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ES2B0FluidMechanicsModelAnswerstoExampleQuestions(SetV)

Question1:UTubemanometer+PitottubeIn figure 1 the flowing fluid is CO2 at 200C. Neglect losses. If and themanometerfluidisMeriamredoil(SG=0.827),estimate and thegasflowrateinm3/h.

Figure1

SOLUTIONEstimatetheCO2densityas

Themanometerreadinggivesthedownstreampressure:

Hence,

NowuseBernoullitofind ,assuming =stagnationpressure

2Or,

Then,

Question2:DimensionalanalysisUnderlaminarconditions,thevolumeflowQthroughasmalltriangularsectionporeofsidelengthbandlengthLisafunctionofviscosity,pressuredropperunitlengthp/L,andb.Using thepi theorem, rewrite this relation indimensionless form.Howdoes the volumeflowchangeiftheporesizebisdoubled?SOLUTIONEstablishthevariablesandtheirdimensions:

, , ,

Then and ,henceweexpect pigroup,foundasfollows:

; ; Solve,

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Question3:DynamicsimilarityWhentested inwaterat200C flowingat2m/s,an8cmdiameterspherehasameasureddragof5N.Whatwillbethevelocityanddragforceona1.5mdiameterweatherballoonmooredinsealevelstandardairunderdynamicallysimilarconditions?SOLUTIONForwaterat200Ctake and .Forsealevelstandardairtake

and .Theballoonvelocityfollowsfromdynamicsimilarity,whichrequiresidenticalReynoldsnumbers:

Or,

Thenthetwosphereswillhaveidenticaldragcoefficients:

Solve

Question4:MomentumconservationA12cmdiameterpipe,containingwaterflowingat200N/s,iscappedbyanorificeplate,asinFigure2.Theexitjetis25mmindiameter.Thepressureinthepipeatsection1is800kPagage.CalculatetheforceFrequiredtoholdtheorificeplate.

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Figure2

SOLUTIONForwatertake .Thisisastraightforwardxmomentumproblem.Firstevaluatethemassflowandthetwovelocities:

Nowapplythexmomentumrelationforacontrolvolumesurroundingtheplate:

Or,

5Question5:Newton`sLawofviscosityThebeltinFigure3movesatsteadyvelocity andskimsthetopofatankofoilofviscosity.Assuminga linearvelocityprofile,developasimple formula for thebeltdrivepower

requiredasafunctionof .Neglectairdrag.Whatpower inwattsisrequiredifthebeltmovesat2.5m/soverSAE30Woilat200C,withL=2m,b=60cm,andh=3cm?

Figure3

SOLUTIONThepoweristheviscousresistingforcetimesthebeltvelocity:

ForSAE30Woil, .Then,forthegivenbeltparameters,

Question6:Heattransfer(conduction)Heatistransferredsteadilytoboilingwaterinthepanthroughitsbottom.Theinnersurfacetemperatureofthebottomofthepanisgivenas .Theradiusofthepanis andthethicknessis .Thetemperatureoftheoutersurfaceistobedetermined.

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Figure4Assumptions

1. Steadyoperatingconditionsexistsincethesurfacetemperaturesofthepanremainconstantatthespecifiedvalues.

2. Thermalpropertiesofthealuminiumpanareconstant.PropertiesThethermalconductivityofthealuminiumisgiventobe SOLUTIONHeattransferareais

Under steady conditions, the rate of heat transfer through the bottom of the pan byconductionis

Substituting,

whichgives