Scilab Code for Unit Operations of Chemical Engineering by

Scilab Code for Unit Operations of Chemical Engineering by Warren L. McCabe, Julian C. Smith, Peter Harriott1 Created by Prashant Dave Sr. Research Fellow


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BookDetailsAuthor:WarrenL.McCabe,JulianC.Smith,PeterHarriottTitle:UnitOperationsofChemicalEngineeringPublisher:McGraw-Hill,Inc.Edition:FifthYear:1993Place:NewDelhiISBN:0-07-112738-01
ContentsListofScilabCode51De nitionsandPrinciples91.1ScilabCode...........................92FluidStaticsanditsApplication112.1ScilabCode...........................114BasicEquationsofFluidFlow134.1ScilabCode...........................135FlowofIncompressibleFluidsinConduitsandThinLayers185.1ScilabCode...........................186FlowofCompressibleFluids206.1ScilabCode...........................207FlowPastImmersedBodies257.1ScilabCode...........................258TransportationandMeteringofFluids298.1ScilabCode...........................299AgitationandMixingofLiquids369.1ScilabCode...........................3610HeatTransferbyConduction4410.1ScilabCode...........................442
11PrinciplesofHeatFlowinFluids4811.1ScilabCode...........................4812HeatTransfertoFluidswithoutPhaseChange5012.1ScilabCode...........................5013HeatTransfertoFluidswithPhaseChange5613.1ScilabCode...........................5614RadiationHeatTransfer6014.1ScilabCode...........................6015Heat-ExchangeEquipment6215.1ScilabCode...........................6216Evaporation6716.1ScilabCode...........................6717Equilibrium-StageOperations7117.1ScilabCode...........................7118Distillation7518.1ScilabCode...........................7519IntroductiontoMulticomponentDistillation8619.1ScilabCode...........................8620LeachingandExtraction9320.1ScilabCode...........................9321PrinciplesofDi usionandMassTranserbetweenPhases10221.1ScilabCode...........................10222GasAbsorption10822.1ScilabCode...........................10823Humidi cationOperations12223.1ScilabCode...........................1223
24DryingofSolids12624.1ScilabCode...........................12625Adsorption13225.1ScilabCode...........................13226MembraneSeparationProcesses14126.1ScilabCode...........................14127Crystallization14627.1ScilabCode...........................14628Properties,HandlingandMixingofParticulateSoilds15528.1ScilabCode...........................15529SizeReduction15829.1ScilabCode...........................15830MechanicalSeparations16230.1ScilabCode...........................1624
ListofScilabCode1.1Example1.1.sce........................92.1Example2.1.sce........................112.2Example2.2.sce........................114.1Example4.1.sce........................134.2Example4.2.sce........................144.3Example4.3.sce........................154.4Example4.4.sce........................165.1Example5.1.sce........................186.1Example6.1.sce........................206.2Example6.2.sce........................226.3Example6.3.sce........................237.1Example7.1.sce........................257.2Example7.2.sce........................267.3Example7.3.sce........................278.1Example8.1.sce........................298.2Example8.2.sce........................308.3Example8.3.sce........................318.4Example8.4.sce........................328.5Example8.5.sce........................338.6Example8.6.sce........................349.1Example9.1.sce........................369.2Example9.2.sce........................379.3Example9.3.sce........................379.4Example9.4.sce........................389.5Example9.5.sce........................399.6Example9.6.sce........................399.7Example9.7.sce........................419.8Example9.8.sce........................425
20P=1.01325*10^5*0.3048/(32.174*0.45359237*12^2);//[lbf/in.^2]2122//(d)23//UsingEq.(1.8),(1.33),(1.37),(1.26),and(1.27)24//Lethp=1hp25hp=550*32.174*0.45359237*0.3048^2/1000;//[kW]
10
Chapter2FluidStaticsanditsApplication2.1ScilabCodeExample2.1Example2.1.sce1clearall;2clc;34//Example2.15rho_A=13590;6rho_B=1260;7Pa=14000;8gc=1;//[ft�lb/lbf�s^2]910//UsingEq.(2.5);Zb=250mmHg11Pb=-(250/1000)*(9.80665/1)*13590;1213//UsingEq.(2.10)14Rm=(14000+33318)/(9.80665*(13590-1260))15disp('mm',Rm,'Thereadinginthemamometeris(Rm)=')
Example2.2Example2.2.sce11
1clearall;2clc;34//Example2.256//(a)7//UsingEq.(2.15)8t=(100*1.1)/(1153-865)9rate_each_stream=(1500*42)/(24*60)10total_liquid_holdup=2*43.8*2311vol=total_liquid_holdup/0.9512disp('gal',vol,'vesselsize=')1314//(b)tankdiameter15Zt=0.90*416ZA1=1.8//[ft];17ZA2=1.8+(3.6-1.8)*(54/72)18disp('ft',ZA2,'tankdiameter=')
12
20//UsingEq.(4.4),21//velocitythroughpipeA22V_Abar=240.7/(3600*0.0233)//[ft/s]2324//velocitythroughpipeB25V_Bbar=240.7/(3600*0.0513)//[ft/s]2627//velocitythrougheachpipeofC28V_Cbar=240.7/(2*3600*0.01414)//[ft/s]2930disp('ft/s',V_Abar,'velocitythroughpipeA=')31disp('ft/s',V_Bbar,'velocitythroughpipeB=')32disp('ft/s',V_Cbar,'velocitythroughpipeC=')3334//(c)35//UsingEq.(4.8),36//massvelocitythroughpipeA37GA=mdot/0.0233//[kg/m^2�s]3839//massvelocitythroughpipeB40GB=mdot/0.0513//[kg/m^2�s]4142//massvelocitythrougheachpipeofC43GC=mdot/(2*0.01414)//[kg/m^2�s]4445disp('kg/m^2�s',GA,'massvelocitythroughpipeA=')46disp('kg/m^2�s',GB,'massvelocitythroughpipeB=')47disp('kg/m^2�s',GC,'massvelocitythroughpipeC=')
Example4.2Example4.2.sce1clearall;2clc;34//Example4.214
5//ApplyingEq.(4.25)6//Pa=Pb,Ua=07//Zb=0,Za=5m89//Thevelocityatstreamlinedischarge10Ub=sqrt(5*2*9.80665)//[m/s]11disp('m/s',Ub,'streamlinedischargevelocity(Ub)=')
Example4.3Example4.3.sce1clearall;2clc;34//Example4.35rho=998;//[kg/m^3]6Da=50;//[mm]7Db=20;//[mm]8pa=100;//[N/m^2]910//(a)11Va_bar=1.0;//[m/s]12Vb_bar=Va_bar*(Da/Db)^2//[m/s]13//UsingEq.(4.29)14//Za=Zb,hf=015pb=pa-rho*(Vb_bar^2-Va_bar^2)/(2*1000)//[kN/m^2]16disp('kN/m^2',pb,'pb=')1718//(b)19//CombiningEqs.(4.14)&(4.15)20//Forxdirection,21//sinceFg=0,wegetEq.(4.30)22theta=%pi/4;23Va_xbar=Va_bar;24Sa=(%pi/4)*(Da/1000)^2;//[m^2]25Sax=Sa;26//FromFIg4.527Vb_xbar=Vb_bar*cos(theta);//[m/s]15
28Sb=%pi/4*(Db/1000)^2;//[m^2]29Sbx=Sb*sin(theta);//[m^2]30//UsingEq.(4.6)31mdot=Va_bar*rho*Sa;//[kg/s]32//SubstitutinginEq.(4.30)33//SolvingforFw,x34beta_a=1;beta_b=1;35Fw_x=mdot*(beta_b*Vb_xbar-beta_a*Va_xbar)-Sax*pa*1000+Sbx*pb*1000//[N]3637//Forydirection,38//Va
ybar=0,Say=039Vb_ybar=Vb_bar*sin(theta);//[m/s]40Sby=Sb*cos(theta);//[m^2]41Va_ybar=0;//[m/s]42Say=0;//[m/s]4344Fw_y=mdot*(beta_b*Vb_ybar-beta_a*Va_ybar)-Say*pa*1000+Sby*pb*1000//[N]
Example4.4Example4.4.sce1clearall;2clc;34//Example4.45gc=32.17;//[ft�lb/lbf�s^2]6rho_w=62.37;//[lb/ft^3],densityofwater7sp_gravity=1.84;8neta=0.60;9hf=10;//[ft�lbf/lb],frictionlosses10Va_bar=3;//[ft/s]11Da=3;//[in.]12Db=2;//[in.]13//FromAppendixcorsssecionalarearespectiveto3in.and2in.diameter14Sa=0.0513;//[ft^2]15Sb=0.0233;//[ft^2]16
16Za=0;//[ft]17Zb=50;//[ft]18Vb_bar=Va_bar*(Sa/Sb);//[ft/s]19g=gc20//UsingEq.(4.32)21Wp=((Zb*g/gc)+Vb_bar^2/(2*gc)+hf)/neta;//[ft�lbf/lb]2223//UsingEq.(4.32)onpumpitself24//stationaisthesuctionconnectionandstationbisthedischarge25//Za=Zb26//Eq.(4.32)becomes27//thepressuredevelopedbypumeisdeltaP=pb�pa28deltaP=sp_gravity*rho_w*(((Va_bar^2-Vb_bar^2)/(2*gc))+neta*Wp)//[lbf/ft^3]2930mdot=Sa*Va_bar*sp_gravity*rho_w;3132//thePower33P=mdot*Wp/550//[hp]
17
Chapter5FlowofIncompressibleFluidsinConduitsandThinLayers5.1ScilabCodeExample5.1Example5.1.sce1clearall;2clc;34//Example5.15//Given6mu=0.004;//[kg/m�s]7D=0.0779;//[m]8rho=0.93*998;//[kg/m^3]9L=45;//[m]1011//Forfittings,formTable5.112sum_Kf=0.9+2*0.2;13//FromEq.(4.29),assumingalpha
a=1,14//sincepa=pb,andVa
bar=015//A=Vb
bar^2/2+hf=g(Za�Zb)16A=9.80665*(6+9);//[m^2/s^2]17//UsingFig5.918f=0.0055;18
19//UsingEq.(5.68),ThereisnoexapnsionlossandKe=0.20//FromEq.(5.66),sinceSaisverylage,Kc=0.4.Hence21Vb_bar=sqrt(294.2/(2.7+2311*f));//[m/s]22//FromAppendix5,crosssectionalareaofthepipe23S=0.00477;//[m^2]24flow_rate=S*Vb_bar*3600//[m^3/hr]
19
Chapter6FlowofCompressibleFluids6.1ScilabCodeExample6.1Example6.1.sce1clearall;2clc;34//Example6.15//Given6gama=1.4;7M=29;8R=82.0568*10^-3;//[atm�m^3/Kgmol�K]9Nma=0.8;10gc=1;//[ft�lb/lbf�s^2]11//AtEntrance12p0=20;//[atm]13T0=555.6;//[K]1415//(a)16//UsingEq.(6.28)17//Pressureatthroat18pt=(1/(1+((gama-1)/2)*Nma^2)^(1/(1-1/gama)))*p0//[atm]19//FromEq.(6.10)20
25//Thevelocityattheentranceofthepipe26ua=Ma_a*Aa//[m/s]27//WhenL
b=L
max,thegasleavesthepipeattheasteriskconditions,where28Ma_b=1;29//UsingEq.(6.43)30A=(gama-1)/2;31Tstar=Tr*(1+A*Ma_a^2)/(1+A*Ma_b^2)//[K]32//UsingEq.(6.44)33rho_star=0.795*Ma_a/sqrt(2*(1+(gama-1)*Ma_a^2/2)/(2.4))//[lb/ft^3]34//UsingEq.(6.39)35pstar=p0*Ma_a/sqrt(1.2)//[atm]36//Massvelocitythroughtheentirepipe37G=0.795*ua//[lb/ft^2�s]38ustar=G/rho_star//[ft/s]3940//(c)41//UsingEq.(6.45)withf
Lmax
rh=4004243err=1;44eps=10^-3;45Ma_ac=rand(1,1);46i=1;47while((err�eps))48A=2*(1+((gama-1)/2)*Ma_ac^2)/((gama+1)*Ma_ac^2);49B=gama*400+1+(gama+1)*log(A)/2;50Ma_anew=sqrt(1/B);51err=Ma_ac-Ma_anew;52Ma_ac=Ma_anew;53end54Ma_ac;55uac=Ma_ac*ua/Ma_a//[ft/s]56Gc=uac*0.795//[lb/ft^2�s]
Example6.3Example6.3.sce1clearall;23
Chapter7FlowPastImmersedBodies7.1ScilabCodeExample7.1Example7.1.sce1clearall;2clc;34//Example7.15//Given6rho_p=2800;//[kg/m^3]7g=9.80665;//[m/s^2]8ac=50*g;//[m/s^2]9//(a)10//Fromappendix2011Dp_100=0.147;//[mm]12Dp_80=0.175;//[mm]13Dp=(Dp_100+Dp_80)/2;//[mm]1415//FromAppendix1416mu=0.801;//[cP]17rho=995.7;//[kg/m^2]18//UsingEq.(7.45)19K=Dp*10^-3*(g*rho*(rho_p-rho)/(mu*10^-3)^2)^(1/3);20//ThisisslightlyabovetheStoke's�lawrange25
21//Assuming22N_rep=4.4;23//FromFig.7.624Cd=7.9;25//FromEq.(7.37)26mu_ta=sqrt(4*g*(rho_p-rho)*Dp*10^-3/(3*Cd*rho))//[m/s]2728//(b)29//Using'ac'inplaceof'g'inEq.(7.45)30K=K*50^(1/3);//Sinceonlyaccelerationchanges31//Etimating32N_rep=80;//FromFig.(7.6)33Cd=1.2;34mu_tb1=sqrt(4*ac*(rho_p-rho)*Dp*10^-3/(3*Cd*rho))//[m/s]35//ForirregularparticlesCdisabout20percentgreater36//thanthatforspheres37Cd=1.2*1.2;38mu_tb2=sqrt(4*ac*(rho_p-rho)*Dp*10^-3/(3*Cd*rho))//[m/s]
Example7.2Example7.2.sce1clearall;2clc;34//Example7.25//Given6g=32.174;//[ft�lb/lbf�s^2]7eps=0.8;8speg_s=4.0;9speg_c=1.594;10Ds=0.004;//[in.]11rho_w=62.37;//[lbf/ft^3]12delta_speg=speg_s-speg_c;13delta_rho=rho_w*delta_speg;//[lbf/ft^3]26
14R=29.92;15gc=32.17;//[ft�lb/lbf�s^2]16//actualsuctiondensity17rho_a=M*pa*(460+60)/(378.7*30*(460+Ta));//[lb/ft^3]18//acualdischargedensity19rho_b=rho_a*pb/pa;//[lb/ft^3]20//averagedensityoftheflowinggas21rho=(rho_a+rho_b)/2;//[lb/ft^3]22//massflowrate23mdot=vdot*M/(378.7*60)//[lb/s]24//developedpressure25dev_p=(pb-pa)*144*14.7/(R*rho);//[ft�lbf/lb]26//velocityhead27vel_head=vb^2/(2*gc);//[ft�lbf/lb]28//UsingEq.(8.1),alpha
a=alpha
b=1,va=0,Za=Zb,29Wp=(dev_p+vel_head)/neta//[ft�lbf/lb]30//UsingEq.(8.4)31Pb=mdot*Wp/550//[hp]
Example8.3Example8.3.sce1clearall;2clc;34//Example8.35//Given6vdot=180;//[ft^3/min]7pa=14;//[lbf/in.^2]8pb=900;//[lbf/in.^2]9Ta=80+460;//[K]10q0=0.063;//[m^3/s]11Cp=9.3;//[Btu/lbmol�F]12gama=1.31;13delta_Tw=20;//[F]14//(a)15neta=0.80;31
21Da=4.026/12;//[ft]22delta_p=h/12*(spg_m-spg_gl)*rho_w*(1);//[lbf/ft^2]23//UsingEq.(8.42)24beeta=sqrt(4*mdot/(0.61*%pi*Da^2*sqrt(2*gc*delta_p*rho_100)));25Do=Da*beeta;//[ft]26//theorificediameter27D=12*Do//[in.]2829//(b)30//UsingFig.8.20,thefractionofdifferentialpressurelossis31fra_prss_loss=0.68;32//Maximumpowerconsumption33P=mdot*delta_p*fra_prss_loss/(rho_ratio*rho_w*spg_O*550)//[hp]
Example8.6Example8.6.sce1clearall;2clc;34//Example8.45//Given6Cpt=0.98;7Ta=200;//[F]8Da=36;//[in.]9pa=15.25;//[in.]10h=0.54;//[in.]11P=29.92;//[in.]12spg_m=13.6;//[specificgravityofmercury]13rho_w=62.37;//[lb/ft^3]14gc=32.174;//[ft�lb/lbf�s^2]15//UsingEq.(8.52)16Pabs=P+pa/spg_m;//[in.]17rho=29*492*31.04/(359*(200+460)*29.92);//[lb/ft^3]34
18//Frommanometerreading19delta_p=h/12*rho_w//[lbf/ft^3]2021//UsingEq.(8.53,maximumvelocity,assumingNmaisnegligible22umax=Cpt*sqrt(2*gc*delta_p/rho)//[ft/s]23//Thereynoldsnumberbasedonmaximumvelocity24mu_air=0.022;//[cP]formAppendix825Nre_max=(Da/12)*umax*rho/(mu_air*0.000672);26//UsingFig5.7,toobtainaveragevelocity27Vbar=0.86*umax//[ft/s]28Nre=Nre_max*0.86;29//Thevolumetricflowrate30q=Vbar*(Da/12)^2*%pi/4*520/660*Pabs/P*60//[ft^3/min]
35
Example9.5Example9.5.sce1clearall;2clc;34//Example9.55//Given6Dt=6;//[ft]7H=8;//[ft]8T=70;//[F]9sp_gr=3.18;10w_fr=0.25;11Da=2;//[ft]12h=1.5;//[ft]13gc=32.17;//[ft�lb/lbf�s^2]14//(a)15//UsingdataofBuurmanetal.inFig.(9.19)16//changeinnc17delta_nc=(104/200)^0.2*(2.18/1.59)^0.45*(33.3/11.1)^0.13;18//changeinP19dalta_P=delta_nc^3;2021//UsingFig.9.1922V=%pi/4*Dt^2*H*7.48;//[gal]23P=3.3*V/1000//[hp]2425//(b)26//FromTable9.3,foracourbladeturbine,27KT=1.27;28Np=KT;29//slurrydensity30rho_m=1/((w_fr/sp_gr)+(1-w_fr))*62;//[lb/ft^3]3132nc=(P*gc*550/(Np*rho_m*Da^5))^(1/3)//[r/s]
Example9.6Example9.6.sce39
18//UsingEq.(9.47)19Vs_barc=0.114*(PgbyV)*(Dt/1.5)^0.17/1000//[m/s]20qg=Vs_barc*At*3600//[m^3/h]21//ThecalculatedfloodingvelocityisbeyondtherangeofthedataonwhichEq.(9.47)22//wasbased,soitmaynotberelaible.BasedonVs
barc,thehighestmeasuredvalue,qg23//wouldbe850m^3/h.
Example9.8Example9.8.sce1clearall;2clc;34//Example9.85//Given6D1=1;//[ft]7D6=68Nre_i=10^4;9Da=4;//[in.]10t1=15;//[s]11P=2;//[hp/gal]1213//(a)14//UsingFig.9.1515//themixingfactorntTisconstantandtimetTisasumedconstant,16//speednwillbethesameinbothvessels.17//UsingEq.(9.24)withconsantdensity18PbyD_ratio=(D6/D1)^2;19//ThePowerinputrequiredinthe6�ftvesselisthen20Pin=2*PbyD_ratio//[hp/1000gal]2122//(b)23//UsingEq.(9.54)withsameinputpowerperunitvolumeinbothvessels24n6byn1=(D6/D1)^(2/3)42
25//blendinginthe6�ftvesselwouldbe26t6=t1*n6byn1//[s]
43
Chapter10HeatTransferbyConduction10.1ScilabCodeExample10.1Example10.1.sce1clearall;2clc;34//Exmple10.15//Given6T1=32;//[F]7T2=200;//[F]8k1=0.021;//[Btu/ft�h�F]9k2=0.032;//[Btu/ft�h�F]10A=25;//[ft^2]11B=6/12;//[ft]12//averagetemperatureandthermalcondutivityofthewall13Tavg=(40+180)/2;//[F]14kbar=k1+(Tavg-T1)*(k2-k1)/(T2-T1);//[Btu/ft�h�F]15delta_T=180-40;//[F]16//UsingEq.(10.5)17q=kbar*A*delta_T/B//[Btu/h]
Example10.2Example10.2.sce44
1clearall;2clc;34//Example10.25//Given6delta1=4.5/12;//[ft]7k1=0.08;//[Btu/ft�h�F]8delta2=9/12;//[ft]9k2=0.8;//[ft]10Tin=1400//[F]11Tout=170//[F]12Rc=0.5;//[ft^2�h�F/Btu]13//(a)14//Consideringunitcrosssectionalarea15A=1;//[ft^2]16RA=delta1/k1;//[ft^2�h�F/Btu]17RB=delta2/k2;//[ft^2�h�F/Btu]18R=RA+RB;//[ft^2�h�F/Btu]19delta_T=Tin-Tout;//[F]overalltemperaturedrop20//UsingEq.(10.9)21q=A*delta_T/R//[Btu/h]2223//(b)24//Thetemperaturedropinoneseriesofresistancesistothe25//individualresistanceastheoveralltemperaturedropistothe26//overallresistance,or27delta_TA=RA*delta_T/R;//[F]28//Temperatureattheinteface29Tf=Tin-delta_TA//[F]3031//(c)Thetotalresistancewillnowincludecontactresistance32R=R+Rc;//[ft^2�h�F/Btu]33//theheatlossfromunitsquarearea34q=delta_T/R//[Btu/h]
45
Example10.3Example10.3.sce1clearall;2clc;34//Example10.35//Given6r1=60/2;//[mm]7r2=(50+r1);//[mm]8k2=0.055;//[W/m�C]9r3=40+r2;//[mm]10k3=0.05;//[W/m�C]11To=30;//[C]12Ti=150;//[C]13//Logrithimicmeanforsilicalayerandcorklayer14rl_s=(r2-r1)/log(r2/r1)//[mm]15rl_c=(r3-r2)/log(r3/r2)//[mm]1617//UsingEq.(10.15)andEq.(10.14)simulataneously18//AndAddingthesetwoEquations19qbyL=(Ti-To)/4.13//[W/m]
Example10.4Example10.4.sce1clearall;2clc;34//Example10.45//Given6k=0.075;//[Btu/ft�h�F]7rho=56.2;//[lb/ft^3]8Cp=0.40;//[Btu/lb�F]9s=0.5/12;//[ft.]10Ts=250;//[F]11Ta=70;//[F]12Tb_bar=210;//[F]1314//(a)46
15Temp_diff_ratio=(Ts-Tb_bar)/(Ts-Ta);16alpha=k/(rho*Cp);17//FromFig.10.618N_Fo=0.52;19tT=N_Fo*s^2/alpha//[h]2021//(b)22//SubstitutinginEq.(10.23)23QTbyA=s*rho*Cp*(Tb_bar-Ta)//[Btu/ft^2]
Example10.5Example10.5.sce1clearall;2clc;34//Example10.55//Given6Ts=-20;//[C]7Ta=5;//[C]8T=0;//[C]9t=12;//[h]10alpha=0.0011;//[m^2/h]1112//(a)13Temp_diff_ratio=(Ts-T)/(Ts-Ta);14//FromFig.(10.8),15Z=0.91;16//thereforedepth17x=Z*2*sqrt(alpha*t)//[m]1819//(b)20//FromEq.(10.27),thepenetrationdistanceis21x_rho=3.64*sqrt(alpha*t)//[m]
47
Chapter11PrinciplesofHeatFlowinFluids11.1ScilabCodeExample11.1Example11.1.sce1clearall;2clc;34//Example11.15//FromAppendix56Di=1.049/12;//[ft]7Do=1.315/12;//[ft]8xw=0.133/12;//[ft]9km=26;//[Btu/ft�h�F]10//UsingEq.(10.15)forLogrithmicmeandiameterDL
bar11DL_bar=(Do-Di)/log(Do/Di);//[ft]12//FromTable11.113hi=180;//[Btu/ft^2�h�F]14ho=300;//[Btu/ft^2�h�F]15hdi=1000;//[Btu/ft^2�h�F]16hdo=500;//[Btu/ft^2�h�F]1748
40Vw_bar=mw_dot/(%pi/4*(Dij^2-Dot^2)*rho_w);//[ft/s]41//Reynoldsnumberforbenzeneandwater42Nre_b=Dit*Vb_bar*rho_b*3600/mu_b;43Nre_w=De*Vw_bar*rho_w*3600/mu_w;44//PrandtlNumberforbenzeneandwater45Npr_b=Cp_b*mu_b/k_b;46Npr_w=Cp_w*mu_w/k_w;4748//PreliminaryestimatesofthecoefficientsareobtainedusingEq.(12.32),omittingthe49//correctionforviscosityratio:50//Benzene51hi=0.023*Vb_bar*3600*rho_b*Cp_b/(Nre_b^0.2*Npr_b^(2/3));//[Btu/ft^2�h�F]52//Water53ho=0.023*Vw_bar*3600*rho_w*Cp_w/(Nre_w^0.2*Npr_w^(2/3));//[Btu/ft^2�h�F]54//UsingEq.(12.39)55//Temperaturedropoverthebenzeneresistance56delta_Ti=(1/hi)/(1/hi+Dit/(Dot*ho))*(Tavg_b-Tavg_w);//[F]57Tw=Tavg_b-delta_Ti;//[F]5859//TheviscositiesoftheliquidsatTw60muw_b=1.45;//[lb/ft�h]61muw_w=2.42*0.852;//[lb/ft�h]62//UsingEq.(12.24),viscosity�correctionfactorsphiare63phi_b=(mu_b/muw_b)^0.14;64phi_w=(mu_w/muw_w)^0.14;65//Thecorrectedcoefficientsare66hi=hi*phi_b;//[Btu/ft^2�h�F]67ho=ho*phi_w;//[Btu/ft^2�h�F]68//Thetemperaturedropoverthebenzeneresistanceandthewalltemperature69delta_Ti=(1/hi)/(1/hi+Dit/(Dot*ho))*(Tavg_b-Tavg_w);//[F]52
70Tw=Tavg_b-delta_Ti//[F]71//Thisissoclosetopreviouslycalculatedwalltemperaturethatasecondapproximation72//isunnecessary73//UsingEq.(11.29),neglectingtheresistanceofthetubewall74Uo=1/(Dot/(Dit*hi)+1/ho);//[Btu/ft^2�h�F]75disp('Theoverallcoefficientis');76disp('Btu/ft^2�h�F',Uo);
Example12.3Example12.3.sce1clearall;2clc;34//Example12.35//Given6L=15;//[ft]7k=0.082;//[Btu/ft�h�F]8Cp=0.48;//[Btu/lb�F]9T1=150;//[F]10T2=250;//[F]11Tw=350;//[F]12//FromTable12.313mu1=6;//[cP]14mu2=3.3;//[cP]15mu_w=1.37;//[cP]16mu=(mu1+mu2)/2;//[cP]17//FromAppendix518D=0.364/12;//[ft]19//viscosity�correctionfactorphiis20phi=(mu/mu_w)^0.14;21//AssumingLaminarflowandGraetznumberlargeenoughtoapplyEq.(12.25)22//UsingEq.(12.25)23//h=k/D2phi(Cpmdot/(kL))^(1/3);24//TouseEq.(12.18)53
Chapter13HeatTransfertoFluidswithPhaseChange13.1ScilabCodeExample13.1Example13.1.sce1clearall;2clc;34//Example13.15//Given6Pa=1;//[atm]7lambda=139.7;//[Btu/lb]8L=5;//[ft]9Tw=175;//[F]10hi=400;//[Btu/ft^2�h�F]11g=4.17*10^8;//[ft/h^2]12Th=270;//[F]13rho_f=65.4;//[lb/ft^3]14kf=0.083;//[Btu/ft�h�F],fromAppendix1315muf=0.726;//[lb/ft�h],fromAppendix916Do=0.75/12;//[ft]17Di=Do-(2*0.065)/12;//[f]18//(a)56
19Twall=205;//[F]20err=50;21h=1.13;22while(err�10)23delta_To=Th-Twall;24//fromEq.(13.11)25Tf=Th-3*(Th-Twall)/4;//[F]26h=h*(kf^3*rho_f^2*g*lambda/(delta_To*L*muf))^(1/4);//[Btu/ft^2�h�F]27//UsingEq.(12.29)28delta_Ti=1/hi/(1/hi+Di/(Do*h))*(Th-Tw);//[F]29Twall_new=Tw+delta_Ti;//[F]30err=Twall_new-Twall;//[F]31Twall=Twall_new;//[F]32end33//Tockeckwhethertheflowisactuallylaminar34Ao=0.1963*L;//[ft^2],fromAppendix635//therateofheattransfer36q=h*Ao*(Th-Twall);//[Btu/h]37mdot=q/lambda;//[lb/ft�h]38disp('[Btu/ft^2�h�F]',h,'coefficientofchlorobenzeneis')394041//(b)42//Forahorizontalcondenser,UsingEq.(13.16)43N=6;44Twall=215;//[F]45err=50;46h=0.725;47muf=0.68;//[lb/ft�h],fromAppendix648while(err�10)49delta_To=Th-Twall;50//fromEq.(13.11)51Tf=Th-3*(Th-Twall)/4;//[F]52h=h*(kf^3*rho_f^2*g*lambda/(6*delta_To*Do*muf))^(1/4);//[Btu/ft^2�h�F]53//UsingEq.(12.29)57
26PbyPc=P/Pc;27//UsingEq.(13.20)28//notingthatlambda,sigmaandrho
Larenearlyconstantandrho
L�rho
V29//qbyA
max~rho
V^(1/2)~P^(1/2)30qbyA_max=qbyA_max*(0.2/2)^(1/2);//[Btu/h�ft^2]31disp('Btu/h�ft^2',qbyA_max,'Themaximumheatfluxis')32//Thecriticaltemperaturedifferencewouldbegreaterthan100[F]and33//thefilmcoefficientwouldbelessthan410[Btu/h�ft^2�F]
59
Chapter14RadiationHeatTransfer14.1ScilabCodeExample14.1Example14.1.sce1clearall;2clc;34//Example14.15//Given6d=150;//[mm]7T1=300+272;//[K]8T3=25+273;//[K]9eps1=0.56;10eps2=1.0;11eps3=eps1;12sigma=5.6721314//(a)15//UsingEq.(14.38)16//q12=sigmaA1F12(T1^4�T2^4)17//q23=sigmaA2F23(T2^4�T3^4)18//Atequilibrium,q12=q2319//FromEq.(14.39)20F12=1/(1/eps1+1/eps2-1)60
21F23=F12;22//A1=A223T2=(100*((T1/100)^4+(T3/100)^4)^(1/4))/2^(1/4);//[K]24disp('F',T2,'thetemperatureoflacqueredsheetis')2526//(b)27//FromEq.(14.38),heatflux28q12byA=sigma*F12*((T1/100)^4-(T2/100)^4);//[W/m^2]29disp('W/m^2',q12byA,'theheatfluxis')
61
approximatelyequaltothefractional20//areaofthewindowftimesthetotalnmberoftubes.Fora25percentbaffle21f=0.195522Nb=f*828;23//Nb~16124Nb=161;25//UsingEq.(15.1),areaofthebafflewindow26Sb=(f*%pi*Ds^2/4)-(Nb*%pi*Do^2/4);//[ft^2]27//UsingEq.(15.3),themassvelocitiesare28Gc=mdot/Sc;//[lb/ft^2�h]29Gb=mdot/Sb;//[lb/ft^2�h]30Ge=sqrt(Gc*Gb);//[lb/ft^2�h]31//UsingEq.(15.4)32ho=k/Do*(0.2*(Do*Ge/(mu_60*2.42))^0.6*(Cp*mu_60*2.42/k)^0.33*(mu_60/mu_140)^0.14);//[Btu/ft^2�h�F]33disp('Btu/ft^2�h�F',ho,'Theindividualheattransfercoefficentofbenzeneis')
Example15.2Example15.2.sce1clearall;2clc;34//Example15.25//Given6Tca=70;//[C]7Tcb=130;//[C]8Tha=240;//[C]9Thb=120;//[C]10//Solution11//UsingEq.(15.7)and(15.8)12neta_h=(Tcb-Tca)/(Tha-Tca);13Z=(Tha-Thb)/(Tcb-Tca);14//FromFig15.7a,thecorrectionfactorisfound15Fg=0.735;16//thetemperaturedropsare63
17//Atshellinlet:18deltaT_i=Tha-Tcb;//[C]19//Atshelloutlet:20deltaT_o=Thb-Tca;//[C]21Log_T=(deltaT_i-deltaT_o)/log(deltaT_i/deltaT_o);22//thecorrectvalueofLog
Tis23Log_T=Fg*Log_T;//[C]24disp('C',Log_T,'Thecorrectmeanemperaturedropis')25//BecauseoflowvalueofFg,a1�2heatexchangerisnotsuitableforthisduty
Example15.3Example15.3.sce1clearall;2clc;34//Exapmle15.35//Given6Tca=70;//[C]7Tcb=130;//[C]8Tha=240;//[C]9Thb=120;//[C]10//Solution11//UsingEq.(15.7)and(15.8)12neta_h=(Tcb-Tca)/(Tha-Tca);13Z=(Tha-Thb)/(Tcb-Tca);14//UsingFig15.7b,thecorrectionfactoris15Fg=0.945;16//thetemperaturedropsare17//Atshellinlet:18deltaT_i=Tha-Tcb;//[C]19//Atshelloutlet:20deltaT_o=Thb-Tca;//[C]21Log_T=(deltaT_i-deltaT_o)/log(deltaT_i/deltaT_o);22//thecorrectvalueofLog
Tis23Log_T=Fg*Log_T;//[C]64
24disp('C',Log_T,'Thecorrectmeanemperaturedropis')
Example15.4Example15.4.sce1clearall;2clc;34//Example15.45//Given6N=28;7xF=0.5/12;//[ft]8yF=0.035/12;//[ft]9km=26;//[Btu/ft�h�F]10AT=2.830;//[ft^2/ft]11Ab=0.416;//[ft^2/ft]12hi=1500;//[Btu/ft^2�h�F]13G=5000;//[lb/h�ft^2]14Tavg=130;//[F]15Tw=250;//[F]16mu=0.046;//[lb/ft�h],fromAppendix817Cp=0.25;//[Btu/lb�F],fromAppendix1518k=0.0162;//[Btu/ft�h�F],fromAppendix1219ID_shell=3.068/12;//[ft],fromAppendix520OD_pipe=1.9/12;//[ft],fromAppendix521//crosssectionalareaofshellspace22Ac=%pi/4*(ID_shell^2-OD_pipe^2)-N*xF*yF//[ft^2]23//Theperimeterofairspace24Ap=%pi*ID_shell+AT;//[ft]25//hydraulicradius26rh=Ac/Ap;//[ft]27//equivalentdiameter28De=4*rh;//[ft]29//ReynoldsNumber30Nre=De*h/mu31//Incomputingmu
wtheresistanceofthewallandthesteamfilm32//areconsiderednegligible,so65
Chapter16Evaporation16.1ScilabCodeExample16.1Example16.1.sce1clearall;2clc;34//Example16.15//Given6mdot=20000;//[lb/h]7xin=0.20;8xout=0.50;9Pg=20;//[lbf/in.^2]10Pabs=1.93;//[lbf/in.^2]11U=250;//[Btu/ft^2�h�F]12Tf=100;//[F]1314//Solution15//theamountofwaterinfeedandthickliquor,frommaterialbalance16w_feed=80/20;//[lb/perpoundofsolid]17w_liquor=50/50;//[lb/perpoundofsolid]18//waterevaporated19w_eva=w_feed-w_liquor;//[lb/perpoundofsolid]67
4950A=q/(U*(259-197))//[ft^2]51disp('ft^2',A,'heatingarearequiredis')
Example16.2Example16.2.sce1clearall;2clc;34//Example16.25//Given6Ti=108;//[C]7Tl=52;//[C]8U1=2500;//[W/m^2]9U2=2000;//[W/m^2]10U3=1000;//[W/m^2]1112//Solution13//Totaltemperaturedrop14delta_T=Ti-Tl;//[C]15//FromEq.(16.13),thetemperaturedropsinseveraleffectswillbe16//approximaelyinverselyproportionaltothecoeficients.Thus17delta_T1=1/U1/(1/U1+1/U2+1/U3)*delta_T;//[C]18delta_T2=1/U2/(1/U1+1/U2+1/U3)*delta_T;//[C]19delta_T3=1/U3/(1/U1+1/U2+1/U3)*delta_T;//[C]20//Consequentlytheboilingpointswillbe21Tb1=Ti-delta_T1;//[C]22Tb2=Tb1-delta_T2;//[C]23disp('C',Tb1,'Theboilingpointinthefirsteffectis')24disp('C',Tb2,'Theboilingpointinthesecondeffectis')
Example16.3Example16.3.sce1clearall;69
2clc;34//Example16.35//Given6mdot_ft=60000;//[lb/h]7xin=0.10;8Tin=180;//[F]9xout=0.5010Ps=50;//[lbf/in.^2]11Tc=100;//[F]1213//Solution14//FromTable16.215U1=700;//[Btu/ft^2�h�F]16U2=1000;//[Btu/ft^2�h�F]17U3=800;//[Btu/ft^2�h�F]18//Thetotalrateofevaporationiscalculatedfromanoverallmaterialbalance19//assumingthesoldsgothroughtheevaporatorwithoutloss20//Table16.321mdot_fs=6000;//[lb/h]22mdot_fw=54000;//[lb/h]23mdot_lt=12000;//[lb/h]24mdot_ls=6000;//[lb/h]25mdot_lw=6000;//[lb/h]26w_evap=mdot_ft-mdot_fs;//[lb/h]
70
20//Tofindoutasintermediatepointontheoperatingline,makinganacetonebalance21//aroundthetoppartofthetower,assumingaparticularvalueofyVthemolesof22//acetoneleftinthegas.23fori=1:3024y(i)=i/(i+Air_in);25//Themolesofacetonelostbythegasinthesecion,mustequaltothemolesgainedby//theliquid26Ace_lost=i-Ace_out;//[mol]27//Hence28x(i)=Ace_lost/(La+Ace_lost);29end30xe=linspace(0.001,0.15,100);31ye=1.9*xe;3233plot(x,y)34plot(xe,ye,'r')35xlabel('x')36ylabel('y')37legend('Operatingline','Equilibriumline')38title('DiagramExample17.1')39//ThenumberofidealstagesdeterminedfromFigis472
Figure17.1:DiagramforExample17.1
Example17.2Example17.2.sce1clearall;2clc;34//Example17.25//Given6Nreal=7;7VbyL=1.5;8m=0.8;9yb=0;73
10xb_star=0;11//xb=0.1xa;1213//(a)14//StrippingFactor15S=m*VbyL;16//Fromanammoniabalance,17//ya=0.9xa/VbyL;18//Also19//xa
star=ya/m20//UsingEq.(17.28)21//N=ln((xa�0.75xa)/(0.1xa�0))/ln(S)22N=log(0.25/0.1)/log(S);23disp(N,'Numberofidealtraysrequiredare')24stage_eff=N/Nreal*100;25disp('%',stage_eff,'StageEfficiencyis')2627//(b)28VbyL=2;29S=m*VbyL;30//Then,31//LetA=(xa�xa
star)/xb32A=exp(5.02);33//Let'f'bethefractionofNH3removed.Thenxb=(1�f)xa.34//Byamaterialbalance35//y=L/V(xa�xb)=1/2(xa�(1�f)xa)=1/2fxa36//xa
star=ya/m=0.5fxa/0.8=0.625fxa37//Thus,38//xa�xa
star=(1�0.625f)xa39//Also,40//xa�xa
star=10.59xb=10.59(1�f)xa41//fromthese42f=0.96243disp('%',f,'percentageremovalobtainedinthiscaseis')
74
Chapter18Distillation18.1ScilabCodeExample18.1Example18.1.sce1clearall;2clc;34//Example18.15//Given6xF=0.50;7P=1;//[atm]8f=0.0001:0.2:1.2;9A=-(1./f-1);10x=[0.01:0.01:1];11fori=1:length(f)12y(i,:)=-A(i)*x+xF/f(i)13end14//FromFig.18.215xB=[0.50,0.455,0.41,0.365,0.325,0.29];16yD=[0.71,0.67,0.63,0.585,0.54,0.5];17//FromFig18.318T=[92.2,93.7,95.0,96.5,97.7,99];19plot(f,T./100,f,xB,f,yD)20xlabel('f�molesvaporizedpermoleoffeed')75
21ylabel('Concentration,molefractionBenzene')22legend('Temperature(C)100','Con.ofBnzeneinliquid','Con.ofBnzeneinvapor')
Figure18.1:ResultsofExample18.1
Example18.2Example18.2.sce1clearall;2clc;34//Example18.276
14Tnb=65;//[C]15rho_v=M*273/(22.4*338);//[kg/^3]16rho_l_0=810;//[kg/m^3],At0C,fromPerry,ChemicalEngineers'Handbook17rho_l_20=792;//[kg/m^3],At20C,fromPerry,ChemicalEngineers'Handbook18rho_l=750;//[kg/m^3],At65C19sigma=19;//[dyn/cm],fromLange'sHandbookofChemistry20//(a)21//Vaporvelocityandcolumndiameter22//UsingFig.18.28,theabscissais23abscissa=LbyV*(rho_v/rho_l)^(1/2);24//for18�in.platespacing25Kv=0.29;26//Allowablevaporvelocity27uc=Kv*((rho_l-rho_v)/rho_v)^(1/2)*(sigma/20)^(0.2);//[ft/s]28//Vaporflowrate29V=D*(R+1)/(3600*rho_v);//[m^3/s]30//Crosssetionalareaofthecolumn31Bubbling_area=V/2.23;//[m^2]32//Ifthebubbleareais0.7ofthetotalcolumnarea33Column_area=Bubbling_area/0.7;//[m^2]34//Columndiameter35Dc=sqrt(4*Column_area/%pi);//[m]36disp('respectively','m',Dc,'and','ft/s',uc,'theallowablevelocityandcolmndiameterare')3738//(b)39//Pressuredrop:40//Areaofoneunitofthreeholesonatrangular3/4�in.pitchis41//1/23/4(3/4sqrt(3/2))in.^2.Theholeareainthissection(halfahole)is42//1/2%pi/4(1/4)^2in.^2.Thustheholeareais%pi/12864/9sqrt(3),or10.08percent43//ofthebubblingarea.82
44//Vaporvelocitythroughholes:45uo=2.23/0.1008;//[m/s]46//UsingEq.(18.58),47//FromFig.18.2748Co=0.73;49hd=51.0*uo^2*rho_v/(Co^2*rho_l);//[mmmethanol]50//Headofliquidonplate:51//Weirheight52hw=2*25.4;//[mm]53//Heightoftheliquidaboveweir:54//Assumingthedowncomerareais15percentofthecolumn55//areaoneachsideofthcolumn.FromPerry,thechord56//lengthforsuchasegmentaldowncomeris1.62timestheradius57//ofthecolmn,so58Lw=1.62*2.23/2;//[m]59//LiqiudFlowrate:60qL=D*(R+1)/(rho_l*60);//[m^3/min]61//FromEq.(18.60)62how=43.4*(qL/Lw)^(2/3)//[mm]63//FromEq.(18.59),with64beeta=0.6;65hI=beeta*(hw+how);//[mm]66//Totalheightofliquid,fromEq.(18.62)67hT=hd+hI;//[mm]68disp('mmmethanol',hT,'pressuredropperplateis')6970//(c)71//Frothheightinthdowncomer:72//UsingEq.(18.62).,Estimating73hf_L=10;//[mmmethanol]74//Then,75Zc=(2*hI)+hd+hf_L;//[mm]76//fromEq.(18.63)77Z=Zc/0.5;//[mm]78disp('mmmethanol',Z,'Frothheightinthedowncomer83
Chapter19IntroductiontoMulticomponentDistillation19.1ScilabCodeExample19.2Example19.2.sce1clearall;2clc;34//Example19.25//Given6P=1.2;//[atm]7Tb=97;//[C]8Td=105;//[C]9f=0.6;1011xF(1)=0.33;12xF(2)=0.37;13xF(3)=0.30;1415//Solution16//(a)1718//FromFig.19.186
19K(1)=2.68/P;20K(2)=1.21/P;21K(3)=0.554/P;22//InEq.(19.12),therighthandsideoftheequationbecomes23RHS=(xF./(f*(K-1)+1));24RHS2=sum(RHS)25disp('C',Td,'flashtemperatureis');26disp('percent',RHS(3),'n�octaneexane','percent',RHS(2),'n�heptane','percent',RHS(1),'n�hexane','Compositionoftheliquidproductis');27y=RHS.*K;28disp('percent',y(3),'n�octane','percent',y(2),'n�heptane','percent',y(1),'n�hexane','Compositionofthevaporproductis');2930//(b)31//Todeterminethetemperatureofthefeedbeforeflashing,32//anenthalpybalanceismadeusing105Casthereferencetemperature.33//Theheatsofvaporizationat105Candtheaverageheatcapacitiesofthe34//liquidfrom105to200Careobtainedfromtheliterature.35Cp=[62,70,78]';//[cal/mol�C],Cp(1)=n�hexane,Cp(2)=n�heptane,andCp(3)=n�octane36delta_Hv=[6370,7510,8560]';//[cal/mol],delta
hv(1)=n�hexane,delta
hv(2)=n�heptane,anddelta
hv(3)=n�octane37//Basedonliquidat105C,theenthalpiesoftheproductare38H_vapor=f*sum((y.*delta_Hv))//[cal]39H_liquid=0;40//Forthefeed41Cp_bar=sum(xF.*Cp)//[cal/mol�C]42T0=H_vapor/Cp_bar+Td;43disp('C',T0,'preheattemperatureis')87
32xB=[0.01,0.544,0.446]';33comp_D=xD.*D;34comp_B=xB.*B;3536disp('mol/h',comp_D(3),'n�octane','mol/h',comp_D(2),'n�heptane','mol/h',comp_D(1),'n�hexane','Thecompositionoftheoverheadproductis');37disp('mol/h',comp_B(3),'n�octane','mol/h',comp_B(2),'n�heptane','mol/h',comp_B(1),'n�hexane','Thecompositionofthebottomproductis');3839//Tofindoutminimumnumberofplates,usingEq.(19.13)[FenskeEquation]40//usingrelativevolativityofthelightkeytotheheavykey,whichisthe41//ratiooftheKfactors.TheKvaluesattheflashtemperatuearetakenfromExample19.242alpha_LK_HK=K(1)/K(2);43Nmin=log((xD(1)/xD(2))/(xB(1)/xB(2)))/log(alpha_LK_HK)-1;44disp('plusareboiler',Nmin,'Theminimumnumberofidealstagesis');
Example19.4Example19.4.sce1clearall;2clc;34//Example19.45//Given6//x(1)=n�pentane,x(2)=n�hexane,x(3)=n�heptaneandx(4)=n�octane7//xF=feed,xD=distillateandxB=bottom8xF=[440506]'./100//[molefraction]9P=1;//[atm]10xD1(2)=0.98;11xD1(3)=0.01;1289
46else47phi=phi-0.01;48end49f=fnew;50end51RDm=f-1;5253//(b)54//Togettheconditionsintheupperinvariantzone,usingEq.(19.24)with55VbyD=RDm+1;56DbyV=inv(VbyD);57VbyF=VbyD*D/F;58LbyV=RDm/(RDm+1);59y_80=DbyV*xD(1:3)./(1-LbyV./K_80(1:3))60y_81_1=[0.046,0.637,0.317]';61x_81_1=y_81_1./K_81;62//Thevaporcompositionforlowerinavariantzoneis63//usingEq.(19.28),forq=1.064BbyVb=0.552;65LbbyVb=1.55;66K_83=[1.52,0.618,0.258]';67y_83=BbyVb*xB(2:4)./(LbbyVb./K_83-1);68y_83_3=[0.662,0.326,0.012]';69x_83_3=y_83_3./K_83;7071disp('respectively','C',81.1,'C',83.3,'ThetempeatureinLowerzoneandUpperzoneis')72disp('respectively',y_83_3(1),'y=',x_83_3(1),'x=','TheLKcompositioninLowerzoneis')73disp('respectively',y_83_3(2),'y=',x_83_3(2),'x=','TheHKcompositioninLowerzoneis')74disp('respectively',y_81_1(2),'y=',x_81_1(2),'x=','TheLKcompositioninUpperzoneis')75disp('respectively',y_81_1(3),'y=',x_81_1(3),'x=','TheHKcompositioninUpperzoneis')
Example19.5Example19.5.sce91
18F=100;//[lbwax+kerosene�freepulp]19//Bymakingamassbalanceoverwax20//wax
in=F(wi(1)/wi(2))+0.0005s(sisthewaxinputwithsolvent)21//wax
out=F(0.002)+(s�200)0.0522//bywax
in=wax
out23s_in=(33.33+9.8)/(0.05-0.0005);//[lb]24//Theconcentrationofthisstreamis,therefore25s_out=200;//[lb]26s_stsol=s_in-s_out;//[lb]27wax_sol=s_stsol*0.05;//[lb]28//Theconcentrationintheunderflowtothesecondunitequalsthat29//oftheoverflowfromthefirststage,or0.05lbofwaxperpound30//ofkerosene.Thewaxintheunderflowtounit2is31wax_uflow_2=s_out*0.05;//[lb]32wax_oflow_21=wax_uflow_2+wax_sol-F*(wi(1)/wi(2))//[lb]3334//Theconcentrationsofthisstreamis,therefore,35ya=wax_oflow_21/871;36yastar=0.05;37xa=yastar;38ybstar=0.2/s_out;39xb=ybstar;40yb=0.0005;4142//Since1stagehasalreadybentakenintoaccount,43//Eq.(17.24),willgiveN�1stages,Hence44N=log((yb-ybstar)/(ya-yastar))/log((yb-ya)/(ybstar-yastar));45disp(N+1,'Thetotalnumberofidealstagesis');
Example20.2Example20.2.sce1clearall;2clc;94
34//Example20.25//Given6F=1000;//[kg]7solv_O=10;//[kg]8solv_B=655;//[kg]9w_out=60;//[kg]10//Solution11//LetsolutionretainedisSR,fromTable20.112SR=[0.5,0.505,0.515,0.530,0.550,0.571,0.595,0.620]';13xb=0:0.1:0.7;14//Letxandybethemassfractionofoilintheunderflowand15//overflowsolutions.1617//Atthesolventinlet,18Vb=solv_O+solv_B;//[kgsolution/h]19yb=solv_O/Vb;20err=1;21i=1;22sr=SR(2);23xb1=0.0;24while(err�0.001)25Lb=sr*F;26xbnew=w_out/Lb;27err=abs(xb1-xbnew);28xb1=xbnew;29sr=SR(i)+(xb1-xb(i))/(xb(i+1)-xb(i))*(SR(i+1)-SR(i));30i=i+1;31end32Lb=sr*F;33//BenzeneintheunderflowatLbis34Underlow_B=Lb-w_out;//[kgsolutions/h]3536//Atthesolidinle37La=400+25;//[kgsolutions/h]95
are73N=4;74disp(N,'Numberofstagesrequiredare')
Figure20.1:DiagramforExample20.2
Example20.3Example20.3.sce1clearall;2clc;34//Example20.397
40nmold=nm;41nm(1)=yH2O/(1-yH2O)*(39.6+100-nm(2));42nm(2)=xMIK/(1-xMIK)*(0.4+60-nm(1));43err=norm(nm-nmold);44end45n=nm(1);46m=nm(2);47Va=139.6+n-m;48yA_a=39.6/Va;49Lb=60.4+m-n;50xA_b=0.4/Lb;5152//Foranintermediatepointontheoperatingline,picking53yA=0.12;54//FromFig.20.10,55yH2O=0.03;56yMIK=0.85;57//Sincetheraffinatephasehasonly2to3pecentMIK,assuming58//thattheamountofMIKintheextractis100,thesameasthesolvent59//fed:60V=100/yMIK;61//Byanoverallbalancefromthesolventinlet(bottom)totheintermediate62//point,63xb=xA_b;64L=Lb+V-Vb;65yb=0;66//AbalanceonAoverthesamesectiongivesxA;67xA=(0.4+117.6*0.12-0)/L;68//ForxAandxMIK=0.03,AbalanceonMIKfromthesolvent69//inlettotheintermediatepointgives70V_revised=101.1/0.85;71L_revised=54.4+118.9-100;72xA_revised=(0.4+118.9*0.12)/73.3;99
18//(a)19//UsingFig.(22.8),fromExample22.1A=Gx/Gy=1and20//Let21A=1;22B=A*sqrt(rho_y/rho_x);23//FormFig22.8,thesuperficialvaporvelocityatflooding24//isuofsqrt(rho
y/(rho
x�rho
y))=0.11,therefore25uof=0.11/sqrt(rho_y/(rho_x-rho_y));//[m/s]26//Theallowablevaporvelocity27uo=uof*0.5;//[m/s]28uo=uo*3.28;//[ft/s]29//thecorrespondingmassvelocity30Gy=uo*rho_y;//[lb/ft^2�s]31//Theallowablemassvelocityintheexamplewas0.236lb/ft^2�s.32//Theincreasebyusingstructuredpackingis33increase=(Gy/0.236)-1;34disp(increase*100,'Thepercentincreaseinmassvelocityis');3536//(b)37//Thepressuredrop38delta_P=20*1.22*(0.5/0.9)^1.8;//[in.H2O]39//Thisis1.2timesthepressuredropof7in.H2OintheIntolaxsaddles.40disp('ThepressuredropwillbegreaterthanIntolaxSaddles')
Example22.3Example22.3.sce1clearall;2clc;34//Example22.35//Given6vdot=4500;//[SCFM]110
44deltaHv=583;//[cal/g]45Qv=deltaHv*H2O_vaporized*18.02;//[cal]46//FromEq.(22.31)47Qsx=Qa-(Qv+Qsy);//[cal]4849Cp=18;//[cal/g�mol�C]50xmax=0.031;51Tb=40;//[C]52Ta=25;//[C]53err=1;54while(err�0.01)55Lb=NH3_abs/xmax;56Tbnew=Qsx/(Lb*Cp)+Ta;57err=Tb-Tbnew;58Tb=Tbnew;59xmax=xmax+0.002;60end61Lmin=Lb-NH3_in;//[molH2O]62La=1.25*Lmin;//[mol]63Lb=La+NH3_in;//[mol]64//Thetemperatureriseoftheliquuidis65Tb=Qsx/(Lb*Cp)+Ta;//[C]66xb=NH3_in/La;//[C]67ystar=0.044;68//Assumingtemperaturetobelinearfunctionofx,so69T=30;70//x=0.0137;71//Usingthedatagivenfor30Candinterpolatingtogetthe72//initialslopefor25andthefinalvalueystarfor35,the73//euilibriumlineisdrawn74y=[0.06,0.03,0.01,0.0002]';75ystar=[0.048,0.017,0.0055,0]';76delta_y=y-ystar;77delta_yL=[0.0125,0.0080,0.00138]';78delta_NOy=[2.4,2.5,7.1]';112
73mu_40=0.0181*10^-2;//[P],Appendix874Dv=7.01*10^-3;//[cm^2/s],fromEq.(21.25)75rho=2.34*10^-2;//[lb/ft^3]76Nsc=mu_40/(rho*Dv);77//FormTable22.1,78fp=1.36;79Hy_EO=1.4*(1.1/0.66)^0.5*1/1.36*(Gy/500)^0.3*(1500/Gx)^0.4;//[ft]80//FormFig.22.19,81Hx_O2=0.9;//[ft]82Gx1=1500;83mu1=0.00656;//[P]84rho1=1;//[lb/ft^3]85//UsingEq.(21.28)86Dv1=2.15*10^-5;//[cm^2/s]87Nsc1=mu1/(rho1*Dv1);88//UsingEq.(22.35),withthecorrectionfactorfpandNsc=381,89//forO2inwaterat25C90Hx_EO=Hx_O2*(Gx/(mu1*100)/(Gx1/0.894))^0.3*(Nsc1/381)^0.5/1.36;//[ft]91//FromFig22.22,theaveragevalueofm92m=1.0;93//FromEq.(22.30)94HOy=1.71+(1*0.96)/1.4;//[ft]9596disp(NOy,'numberoftransferunitsrequired')97disp('ft',D,'diameterofthecolumn')98disp('ft',HOy,'packingheight')
Example22.6Example22.6.sce1clearall;2clc;34//Example22.65//Solution6rho_m=62.2/18;//[mol/ft^3]118
7//kya=0.025Gy^0.7Gx^0.258H2ObySO2=2*0.98964/0.01036;9//and10xb=1/(H2ObySO2+1);11//ThemolalmassvelocityofthefeedgasGmis12Gm_in=200/29*(1/0.8);//[mol/ft^2�h]13SO2_in=Gm_in*0.2;//[mol/ft^2�h]14Air_in=Gm_in*0.8;//[mol/ft^2�h]15Air_out=Air_in;//[mol/ft^2�h]16SO2_out=Air_out*(0.005/(1-0.005));//[mol/ft^2�h]17SO2_abs=SO2_in-SO2_out;//[mol/ft^2�h]18H2O_in=H2ObySO2*SO2_abs;//[mol/ft^2�h]19//Operatingline20x=0:6;21x=x/10^3;22A=x./(1-x);23B=H2O_in/Air_in*A+(0.005/0.995);24y=B./(B+1);25plot(x,y)26xgrid();27xlabel('x');28ylabel('y');29//legend('20C','30C','40C');30title('xvsy');31Gxbar=H2O_in*18.02+SO2_abs*64.1/2;//[lb/ft^2�h]32kxa=0.131*Gxbar^0.82;//[mol/ft^3�h]33//Thegasfilmcoefficientsarecalculatedforthebottom34//andthetopofthetower:35//Atbottom:36Gy_B=(Air_in*29)+(SO2_in*64.1);//[lb/ft^2�h]37kya_B=0.025*Gy_B^0.7*Gx^0.25;//[mol/ft^3�h]38//Attop:39Gy_T=(Air_out*29)+(SO2_out*64.1);//[lb/ft^2�h]40kya_T=0.025*Gy_T^0.7*Gx^0.25;//[mol/ft^3�h]41//Assuming42yLbar=0.8243C=kxa*yLbar/kya_B;119
Chapter23Humidi cationOperations23.1ScilabCodeExample23.1Example23.1.sce1clearall;2clc;34//Example23.15//Given6T=320;//[F]7P=1;//[atm]8//(1)=CO2,(2)=H2O,(3)=O2,(4)=N29y_in=[0.14,0.07,0.03,0.76]';10Tw=80;//[F]11//Solution12//(a)13//Basis14F=100;//[mol],ofgas15Ts=120;//[F]16Cps=[9.72,8.11,7.14,6.98]';17n_in=F*y_in;//[mol]18nCp=n_in.*Cps;//19sum_nCp=sum(nCp);20sum_n_in=sum(n_in);//[mol]122
21Tavg=(Ts+T)/2;//[F]22lambda_s=1025.8*18;//[Btu/lbmol],atTs,fromAppendix723//Makingaheatbalanceforzmolesofwaterevaporated24z=sum_nCp*(T-Ts)/(lambda_s+18*(Ts-Tw));25//Totalmolesofwaterinexitgas26n_out(2)=z+n_in(2);//[mole]27//Partialpressureofthewaterintheexitgas28PH2O=n_out(2)/107.76*760;//[mmHg]29//Butat120F,PH2Oprime=87.5mmHg(Appendix7).Saturation30//temperatureTsmustbegreaterthan120F.Trying31Ts=126;//[F]32Tavg=(Ts+T)/2;//[F]33lambda_s=1022.3*18;//[Btu/lbmol],atTs,fromAppendix734//Makingaheatbalanceforzmolesofwaterevaporated35z=sum_nCp*(T-Ts)/(lambda_s+18*(Ts-Tw));36//Totalmolesofwaterinexitgas37n_out(2)=z+n_in(2);//[mole]38//Partialpressureofthewaterintheexitgas39PH2O=n_out(2)/107.76*760;//[mmHg]40//ThisiscloseenoughtothevalueofPH2Oprime41disp('F',Ts,'Adiabaticsaturationtemperature');4243//(b)44//forTin=Ts,byheatbalance45z=sum_nCp*(T-Ts)/(lambda_s);46n_out(2)=z+n_in(2);//[mole]47//Partialpressureofthewaterintheexitgas48PH2O=n_out(2)/107.85*760;//[mmHg]49//Thisishigherthanthevaporpressureofwaterat126F,50//103.2mmHg,andTs�126F.Trying51Ts=127;//[F]52Tavg=(Ts+T)/2;//[F]123
53lambda_s=1021.7*18;//[Btu/lbmol],atTs,fromAppendix754//Makingaheatbalanceforzmolesofwaterevaporated55z=sum_nCp*(T-Ts)/(lambda_s);56//Totalmolesofwaterinexitgas57n_out(2)=z+n_in(2);//[mole]58//Partialpressureofthewaterintheexitgas59PH2O=n_out(2)/107.76*760;//[mmHg]60//Thus127istoohighand126istoolow.Hence,61Ts=(126+127)/2;//[F]62disp('F',Ts,'Adiabaticsaturationtemperature');
Example23.3Example23.3.sce1clearall;2clc;34//Example23.35//Given6Hair_in=0.022;7Tair_inpre=70;//[F]8mdot=15000;//[lb/h]9//Solution10//UsingFig.23.1011Tair_inreh=85;//[F]12Tair_outreh=130;//[F]13Hin=0.0030;14hya=85;15Ts=81;//[F]16Tair_outpre=168;//[F]17humid_heat1=0.241;//[Btu/lb�F]18//Heatrequiredtopreheattheairis19Qpre=humid_heat1*mdot*(Tair_outpre-Tair_inpre);//[Btu/h]20humid_heat2=0.250;//[Btu/lb�F]21//Heatrequiredinthereheateris124
Chapter24DryingofSolids24.1ScilabCodeExample24.1Example24.1.sce1clearall;2clc;34//Example24.15//Given6Twb=80;//[F]7Tdb=120;//[F]8v=3.5;//[ft/s]9rho=120;//[lb/ft^3]10Xe=0;11Xc=0.09;12lambda=1049;//[Btu/lb]13M=29;14B=24;//[in.]15D=2;//[in.]16Dc=2;//[ft]17//Solution18//(a)19//massvelocity20G=v*M*492*3600/(359*(460+120));//[lb/ft^2�h]126
21//thecoefficent,byEq.(24.13),infpsunits,is22h=0.01*G^0.2/2^0.2;//[Btu/ft^2�h�F]23//SubstitutinginEq.(21.15)gives24Rc=1.94*(Tdb-Twb)/(lambda);//[lb/ft^2�h]25disp('lb/ft^2�h',Rc,'Dryingrateduringtheconstantperiodis')2627//(b)28//Sincedryingisfrombothfaces,area29A=Dc*(B/12)^2;//[ft^2]30//Therateofdrying31mvdot=Rc*A;//[lb/h]32//Volumeofthecake33Vc=(B/12)^2*D/12;//[ft^3]34//massofthebone�drysolidis35mdot_bd=rho*Vc;//[lb]36//Thequantityofmoisturetobevaporizedis37X2=0.20;38X1=0.10;39Q=mdot_bd*(X2-X1);//[lb]40//Dryingtime41tT=Q/mvdot;//[h]42disp('h',tT,'dryingtime')
Example24.2Example24.2.sce1clearall;2clc;34//Example24.25//Given6X1=0.25;7X=0.05;8Dvprime=8.3*10^-6;//[cm^2/s]9D=25.4;//[mm]1011//Solution12s=D/(2*10);//[cm]127
13tT=4*s^2/(%pi^2*Dvprime)*log(8*X1/(%pi^2*X))/3600;//[h]14disp('h',tT,'dryingtimeis')
Example24.3Example24.3.sce1clearall;2clc;34//Example24.35//Given6Tw=80;//[F]7Tdb=120;//[F]8v=3.5;//[ft/s]9rho=120;//[lb/ft^3]10Xe=0;11Xc=0.09;12lambda=1049;//[Btu/lb]13M=29;14B=24;//[in.]15D=2;//[in.]16Dc=2;//[ft]17X2=0.20;18X1=0.10;19Dcyl=1/4;//[in.]20L=4;//[in.]21Vbar=3.5;//[ft/s]22Thb=120;2324//Solution25//SincetheXcislessthan10percent,alldryingtakesplace26//intheconstant�rateperiodandthevaporrizationtemperature,27//asbefore,is80F.28//FromExapmle24.1,massofwatertobeevaporated29mdot=8*(X2-X1);//[lb]30//Thequantityofheattobetransferred128
31QT=mdot*lambda;//[Btu]32//massofthedrysoildinonecylinderis33mp=%pi/4*(Dcyl/12)^2*(L/12)*rho;//[lb]34//surfaceareaofonecylinderis35Ap=%pi*(Dcyl/12)*(L/12);//[ft^2]36//Totalareaexposedby8lbsolids37A=8/mp*Ap;//[ft^2]38//Theheattransfercoefficientisfoundfromthe39//equivalentformofEq.(21.62)40//hDbyk=1.17Nre^0.585Npr^(1/3)41//Forairat1atmand120F,thepropertiesare42rho_a=M/359*492/580;//[lb/ft^3]43mu_a=0.019;//[cP],fromAppendix844k_a=0.0162;//[Btu/ft�h�F],fromAppendix1245Cp_a=0.25;//[Btu/lb�F],fromAppendix1546Nre=1/48*Vbar*rho_a/(mu_a*6.72*10^-4);47Npr=mu_a*2.42*Cp_a/k_a;48//FormEq.(21.62)49h=(k_a*1.17*Nre^0.585*Npr^(1/3))/(1/48);//[Btu/ft^2�h�F]50mdot_g=v*3600*rho_a;//[lb]51//FromFig.23.252cs=0.25;53delta_Thb=Thb-Tw;//[F]54delta_Tha=8.24;//[F]55//Theheattransferredformthegastoathinsectionofthebed56delta_TL=(delta_Thb-delta_Tha)/log(delta_Thb/delta_Tha);//[F]57//rateofheattransfer58qT=h*A*delta_TL;//[Btu/h]59//dryingtime60tT=QT/qT;//[h]61disp('h',tT,'Requireddryingtimeis')
Example24.4Example24.4.sce1clearall;129
2clc;34//Example24.45//Given6msdot=2800;//[lb/h]7Xa=0.15;8Xb=0.005;9Ti=80;//[F]10To=125;//[F]11Thb=260;//[F]12Hb=0.01;//[lbwater/lbdryair]13G=700;//[lb/ft^2�h]14Cps=0.52;//[Btu/lb�F]1516//Solution17//Countercurrentoperationwillbeused.18//Assuming19Nt=1.5;//NTU20//FromFig.23.221Twb=102;//[F]22//FromEq.(2.48)23Tha=(Thb-Twb)/exp(Nt)+Twb;//[F]24Tsb=To;//[F]25lambda=1036;//[Btu/lb],at102F,fromAppendix726Cpv=0.45;//[Btu/lb�F],fromAppendix1527Cpl=1.0;//[Btu/lb�F]28//FromEq.(24.9)29mvdot=msdot*(Xa-Xb);//[lb/h]30//TheheatdutyisfoundformsubstitutioninEq.(24.1)31qTdot=Cps*(To-Ti)+Xa*Cpl*(Twb-Ti)+(Xa-Xb)*lambda+Xb*Cpl*(To-Twb)+(Xa-Xb)*Cpv*(Tha-Twb);//[Btu/lb]32qT=qTdot*msdot;//[Btu/h]33//Theflowrateoftheenteringairisfoundfromaheatbalanceandthehumidheatcsb.34//FromFig.23.235csb=0.245;//[Btu/lb�F],36mgdot=qT/(csb*(Thb-Tha)*(1+Hb));//[lb/hofdry130
Chapter25Adsorption25.1ScilabCodeExample25.1Example25.1.sce1clearall;2clc;34//Example25.15//Given6ya=0.002;7T=20+273;//[K]89//Solution10//(a)11M=86.17;12//fromPerry'sChemicalEngineers'Handbook,6thed.13Pprime=120;//[mmHg]14fs=Pprime;//[mmHg]15rho_L=0.615;//[g/cm^3],atnormalboilingpoint(68.7C)16P=760;//[mmHg]17p=ya*P;//[mmHg]18f=p;//[mmHg]19V=M/rho_L;//[cm^3/gmol]132
18cbyc0=[0.005,0.01,0.027,0.05,0.1,0.2,0.29,0.56,0.0019,0.003,0.0079,0.018,0.039,0.077,0.15,0.24];19t1=t(1:8);20t2=t(9:16);21cbyc01=cbyc0(1:8);22cbyc02=cbyc0(9:16);23plot(t1,cbyc01,t2,cbyc02);24xgrid();25xlabel('t,Hours');26ylabel('c/c0');27title('BrakthroughcurvesforExample25.2');28legend('L=8cm','L=16cm');2930//(a)31FA=u0*c0*10^-6/22400*273/298*737/760*M*3600;//[g/cm^2�h]32//Thetotalsoluteadsorbedistheareaabovethegraphmultiplied33//byFA.Forthe8�cmbed,theareais34Area_bed=4.79;//[h]35//Thisareacorrespondstotheidealtimethatwouldberequiredtoadsorb36//thesameamountifthebreakthroughcurvewereaverticalline.Themass37//ofcarbonperunitcross�sectionalareaofthebedis38Ac=8*rho_b;//[g/cm^2]39//Thus,40Wsol=FA*Area_bed/Ac;//[gsolute/gcarbon]41//Atthebreakpoint,where42cbyc0_break=0.05;43//and44t_break=2.4;//[h]45Area_bed_break=2.37;//[h]46//Theamountadsorbeduptothebreakpointisthen47Wb=FA*t_break/Ac;//[gsolute/gcarbon]48ratio_W=Wb/Wsol;134
45//Ifthediffusionintotheparticleoccuredonlyinthegasphase,the46//maximumpossiblevalueofDewouldbeaboutDv/4,whichleadsto47kc_int2=10*Dv/(4*Dp);//[cm/s]48disp('Kcaisslightlylessthanhalfthepredictedvalueofkca');
Example25.4Example25.4.sce1clearall;2clc;34//Example25.45y=0.0012;6vdot=16000;//[ft^3/min]7P=760;//[mmHg]8rho_b=30;//[lb/ft^3]9Lun=0.5;//[ft]1011//Solution12//(a)13//Formthehandbook14Pprime=151;//[mmHg]15fs=Pprime;//[mmHg]16rho_L=0.805;//[g/cm^3],at20C17Tnb=79.6;//[C]18rho_e=0.75;//[g/cm^3]19M=72.1;20V=M/rho_e;21p=y*P;//[mmHg]22f=p;//[mmHg]23//At35C24T=35+273;//[K]25A=T/V*log10(fs/f);26//FormFig.25.4,27//thevolumeadsorbed28V_ads=24;//[cm^3/100gcarbon]138
29Wsat=V_ads*rho_e;//[g/100gcarbon]30W0=1/3*Wsat;//[g/100gcarbon]31Working_capacity=Wsat-W0;//[g/100gcarbon]32//or33Working_capacity=Working_capacity/100;//[lb/lbcarbon]34disp(Working_capacity,'Workingcapacityofthebedis')3536//(b)37u0=1;//[ft/s]38A=vdot/u0;//[ft^2]39D=sqrt(4*A/%pi);//[ft]40Abed=10*27;//[ft^2]41L1=4;//[ft]42c0=y/359*273/298*72.1;//[lb/ft^3]43//FormEq.(25.3)44tstar=L1*rho_b*(Working_capacity)/(u0*c0*3600);//[h]45Lu1=L-Lun;//[ft]46tb1=Lu1/L*tstar;//[h]4748//if49L2=3;//[ft]50Lu2=L2-Lun;51tb2=Lu2/L*tstar;//[h]52//checkingfordelta
P53//UsingEq.(7.22)54phi_s=0.7;//fromTable28.155eps=0.35;//fromTable7.156mu=1.21*10^-5;//[lb/ft�s]57rho=0.074;//[lb/ft^3]58//Fora410�meshcarbon59Dp=1.108*10^-2;//[ft]60deltaPbyL=150*1*mu*(1-eps)^2/(32.2*phi_s^2*Dp^2*eps^3)+(1.75*rho*1^2*(1-eps)/(32.2*0.7*Dp*eps^3));//[lbf/ft^2�ft]61deltaPbyL=deltaPbyL*12/62.4;//[in.H2O/ft]139
Chapter26MembraneSeparationProcesses26.1ScilabCodeExample26.1Example26.1.sce1clearall;2clc;34//Example26.15//Given6alpha=5;7per=0.2;//[scf/ft^2�h�atm]8Pf=150;//[lbf/in.^2]9Pp=15;//[lbf/in.^2]1011//Solution12//(a)13R=Pp/Pf;14//Atthefeedinlet15xin=0.209;16//UsingEq.(26.17)17A=alpha-1;18B=1-alpha-1/R-xin*(alpha-1)/R;141
19C=alpha*xin/R;20yi_in=(-B-sqrt(B^2-4*A*C))/(2*A);21//Atthedischargeend22xd=0.05;23//UsingEq.(26.17)24A=alpha-1;25B=1-alpha-1/R-xd*(alpha-1)/R;26C=alpha*xd/R;27yi_d=(-B-sqrt(B^2-4*A*C))/(2*A);2829//Foranapproximatesolution,theseterminalcompositionsare30//averagedtogive31ybar=(yi_in+yi_d)/2;32//Fromanoverallmaterialbalance33//Basis34Lin=100;//[scfh]35V=(Lin*xin-Lin*xd)/(ybar-xd);36//disp(ybar,'andpermeatecompositionis','percent',V/Lin100,'Thepermeateinthefeedis');373839//Formoreaccuratecalculation40j=2;41yi_in(1)=0.5148;42x(1)=0.209;43y(1)=0.5148;44L=Lin;45deltaV=[];46deltaVybar=[];47ybar=[];48fori=0.2:-0.01:xd49x(j)=i;50A=alpha-1;51B=1-alpha-1/R-x(j)*(alpha-1)/R;52C=alpha*x(j)/R;53yi_in(j)=(-B-sqrt(B^2-4*A*C))/(2*A);54ybar(j-1)=(yi_in(j-1)+yi_in(j))/2;142
55deltaV(j)=L*(x(j-1)-x(j))/(ybar(j-1)-x(j));56V=sum(deltaV);57L=Lin-V;58deltaVybar(j)=deltaV(j-1)*ybar(j-1);59deltaVybarsum=sum(deltaVybar);60y(j-1)=deltaVybarsum/V;61j=j+1;62end63disp(y($),'andpermeatecompositionis','percent',V/Lin*100,'Thepermeaterecovered');;646566//(b)67//ThemembraneareaobtainedfromthefluxofAusing68//Eq.(26.29)and(26.13)69//forthefirstincrementx=0.209tox=0.270deltaybar1=1.4856;//[scfh],forLin=100scfh71//Atx=0.20972A1=0.209-0.1*0.5148;73//Atx=0.274A2=0.2-0.1*(0.50);75Aavg=(A1+A2)/276QAP1=0.2*10;//scfh/ft^377//forspecifiedflowof300scfh78deltaA=1/2*1.486/Aavg*180;//[ft^2]79//Thecalculationcontinuedwithincrementsof0.0180A=211/2.0*180;//[ft^2]81disp('ft^2',A,'Themembraneareaneededis')
Example26.4Example26.4.sce1clearall;2clc;34//Example26.45//Given6F=10;//[gal/day�ft^3]143
1415//Solution16//(a)17//Jwbasedonarea18Jw=4.72*10^-4*Do/Di*10^-2;//[m/s]19dt=200*10^-6;//[m]20D=dt;//[m]21//FromEq.(26.53)22Vbar=4*(Jw)*L/Di;//[m/s]23//FromEq.(26.56)24delta_ps=(Vbar*32*mu*L)/(D)^2*(1/2)/10^5;//[atm]25disp('atm',delta_ps,'pressuredrop=','m/s',Vbar,'exitvelocity=');2627//(b)28//Ifthefibresareopenatbothends,theeffectivelengthis1.5mand29//theexitvelocityishalfasgreat.Thepressuredropisone�fourthas30//largeasitwas:31deltaP=delta_ps/4;//[atm]32disp('atm',deltaP,'pressuredrop(ifbothendsareopen)=')
145
20M2=246.5;//[MgSO4.7H2Omolecularweight]21M2_in=wA*F_in*M2/M1;//[kg]22H2O_free=F_in-H2O_evp-M2_in;//[kg]23ML=100;//[kg]24M2_in100=ML*xA*M2/M1;//[kg]25H2O_free100=ML-M2_in100;//[kg]26M2_ML=M2_in100/H2O_free100*H2O_free;//[kg]27FC=M2_in-M2_ML;//[kg]28disp(FC,'kilogramsofcrystalsobtainedperkilogramoforiginalmixture=')
Example27.2Example27.2.sce1clearall;2clc;34//Example27.25//Given6//A=MgSO4,B=MgSO4.7H2OandC=H2O7T=120;//[F]8wA=0.325;910//Solution11//FromFig27.412//EnthalpycoordinateofthepointwA13H1=-33;//[Btu/lb]14//EnthalpycoordinateofthefinalmagmaatconcentrationwA15H2=-78.4;//[Btu/lb]16//Perhundredpoudsoforiginalsolutionthechangeinenthalpy17F=100;//[lb]18delta_H=F*(H1-H2);//[Btu]19//Applying"center�ofgravityprinciple"to70FisotherminFig.27.320C_ML=0.259;21C_CRY=0.488;22//Crystalsare147
2clc;34//Example27.45//Given6alpha=1+0.029;7//FromExample27.38sigma=2.5;//[erg/cm^3]9T=300;//[K]10N=6.0222*10^23;11R=8.3134*10^7;//[erg/gmol�K]12M=74.56;//[Molecularweight]13rho=1.988;//[g/cm^3]14nu=2;15VM=M/rho;//[cm^3/gmol]1617//UsingEq.(27.9)18L=4*VM*sigma/(2*R*T*log(alpha))*10^7;//[nm]19disp('nm',L,'sizeofnuclues(L)=');
Example27.5Example27.5.sce1clearall;2clc;34//Example27.55//Let:A=MgSO4;B=MgSO4.7H2O;C=H2O6//Given7xA=0.31;8T=86;//[F]9Tb=2;//[F]10vbys=0.15;11//PB=12rho_cr=105;//[lb/ft^3]13rho_ml=82.5;//[lb/ft^3]1415//Solution16//Basis:17F=10000;//[lb/h]149
15Lpr=L;//[ft]16//UsingEq.(27.28)17//drawdowntime18tou=Lpr/(3*G);//[h]19//volumeoftheliquidinthecrystallizer20Vc=tou*Q;//[ft^3]21//Totalmagmavolume22Vmagma=Vc/0.85*7.47;//[gal]23disp('gal',Vmagma,'Themagmavolumeinthecrystallizerbe');24//UsingEq.(27.44)25//Thenucleationrateis26C=10000;//[lb/h]27rho_c=105;28B0=9*C/(2*rho_c*Vc*Lpr^3);//[nuclei/ft^3�h]29disp('nuclei/ft^3�h',B0,'Thenucleationratenecessaryis');30//UsingEq.(27.40),thezero�sizeparticledensityis31n0=B0/0.0018;//[nuclei/ft^4]32L1=(0:8)*10^-3;33//UsingEq.(27.27)34//LetA=log10(n),B=log10(n0)35B=log10(n0);36A=B-1.1*10^3*L1/(2.3026);37figure(1);38plot(L1*10^3,A);39xgrid();40xlabel('Lx10^3ft');41ylabel('logn');42title('Populationdensityvslength');4344//FromFig.27.15cforvaluesofzcorrespondingtomeshopenings.45L1=[11,14,16,19,23,27,33,38,46,54,65,78]'*10^-2;46z=L1/(tou*G*100);//[mm]47t=0;48functionf=fun(z,xm)151
49f=z^3*exp(-z)/6;50endfunction51[xm]=ode(0,0,z,fun);52fori=1:length(xm)53Diff(i)=z(i)^3*exp(-z(i))/6;54end55figure(2);56subplot(2,1,1);57plot(z,xm);58xgrid();59xlabel('z');60ylabel('xm');61title('cumulativemassdistribution');62subplot(2,1,2);63plot(z,Diff)64xgrid();65xlabel('z');66ylabel('dxm/dz');67title('differentialmassdistribution');152
Figure27.2:Size-distributionrelationsforExample27.6
154
37end38end3940fori=1:length(Dpn)-141forj=1:length(Dpu)-142if(ji)43delta_B(i,j)=0;44else45delta_B(i,j)=B(i,j)-B(i,j+1);46end47end48end49disp(delta_B,'individualbreakagefunctions');5051//(c)52deltaT=30;//[s]53//UsingEq.(29.15)54x=[];55x(:,1)=xn0;56forn=1:length(xn0)57fort=1:72058if(n==1)59x(n,t+1)=x(n,t)*(1-Su(n)*deltaT);60else61x(n,t+1)=x(n,t)*(1-Su(n)*deltaT)+deltaT*Su(n-1)*delta_B(n-1,n-1)*x(n-1,t);62end63end64end65time=linspace(0,6,721);66fori=1:length(xn0)67plot2d(time,x(i,:),style=i);68xgrid();69xlabel('time(h)');70ylabel('massfraction(xa)');71title('Massfractions');72legend('x1','x2','x3','x4','x5','x6','x7');73end160
Chapter30MechanicalSeparations30.1ScilabCodeExample30.1Example30.1.sce1clearall;2clc;34//Example30.15//Given6//FromTable30.17Dp=[4.699,3.327,2.362,1.651,1.168,0.833,0.589,0.417,0.208,0.0000001]';//[mm]8F=[0,0.025,0.15,0.47,0.73,0.885,0.94,0.96,0.98,1.0]';9O=[0,0.071,0.43,0.85,0.97,0.99,1.00]';//[1to7]10U=[0.0,0.195,0.58,0.83,0.91,0.94,0.975,1.00]';//[3to10]1112//Solution13plot(Dp,F)14plot(Dp(1:7),O,'r')15plot(Dp(3:$),U,'g')162
41//UsingEq.(30.24)42alpha=A^2*gc/(c*muw)*deltaP.*(Kc)/10^11;//[ft/lb10^�11]43figure(2);44plot2d(deltaP,Rm);45xgrid();46xlabel('deltaP(lbf/ft^2)');47ylabel('Rm(ft^�110^�10)');48title('RmvsdeltaP');49figure(3);50plot2d(log(deltaP),log(alpha));51xgrid();52xlabel('deltaP(lbf/ft^2)');53ylabel('alpha(lb/ft10^�11)');54title('alphavsdeltaP');55//Form30.1756disp(Rm,'Rm(ft^�110^�10)=');57disp(alpha,'alpha(lb/ft10^�11)=');58alpha0=1.75*10^11/1000^0.26;59disp('alpha=2.910^10deltaP^2.6','EmpericalEquationforthecake');166
Figure30.3:Rmvs.deltaPforExample30.2168
20//For21c1=10;//[g/L]22v=10^-3;//[cm/s]23//UsingEq.(30.53)24cs=c1*exp(v/kc);//[g/L]25deltaPi=horner(pi,cs);26Qm=250/36000;//[cm/s�atm]27//UsingEq.(30.50)28deltaP=v/Qm+deltaPi;//[atm]29//UsingEq.(30.53)30cs=400;31vmax=kc*log(cs/c1);//[cm/s]32deltaP=vmax/Qm+horner(pi,cs);//[tm]33c=[10,20,40];34V=[];35deltaP=[];36forj=1:length(c)37c1=c(j);38i=1;39vmax=kc*log(cs/c1)*10^4;40h=(vmax-1)/1000;41forv=1:h:vmax42cs=c1*exp(v*10^-4/kc);//[g/L]43deltaPi=horner(pi,cs);//[atm]44deltaP(j,i)=v*10^-4/Qm+deltaPi;//[atm]45V(j,i)=v*10^-4;46i=i+1;47end48end49V=V*36000;50forl=1:length(c)51figure(1)52plot2d(deltaP(l,:),V(l,:),style=l);53xgrid();54xlabel('deltaP(atm)');55ylabel('Permeateflux(L/m^2�h)');56title('Effectivepressuredropandconcentrationonflux')171
Figure30.5:E ectofpressuredropandconcentrationon uxforExam-ple30.4
Example30.5Example30.5.sce1clearall;2clc;34//Example30.55//Given6D=1.5;//[cm]7Nre=25000;8Qm=40;//[L/m62�h]173

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