化工应用数学电子教案.ppt

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1、化工应用数学建立數學模式Theconservationlawsmaterialbalanceheatbalanceenerybalance(rateof)input-(rateof)output=(rateof)accumulation範例說明Asingle-stagemixersettleristobeusedforthecontinuousextractionofbenzoicacidfromtoluene,usingwaterastheextractingsolvent.ThetwostreamsarefedintoatankAwheret

2、heyarestirredvigorously,andthemixtureisthenpumpedintotankBwhereitisallowedtosettleintotwolayers.Theuppertoluenelayerandthelowerwaterlayerareremovedseparately,andtheproblemistofindwhatproportionofthebenzoicacidhaspassedintothesolventphase.watertoluene+benzoicacidtoluene+benzoi

3、cacidwater+benzoicacid簡化（理想化）Sm3/stolueneykg/m3benzoicacidRm3/stoluenexkg/m3benzoicacidSm3/swaterRm3/stolueneckg/m3benzoicacidRateequationfortheextractionefficiency:y=mxMaterialBalance:Inputofbenzoicacid=outputofbenzoicacidRc=Rx+SySamemethodcanbeappliedtomulti-stages.隨時間變化Fun

4、tionoftime非穩定狀態(unsteadystate)Inunsteadystateproblems,timeentersasavariableandsomepropertiesofthesystembecomefunctionsoftime.Similartothepreviousexample,butnowassumingthatthemixerissoefficientthatthecompositionsofthetwoliquidstreamsareinequilibriumatalltimes.Astreamleavingthe

5、stageisofthesamecompositionasthatphaseinthestage.Thestateofthesystematageneraltimet,wherxandyarenowfunctionsoftime.Sm3/stolueneykg/m3benzoicacidRm3/stoluenexkg/m3benzoicacidSm3/swaterRm3/stolueneckg/m3benzoicacidV1,xV2,yMaterialbalanceonbenzoicacidSm3/stolueneykg/m3benzoicaci

6、dRm3/stoluenexkg/m3benzoicacidSm3/swaterRm3/stolueneckg/m3benzoicacidV1,xV2,yInput-output=accumulation單位時間的變化t=0,x=0MathematicalModelsSaltaccumulationinastirredtankt=0Tankcontains2m3ofwaterQ:Determinethesaltconcentrationinthetankwhenthetankcontains4m3ofbrineBrineconcentration

7、20kg/m3feedrate0.02m3/sFlow0.01m3/s建立數學模式VandxarefunctionoftimetDuringt:balanceofbrinebalanceofsaltBrineconcentration20kg/m3feedrate0.02m3/sBrine0.01m3/sVm3xkg/m3解數學方程式Solvex=20-20(1+0.005t)-2V=2+0.01tMathematicalModelsMixingPurewater3l/minMixture2l/minMixture3l/minMixture4l

8、/minMixture1l/minTank1Tank2t=0Tank1contains150gofchlorinedissolvedin