Fluid Mechanics.docx
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FluidMechanics
FluidMechanics
TABLEOFCONTENTS
1OBJECTIVES1
BasicDefinitions1
Pressure1
Flow1
EnergyinaFlowingFluid1
OtherPhenomena2
TwoPhaseFlow2
FlowInducedVibration2
2BASICDEFINITIONS3
Introduction3
Pressure3
Density4
Viscosity4
3PRESSURE6
3.1PressureScales6
Example3.1:
6
Example3.2:
7
Example3.3:
7
3.2PressureDifferential7
Example3.4:
8
Example3.5:
8
3.3FactorsAffectingPressureofFluids9
4FLOW11
LaminarversusTurbulentFlow11
MassandVolumetricFlowRate12
TheContinuityPrinciple13
Example3.6:
14
Example3.7:
14
4.4EffectofPressureandTemperature15
5ENERGYINAFLOWINGFLUID16
Energy,PressureandHeadofFlowingFluid16
5.1.1Example5.1:
19
EnergyLossandHeadLoss19
ConservationofEnergyinFlowingLiquid20
PressureandVelocityChangesinaFluidSystem21
6OTHERPHENOMEMON26
Siphon26
LoopSeal27
Buoyancy28
7TWO-PHASEFLOW29
Cavitation30
WaterHammer31
SteamHammer33
MinimisingWaterorSteamHammer34
SolidOperation35
FLOW-INDUCEDVIBRATIONS37
SUMMARY38
ASSIGNMENTQUESTIONS39
1OBJECTIVES
BasicDefinitions
Definethefollowingtermsandstatetheirunitsofmeasurement:
pressure,density,andviscosity.
Pressure
Convertagivenvalueofpressureexpressedontheabsolute,gaugeorvacuumscaletotheappropriatevaluesoneitheroftheothertwoscales.
Givenapressuredifferentialactingonagivenarea,calculatetheforceproduced.
Statethefactorsaffectingpressureofliquidsandgases.
Flow
Describethedifferencebetweenlaminarflowandturbulentflowwithrespecttothevelocityprofileandpulsations.
Definemassandvolumetricflowrates.
Statetherelationshipsbetweenmassandvolumetricflow.
Statethecontinuityprincipleandapplyittodeterminethechangetoafluid'svelocity.
Explaintheeffectofpressureandtemperatureonvolumetricflowrateforliquidsandgases.
EnergyinaFlowingFluid
Definethefollowingtermsregardingasystemwithflowingliquid:
Elevationhead,pressureheadandvelocityhead,
Staticpressure,dynamicpressureandtotalpressure,and
Energylossandheadloss.
Statetheeffectoffluidviscosityandvelocityonaheadlossinturbulentflow.
Statetheeffectoftemperatureonviscosityofliquids.
Explaintherelationshipbetweenelevationhead,pressureheadandvelocityheadinafluidsystemwithenergylossesandadditions.
Givenasimplefluidsystemcomprisedofpipingwithconstantorvaryingelevationanddiameterandacombinationofelbows,orifices,venturis,valves,tanksandafluidmover(e.g.,pump),determinethedirectionofpressureandvelocitychangesalongthesystem,andexplainwhythesechangesoccur.
OtherPhenomena
Describethefollowingterms:
siphon,loopseal,andbuoyancy.
Explaintheadverseeffectsofgasorvapouraccumulationinasiphon.
TwoPhaseFlow
Definetwo-phaseflow.
Describethedifferentformsoftwophaseflow.
GiveexamplesofdifferentformsoftwophaseflowinaCANDUplant.
Definecavitation.
Explainhowcavitationcanoccurinafluidsystem.
Explainhoweachofthefollowingcanproducelargepressurespikesinafluidsystem:
waterhammer,steamhammer,andsolidoperation.
Explainhowthefollowingoperatingpracticesminimisetheriskofwaterorsteamhammer:
Drainingofasteamorgassystem,
Ventingandslowprimingofaliquidsystem,
Slowoperationofvalves,
Startinguporshuttingdownacentrifugalpumpwithits
dischargevalveclosedorcrackopened,
Delaybetweenpumpstart-upsandshutdowns,and
Applyingcoolingwatertoheatexchangersfirst.
FlowInducedVibration
Explainhowaflowingfluidcancauseequipmentvibration.
2BASICDEFINITIONS
Introduction
FluidsystemsarethebackboneofnuclearpowerplantsandtheCANDUstationsarenoexception.Wewillusethetermfluidasagenerictermforbothliquidsandgases.
Thefluidsystemsareusedprimarilyasheattransportvehicles.Anexamplewouldbethegeneratorstatorcoolingsystem.Heatgeneratedinthestatorwindingsistransferredtotheclosed-loopstatorcoolingsystemandthentothelow-pressureservicewater.
Thismoduleisdesignedtohelpyouunderstandprocessesthatoccurinindividualfluidhandlingpartsanddevicesaswellasentiresystems.
Inthismodule,wewillreviewbasicterms,conceptsandlawsoffluidmechanicsandapplythemtoassortedfluid-relatedprocessesinnuclearpowerplants.
Pressure
Pressureisoneofthebasicpropertiesofallfluids.Pressure(p)istheforce(F)exertedonorbythefluidonaunitofsurfacearea(A).
Mathematicallyexpressed:
F
p=A
ThebasicunitofpressureisPascal(Pa).Whenafluidexertsaforceof1Noveranareaof1m2,thepressureequalsonePascal,i.e.,1Pa=1N/m2.
Pascalisaverysmallunit,sothatfortypicalpowerplantapplication,weuselargerunits:
1kilopascal(kPa)=103Pa,and
1megapascal(MPa)=106Pa=103kPa.
Density
Densityisanotherbasicfluidproperty.Density(p-Greekro)isdefinedasmass(m)ofaunitofvolume(V).Itsbasicunitiskg/m3.
Mathematicallyexpressed:
m
p=V
Forallpracticalpurposes,liquidsareconsideredtobeincompressible,i.e.,theirvolumeanddensityarenotaffectedbypressure.Althoughitisnotabsolutelytrue,thechangesarenegligible.Theeffectoftemperatureondensityofliquids,however,cannotbeignoredbecauseliquidsexpandandcontractwhentemperaturechanges.
Bothpressureandtemperatureaffectdensityofgases.Whentemperatureiskeptconstant,anincreaseinpressurewillincreasedensity.Whenpressureiskeptconstant,anincreaseintemperaturewilldecreasedensity.
Viscosity
Viscosityisanotherfluidpropertyweneedtounderstandbeforediscussingsomeotheraspectsofmechanicalequipment,suchaspressurelossesinpipingduetofrictionorbearinglubrication.
Viscosityisameasureofthefluid'sresistancetoflowduetoitsinternalfriction.
Viscosityismeasuredintwoways:
dynamic(absolute)andkinematic.Thesetwoparametersarerelatedsincethekinematicviscositymaybeobtainedbydividingthedynamicviscositybydensity.
Inthismodule,forsimplicity,wewillonlyusetheabsoluteviscositywhenexplainingfluidfrictioninpipingsystems.When,inthefollowingtextwementionviscosity,itisthedynamicviscosity.
Dynamic(absolute)viscosity(n-Greekmu)isthemeasureofthetangentialforceneededtoshearoneparallelplaneoffluidoveranotherparallelplaneoffluid.Thethicker/moreviscousthefluid,thelargertheareaofcontact,andthelargerthevelocitychangebetweenthelayersofthefluid,thelargerthetangentialforce.
Thebasicunitisthepascal-second(Pa-s).Theviscosityofafluidequals1Pa-sifaforceof1Nisneededtosheara1m2planeofthisfluidwhenthevelocitychangebetweenthelayersofthefluidis1m/sper1m.Athousandtime'ssmallerunitiscalledcentipoise(cP).Togiveyousomefeelforthisunit,theviscosityofwaterat20?
Cisabout1cP.
Viscosityofliquidsismuchlargerthanviscosityofgasesorsteam.Forallfluids,viscosityincreaseswithrisingpressure.Theeffectoftemperatureismuchbigger,though,anditdependsonthetypeoffluid:
risingtemperaturelowerstheviscosityofaliquid,andincreasestheviscosityofagas.Thisdifferenceisexplainedbelow.
Theresistanceoffluidtoshear(i.e.,viscosity)dependsuponitscohesionanditsrateoftransferofmolecularmomentum.Cohesionreferstotheattractiveforcesbetweenneighbouringmolecules.Whenthefluidexpandsduetoincreasedtemperature,themoleculesgetfurtherapart,andcohesiongetsweaker.Transferofmolecularmomentumiscausedbyrandommovementsoffluidmoleculesbackandforthbetweendifferentlayers.Thistransfertendstoequalizethevelocitiesofadjacentlayers,andthus,itresiststheirrelativemotion.Inliquids,moleculesaremuchmorecloselyspacedthaningases.Therefore,cohesionisthedominantcauseofviscosity,andsincecohesiondecreaseswithtemperature,viscositydoeslikewise.Agas,ontheotherhand,hasverysmallcohesiveforces.Mostofitsresistancetoshearistheresultofthetransferofmolecularmomentum.Thehigherthetemperature,thelargerthistransfersbecausemoleculesmovefaster.Therefore,theviscosityofagasincreaseswithrisingtemperature.
3PRESSURE3.1PressureScales
Sinceweliveinanatmosphereofpressurisedair,wehavetodecideonthedatum,wherethepressurewouldbezero.
Onecommonlyusedscaleistheabsolutescale.Itstartsatthepointofnopressureatall,i.e.,theabsolutezeropressure.Readingstakenonthisscalearecalledabsolutepressureandhavesuffix(a)added,e.g.,4MPa(a).
Ascalewithzeroatatmosphericpressureisknownasthegaugescale.Readingsmadeonthisscalearecalledgaugepressure.Thenamereflectsthefactthatmostgaugesreadzeroattheatmosphericpressure.Todistinguishreadingsonthisscale,weusesuffix(g).Thegaugescaleisthemostcommonscaleusedinourplants.
Sinceatmosphericpressurechangesconstantly,itmaybedifficulttopinpointthegaugepressurezeropoint.Therefore,weusestandardatmosphericpressuresetat101.3kPa(a).Withatmosphericpressurechangesbeingrelativelysmallcomparedwithpressuresusedintheindustry,smallvariationsareignored.
Wenowcancorrelatethetwodiscussedscales:
p(a)=p(g)+atmosphericpressure
3.1.1Example3.1:
Ifinstrumentairgaugepressureis580-kPa(g),whatisitsabsolutevalue?
p(a)=580kPa(g)+101.3kPa=681.3kPa(a)
Thethirdscale,sometimesusedinourplantsforsystemsatlowerthanatmosphericpressure,isthevacuumscale.Vacuumisthedifferencebetweentheatmosphericpressure