流体力学与传热习题参考解答英文.docx
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流体力学与传热习题参考解答英文
1.Waterispumpedataconstantvelocity1m/sfromlargereservoirrestingonthefloortotheopentopofanabsorptiontower.Thepointofdischargeis4meterabovethefloor,andthefrictionlossesfromthereservoirtothetoweramountto30J/kg.Atwhatheightinthereservoirmustthewaterlevelbekeptifthepumpcandeveloponly60J/kg?
22
U22P2u,R
w=Z2g+-hf（Z0+1丄）
22
ZZ2Z!
431m
2.Thefluid（density1200kg/m）ispumpedataconstantrate20m3/hfromthelargereservoirtotheevaporator.Thepressureabovethereservoirmaintainsatmospherepressureandthepressureoftheevaporatorkeeps200mmHg（vacuum）.Thedistancebetweenthelevelofliquidinthereservoirandtheexitofevaporatoris15meterandfrictionallossinthepipeis120J/kgnotincludingtheexitofevaporator,whatisthepumpeffectiveworkandpowerifthediameterofpipeis60mm?
乙g+^
hf
2.67x104N/m2
hf120J/kg
2005
10F2x1.013x105
760
1200Kg/m360
U2
V
A
20
1.97m/s
3600*
n/4*0-062
Z1
0
Z2
15
2.67x10
1.972
W
15x9.81
120246.88J/kg
1200
2
NW
Q
246.88x1200x20/3600=1646W
hf=6.5U2
whereUisthevelocityinthepipe,find
a.watervelocityatsectionA-A'.
b.waterflowrate,inm3/h.
\L
8mAK
23
V=UA=2.9n/4x01x360082m/h
1Z1g+U/2
U22
Z2g+2
hf
U1
0
12Z1
6m
Z20
hf
6.5U2
6x9.81
u2
6.5U2
2
U2.9m/s
4.Waterpassesthroughthevariablepipe.Thevelocityinthesmallpipeis2.5m/s.TheverticalglasstubesareinsertedrespectivelyatthesectionAandBtomeasurethepressure（seefig.）Ifthefrictionlossbetweentwosectionis15J/kg,whatisthewatercolumndiffereneebetweentwoglasstubes?
Bytheway,drawtherelativeliquidcolumnheightoftwotubesintheFig.
a乙g+U；
bZbg+U；hf
2
乙二Zb
・・2
・・2
ab
Ub
Uahhf
1.232/2
2.52/21512.63
2
2f
12.63
3
Pa&
Rg
R=
3
1.29x10m
9.8x10
UaAaUbAb
Ub2.5*（33/47）21.23m/s
5.Acentrifugalpumptakesbrine（density1180kg/m3,viscosity1.2cp）fromthebottomofasupplytank
anddeliversitintoanothertank.Thelinebetweenthetanksis300mof25mmdiameterpipe（innerdiameter）.Theflowrateis2m3/h.Inthisline,therearetwogatevalves,fourelbows（90o）andonereturnbend,whatisthefrictionlossiftheroughnessofpipeis0.025mm?
lU2
hfhfsthflocal4fdV
v2m3/h=1.2cp=1.2x10-3Pa.s
k=0.025mmk/d=0.025/25=0.001
kc=0.4kl=1kr=2x0.07=0.14
kel4x0.753kre15-2.2
uv/A2/（3600x/4x0.0252）1.13m/s
Re山2.78x104f0.063
2
hf4x0.0063x300/0.025x1.132/2+
（0.4+1+2x0.07+4x0.7+1.5）x1.132/2=197.86J/kg
1000
V0uos00.61x/4x0.00012x2gx0.6x（13600
5.8x10m3/s
7.Waterflowsthroughapipewithadiameterdi100mmasshowninfigure.
a.whenthevalveisclosed,Ris600mmandhequals1500mm.Whilethevalveopenspartially,R=400mmandh=1400mm,f=0.00625（Finningfactor）andkc=0.5（contractioncoefficient）,whatistheflowrateofwater,inm3/h?
b.Ifthevalveopensfully,whatisthepressureofsection2-2',inN/m2?
Theequivalentlengthofthevalveis1.5mandtheFanningfactorfkeepsthesame?
（H2o=1000kg/m3,Hg=13600kg/m3）
2
2
g乙
u11
2
gZ2
u22
2
hf1-2
1
02
g（Hg
RH2oh）
39630N/m
2
2
lu
u
u1
0Z2=0
hf1-2
4f+k
c2.13u
d22
WecangetZ1fromthevalveclosed
h=1.5mR=0.6mZ1HggR/H2Oh6.66m
1
L玄
9.81x6.66u2/22.13u239630/1000
hf1-3
'and3-3',wehave
u=3.13m/sVh3600x/4x0.12x3.1388.5m/h
（2）whenthevalveopensfully,forsection1-1
2
2
d二
lin^B
jlJORinii
Forparallelpipeline
2.72
hfAhfBVtotaiVA+VB
hfA4fA
（l+^e）UA4x0.0075x10/0.053/2（2722）2
dA23600x/4x0.053"
0.333J/kg
（l+le）Ub22
hfB4fB
dB
—4x0.0045x2/0.3/2xuB0.333
2
uB2.36m/sVB=uBAB2.36x/4x0.232600m3/h
10.Aflatfurnacewallisconstructedof120mmlayerofsil-o-celbrick,withathermalconductivity0.08w/（moC）,backedbya150mmofcommonbrick,ofconductivity0.8w/（moC）,thetemperatureofinnerfaceofthewallis1400o,andthatoftheouterfaceis200C.
a.Whatistheheatlossthroughthewallinwpersquaremeter.
b.
Toreducetheheatlossto600w/m2byaddingalayerofcorkwithk0.2w/（moC）ontheoutsideofcommonbrick,howmanymetersofcorkarerequied?
0.120.15
b.600=（1400-200）/（0.12/0.08+0.15/0.8+x/0.2）x=0.0625m
13.Airatthenormalpressurepassesthroughthepipe（d20mm）andisheatedfrom20oCto100oC.Whatisthefilmheattransfercoefficientbetweentheairandpipewalliftheaveragevelocityofairis10m/s?
Thepropertiesofairat60oCareasfollows:
density1.06kg/m3,viscosity0.02cp,conductivity0.0289w/（moC）,andheatcapacity1kJ/kg-K
ud10x0.02x1.0644
0.02x10
Re=l1.06x1010
2
39.66x0.0289心02=57.22w/m.k
14.Ahotfluidwithamassflowrate2250kg/hpassesthrougha25x2.5mmtube.Thephysicalpropertiesoffluidareasfollows:
k=0.5w/（moC）,Cp=4kJ/kg-K,viscosity10-3N-s/m2,density1000kg/m3Find:
a.Heattransferfilmcoefficienthi,inw/（m2-K）.
b.
Iftheflowratedecreasesto1125kg/handotherconditionsarethesame,whatistheih
c.Ifthediameteroftube（insidediameter）decreasesto10mm,andthevelocityukeepsthesameasthatofcasea,calculateh.
d.Whentheaveragetemperatureoffluidandquantityofheatflowpermeteroftubeare40oCand400w/m,respectively,whatistheaveragetemperatureofpipewallforcasea?
e.Fromthisproblem,inordertoincreasetheheattransferfilmcoefficientandenhanceheattransfer,whatkindsofmethodscanyouuseandwhichisbetter,explain?
Hint:
forlaminarflow,Nu=1.86[RePr]1/3
1/3
4
220.1
forturbulentflowNu=0.023Re0.8Pr1/3
hi25500X0.5183159w/m2k
Nu0.023Re0.8Pr1/3hi=6347w/m2k
⑷Q=hiAi（t-tw）=400=500x2x0.02（t-tw）
t=40Ctw39.41C
（5）theremethods:
increaseuorhiordecreasedThefirstisbetter
thepipeandthehotfluidgoesthroughtheoutside.Theinletandoutlettemperaturesofcoldfluidare20and80o,andtheinletandoutlettemperaturesofhotfluidare150and90,respectively.Thehi（filmcoefficientinsidepipe）is700w/（m2°C）andoverallheattransfercoefficientUo（basedontheoutsidesurfaceofpipe）is300w/（m2oC）,respectively.Iftheheatlossisignoredandtheconductivityofpipewall（steel）istakenas45w/（moC）,find:
（1）heattransferfilmcoefficientoutsidethepipeho?
（2）thepipelengthrequiredforcounterflow,inm?
（3）whatisthepipelengthrequirediftheheatingmediumchangestosaturatedvapor（140oC）anditcondensestosaturatedliquidandotherconditionskeepunchanged?
（4）Whentheexchangerisusedforayear,itisfoundthatitcannotmeettheneedofproduction（theoutlettemperatureofcoldfluidcannotreach80°C）,explainwhy?
11d0lmdo1230.002x23
h。
Vohidikdm300700x1945x21
1/h0=1/U0-（do/hidi+bdo/kdm）=1/300-23/700*19-0.002*23/45*21
2
h0642.9w/mk
LMTD=70°C=t1+12Q=UoAoTm=mcCp（Tcb-Tca）
2
300*2*0.023*70L=500/3600*1000*（80-20）
L=5.4m
8020
14020ln
14080
（d）scaleisformedontheoutside,V0isdecreased
16.
Waterflowsturbulentlyinthepipeof①25x2.5mmshelltubeexchanger.Whenthevelocityofwateruis1m/s,overallheattransfercoefficientUo（basedontheoutersurfaceareaofpipe）is2115w/（moC）.Iftheubecomes1.5m/sandotherconditionskeepunchanged,Uois2660w/（moC）.Whatisthefilmcoefficienthooutsidethepipe?
（Heatresistancesofpipewallandscaleareignored）
17.Waterandoilpassparallellythroughanexchangerwhichis1mlong.Theinletandoutlettemperaturesofwaterare15and40°C,andthoseofoilare150and100°C,respectively.Iftheoutlettemperatureofoil
decreasesto80PC,andtheflowratesandphysicalpropertiesandinlettemperaturesofwaterandoilmaintainthesame,whatisthepipelengthofnewexchanger?
（Heatlossandpipewallresistanceareneglected）
QWhChT1-T2WcCct2t1VAtm
WhChT1-T2'WcCct2't1
150
100
40
15
t2
50C
150
80
t2
15
L2
T1
T2'
tm1
150
8092.5
4OC
L1
T1
T2
tm2
150
1.85
10069.8
L2
1.85mL1=1m
tm1
92.5tm269.8
18.Airwhichpassesthroughthepipeinturbulentflowisheatedfrom20to80°C.Thesaturatedvaporat
mc1Cpc（Tcb
116.3oCcondensestosaturatedwateroutsidethepipe.Ifairflowrateincreasesto120%oftheoriginandinletandoutlettemperaturesofairstayconstant,whatkindofmethodcanyouemployinordertodothat?
（Heatresistaneeofpipewallandscalecanbeignored）
h12Ai
Tm2
mc2Cpc（Tcb
Tca）
hi2Tm2
mc2
1.2
1.20.8
Tm2
hi1Tm1
md
Tm1
Tm1
8020
ln（116.3
20）/（116.380）
Tca）
Tm2
ln（Th20）/（Th80）
8020
Th=118.5oC
19.
Waterflowsthroughthepipeofa①25x2.5mmshell-tubeexchangerfrom20to50oC.Thehotfluid（Cp1.9kJ/kgoC,flowrate1.25kg/s）goesalongtheshellandthetemperatureschangefrom80to30oC.Filmcoefficientsofwaterandhotfluidare0.85kw/（moC）and1.7kw/（moC）.WhatistheoverallheattransfercoefficientUoandheattransferareaifthescaleresistancecanbeignored?
（theconductivityofsteelis45w/（moC）.
W=1.25Kg/sCp=1.9Kj/kgC
21.Afilterpress（A=0.1m2）isusedforfilteringslurry.Thevacuuminsidethefilteris500mmHg.Oneliterfiltratecanbegotafterfilteringof5minand0.6moreliterfiltrateisobtainedafter5moremin.Howmuchfiltratewillbegotafterfilteringof5moremin?
22
forfilterpressV2VVe=KA
22
5min12Ve0.1x5K⑴
22
10min1.62x1.6Ve0.1x10K
（2）
From
（1）
（2）,wecanseeVe=0.7K=48
.2
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