.MCAD 308000000 \  docDocumentMmcObject[ pp "d2_graph_format graphData% axisFormat)L)Ltrace2D&&&&&&&&& & & & & &&& dim_formatTmasslengthtimecharge temperature luminosity substanceNumericalFormatQdii shpRectVF}mcDocumentObjectState\ mcPageModelK????mcHeaderFooterI@I CHeaderFooterJ@J@J@JMbP?MbP? TextState? TextStyle>@ Arial 0,128,128Serial_ParPropDefaultW?Normalfont_style_listO font_styleP  VariablesTimes New Roman@P  ConstantsTimes New Roman@P TextArial@P Greek VariablesSymbol@P User^1Arial@P User^2 Courier New@P User^3System@P User^4Script@P User^5Roman@P User^6Modern@P User^7Times New Roman@P SymbolsSymbol@P Current Selection FontArial@P Undefined Font@P HeaderArial@P FooterArial@P Rotated Math FontTimes New Romank TextRegion* docRegionGshpBoxU-$<X  CharacterMap-RangeMap;AInstructions: 1) Uncheck "automatic calculation" in the Math menu. 2) Enter tabular data for xy-diagram here. If you need more or fewer rows use the "matrix" tool (View-Toolbars-Matrix). If you wish to use a function y=y(x) instead, replace definitions of yeq(x) and xeq(y) below. 3) All other parameters are entered next to the McCabe-Thiele diagram at the very end of this document. You can move there end now by pressing Ctrl-End. ChrPropMap7  RangeElem<  ChrPropData8 RangeData=eArial255,0,0 < 8u255,0,0  ParPropMap9 <  ParPropData:@W,EmbedMap1<LinkMap/<LinkData0@NormalArial eqRegionB@U YE'tree @ p@@ @@dxes@@p@@0@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A @@0A!@@@ "@@ 1 #@@.8 $@@.7 %@@.6 &@@.5 '@@.4 (@@.3 )@@.2 *@@.1 +@@.05 ,@@0 -@B@UxE.@@ p/@@ .0@@d/yes1@@p/2@@013@@0A24@@0A35@@0A46@@0A57@@0A68@@0A79@@0A8:@@0A9;@@0A:<@@0A;=@@@<>@@<1 ?@@;.8 @@@@:.725 @A@@9.656 @B@@8.586 @C@@7.513 @D@@6.428 @E@@5.322 @F@@4.186 @G@@3.102 @H@@20 @I@B@U Xmh@J@@ p@K@@ @J@L@@@@K@M@@d@L SplineFit@N@@p@L@O@@ @N@P@@ @@O@Q@@d@PxArray@R@@@PyArray@S@@@Ox@T@@@K@U@@d@Tinterp@V@@p@T@W@@ @V@X@@ @@W@Y@@ @@X@Z@@@@Y@[@@d@Zpspline@\@@p@Z@]@@ @\@^@@d@]xArray@_@@@]yArray@`@@@YxArray@a@@@XyArray@b@@@Wx@c@B@U v?@d@@ p@e@@ @d@f@@@@e@g@@d@fyeq@h@@p@f@i@@@hx@j@@@e@k@@d@j SplineFit@l@@p@j@m@@ @l@n@@ @@m@o@@d@nxes@p@@@nyes@q@@@mx@r*@U^w^ v$v$-@lIf you wish to specify something else for yeq(x), you will also need to specify the inverse function xeq(y).7l@s@B@U <A?@@ pA@@@ A?AA@@dA@xprimeAB@@A@AC@@dABrootAD@@pABAE@@ ADAF@@@AEAG@@@AFAH@@dAGyQLAI@@pAGAJ@@AIxAK@@AFAL@@dAKyeqAM@@pAKAN@@AMxAO@@AExAP@B@UIAQ@@ pAR@@AQAS@@dARxprimeAT@@ARAU@@+@ATSerial_DisplayNodeXAV@@AT _n_u_l_l_3JAW*@U @%$"(-@TRmin usually (but not always) occurs at intersection of Q-line and equilibrium curve7T9TAXZ>d-@Step off stages in rectifying section until xi drops below the intersection of q-line and the ROL. (xi,yi) is a point on the quasi-equilibrium curve while (xi-1,yi) is a point on the operating line. 7-B4<-B58B3 0,128,128B6<B78B3_ 0,128,128B4B8<8B98B3 0,128,128B6B:<B;8B3_ 0,128,128B8B<<B=8B3 0,128,128B:B><B?8B3_ 0,128,128BBB<BC8B3_ 0,128,128B@BD<BE8B3 0,128,128BBBF<BG8B3_ 0,128,128BDBH<%BI8B3 0,128,128BFBHB49BJ<BK:@W,1BL</BM<BN0@NormalArial BO@B@U 8BP@@ pBQ@@ BPBR@@dBQMrectBS@@BQBT@@@BSBU@@@BTBV@@H@BUBW@@dBViBX@@BV0BY@@HBUBZ@@@BYB[@@dBZxB\@@BZ0B]@@BYx.DB^@@BTB_@@@B^B`@@@B_Ba@@H@B`Bb@@dBaiBc@@BaBd@@dBciBe@@Bc1Bf@@HB`Bg@@@BfBh@@dBgyBi@@BgiBj@@BfBk@@dBjyROLBl@@pBjBm@@BlBn@@dBmxBo@@BmBp@@dBoiBq@@Bo1Br@@HB_Bs@@@BrBt@@dBsxBu@@BsiBv@@BrBw@@dBvxQECBx@@pBvBy@@ BxBz@@@ByB{@@dBzxB|@@BzB}@@dB|iB~@@B|1B@@ByB@@dByB@@BiB@@(B^B@@@BB@@dBxB@@BiB@@BxiB@@BSB@@dBaugmentB@@pBB@@ BB@@dBxB@@ByB*@U @,6&<-@|Since a programming loop can only return a single matrix, we combine the two column vectors x and y into one 2-column matrix7|9|B<|B:@W,1B</|B<|B0@NormalArial B@B@U &Kk@HB@@ pB@@BB@@@BB@@dBMrectB@@BB@@@BB@@@BB@@5BB@@<@BB CVSEqItem EqItemBBB CVSComboItemCVSItem< YCCVSOleClientItem ࡱ> Root EntryaB.dK8{xkContents9OlePres000(R KQ MS Sans Serif T1c$.Arialb `YYDArialb `YYDB@@B@XB@@B _n_u_l_l_B@B@U ~6B@@ pB@@ BB@@dBNrectB@@BB@@@BB@@dBrowsB@@pBB@@BMrectB@@B1B@B@U~B@@ pB@@BB@@dBNrectB@@BB@@+@B@XB@@B _n_u_l_l_B@B@U }"B@@ pB@@ BB@@dBx0B@@BB@@dBMrectB@@ BB@@dBNrectB@@B0B@B@UB@@ pB@@BB@@dBx0B@@BB@@+@B@XB@@B _n_u_l_l_B*@U  @?H P-@Step off stages in stripping section until xi drops below xB. (xi,yi) is a point on the quasi-equilibrium curve while (xi-1,yi) is a point on the operating line. 7,B<,B8B 0,128,128B<B8B_ 0,128,128BB<B8B 0,128,128BB<B8B_ 0,128,128BB<B8B 0,128,128BB<B8B_ 0,128,128BB<B8B 0,128,128BB<B8B_ 0,128,128BB<4B8B 0,128,128BB<B8B_ 0,128,128BB<B8B 0,128,128BB<B8B_ 0,128,128BB<%B8B 0,128,128BBB9B<B:@W,1B</B<B0@NormalArial B@B@U  ;B@@ pB@@ BB@@dBMstripB@@BB@@@BB@@@BB@@H@BB@@dBiB@@B0B@@HBB@@@BB@@dBxB@@B0B@@Bx0B@@BB@@@BB@@@BB@@H@BB@@dBiB@@BB@@dBiB@@B1B@@HBB@@@BB@@dByB@@BiB@@BB@@dBySOLB@@pBC@@BC@@dCxC@@CC@@dCiC@@C1C@@HBC@@@CC@@dCxC@@CiC @@CC @@dC xQECC @@pC C @@ C C @@@C C@@dC xC@@C C@@dCiC@@C1C@@C C@@dCyC@@CiC@@(BC@@@CC@@dCxC@@CiC@@Cx.BC@@BC@@dCaugmentC@@pCC@@ CC@@dCxC@@CyC *@U    @,6&<-@|Since a programming loop can only return a single matrix, we combine the two column vectors x and y into one 2-column matrix7|9|C!<|C":@W,1C#</|C$<|C%0@NormalArial C&@B@U 9 C'@@ pC(@@ C'C)@@dC(NstripC*@@C(C+@@@C*C,@@dC+rowsC-@@pC+C.@@C-MstripC/@@C*1C0@B@U  C1@@ pC2@@C1C3@@dC2NstripC4@@C2C5@@+@C4@XC6@@C4 _n_u_l_l_C7@B@U  > C( C8@@ pC9@@C8C:@@@C9C;@@dC:MstripC<@@C9C=@@+@C<@XC>@@C< _n_u_l_l_C?@B@U T Yi !d C@@@ pCA@@ C@CB@@dCAMCC@@CACD@@dCCstackCE@@pCCCF@@ CECG@@dCFMrectCH@@CFCI@@dCH submatrixCJ@@pCHCK@@ CJCL@@ @CKCM@@ @CLCN@@ @CMCO@@dCNMstripCP@@CN1CQ@@CMNstripCR@@CL0CS@@CK1CT*@UU  d  J=6=6-@Combine Mrect and Mstrip into one matrix. "submatrix" is used to eliminate the first row from Mstrip which duplicates last row of Mrect.79CU<CV:@W,1CW</CX<CY0@NormalArial CZ@B@U O  !C[@@ pC\@@ C[C]@@dC\xC^@@4C\C_@@dC^MC`@@C^0Ca@B@U "Cb@@ pCc@@ CbCd@@dCcyCe@@4CcCf@@dCeMCg@@Ce1Ch*@U   # JAHAH-@Partition M into two column vectors: x and y. xi and yi are the mole fractions of the more volatile component in the liquid and vapor streams leaving stage i. 780Ci<0Cj8Ch 0,128,128Ck<Cl8Ch_ 0,128,128CiCm<Cn8Ch 0,128,128CkCo<Cp8Ch_ 0,128,128CmCq@@D<1D?@B@Uz  TD@@@ pDA@@ D@DB@@dDAxB.calcDC@@DADD@@dDCxDE@@DCNDF*@U  W -@<-----------This line should be at top of window. Adjust View/Zoom until line does not fold but nearly spans width of screen----------->7DG<DH8DFl Arial9DI<DJ:@W1DK</DL<DM0@NormalArial DN@B@U  DO@@ pDP@@DODQ@@@DPDR@@@DQDS@@@DRDT@@tDS1DU@@DSDV@@tDU4.324DW@@DUDX@@tDW10DY@@KDWDZ@@DY3D[@@DRD\@@dD[yprimeD]@@D[ _n_u_l_l_D^@@ DQD_@@ @D^D`@@ @D_Da@@ @D`Db@@ @DaDc@@@DbDd@@dDcyeqDe@@pDcDf@@DeziDg@@DbziDh@@DaDi@@dDhyRDj@@Dhi2Dk@@D`Dl@@dDkyQDm@@Dki2Dn@@D_Do@@dDnySDp@@Dni2Dq@@D^Dr@@dDqysDs@@DqjDt@@DPDu@@@DtDv@@@DuDw@@tDv1Dx@@Dv0Dy@@DuDz@@dDyxprimeD{@@Dy _n_u_l_l_D|@@ DtD}@@ @D|D~@@ @D}D@@ @D~D@@ @DD@@dDziD@@DziD@@DD@@dDxRD@@Di2D@@D~D@@dDxQD@@Di2D@@D}D@@dDxSD@@Di2D@@D|D@@dDxsD@@DjD &% )|)|&&equilibrium curve&y=x line&Rectifying section oper. line&Q line&Stripping section oper. line&stepping off stages&&& & & & & &&&D*@U M  n YY- Enter values:7 D< D8D 0,128,1289 D< D:@W,1D</ D< D0@NormalArial D*@U* ** \ -AIf you need to change more than one of these values, uncheck the "Automatic Calculation" line in the Math menu After all values have been entered, then you can press F9 to update results If flashing-lightbulb icon stays on more than a few seconds, program is probably caught in a loop taking an infinite number of steps. Press "Escape" to abort calculation; then check input variables7D<D8D}255,0,09D<D:@W1D</D<D0@NormalArial D@B@U# 9 4 lD@@ pD@@DD@@dD\hD@@D1D*@UX% 7 X4  h-Murphree plate efficiency7D<D8D 0,128,1289D<D:@W,1D</D<D0@NormalArial D@B@UB 3] R cD@@ pD@@DD@@dDx.DD@@D0.79D*@UXC U XR  -Mol frac in distillate7D<D8D 0,128,1289D<D:@W,1D</D<D0@NormalArial D@B@U` 1{ p dD@@ pD@@DD@@dDx.FD@@D0.25D*@UXa s Xp  jj-Mol frac in feed7D<D8D 0,128,1289D<D:@W,1D</D<D0@NormalArial D@B@U 2  eD@@ pD@@DD@@dDx.BD@@D0.01D*@UX  X  -Mol frac in bottoms7D<D8D 0,128,1289D<D:@W,1D</D<D0@NormalArial D@B@U   fD@@ pD@@DD@@dDqD@@D0.3D*@UX  X  $$-,Thermal conditions of feed (liquid fraction)7,D<,D8D 0,128,1289,D<,D:@W,1D</,D<,D0@NormalArial D@B@UX   gD@@ pD@@DD@@dDR.minD@@DD@@+@D@XD@@D _n_u_l_l_D@B@U/]D@@ pD@@DD@@dDRD@@D8.618D*@UX7X^ x6x6-.Reflux ratio (to obtain total reflux, use R=0)7.D<.D8D 0,128,1289.D<.D:@W,1D</.D<.D0@NormalArial D*@UGYV_ -!After N steps, this is actual xB:7 !D< D8Dw 0,128,128D<D8D 0,128,128DDD9!D