequationforlaminarflow

2

substitutingequation2foruintoequation1andintegrating

3

rearrangingequation3gives

1.8.Inaverticalpipecarryingwater,pressuregaugesareinsertedatpointsAandBwherethepipediametersare0.15mand0.075mrespectively.ThepointBis2.5mbelowAandwhentheflowratedownthepipeis0.02