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105Pa,p2=-33332Pa
Problem4作业1.3
ppt1-2
InaNewtonianfluid,therelationshipbetweenthesheartressandshearrateis(
)
●Keepingthepressureconstant,theviscosityofagaswill(increase)asthetemperaturerising,andtheviscosityofaliquidwill(decrease)asthetemperaturerising
●theeffectofthesolidboundaryontheflowisconfinedtoalayerofthefluidimmediatelyadjacentto(wallofsolid)
●Atlowflowratesthepressuredropinthefluidisproportionaltothe(velocity);
athighratesitincreasesasthe(squareofthevelocity).
●Mechanicalenergyisfinallyconvertedto(heat)wheneddiesinfluidareobliteratedbyviscousaction,whichmayleadtoalarge(friction)lossinthefluid.
●Potentialflowhastwoimportantcharacteristics:
(1)neithercirculationsnoreddiescanformwithinthestream
(2)frictioncannotdevelop
ppt1-3
Ø
Bernoulli'
sequationhasfollowingrestrictions
1)idealfluid
2)densityisconstant
3)steady-stateflow
Thetotalenergybalanceisnotoftenusedwhen(appreciableenthalpy)changesoccuror(appreciableheat)isexchangedbetweenthesystemandtheenvironment.
Mechanicenergyincludes(workterm),(potentialenergy),(kineticenergy),and(flowworkpart)oftheenthalpyterm.
4.ExperimentontheconversionofmechanicalenergyshowninFig..
作业1.5
Waterfromthereservoirflowsthroughthepipe,whichthethroatdiameterisd.theratioofDtodequals2,theverticaldistancehbetweenthetankAandaxisofthepipeis1m.
HowmuchtheHisneededifthewateratthetankAislefttothethroatofthepipe?
Assumingthatfluidflowisapotentialflow.
作业1.8
Movingthewaterfromonecontainerintotheotherplacebymeansofapipeofconstantcross-sectionalareaisshownasinfigure.Find
(1)ThevelocityatstationA,B,C,D
(2)ThepressureatstationA,B,C,D
(3)ThemechanicalenergyinstationA,B,C
Assumingthatthewaterflowsthroughthepipewithoutfrictionlosses.
Solution:
1)towriteBernoulliequation1.3-26fromstation1tostationD
simplifying
Andgives
VD=9.9m/s
Fromcontinuityequation
VA=VB=VC=VD=9.9m/s
2)gaugepressurePD=0
writingBernoulliequationbetweenstationsc-dgives
,
PC=-3×
9.81×
1000=-294300Pa
Similarly
PB=1×
1000=9810Pa
PA=-4×
1000=-392400Pa
Totalmechanicalenergymaintainconstantwhenthefluidflowsfromthecontainertotheexit
5=49.05J/kg
ppt1-4
Theaveragevelocityis(0.5)timesthemaximumvelocityatthecenterforlaminarflow.
Theaveragevelocityis(0.8)timesthemaximumvelocityatcenterforturbulentflow
Themaximumvalueofthemomentumfluxoccurs(attheinterfacebetweenthefluidandthewallofsolid)foralaminarflow.
Themaximumvalueofthevelocityoccurs(atthecenterofthetube)foralaminarflowinpipe.
Inlaminarflowthevelocitydistributionwithrespecttoradiusis(parabola)withtheapexatthecenterlineofthepipe
Thepressuredropis(proportional)totheaveragevelocityforthelaminarflow
ppt1-5
•Forlaminarflow,theaveragevelocityinapipeismaximumvelocity,forturbulentflowaveragevelocityismaximumvelocity.
•Forlaminarflowinapipe,theflowrateisconstant,whendiincreases,thefrictioncoefficientwill(increse),andfrictionlosswill(reduce).
•Whenthepipeinstallationchangesfromhorizontaltoverticalpositionandthevelocitykeepsunchanged,thefrictionallosswillbeC.
A).increased;
B).decreased;
C).thesame;
D).uncertain
•Inlaminarflow,thevelocitydistributionwithrespecttoradiusis()atthecenterlineofthepipe
•Roughnesshas(noeffect)onthefrictionfactorforlaminarflowunlesskisverylarge.
•Forlaminarflow,thefrictioncoefficientisproportionaltoa(reciprocalofRe)
•Forturbulentflow,thefrictioncoefficientisafunctionofboth(roughnessandRe)
•Forcompletelyturbulentflow,thefrictioncoefficientisafunctionof(relativeroughness)
1250cm3/sofwateristobepumpedthroughasteelpipe,25mmdiameterand30mlong,totank12mhigherthanitsreservoir.Calculateapproximatelythepowerrequired.Whatpowermotor(inkW)wouldyouprovide?
Theroughnessofasteelpipewillbetakenas0.045mm;
theefficiencyofthepumpis50%
turbulentflow
frommoodyfigure
作业1.9
Liquidflowsthroughthetube,showninFig.thelengthofabequalscd,andthediameterandroughnessoftubearesame.Find:
(1)theexpressionsofΔpab/(ρg),hfab,Δpcd/(ρg)andhfcd,respectively.
(2)therelationshipbetweenreadingsR1andR2intheUtube.
两水池的水位差H=24m,l1=l3=l4=100m,d1=d2=d4=100mm,
d3=200mm,沿程阻力系数λ1=λ2=λ4=0.025,
λ3=0.02,除阀门外,忽略其他局部阻力。
(1)阀门局部阻力系数ζ=30,求管路中的流量;
(2)关闭阀门,其他条件不变,求管路中的流量。
解:
假设2、3的l相等
1)由
得
流量
总摩擦阻力损失
故u3=0.575m/su1=3m/sQ=0.024m3/s
2)
得u1=2.5m/sQ=0.0196m3/s
ppt1-7
●orificeandventurimetersmeasuretheaveragevelocityoftheentirestreamoffluid
●Thepitottubemeasuresthelocalvelocityoffluid.
●Rotametermustbeverticallyinstalledinthepipeline,andthefluidmustflowupwardthroughthetaperedtubeandsuspendsfreelyafloat.
vIntheorificeandventurimeter,thevariationofvelocitythrough(constant)areageneratesa(variable)pressuredrop.
vIntherotameter,thevariationofflowratethrough(variable)areageneratesa(constant)pressuredrop.
vForaorifice,nozzleandventurimeter,whentheReynoldsnumberisgreaterthancriticalRe,thenorificecoefficientCois(onlydependent)oftheReynoldsnumberforagivenβ
Sulphuricacidofspecificgravity1.3isflowingthroughapipeof50mminternaldiameter.Athin-lippedorifice,10mm,isfittedinthepipeandthedifferentialpressureshownbyamercurymanometeris10cm.Assumingthattheleadstothemanometerarefilledwiththeacid,calculate(a)theweightofacidflowingpersecond,and(b)theapproximatepressuredropcausedbytheorifice.Thecoefficientoftheorificemaybetakenas0.61,thespecificgravityofmercuryas13.6,andthedensityofwateras1000kg/m3
(a)themassflowratemisgivenby
Or,where
isapproximatelyunity,m=0.268kg/s
(b)theapproximatepressuredropcausedby(13600-1300)×
0.1=12066.3Pa
Waterflowsthroughanorificeof25mmdiametersituatedina75mmpipeattherateof300cm3/s.whatwillbethedifferenceinlevelonawatermanometerconnectedacrossthemeter?
Taketheviscosityofwateras1mNs/m2.
Thevelocityflowingthroughhole
velocityflowingpipe
theratioofarea:
m=0.11
so
Co=0.61
R=51.2mm
Wateristransportedbyapumpfromreactor,whichhas200mmHgvacuum,tothetank,inwhichthegaugepressureis0.5kgf/cm2,asshowninFig.Thetotalequivalentlengthofpipeis200mincludingalllocalfrictionalloss.Thepipelineis57×
3.5mm,theorificecoefficientofCoandorificediameterdoare0.62and25mm,respectively.Frictionalcoefficientis0.025,Find:
DevelopedheadHofpump,inm.(thereadingRofUpressuregaugeinorificemeteris168mmHg)
Pr=-200×
13.6×
9.81=-26683.2PaPt=49035Pa,
PressuredropinU
∆p=0.168×
(13600-1000)×
9.81=20765.8Pa
fromcontinuityequation:
1.6m/s
skinfrictionloss
developedhead
ppt2-1
●Ifacentrifugalpumpoperatesonair,then,itcann’tdrawliquidfromaninitiallyemptysuctionline。
●Positive-displacementpumpsarenotsubjecttoairbinding.
●Beforeacentrifugalpumpstartsup,closethevalveindischargeinotherto(reduce)thestart-uppowerrequired
●Whenthetemperatureoffluidtobetransportedincreases,themaximumliftofsuctionwill(B).Ifthevelocityofsuctionpipedecreases,themaximumsuctionliftwill(A).Iftheflowrateremainsconstantbutthediameterofsuctionpipedecreases,themaximumsuctionliftwill(B)
A)increase;
B)decrease;
C)keepthesameD)beuncertain
●Whenthesuctionpressureis(close)tothevaporpressure,thecavitationwilloccur
●Thedifferencebetweenthetheoreticalandactualcurvesresultsfrom(shockloss);
(frictionloss);
and(recirculationloss).
•Whenhigherdevelopedheadisrequired,thebestselectionis(B).
A)operationinseriesB)multistagecentrifugalpumpC)throttledbyvalve
●(×
)OnepumpcandevelopmoreHthanthattwosamepumpswhichworkinseries.
●Themethodsofadjustingvolumeflowrateofcentrifugalpumpare
(1)changesinrevolutionofpump;
(2)changeofdiameterofimpeller;
(3)adjusttheopeningof