Dedication
Toallthosewhocontemplatenature,savoritsbeauty, andlearnandliveitssimplicity.
“Natureispleasedwithsimplicity.Andnatureisnodummy.”
–IsaacNewton.
Part1 Introduction
1.Thermofluids3
1.1WhatisThermofluids?4 1.1.1Thermodynamics4 1.1.2Fluidmechanics6 1.1.3Heattransfer8
1.2Thermodynamics,fluidmechanics,andheattransfer9
1.3Dimensionsandunits10
1.4Organizationofthebook14 Problems15 References16
2.Energyandthermodynamics19
2.1Thestudyofenergy19
2.2Theconservationofenergy22
2.3Thequalityofenergy24
2.4Thermodynamicsystems27
2.5Thermodynamicstate,equilibrium,andproperties28 Problems29 References30
3.Movingfluids33
3.1Whatisafluid?34
3.2Thecontinuumfluid36
3.3Naturethrivesinmovingfluids37
3.4Whatisviscosity?37
3.5Newtonianfluids40
3.6Aclassificationoffluidmotions43 3.6.1Fluidviscosity43
3.6.2Fluidcompressibility44
3.6.3Flowspace44
3.6.4Steadyversusunsteadyflow44
3.6.5Laminarversusturbulentflow45
3.7Fluidmechanicstextbooks45 Problems46 References47
4.Thetransferofthermalenergy51
4.1Whatisthermalenergy?51
4.2Specificheats54
4.3Heattransferversusthermodynamics57
4.4Thethreeheattransfermechanisms58
4.4.1Conduction59
4.4.2Convection60 4.4.3Radiation61 Problems63 References64
Part2
AnEcologicalViewonEngineering Thermodynamics
5.Thefourlawsofecology69
5.1Whatisecology?69
5.2Thefourlawsofecology72
5.3Animalthermoregulation75
5.4Learningfromintelligentdesigns78
5.4.1Natural-convection-enabledairtransport78
5.4.2Wearingpolarbearhair79
5.4.3Ecologicalbuildings79
5.4.4Intelligentdesignsarecomplexandintegrated80 Problems80 References81
6.Thefirstlawofthermodynamics85
6.1Energy86
6.2Thermodynamicsystems90
6.3Heatandworktransfer92
6.4Conservationofenergy93
6.5Movingboundarywork99
6.6Enthalpy101
6.7Thermodynamiccycle103 Problems105 References106
7.Thesecondlawofthermodynamics109
7.1Introduction110
7.2One-wayenergyflow112
7.3Entropy114
7.4Heatsourceandsink117
7.5Heatengine118
7.6Reverseheatengines127 Problems130 References132
Part3 EnvironmentalandEngineeringFluidMechanics
8.Fluidstatics135
8.1Whatispressure?136
8.2Fluidstatics137
8.3Hydrostaticpressure140
8.4Measuringpressure144
8.5Hydrostaticforceonasurface147
8.5.1Curvedtwo-dimensionalsurfaces152
8.6Buoyancy153
8.6.1Immersedbodies155
8.6.2Floatingbodies156 Problems157 References158
9.Bernoulliflow161
9.1Streamline,streakline,andpathline162
9.1.1Streamline162
9.1.2Streakline162
9.1.3Pathline163
9.2Streamline,streamtube,andBernoulli’sWig164
9.3TheBernoulliequation166
9.4Bernoulli’spressures168
9.5Flowratemeasurements172
9.6Energylineandhydraulicgradeline174 Problems177 References179
10.Dimensionalanalysis181
10.1Dimensionalhomogeneity182
10.2Scalinganddimensionalanalysis183
10.3BuckinghamPitheorem186
10.4Prevailingnondimensionalparametersinfluidmechanics188
10.5Someremarksondimensionalanalysis194
x Contents
Problems194 References196
11.Internalflow199
11.1Flowinachannel200
11.2TheReynoldsnumberandthetypeofpipeflow200 11.3Developingpipeflow203
11.3.1Laminarpipeflowentrancelength204
11.3.2Turbulentpipeflowentrancelength205
11.3.3Pressureandshearstress206
11.4Fullydevelopedhorizontalpipeflow208
11.4.1Pressuredrop208
11.4.2Velocityprofile210
11.4.3Volumetricflowrateandaveragevelocity211
11.5Fullydevelopedinclinedpipeflow212
11.6Energyconservationandheadlossinpipeflow214
11.6.1Headloss215
11.7Majorandminorlossesinpipeflow216
11.7.1TheMoodychart(diagram)219 Problems223 References225
12.Externalflow227
12.1Everydayexternalflow228
12.2Liftanddrag229
12.3Boundarylayer231
12.3.1Disturbanceboundarylayer232
12.4Flatplateboundarylayerdevelopment233
12.4.1Laminarboundarylayer235
12.4.2Transitionalboundarylayer237
12.4.3Turbulentboundarylayer237
12.5Bluffbodyaerodynamics239
12.5.1Steadyflowacrossasmoothcircularcylinder240
12.5.2Vortexshedding243
12.5.3Streamlining247 Problems248 References249
13.Steadyconductionofthermalenergy255
13.1Fourier’slawofheatconduction256
13.2Fromelectricresistancetothermalresistance260
13.3One-dimensionalheatconductionincylindricalcoordinates261
13.4Heatconductionradiallythroughasphere263
13.5Steadyconductionthroughmultilayeredwalls264
13.5.1Thermalcontactresistance265
13.6Multilayeredinhomogeneouswalls267
13.6.1Parallel-pathmethod269
13.6.2Isothermal-planemethod270 Problems271 References273
14.Transientconductionofthermalenergy275
14.1Alumpedsystemwithhomogeneoustemperature276 14.2Biotnumber282
14.3One-dimensionaltransientproblems284
14.4Semi-infinitesolid290 Problems293 References294
15.Naturalconvection295
15.1Naturalconvectionandthermals296
15.2Thermalexpansionandbuoyancyforce299
15.3Nondimensionalparametersinnaturalconvection301
15.4TheclassicalRayleigh–Bernardconvection304
15.5Continuousthermalplumesandbuoyantjets308
15.6Freeconvectionalongaverticalplate309
15.7Otherfreeconvectioncases313 Problems316 References317
16.Forcedconvection319
16.1Whatistheforcebehindforcedconvection?320
16.2Theconvectionheattransfercoefficient323
16.3Forcingheattoconvectfromaflatsurface324
16.4Primaryparametersinforcedconvection330
16.5Nusseltnumber,Reynoldsnumber,andPrandtlnumber333
16.5.1Nusselt–Reynoldsencounter333
16.5.2Nusseltnumber333
16.5.3Prandtlnumber334
16.6Nu–Re–Prrelationships336
16.6.1Constanttemperatureflatplate336
16.6.2Uniformheatfluxflatplate338
16.7Relatingheatconvectionwithflowshearatthewall340
16.8Forcedconvectionaroundacircularcylinder343
16.9Othernondimensionalparametersofforcedconvection345
16.10Internalforcedconvection347
16.10.1Pipeflowregimes348
16.10.2Hydrodynamicandthermalentrancelengths348
16.10.3Uniform-heat-fluxpipe349
16.10.4Constant-surface-temperaturepipe350
16.10.5Nusseltnumberandpumpingcostforlaminar andturbulentforcedconvectioninapipe350 Problems353 References355
17.Thermalradiation357
17.1TheradiatingSun357
17.2Allbodiesaboveabsolutezeroradiateheat361
17.3Absorptivity,transmissivity,andreflectivity362
17.4Vieworshapefactors365
17.5Furtherreadingonthermalradiation369 Problems369 References371
18.Heatexchangers373
18.1Naturethrivesbyexploitingeffectiveheatexchangers374
18.1.1Indirect(noncontact)heatexchanger376
18.1.2Directcontactheatexchanger377
18.2Counter-flow,parallel-flow,andcrossflowheatexchangers378
18.3Movingalongaconstant-temperaturepassage380
18.4Heatexchangebetweenahotstreamandacoldstream382
18.4.1Heatcapacityrate383
18.5Logmeantemperaturedifference384
18.5.1Parallel-flowheatexchanger386
18.5.2Counter-flowheatexchanger387
18.5.3Correctionfactor388
18.6Heatexchangereffectivenessandnumberoftransferunits389 Problems392 References393 Index395
Christmastreeworms
Christmastreewormshaveanarrayofphotoreptorsoneponymousfeeding appendages.Theyabsorblightmaximallyat464nminwavelength,probably functioningasasilhouette-detectingintruderalarm[Boketal.,2017].Thisalert systemapparentlycanbebreachedinturbulentwaters,whereCaribbeansharpnosepufferspreyChristmastreewormswiththeirlongsnoutandlargefused frontteeth[Hoeksema&tenHove,2017].Assuch,thisnaturalphenomenon illustratesthespectacularworkingsofengineeringthermofluids;radiation,fluid turbulence,andothers.
M.J.Bok,M.L.Porter,H.A.tenHove,R.Smith,D-E.Nilsson,“Radiolareyes ofSerpuidWorms(Annelida,Serpulidae):structures,functionandphototransduction,”BiologyBulletin,233:39-57,2017.
B.W.Hoeksema,H.A.tenHove,“AttackonaChristmastreewormbya CaribbeansharpnosepufferfishatSt.Eustatius,DutchCaribbean,”Bulletinof MarineScience,93(4):1023-1024,2017.
Caribbeansharpnosepuffershavealongsnoutandlargefusedfrontteeth, well-suitedtoprey.Christmastreewormspossiblyfailedtodictateandretract inturbulentwaters.
Listoffigures
Fig.1.1 Asimplifiedillustrationofthecycleoflifesustainedviatheorderly transferofenergyoriginatingfromthesun(createdbyS.Akhand).
Fig.1.2 Anillustrationoftherelativesizesandsurvivalwaterdepthsofagiant squid,adolphinandahuman(createdbyY.Yang).
Fig.1.3 Agiraffe’sbigheartversusafist-sizedhumanheart(createdbyY.Yang). WilliamHazlittstatedthat,“Theseatofknowledgeisinthehead,of wisdom,intheheart.”
Fig.1.4 Afennecfoxequippedwithfan-likeearsaboundinginheat-transferring bloodvesselstostaycoolintheSaharaDesert(createdbyS.Akhand). Therearemanybloodvesselsbringingwarmbloodtothebigearsand returningcoolerbloodafterdissipatingheatthroughtheextendedsurface areaintotheambientair.
Fig.1.5 Heightversuslength(createdbyY.Yang).Dr.JASmeasuresalamppost tothedesiredlengthandasksT.-E.Barutocutofftheexcesslength.T.-E. Barusees“height”butnot“length.”
Fig.2.1 Alivinghumanbodyisaheatengine(createdbyO.Imafidon).Food providesthefueltogenerateworkandheat.Theunusedenergyfromthe excessfoodisstoredasfatforfutureusage.
Fig.2.2 Comparingthequalityofelectrical,mechanical,andthermalenergy (createdbyO.Imafidon).Theeaseintransformingtheformofenergyto otherformsindicatesthequalityoftheenergy.
Fig.2.3 Ahierarchyoffoodenergychain(createdbyO.Imafidon).Consuming thefoodofthelowerlevelismoreefficientandenvironmentallyfriendly because90%lossesarecompoundedupthepyramid.
Fig.3.1 Fluidsversussolids(createdbyF.Fashimi).Fluidscannotsustainashear force,thatis,afluidcontinuestomoveunderashearforce.Asolid deformsunderashearforcetoacertainamountandstops.
Fig.3.2 Themovingfluidwithastablevortexringaboveaflyingdandelionseed (createdbyX.Wang).Theappropriateporosity,shape,density,orweight anditsdistribution,anddimensionsfurnishtherightconditionsfora stablevortexringabovetheseed,empoweringtheseedtotravelfarand wideridingontheomnipresentatmosphericwind.
Fig.3.3 Ablackflylarvacapitalizingonflowvorticesandflow-inducedvibrations toscoopupfoodandconvectitintoitscephalicfans(createdbyY.Yang). Thecephalicfansdanceinharmonywiththeorganizedflowstructures thatsweepupfood,andsynchronouslyconveyingthefoodtothefans.
Fig.3.4 Arotationalrheometerformeasuringfluidviscosity(createdbyF. Fashami).Withknowngap,dgap = Ro –Ri ,innerradius,Ri ,inner cylinderlength,L,thetorque,Tq ,requiredtospintheinnercylinderata prescribedspeed,Srpm ,yieldsthefluidviscosity, μ.
Fig.3.5 ShearingarubberblockversusaNewtonianfluid,ofwidthW(createdby Y.YangandD.Ting).Therubberblock,beingasolid,deforms,while water,beingafluid,movescontinuously.
5
7
8
9
11
21
24
26
34
38
39
39
41
Fig.3.6 ShearstressversusshearingstrainratefortypicalNewtonianfluids (createdbyO.Imafidon).Theslopecorrespondstotheviscosity.With increasingtemperature,from20°Cto30°C,theslopecorrespondingto waterdecreases.Inotherwords,theviscosityofmostNewtonianfluids decreaseswithincreasingtemperature.
Fig.3.7 Laminarsteadyversusunsteadywakedownstreamofasquarecylinder (createdbyX.Wang).Thelocalflowissteadywhenitsfeaturesdonot changewithrespecttotime,anditisunsteadyiftheflowcharacteristics varywithtime.Thetwocounter-rotatingvorticesremainstationary behindthecylinderataReynoldsnumberof45.Thesevorticesshed alternativelyataslightlyhigherReynoldsnumberof50.
Fig.3.8 Risingincensesmokechangingfromlaminartotransition,toturbulent flowasitrises(createdbyX.Wang).
Fig.4.1 Creatingdisorderbymeltingandevaporatingicecubeswithheatina fryingpan(createdbyX.Wang).Iceismorerigidandthusorderlythan water,andwaterismoreorderlythansteam.Theprogressivelymore energeticH2 Oisdrivenbytemperature,thehigherthetemperature,the moredisorderaretheH2 Omolecules.
Fig.4.2 H2 Omoleculesbecomeprogressivelymoredisorderedfromicetowater tosteam,withincreasingtemperature(createdbyM.Abbasi).Aunique featureaboutH2 Oisthatthemoleculesaremorelooselypackedinthe solidphase,ice,thanintheliquidphase,water.Atthesametime,the moleculesaremorerigidlyheldtogetherinicethaninwater.The crystallinelatticeiniceisdominatedbyaregulararrayofhydrogen bonds,spacingthemoleculesfartherapartthantheyareinliquidwater. Liquidwatercontainstheintermolecularforce,thatis,thehydrogenbond occursbetweenthepartiallynegativeoxygenofawatermoleculeandthe partiallypositivehydrogenonaneighboringwatermolecule.
Fig.4.3 Adrinkingbirdoperatesasaheatengine(createdbyA.Raj).Theambient airsuppliestheheattooperatethisheatengine.Aportionofthissupplied heatisutilizedtoevaporatewaterfromthehead,causingtheliquidtorise upviatheinnerstemtothehead.Theremainingheatiswasted,for example,byheatingtheheadwhenthebottomendofthestemisopened upabovetheliquidsurface,orbyheatingtheotherpartsofthebird’sbody.
Fig.4.4 Modulatingtemperatureviaseabreezeandlandbreeze(createdbyA. Raj).Thehighheatcapacityofwaterbuffersanddampenstemperature fluctuationsinnear-waterneighborhood.Duringtheday,theland,dueto itslowerheatcapacity,isheatedupfasterthanthewaters,bytherising sun,asthehotairrisesonland,thecoolerairabovethewatersbreezes andcoolstheland.Aftersunset,thelowerheatcapacitylandcoolsoff fasterthanthehigherheatcapacitywater,andthewindcirculation reversesintolandbreeze.
Fig.4.5 Specificheatcapacityofairatconstantvolumeversusconstantpressure (createdbyF.Kermanshahi).Forcompressiblefluidlikeairthespecific heatcapacityatconstantpressureislargerthanthespecificheatcapacity atconstantvolumebytheexpansionworkofpushingthesystem boundarysuchasamovablepiston.
43
45
47
52
53
54
55
57
Fig.4.6 Therateofheatconductionisproportionaltothesurfaceareaavailable forheattransferandthe(negative)temperaturegradient(createdbyF. Kermanshahi).Notethatheattransferspontaneouslyfromhightolow temperature,thatis,inthenegative-temperature-gradientdirection. 60
Fig.4.7 Theheattransferofbarbequingfishfillets(createdbyX.Wang).Toputit concisely,heatisconductedfromthehotgrilltothefishaswitnessedby thebeautifulgrilllines.Heatisconvectedfromthefiretothefishvia mostlyinvisibleenergetichotplumesofdifferentsizes.Atthesametime, heatisradiatedfromthesootyfireandthehotinnersurfacestothe respectivefishsurfacethatisinview.
Fig.5.1
Fig.5.2
Acold-bloodedfrogadjustingitselftoitssurroundings(createdbyS. Akhand).Theleftfigureshowsthatthebodytemperatureofthefrogis lowbecauseitisinacoolautumnenvironment.Therightfigureexhibits thatthebodytemperatureofthefrogishighbecauseitssurroundingsis hot,duringahotsummerday.
Anillustrationofthe“BoilingFrog”fable(createdbyS.F.Zinati).Ifwe putalivefrogintoapotofhotwater,itwilljumpoutimmediately.Onthe otherhand,ifweplaceitinapotofroom-temperaturewater,andheatit upslowly,thefrogwilladjustitsbodytemperaturetothatoftheslowly increasingwatertemperature.Accordingtothe“BoilingFrog”narrative, iftheriseinwatertemperatureissufficientlyslow,thefrogwilleventually beboiledtodeathwithoutrealizingthewateristoohotforittostay.
Fig.5.3 Thesimplifiedfoodchain(createdbyS.Akhand).Afalloutofthesecond lawofthermodynamicsisthateventhemightyeagle,thekingofthesky, diesanddecomposes.Ittakesthealways-givingsuntotransformthe compostbackintoallkindsofheartyplantsthatprovidehighqualityfood and/orenergy.Notethatfoodwebisamoreaccuratedescriptionthat illustratesthecomplexityinvolved,asmostorganismshaveamorediverse appetitethanonefood.
Fig.5.4 Ectothermssurvivechangesintheirenvironmentprimarilyviabehavioral thermoregulation(createdbyS.Akhand).Alizardtakesadvantageofthe ground,shade,andthesunappropriatelytoachieveacomfortablethermal condition.
Fig.6.1 Thedifferentformsofenergyincludemechanical,thermal, electromagnetic,electrical,chemical,andnuclear(createdbyS.Akhand). Notincludedintheillustrationarekineticenergyandpotentialenergy.
Fig.6.2 Thermodynamicsystems(A)opensystem,(B)closedsystem,and(C) isolatedsystem(createdbyX.Wang).Bothmassandenergycanenteror leaveanopensystem.Onlyenergycancrosstheboundaryofaclosed system.Nothingcanenterorexitanisolatedsystem.
Fig.6.3 Theconservationofenergybetweenpotentialandkineticenergyofa frictionlessskateboarderisanalogoustothatofapendulum(createdby Y.Yang).Intheidealfrictionlesssituation,thesumofpotentialenergy andkineticenergyisaconstant.
Fig.6.4 Moving-boundaryworkofapiston-cylinderclosedsystem(createdby F.Kermanshahi).Notethatworkisapath-dependenttransientprocess, whereadifferentpathleadstoadifferentamountofwork.Expansion alongPathAleadstomoreworkthanalongPathBandPathC.
Fig.6.5 TheCarnotenginecycle(createdbyY.Yang).Isothermalheatadditionof amountQH atthehighertemperature,TH .Adiabatic(Q=0)expansion, decreasingpressureasthevolumeincreases.Isothermalheatrejectionof amountQL atthelowertemperature,TL .Adiabaticcompressionprocess backtoitsinitialstate.
Fig.7.1 Thefourlawsofthermodynamicsillustrated(createdbyO.Imafidon). Thezerothlawdealswiththermalequilibrium.Thefirstlawisaboutthe conservationofenergy.Thesecondlawisconcernedwiththenaturalflow
62
71
71
73
77
87
91
95
99
103
Fig.7.2
directionofenergy.Accordingtothethirdlaw,theabsolutezero temperaturecorrespondstozeroentropyforaperfectcrystal.
Decreasingorderand,thus,increasingentropyfromsolidtoliquidto gaseousphase(createdbyX.Wang).Inthesolidphase,theH2 O moleculesarerigidlyconfinedwithintheicecubes.Theyarefreetomove aroundwithinthespreadofthewaterinthepanwhentheicecubesmelt. BoilingthewaterintosteamgrantsfullfreedomtotheH2 Omolecules, allowingthemtoroameverywhereintotheenvironment.
Fig.7.3 Anisolatedsystemoficecubesinhotwater(createdbyS.Zinati).The entropyoftheentiresystemincreasesasthehotwaterlosesthermal energytomelttheicecubes.
Fig.7.4 Aheatengine(createdbyO.Imafidon).Aportionoftheheatfromthe high-temperaturereservoir,QH ,isconvertedintousefulwork,W,while theremainingunusedheatisdissipatedintothelow-temperaturereservoir aswasteheat,QL
Fig.7.5 Asteampowerplantisaheatengine(createdbyF.Kermanshahi). High-temperatureheatfromahigh-temperaturereservoirentersthe system(heatengine)atQH .Steamproducedbytheboilerspinsthe turbine,leadingtoanetusefulpoweroutputofWnet ;thisisthenetpower afteraportionofitisemployedtooperatethepump.Theremaining unusedheatisdissipatedintothelow-temperaturereservoir,atarateQL , viathecondenser.
Fig.7.6
Athermoelectricgeneratorasaheatengine(createdbyO.Imafidon). ThermalenergyentersthesystemfromtheheatsourceatTH viathehot leg.Partofthisenergyisharnessedtorotatethefan.Theremaining untappedthermalenergyleavesthesystem,viathecoldleg,intotheheat sinkatTL .
Fig.7.7 ACarnotheatengine(createdbyO.Imafidon).Itisanideal,or theoreticallymost-efficient,engine,settingthelimitforrealenginesto strivefor.
Fig.7.8 Areverseheatengine(createdbyO.Imafidon).Workinput,Win ,is requiredtomoveheatfromalower-temperatureregionatTL toa higher-temperaturezoneatTH .Forheatpumps,thedesiredoutputisQH , theheatforwarmingupazonethatisatahighertemperaturethanthe regionwherethethermalenergyisextractedfrom.Ontheotherhand,the thermalenergyremovalfromacoolerregionQL isthedesirableoutput forrefrigeratorsandairconditioners,andthedumpingofthisheatintoa higher-temperaturereservoirismadepossibleviaareverseheatengine withappropriateworkinput.
Fig.8.1 Pressureisforceperunitarea(createdbyY.Yang).A0.102-kgapple undernormalgravityproduces0.102 × 9.81 = 1kg m/s2 = 1Nofforce orweight.Therightfigureillustratesthatthis1Nforceisexertedon Newton’shatand,thus,head.Ifthis1-Nforceisdistributedoverasurface areaof1m2 ,thenthecorrespondingpressureonthesurfaceis1Pa.
Fig.8.2
Forcesactingonasmallwedge-shapedfluidelementofafluidatrest (createdbyD.Ting).Theinfinitesimalfluidelementhasaunitwidthinto thepage.Thezdirectionispointingverticallyupand,hence,gravityis actinginthenegativezdirection.
Fig.8.3 AneverydayworkingsofPascal’slaw,apressureappliedatapointinan enclosedfluidisdistributedequallythroughoutthefluidinalldirections (createdbyX.Wang).Thevolumeoffluidisrelativelysmall,withno appreciablevariationinhydrostaticpressure,and,therefore,itcanbe consideredasapointforallpracticalpurposes.
111
114
115
119
120
121
123
128
137
138
139
Fig.8.4 AnengineeringapplicationofPascal’slaw,whereapressureappliedata pointinanenclosedfluidisdistributedequallythroughoutthefluidinall directions(createdbyF.Fashami).Foracarjack,thepressurethroughout theenclosedfluidisthesame,otherthanapossiblesmalldifferencein hydrostaticpressureduetodifferingheight,ifany,betweenPoint1and Point2.WithoutanyheightdifferencebetweenPoint1andPoint2,we haveF1 = F2 A1 /A2 .Thissaysthatarelativelysmall,appliedforce,F1 , canresultinalargeF2 forliftingacar,whenA2 ismuchlargerthanA1 .
Fig.8.5 Hydrostaticpressureillustrated(createdbyX.Wang).Thepressure increaseslinearlywithdepth,orheight,h.Thehigherthepressure,the strongerthejet.
Fig.8.6 Shrinkingaballoonusinghydrostaticpressure(createdbyX.Wang).An interestingexperimentistousealongballoonandpositionitverticallyin awatercolumn.Theincreasinghydrostaticpressurewithdepthwillresult inashrinkingcrosssectionwithwaterdepth.
Fig.8.7 Thehydrostaticpressuredependsontheheightofthefluidcolumnand nottheshapeofthecontainerorthesurfaceareaonwhichthepressure acts(createdbyX.Wang).Itgoeswithoutsayingthatthehydrostatic pressureisalsoafunctionofthefluiddensity,theactinggravity,andthe surroundingpressurethatactsonthefreesurface(butnottheareaofthe freesurface).
Fig.8.8 Measuringthestaticpressuredifferenceusingamanometer(createdbyF. Kermanshahi).Ingeneral,thedensityofthemovingfluidintheconduitis ordersofmagnitudelessthanthatofthemanometerfluidintheUtube and,hence,P1 -P2 = ρ L gh,where ρ L isthedensityofthemanometer liquid,andhistheheightdifferenceofthemanometerliquidinthetwo armsofthemanometer.
Fig.8.9 Measuringtheatmosphericpressureusingabarometer(createdbyX. Wang).Theweightoftheatmosphericairexertsaforceonthefree surfaceofthebarometricfluid,suchasmercury,inthereservoiratthe baseandtheresultingpressurekeepsthecolumnoffluidstandinginside thecolumnatthecorrespondingheight.Notethatthepressureactingon thefreesurfaceatthetopofthecolumnofthebarometricfluidinthetube isvirtuallyzero.Toputitanotherway,theonlypressureactingonthe columnofbarometricfluidinsidethetubeisthehydrostaticpressure inducedbytheweightofthefluidcolumn,andthisiscounterbalancedby theatmosphericpressureactingonthefreesurfaceofthebarometricfluid inthereservoir.
Fig.8.10
Fig.8.11
Fig.8.12
Hydrostaticforceontheflatsurfacesofacylindricaltank(createdbyF. Fashami).Here,thegagepressure,P,istakenasthepressurewithrespect totheatmosphericpressure,thatis,P = 0indicatesthatthepressureis atmospheric,andtheverticallyupwardactingatmosphericpressure cancelsoutthedownwardactingpressure.Thebottomsurfacemustbe abletowithstandanetforceof ρ ghAorapressureof ρ gh,inorderforthe tanktoholdwater.
Hydrostaticforceactingonaflatsurfacesubmergedinafluid(createdby O.Imafidon).Thecentroid,CG ,at(xC ,yC ),isthegeometriccenterofthe plateandthecenterofpressure,CP ,at(xR ,yR ),isthepointwherethe resultantforceacts.
Hydrostaticforceonatwo-dimensionalcurvedsurface(createdbyO. Imafidon).Theforceactinginthehorizontaldirectionisfromthe hydrostaticpressurethatincreaseslinearlywithdepthbelowthefree
140
141
142
143
144
146
148
149
Fig.8.13
Fig.8.14
surface.Theforceactingintheverticaldirectionisthatduetotheweight ofthevolumeoffluidsittingontopofthesurface. 153
Atequilibriumintheverticaldirection,thedownwardweightofthe rubberduckyisequaltotheupwardbuoyantforce(createdbyX.Wang). Thisbuoyantforceisequaltotheweightofthedisplacedfluid(water)by therubberducky. 154
Neutrallybuoyantrubberducky(createdbyX.Wang).Whenthecenterof gravityoftherubberducky,CG ,isbelowthecenterofbuoyancy,CB ,the rubberduckyisstable.Itwillrestoretoitsuprightpositionwhenitis tilted,thatis,thegravitywillweightheheavierbasedownwardwhilethe buoyancywillliftthelightertopupward. 155
Fig.8.15
Acanoeistinacanoe,wherethecenterofgravityisabovethecenterof gravity(createdbyX.Wang).Itis(A)neutrallystablewhenthe meta-center,M,coincideswiththecenterofgravity,G,(B)stablewhen themeta-centerisabovethecenterofgravity,and(C)unstablewhenthe meta-centerisbelowthecenterofgravity.
Fig.9.1 Streamlines(leftfigure),streaklines(middlefigure),andpathlines(right figure)aroundacircularcylinderatReynoldsnumberbasedonthe cylinderdiameterof500(createdbyX.Wang).Forsteadyflow,the streamline,streakline,andpathlineareidentical.
Fig.9.2 Describingastreamlineintermsofthevelocitycomponentsinasteady, two-dimensionalflow(createdbyX.Wang).Overashortperiodoftime, Dr.JASmovesfromPoint1withcoordinates(x,y)toPoint2with coordinates(x+dx,y+dy).ThischangeinDr.JAS’positionisrealizedby thevelocityvectorV,whosexcomponentisuandycomponentisv.
Fig.9.3 Bernoulli’swigasastreamtube(createdbyK.Esmaeilifoomani,editedby D.Ting).Eachstrandofhairisastreamline,throughwhichnofluid crosses.Forsteadyflows,thestreamlinesarefixedlinesinspace.For unsteadyflows,thestreamlineschangewithrespecttotime.Atany momentintime,themasspassingthroughanycross-sectionofa streamtuberemainsconstant.
Fig.9.4
AstraightforwardderivationoftheBernoulliequationfora two-dimensionalstreamline,basedonNewton’ssecondlawofmotion, F = ma(createdbyX.Wang).Theforcesactingontheinfinitesimal streamlineelementarethepressureforcesactingnormaltothetwoends andtheweightofthefluidelement.Thesumoftheseforcesisequaltothe massoftheelementtimesitsacceleration.
Fig.9.5 TheBernoulliequationcanbeviewedaspressures,wherethetotal pressureisthesumofstaticpressure,dynamicpressure,and“hydrostatic pressure”onmovingfluid(createdbyX.Wang).Staticpressure,PS , representsthepressureofthefluidwhenmovingatthesamevelocityas thefluid.Thedynamicpressure, 1 2 ρ U2 ,isthekineticenergyperunit volumeofthemovingfluid.The“hydrostaticpressure”onthemoving fluid, ρ gz,accountsforchangesintheelevation.
Fig.9.6
Pitot-statictubeoperationisbasedontheBernoulliprinciple(createdby X.Wang).Thedifferencebetweenthestagnationpressure,P0 ,andthe staticpressure,PS ,isthedynamicpressure, 1 2 ρ U2 ,fromwhichthe velocitycanbedetermined.Thespecifics,suchasstagnationportsize, numberandlocationsofthestaticports,andthedistancebetweenthe90° bend,havebeenoptimizedtoprovidethemostaccuratemeasurements thatareleastsensitivetosmallmisalignmentsoftheprobe.
156
162
164
165
166
169
170
Fig.9.7 Commonvolumetricflow-ratemeasurementmeters:(A)venturi,(B) nozzle,and(C)orificeflowmeters(createdbyA.Raj).Thesmooth contractionfollowedbyagradualexpansionofaventuriflowmeter disturbstheflowmarginallyand,thus,resultsinminimalpressuredrop. Anorificeinterfereswiththeflowabruptly,leadingtoasubstantial pressuredrop.
Fig.9.8 Anillustrationofstaticandflowingfluidheads,totalingtheBernoulli Head(createdbyO.Imafidon).Intheabsenceoflossesorgainsthetotal (Bernoulli)headisconserved.(A)Demonstratesaflowalongthesame elevation,wheretheincreaseinvelocityheadwithdecreasing cross-sectionalareaofthepipeisequaltothedecreaseinthepressure head.Forthefixedcross-sectionpipein(B),thevelocityheadremains unchangedduetocontinuity.Thepressureheaddecreasesasthepipeis elevatedbutthehydraulicgradelineremainsfixedintheidealfrictionless flow.
Fig.9.9 Thevariationoffluidheadalongtheflowpassageofarealfluid(created byO.Imafidon).Withfiniteviscosity,wehavefinitelosses;therefore,the totalheaddecreasesalongtheflowpassage.Fortheuniformcross-section straightpipe,(A),thetotalheaddecreaseslinearlywithpipelength.(B) showsthatareductioninpipecross-sectionincreasesheadloss,along withincreasingflowvelocity.(C)showsthatthepumpinputsenergyinto thefluidandhence,increasesthefluidhead.
Fig.9.10 Energygradelinefromalowerelevationtanktoahigheroneviaa uniformpipeequippedwithapump(createdbyF.Kermanshahi).
Fig.10.1 Animalmetabolicrateversusbodymass(createdbyY.Yang).Dataare takenfromtheappendixof McNab(2008).Withinthescatterofthedata, thelog–logrelationshipbetweenthemetabolicrateandbodymassof mammalsextendsfromthetinyEtruscanshrews,whereanaverageadult hasabodymassoflessthan2g(Animalia,2021),tothegreatWeddell sealsthatweighbetween400and500kgwhenfullygrown(Antarctica, 2021).
Fig.10.2
Fig.10.3
Fig.10.4
Nondimensionalstridelengthversusrunningspeedofvariousanimals (createdbyY.Yang).Dataaretakenfromvarioussources;see,for example,(Alexander,1989, 2004).Asexpected,thelongerthenormalized stridelength,thehigherthenormalizedrunningspeed.Studies,including thoseconductedby Montanari(2017), Sellersetal.(2017),and Celine (2021),indicatethatdinosaurs,suchasTyrannosaurusrex,cannotoutrun humans.Wecaninferthisfromtherelation,Lstride /Lleg ∝ [U/(Lleg g)] 1 2 , thatthisisbecausethemuchlongerlegs,Lleg ,ofthedinosaursdonotlead toaproportionalincreaseinthestridelength,Lstride .Itfollowsthatthe speed,U,doesnotincreaseinproportiontoLleg .
Nondimensionalvortexsheddingfrequency,StrouhalnumberSt = fs D/U, asafunctionofReynoldsnumberforacircularcylinder(createdbyO. Imafidon).NotethatforReynoldsnumberbetween200and100,000the Strouhalnumberremainsapproximatelyunalteredat0.2.
Laminarrisingsmoketransitionsintoturbulentsmokeasitrises(created byX.Wang).Thebuoyantacceleration,whichisofequalmagnitudeto thegravitationalacceleration,causesthelaminarsmoketobecomea turbulentplumebeforetheaccelerationeventuallyslowsasthesmoke losesheattothesurroundings.Thesmokeontheleftiscoolerthantheone ontheright.Withasmallertemperaturedifferencebetweenthesmokeand theambientair,theleftsmokeislargelylaminar.Fortherightsmoke,the
172
175
176
179
184
185
189
largertemperaturedifferencepowersittoacceleratesupwardrapidlyand, hence,transitionsintoaturbulentsmokequickly. 190
Fig.11.1 Laminar,transitional,andturbulentflowregimesforpipeflow(createdby Y.Yang).Typically,theflowissteadyandlaminarforRe < 2100,itis transitionalfor2100 < Re < 4000,anditbecomesfullyturbulentforRe > 4000. 202
Fig.11.2 Thedevelopmentofpipeflowwithauniformvelocityattheentrance (createdbyY.Yang).Theboundarylayerisdefinedbythelayerfromthe wallwherethevelocityislessthan99%thefreestreamvelocity.Theflow becomesfullydevelopedwhentheboundarylayerreachesthecenterof thepipe.Theparabolicprofilesignifiesthattheflowislaminar;a turbulentprofileisfullerorflatter.
203
Fig.11.3 Thevariationofpressuredropandwallshearforadevelopinghorizontal pipeflow(createdbyY.Yang).Therateofpressuredropwithdistance decreasesintheentranceregion.Itreachesaconstantvalueoncetheflow isfullydeveloped.Thecorrespondingwallshearremainsconstantbeyond theentrancelength. 207
Fig.11.4 Fullydevelopedflowinahorizontalpipe(createdbyX.Wang).Notethat thevelocityprofileremainsunchangedalongthepipe.Thesmooth, parabolicprofilecorrespondstolaminarflowatRe = 500,whiletheflatter oneisturbulentatRe = 3000.
Fig.11.5 ForcesactingonacylindricalfluidelementoflengthL(createdbyO. Imafidon).Thenetforceiszerobecausethefluidismovingataconstant velocity,thatis,theaccelerationiszero,accordingtoNewton’ssecond lawofmotion.
Fig.11.6 ForcesactingonacylindricalfluidelementoflengthLataninclination angle, θ (createdbyO.Imafidon).Comparedtothehorizontalcase,the specificweightofthefluid, γ = ρ g,istheadditionalterm.
Fig.11.7 Energyperunitmassofamovingfluidinapipe(createdbyD.Ting).The threecomponentsarepressureenergy,kineticenergy,andpotentialenergy.
Fig.11.8 Turningorguidevanesforreducingminorheadloss(losscoefficient,KL ) ina90°bend(createdbyX.Wang).Theguidevaneseliminateorlessen theformationofrecirculatingflowand,hence,theassociatedlosses.
Fig.11.9 Thesetupformeasuringthelosscoefficientofanairfilter(createdbyF. Kermanshahi).Therearewellestablishedstandardstospecifyexactly howthemeasurementsshouldbeconducted,includingthedefinite locationstoflushmountthepressuretaps.
Fig.11.10 MoodychartorMoodydiagram(createdbyY.Yang).Notethatforfully developedlaminarpipeflow,thefrictionfactor,f = 64/Re.
Fig.11.11 Waterdeliveryfromatank(createdbyF.Kermanshahi).Theentranceinto thepipe,thefour90°elbows,thevalve,andtheexitintotheatmosphere contributetominorlosses.
Fig.12.1 Atwo-dimensionalairfoilwhereliftanddragaredescribed(createdbyS. Khademi).Theflow(friction)alwaystriestodragtheobjectalong.Liftis producedbythepressuredifference;pressureisnegativeontheupper surfaceandpositiveonthelowersurfaceand,thus,pushestheairfoil upward,creatinglift.
Fig.12.2 Boundarylayeroverathinplateat(A)averylowfreestreamvelocity and/orhighviscosityand(B)averyhighfreestreamvelocity(createdby O.Imafidon).Whenyourideonaslow-movingfluidparticlealongthe streamlinethatwillmeettheleadingedgeheadon,youwillslowdown aheadoftheleadingedge,asmanyfluidparticlesaheadofyoualsoslow
209
210
212
215
217
218
220
222
230
Fig.12.3
Fig.12.4
Fig.12.5
downtoastopatthestagnationpointatthepointededge.Ontheother hand,ifyourideonafast-movingfluidparticleaheadofthepointededge, you,likeallotherfast-movingparticlesaheadofyou,aremovingsofast thatyoudonotslowdownuntilviscositywithintheformingboundary layeronthetoporlowersurfacedragsyoudown.
Disturbanceboundarylayer(createdbyN.Bhoopal).Thedisturbance boundarylayerisdefinedbyU = 0.99U∞ .Interestedreaderswouldenjoy watching Lesics(2021),especiallyfrom4:20min.intothevideoclip.
Boundarylayerdevelopment,fromlaminartotransitiontoturbulent,over aflatplate(createdbyO.Imafidon).Duetoinherentimperfections,such asdisturbancesintheflowandsurfaceroughness,thecriticalReynolds number,Rec ≈ 5 × 105 inpractice.
Dr.JAS’flat-bottomcanoefordemonstratingfrictiondrag(createdbyA. Raj).Thepressuredragisminimizedviastreamlining.Specifically,the incomingflowisguidedalongagraduallydecliningsmoothplateandthe flowleavestheendofthecanoesmoothlyoveraplatewithasmallincline.
Fig.12.6 Boundarylayeraroundacircularcylinderinsteadyflow(createdbyO. Imafidon).Theflowseparatesfromthesurfaceofthecylinderduetoan adversepressuregradient.Thisissomewhatlikesomeoneridingonafluid particlerollercoasteralongthecurvedstreamlinearoundthesideofthe cylinderand“flyingoff”thetrackattheseparationpoint.
Fig.12.7
Flowregimesofatwo-dimensional,circularcylinderinsteadyflowfor Re = 1to1 × 104 (createdbyY.Yang).Regime1:creepingflow(Re 5);Regime2:closednear-wake,standingvortexpair(5 Re 45); Regime3:periodiclaminarvortexstreet(45 Re 190);Regime4: transitioninshearlayers(190 Re 3 × 105 );Regime5:criticalregime (3 × 105 Re 3 × 106 );Regime6:postcriticalregime(Re 3 × 106 ).
Fig.12.8 AmapofabuoyantvortexringintermsofRe,Bo,andWe(createdbyX. Yan).Atthelowend,itindicatesthatsomeminimuminertialand/or gravitationalforceisrequiredforthecreationofabuoyantvortexring.At thehighend,itsuggeststhattoomuchdragand/orinertiawillleadto disintegrationoftheturbulentvortexring.
Fig.12.9
Dragcoefficient,CD ,andStrouhalnumber,St,versustheReynolds, number,Re,forcommonbluffbodiessuchasasmoothsphereanda smoothcircularcylinder(createdbyO.Imafidon).Notethatoverawide rangeofReynoldsnumbersbetween103 and105 ,bothCD andStremain largelyunchanged.
Fig.13.1 Steadyheatconductionthroughahomogeneoussolid,Fourier’slawof heatconduction(createdbyD.Ting).Wemayenvisiontheflowofheat similartolavafallingdownthemountain,thesteepertheslope,thehigher theflowrate.
Fig.13.2 Thermalconductivityandthermalqualityofwintercoats(createdbyX. Wang).Ifbothwintercoatsresistheattransfersothattheresultingheat transferrateisthesame,thenthethinnercoatwithalowerthermal conductivityisabetter-qualityovercoat.
Fig.13.3 One-dimensional,steadyheatconductionthroughapassivehomogeneous wall(createdbyD.Ting).Thewallispassivebecauseitisneither generatingheat(notaheatsource)norisitabsorbingheat(notaheat sink).Itishomogeneousinthesensethatthethermalproperties,suchas thethermalconductivity,areuniformthroughoutthewall.
232
233
233
236
241
242
245
246
256
258
259
Fig.13.4
Fig.13.5
Fig.13.6
Fig.13.7
Thermalresistantconceptofheattransfer(createdbyD.Ting). Temperaturepotentialisanalogoustoelectricvoltage,andthethermal energyflowrateisakintothecurrentflowrate.
One-dimensionalradialheatconductionthroughthewallofalong cylindricalpipe(createdbyD.Ting).Notethattheavailableheattransfer areaincreaseswithradius.Therefore,insulatingatasmallerradial circumferenceismoreeffectivecomparedtoinsulatingatalargerradial location.
One-dimensionalheatconductionthroughathree-layerwall(createdby D.Ting).Understeady-stateconditions,theheatthatisconductedthrough thefirstlayerpassesthesecondandthirdlayers.Itfollowsthattheheat transferrateatanypointalongthepathisthesame.
Thermalcontactresistance(createdbyX.Wang).Theimperfectcontact hasvoidsthataretypicallyofsignificantlylowerthermalconductivity.For thatreason,thetransferofheatissloweddown,andthisismanifestedasa temperaturedrop, Tcontact = T1,R T2,L ,fromthewarmerlayertothe coolerone.
260
Fig.13.8
Fig.13.9
Fig.13.10
Fig.14.1
Heattransferviatheparallel-pathmethod(createdbyY.Yang).The parallel-pathmethodassumesperfectlyone-dimensionalheatflow, resultinginlowerandhigherheattransferratesthroughthepassage consistingoflessandmoreconductivematerials,respectively.Forthe caseshown,Q stud /Astud islargerthanQ insul /Ainsul
Aschematicofawood-framewallsectionofatypicalresidentialbuilding inNorthAmerica(createdbyD.Ting).Thermalenergytravels considerablyfasterthroughthesupportingstructures,suchasstuds,as comparedtothe“pink”insulation.Forthisreason,someofthethermal energyintheproximityofthestudstravelsthroughthestudsinsteadof themorerestrictivepathmadeofinsulation.
Equivalent-circuitdiagramfortheisothermal-planemethod(createdbyY. Yang).Theisothermal-planemethodassumesthatthetemperatureatany cross-sectionalongthedecreasingtemperatureheat-transferpathisatthe sametemperature.
Acold-bloodedcreaturesuchasalizardisatthesametemperatureasits environment(createdbyO.Imafidon).Treatingthelizardasalumped systemimpliesthattheentirebodyofthelizardisatahomogeneous temperatureasthelizardadjuststochangesinitsenvironment.This lumpedsystemassumptionisvalidonlywhenthechangeinthe environmentaltemperatureissufficientlyslow.Thisistrueinreallife, exceptinsituationssuchaswhentheenvironmentbecomesunbearably hotsuchasunderscorchingsuninadesert,thelizarddivesintothesand toavoidbeingtoasted.
Fig.14.2 Duetoitsexcellentwaterconductivity,abambootreecanbeconsidered asaone-dimensional(vertically)lumpedsystemintermsofwater distribution(createdbyN.Bhoopal).Likewise,wecanapproximatea copperrodasalumpedsystemintermsofheatdistribution,becauseofits superiorthermalconductivity.
Fig.14.3 Theenergybalanceofathermocouplejunctionintheformofabead (createdbyF.Kermanshahi).Therateofenergyincreaseinthebeadis equaltothenetrateofheatgain.Thisincreaseinenergycontent,dE/dt,is reflectedintemperatureriseaccordingtodE/dt = mcP dT/dt.
261
264
266
268
269
271
276
278
279
Fig.14.4
Fig.14.5
Fig.14.6
Plotoftheresponse,T(t) T∞ = [T0 T∞ ]exp{ hAt/(mcP )} = [T0 T∞ ]exp( t/τ ),ofathermocouplejunctionsubjectedtoastep changefromT0 = 22°CtoT∞ = 88°C(createdbyX.Wang).
Asinglezonebuildingmodeledintermsofacapacitorandaresistor (createdbyX.Wang).Thecapacitance,C,describesthethermalmassof thebuilding,whiletheresistance,R,representstheoverallheat transmissionresistanceofthebuildingenvelope.Inthesummertime,Q’is negative,indicatingtherateofcooling,thatis,heatremovalrate.
Biotnumberillustrated(createdbyX.Wang).Whenthe within-the-systemthermalconductionresistanceissmallcomparedtothe surfaceconvectiveresistance,anychangeinsurfacetemperatureis promptlytransmittedthroughtheentiresystemand,hence,thesystemhas ahomogeneoustemperature.Withthatinmind,thissmall-Bicondition grantstheutilizationofthelumpedparameterassumption.
280
Fig.14.7
Fig.14.8
One-dimensionaltransientheatconductionthroughthethicknessofa largeplatewithbothsidesexposedtoachangeinthesurrounding temperature(createdbyX.Wang).Fortheparticularcaseshown,theplate isinitiallyatequilibriumwiththeambientatT0 ,andattimet = 0,the ambienttemperaturedropstoT∞ ,andtheplatestartstorespondtothat stepchange.Thechangeinthetemperaturedistributioninsidetheplate withincreasingtime,t,isofsignificantpracticalimportance.
Asemi-infinitewallsubjectedtoachangeinambientand,thus,surface temperature(createdbyX.Wang).Thewallissothickthatthe temperatureatlargexremainsfixedatT0 .
Fig.14.9 Solutionforasemi-infinitewallsubjectedtoachangeinsurface temperature(createdbyX.Wang).(A)Errorfunction,erf,versus similarityvariable,x/ (4α t),whereuisavariable.(B)Nondimensional temperature, θ ,asafunctionofthesimilarityvariable,x/ (4α t), accordingtothecomplementaryerrorfunction,erfc.
Fig.15.1 Aflockofbirdsridingonathermal(createdbyS.Akhand).Thefigure equallyillustratesmultiplesnapshotsofonevulturerisingonathermalin aroughlycircularmotion.
Fig.15.2 AbeautifuldisplayofcumuluscloudsabovetheDetroitriver(phototaken byX.Wang).
Fig.15.3 Asphericalvolumeofhotairinacooler,stagnantenvironment(created byD.Ting).Intheidealcase,weassumethevolumeofhotairstaysasa spherewithauniformtemperature.
Fig.15.4 Buoyanthotair,heatedviaanelectricresistor,beingopposedbyits viscousstagnantsurroundings(createdbyD.Ting).Thebuoyantforceof theheatedlighterairhastobegreaterthantheviscousforceimposedby thesurroundingstagnantairbeforethevolumeofhotaircanrise.
Fig.15.5 AsnapshotofRayleigh–Bérnardconvectionbasedonatwo-dimensional simulationofairina0.2mhighand0.5mwidecavity(createdbyX. Wang).Thebaseisat20°Cwhiletheairisat10°C.
Fig.15.6 Arectangularenclosure(orcavity)withshorterdimensionLS andlonger dimensionLL (createdbyD.Ting).Thelowerhorizontalplaneisheated untiltheRayleighnumberislargerthanthecriticalvaluetoformlaminar Rayleigh–Bérnardcells.FurtherincreaseintheRayleighnumberbeyond thelaminar-to-turbulentcriticalvalueleadstorandomturbulentmotion drivenbyintensenaturalconvection.
Fig.15.7 Acontinuousthermalplumeofair(createdbyX.Wang)generatedfroma 0.01mdiametercylinderat380Kin293Kambientairmovingupwardat
281
283
285
291
292
297
298
300
301
305
306
