Fluid Mechanics.docx

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