Dimensionamiento de Un Reactor Para La Produccion de Metanol-idealizado

\@JQLTYJHGH G\XÙ@EOG HL @GZGTJX

IJL@IJGY DÇYJIGY L J@KL@JLTÏGY 

HJYL×E HL TLGIXETLY J 

HJOL@YJE@GOJL@XE HJOL@YJE@GOJL@XE HL \@ TLGIXET RGTG CG RTEH\IIJÙ@ HL OLXG@EC

Gc|o`e= 

Alt`g`he Ke`}çcl} Ifçql} 

RTEALYET= 

Htg. Loog G`xe`jg Mç|tlk|j Olhj`g 

Alifg l`xtlkg= 71 hl `eqjlodtl `eqjlodtl hlc 4277

Hjol`yje`gojl`xe hl |` tlgixet rgtg cg rteh|iijù` hl olxg`ec Hlyitjrijù` z |ye hlc rteh|ixe  Lc olxg`ec e gciefec Olxïcjie# r|lhl edxl`ltyl hl |`g gorcjg qgtjlhgh hl a|l`xly ieoe ret lmlorce# lc kgy hl yï`xlyjy# e xgodjê` ret olhje hl cg oghltg# g|`w|l lyxg xêi`jig ly o|z g`xjk|g z y| rteh|iijù` ly o|z dgmg# hghe w|l lc olxg`ec edxl`jhe ly |` y|drteh|ixe hlc igtdù` qlklxgc# z igyj xehe lc rteh|ixe ly rtlijygol`xl igtdù` qlklxgc Tedltx Dezcl ly rtly|`xgol`xl lc rtjolte l` cektgt edxl`lt lc olxg`ec Ce gjycù hl cg hlyxjcgijù` ylig hl oghltg Dltxflcex l` y| lyx|hje hl fjhteigtd|tey z hltjqghey fgcekl`ghey ce edx|qe ret ygre`jajigijù` hlc icet|te hl olxjce Lc ý`jie oêxehe qjgdcl rgtg cg edxl`ijù` hl olxg`ec ltg cg hlyxjcgijù` ylig hl cg oghltg# rlte l` cg Dghjyifl G`jcj` |`h Yehg Agdtjn yl lyx|hjù# dgme cg hjtliijù` hl Gc{j` ojxxgyif# cg fjhtekl`gijù` hlc ùvjhe hl igtde`e g rtlyjù` z ie` lcce cg yï`xlyjy hlc olxg`ec Hl lyxg og`ltg lc olxg`ec yl ie`qjtxjù l` |` rteh|ixe qgcjeye rgtg cg j`h|yxtjg# hldjhe g cg ktg` ig`xjhgh hl |yey z grcjigije`ly w|l xjl`l Lc rtj`ijrgc |ye ly rgtg edxl`lt aetogchlfjhe &rgtg rcçyxjiey lxi*> ylk|jhe hl extey# ieoe edxl`ijù` hl rcgyxjajig`xly# ieoe j`xltolhjgtje rgtg o|ifgy extgy yï`xlyjy# ieoe hjyecql`xl# g`xjie`klcg`xl# rgtg aetogt recjêyxltly# rlkgol`xey z iecetg`xly hl g`jcj`g# gyï ieoe gkl`xl hl olxjcgijù` Fgdcg`he l` xlogy oçy tlijl`xly# lc olxg`ec yl rtlxl`hl rtlxl`hl |ygt  ieoe ieod|yxjdcl# yl r|lhl ie`qltxjt l` kgyecj`g kgyecj`g hl gcxe eixg`gml g o|z dgme ieyxl# ie` cg ql`xgmg w|l `e ie`xjl`l y|ca|tey z ie`xgoj`g ol`ey Cg i|lyxjù` ly w|l lc olxg`ec `e yl edxl`htïg hl cg fjhtekl`gijù` hl ùvjhe hl igtde`e yj`e hl djeogyg Lorclg`he |` rgtçolxte hl |`g xe`lcghg hl djeogyg ylig# hl lyxg rehtïg` rteh|ijtyl gctlhlhet hl ;22 cjxtey hl olxg`ec# g aj`gc hl i|l`xgy# lyxl ly |` |ye w|l gý` lyxç l` rteilye hl ylt qjgdcl z ieorlxjxjqe

Lyx|hje rtlcjoj`gt hl oltighe Cg j`h|yxtjg hlc olxg`ec `e lyxç o|z hlygtteccghg l` Oêvjie# yl rteh|il` gctlhlhet hl 711 ojcce`ly hl kgce`ly g`|gcol`xl Ret ce xg`xe Oêvjie `e lvretxg olxg`ec hldjhe g y| dgmg rteh|iijù`# rlte yï joretxg# ylký` hgxey hlc J@LKJ# l` 422;# Oêvjie ieortù 7726 ojcce`ly o jcce`ly hl hùcgtly hl olxg`ec# l` 4226 7728 ojcce`ly hl hùcgtly z l` 422: yece <74 ojcce`ly hl hùcgtly Fgdcg`he g `jqlc o|`hjgc# cg rteh|iijù` hl olxg`ec yl lvxjl`hl rtçixjigol`xl ret xehe lc kcede# hlyhl Gyjg# Goêtjig hlc `etxl z y|t# Çatjig z etjl`xl olhje Ie` oçy hl :2 rcg`xgy l` xehe lc o|`he# cg igrgijhgh hl rteh|iijù` ly hl ;< ojcce`ly hl xe`lcghgy Lc olxg`ec ly |` rteh|ixe kcedgc# z ighg hïg fgz oçy hl 62#222 xe`lcghgy l`qjghgy hl |` ie`xj`l`xl g exte Cg hlog`hg g`|gc hl olxg`ec a|l hl gctlhlhet hl 8< ojcce`ly hl xe`lcghgy z yl lyrltg w|l l` lyxl g÷e# lyxg hlog`hg lvilhg cgy <2 ojcce`ly hl xe`lcghgy

Oêxehey hl rteh|iijù`  Cg rteh|iijù` hl olxg`ec g`xltjetol`xl yl fgiïg olhjg`xl cg hlyxjcgijù` ylig hl oghltg# rlte gix|gcol`xl# g `jqlc j`h|yxtjgc lvjyxl` qgtjey rteilyey dgyghey l` lc lorcle hl igxgcj}ghetly ]j`i / Iteoe &Rteilye DGYA g gcxg rtlyjù`* z hl iedtl  ’ ùvjhe hl ]j`i &rteilye JIJ g dgmg rtlyjù`* w|l hg` ylclixjqjhghly y|rltjetly gc ::, 4F4 . IE  IF9EF Cg rtlyl`ijg hl |` rlw|l÷e retil`xgml hl IE 4 yl j`ic|zl l` qgtjey rteilyey &c|tkj z extey* ce i|gc agqetlil cg aetogijù` hl olxg`ec Cey rtjoltey igxgcj}ghetly a|lte` hlygtteccghey ret DGYA l` 7:49# w|l ie`yjyxïg` l` |`g ol}icg feoekê`lg hl ùvjhey hl iteoe z ij`i w|l rltojxïg` erltgt g 922  ’ 822 ½I z 922  ’ 9<2 gxo L` cg hêighg hl cey 12# cg lortlyg JIJ hlygtteccù cey igxgcj}ghetly hl iedtl w|l tlqec|ije`gte` cg j`h|yxtjg hlc olxg`ec> hldjhe g w|l ie` lccey yl rehïg erltgt g rtlyje`ly z xlorltgx|tgy yl`yjdclol`xl j`altjetly# l`xtl <2 z 722 gxo z 482  ’ 4;2 ½I Lc rteilye JIJ rgtg cg edxl`ijù` hl olxg`ec g dgmg rtlyjù` j`xteh|ijhe l` 7:11 ie`xj`|g yj` xl`lt tjqgcly j`olhjgxey Ly ret lye w|l rgtg lyxl xtgdgme yl lcjkjù lc rteilye g dgmg rtlyjù` &JIJ* Rteilye Dgya 

L` lc rteilye DGYA yl |xjcj}g |` igxgcj}ghet hl It 4E9/]`E g 9<2 ½I z 922 gxo Cg tlgiijù` ly lvexêtojig z `lilyjxg tlatjkltgijù`> cey kgyly w|l ygcl` hlc tlgixet yl l`atïg` rgtg ie`hl`ygt lc olxg`ec aetoghe# z cey `e ie`hl`yghey yl tlijicg` Lc olxg`ec yl r|tjajig ret hlyxjcgijù` atgiije`ghg z yl edxjl`l ::, hl r|tl}g

Rteilye JIJ 

Lc rteilye JIJ ghojxl gcjol`xgije`ly hl fjhteigtd|tey cïw|jhey# kgyleyey e yùcjhey Lc kgy hl yï`xlyjy r|lhl edxl`ltyl ret tlaetoghe ie` qgret e ie` evjhgijù` rgtijgc L` lc rteilye hl tlaetoghe ie` qgret# cg gcjol`xgijù` yl hly|ca|tg ret  rteilyey igxgcïxjiey e hl gdyetijù`# yl ol}icg ie` qgret z yl cclqg g |` tlaetoghet x|d|cgt Lc kgy hl yï`xlyjy edxl`jhe ygcl hlc tlaetoghet g 622 /662 ½I z rgyg g cg yliijù` hl tli|rltgijù` hl igcet Hlyr|êy hl l`atjgtyl fgyxg xlorltgx|tg godjl`xl# lc kgy yl j`xteh|il l` lc ijice hl yï`xlyjy hl olxg`ec> ijti|cghet# tlgixet# igodjghet hl igcet# l`atjghet z ylrgtghey Lc rteh|ixe edxl`jhe yl hlyxjcg l` hey e xtly iec|o`gy rgtg gcig`}gt cg igcjhgh hlylghg Lc rteilye g`xltjetol`xl lvrcjighe yl o|lyxtg l` cg yjk|jl`xl jogkl`

Cgy rtj`ijrgcly igtgixltïyxjigy hlc rteilye ye`= |` igxgcj}ghet dgyghe l` iedtl gcxgol`xl lyxgdcl ie` |` xjlore hl qjhg y|rltjet g 8 g÷ey# w|l erltg g <2/722 gxo z 422/922 ½I> |` hjyl÷e yl`ijcce hlc tlgixet z |` yjyxlog hl tli|rltgijù` hl igcet z hl hlyxjcgijù` erxjoj}ghey Lc tlgixet ly hl clife ac|jhj}ghe> ly |` hlrùyjxe g rtlyjù` w|l ie`xjl`l lc clife hl igxgcj}ghet# hexghe ie` yjyxlogy rgtg cg igtkg hlc igxgcj}ghet ret cg igtkg y|rltjet z rgtg y| hlyigtkg ret cg rgtxl j`altjet Cg tlgiijù` yl rgtg g hjaltl`xly `jqlcly ret j`zliijù` hl kgy atje# z lc ýcxjoe l`atjgojl`xe yl tllorcg}g fgdjx|gcol`xl ret |` j`xltigodjghet hl igcet w|l rtligcjl`xg cg gcjol`xgijù` gc rtjolt clife Cgy igrgijhghly hl cgy rcg`xgy Qgtjg` l`xtl <2 z 4<222 x%hïg L` lc igye hl w|l yl lorcll lc rteilye hl evjhgijù` rgtijgc# yj yl hjyre`l hl gcjol`xgije`ly rlyghgy e igtdù`# êyxgy yl evjhg` rgtijgcol`xl ret evïkl`e z qgret Lc kgy rteh|ixe# w|l ie`xjl`l ktg`hly ig`xjhghly hl F 4 z IE# m|`xe ie` IE4 z gck|`gy jor|tl}gy# yl xtgxg rgtg lqjxgt cey ieor|lyxey hl g}|atl &w|l l`ql`l`gtïg` gc igxgcj}ghet*# z rgtg gm|yxgt gc ùrxjoe cg tlcgijù` F 4%IE Ieoe l` cey rteilyey hl evjhgijù` rgtijgc r|lhl` erltgt g rtlyje`ly j`xltolhjgy# r|lhl` y|rtjojtyl l` lyxgy j`yxgcgije`ly cg lxgrg hl ieortlyjù` hlc kgy hl yï`xlyjy

Oêxehe JIJ hl rteh|iijù` hl olxg`ec / Jorgixe godjl`xgc L` lyxl rteilye yl |yg` qgtjey fjhteigtd|tey cïw|jhey# kgyleyey e yùcjhey# rlte kl`ltgcol`xl yl |yg lc kgy hl yï`xlyjy# w|l yl edxjl`l ret tlaetoghe ie` qgret e ret evjhgijù` rgtijgc Lc tlaetoghe yl fgil g rgtxjt hl kgy `gx|tgc# lc i|gc xjl`l rlw|l÷gy ig`xjhghly g}|atl w|l hldl` ylt tloeqjhgy g`xly hl l`xtgt gc tlaetoghet Cey ieor|lyxey hl g}|atl ye` xtg`yaetoghey g y|ca|te hl fjhtùkl`e rgtg c|lke ylt gdyetdjhey ret lc gdyetdlhet hl g}|atl Hl `e og`lmgtyl lyxey tlyjh|ey r|lhl` tlrtlyl`xgt |` rtedclog gc godjl`xl Ieoe xehe rteilye dgyghe a|`hgol`xgcol`xl l` cg rlxtew|ïojig# kl`ltgcol`xl cg `lilyjhgh hl j`y|oey fgil w|l cgy j`yxgcgije`ly hl lyxey rteilyey yl l`i|l`xtl` o|z iltig hl tlaj`ghetgy hl rlxtùcle# j`ic|ye l` eigyje`ly lyxey ojyoey rteilyey aetog` rgtxl j`xlktgc hl lccgy Tlajtjê`heyl gc jorgixe l` lc gjtl# kl`ltgcol`xl lyxçy rcg`xgy rteqeig` |`g ie`xgoj`gijù` ie` ieor|lyxey hl g}|atl# fjhteigtd|tey qecçxjcly z ùvjhey hl `jxtùkl`e z ylk|tgol`xl oe`ùvjhe hl igtde`e Yj djl`# l` lyxl rteilye yl |yg yecgol`xl kgy `gx|tgc# ly joretxg`xl tliethgt  cgy lojyje`ly ig|yghgy ret cey ieod|yxjdcly w|l yl |yg` rgtg cey lw|jrey w|l yjtql` gc rteilye# ieoe ret lmlorce cgy igchltgy# oexetly hl ieod|yxjù` j`xlt`g# x|tdj`gy# j`ij`ltghetly lxi Tlyrlixe gc gk|g# xeog`he l` i|l`xg w|l lc gk|g yl tlw|jltl xg`xe rgtg cey rteilyey l` yj# ieoe rgtg xtg`yaltl`ijg xêtojig# xehg j`yxgcgijù` hl lyxl xjre tlw|jltl |` gdgyxlijojl`xe gd|`hg`xl hl gk|g# rgtxl hl cg i|gc ly hlygcemghg ieoe gk|g tlyjh|gc ie` hjqltyey ie`xgoj`g`xly l` lccg Lc jorgixe godjl`xgc gc y|lce yl hg ret ogc og`lme hl tlyjh|ey# cg ie`xgoj`gijù` yl hg i|g`he lyxey yl ajcxtg` gc y|lce# retw|l yl ieceigte` l` xg`w|ly z reyxltjetol`xl a|lte` l`xlttghey \`g –ie`xgoj`gijù`‟ w|l kl`ltgcol`xl `e yl xeog l` i|l`xg# ly cg

ie`xgoj`gijù` ret t|jhe Cey fet`ey z igchltgy |yghey l` cey rteilyey# gyï ieoe cey ieortlyetly z oexetly ye` lojyetly hl t|jhe

Hgxey ij`êxjiey z xltoehj`çojiey Cg tlgiijù` hl yï`xlyjy hl olxg`ec ly a|ltxlol`xl lvexêtojig= 4F4 . IE

⟻

IF9EF

Ie` igcet hl tlgiijù` hl ΘF²4:6 ? /:7 NM%oec

Xgodjê` yl hg cg ie`qltyjù` hlc IE 4 g|`w|l lyxg tlgiijù` ei|ttl l` ol`et  rteretijù` Ieoe yl r|lhl edyltqgt l` cg tlgiijù`# lyxg ly tlqltyjdcl# z cgy gcxgy rtlyje`ly z dgmgy xlorltgx|tgy agqetlil` lc hlyrcg}gojl`xe hlc lw|jcjdtje fgijg cg aetogijù` hl olxg`ec Ret ce xg`xe# l` lc rteilye ly `lilygtje erltgt  g lclqghgy rtlyje`ly z dgmgy xlorltgx|tgy# ie`xg`he xgodjê` ie` lc |ye hl

igxgcj}ghetly ce y|ajijl`xlol`xl gixjqey# r|ly gc xtgdgmgt ie` dgmgy xlorltgx|tgy cg qlceijhgh hl tlgiijù` hjyoj`|zl o|ife

Ieor|lyxe F4 IF9EF &olxg`ec* IE

Igrgijhgh igcetïajig &g 722²I* 466; M%N-oec <7 M%N-oec 4:9: M%N-oec

Igrgijhghly igcetïajigy  igci|cghgy hl xgdcg D.4 hl –Rtj`ijrjey lclol`xgcly hl cey rteilyey w|ïojiey‟ 

Cg ie`yxg`xl lyrliïajig hl qlceijhgh hl cg tlgiijù` l` a|`ijù` hl cg xlorltgx|tg# lyxç hghg ret cg yjk|jl`xl lvrtlyjù`=

   -

He`hl T ? 69788 M- oec /7- ²N/7 z X lyxç l` ²N L` dgyl g lyxg lvrtlyjù`# yl edx|qjlte` cey qgcetly hl n z yl ieceigte` l` cg xgdcg 7# i|zey hgxey yl rtlyl`xg` ktgajighey G rgtxjt hl cg ktçajig yl hlxltoj`ù lc qgcet hl cg ie`xg`xl hl Gttfl`j|y &G* z cg l`ltkïg hl gixjqgijù` &L*. Xgdcg 7

7%x

C`&n*

2.22477

/2<68:

2.2242;

/222:;8

2.2242469:

2<87:

2.227:662;

72;7

2.227:8:9

7<62<

2.227:74

42;

2.2276;17

4<826

2.2276871

4::8

2.227626

989

8 9< 9

z ? /7944;v . 4;9<1 T´ ? 2::::

4<     *     n     &    `     c

4

c`n

7< 7 2< 2 2227;< 22276 22276< 2227: 2227:< 7%x 

2224

22242< 22247 22247<

L` dgyl g cg ktçajig=

G &ie`yxg`xl hl Gttfl`j|y * ? ;<:-7277 L &l`ltkïg hl gixjqgijù` * 72:#:1:4;6 M % oec- N Li|gijù` hl qlceijhgh 

Cg li|gijù` hl qlceijhgh ly cg yjk|jl`xl# y|re`jl`he w|l cg tlgiijù` ly lclol`xgc z xeog`he l` i|l`xg w|l ly tlqltyjdcl=

    -

Lvjyxl` o|ifey j`xl`xey ret fgilt |` oehlce ij`êxjie hl cg yï`xlyjy hl olxg`ec> |`g li|gijù` hl qlceijhgh dgyghg l` hgxey lvrltjol`xgcly ly cg yjk|jl`xl=

   

He`hl n ly cg ie`yxg`xl lyrliïajig hl qlceijhgh z N lw ly cg ie`yxg`xl hl lw|jcjdtje hl cg tlgiijù`. Lc qgcet hl xêtoj`e –`‟ yl hlxltoj`ù lorïtjigol`xl z

xjl`l qgcet hl /79 Z cgy rtlyje`ly iettlyre`hl` g cgy rtlyje`ly rgtijgcly hl ighg ieore`l`xl

Ie`qltyjù` oçvjog Rgtg edxl`lt cg ie`qltyjù` oçvjog l` lc lw|jcjdtje# yl fg` flife gck|`gy ie`yjhltgije`ly l` dgyl g cgy ie`hjije`ly l` w|l yl cclqg g igde lc rteilye Cgy ie`yjhltgije`ly ye`= Ni g 422 ²I ? 2;6:; X? 422 ²I R ? 722 gxo Lc qgcet hl Ni yl edx|qe ie` gz|hg hl cg yjk|jl`xl li|gijù`=

       

He`hl X hldl lyxgt l` nlcqj` Edxl`jl`he lc g`xjcekgtjxoe z lorclg`he cg li|gijù` w|l tlcgije`g N r ie` NI

He`hl X hldl lyxgt l` nlcqj`# z T ? 226421 C-gxo%&oec - n* Ly gyï ieoe yl edxjl`l lc qgcet hl N i g 422 ²I Yl ie`yjhltg w|l lc tlgixet ly jyexêtojie z w|l `e fgz igïhg hl rtlyjù`  Ghloçy w|l cg gcjol`xgijù` ly lyxlw|jeoêxtjig z w|l cg tlgiijù` yl cclqg g igde l` agyl kgy Rgtxjl`he hl cg tlgiijù`=

4F4 . IE

IF9EF

Y|re`jl`he w|l cg tlgiijù` ly lclol`xgc=

   

                           

Y|yxjx|zl`he cey qgcetly hl cgy ie`il`xtgije`ly l` cg li|gijù` hl N i=

          -        Ret clz hl kgyly jhlgcly yl hlxltoj`ù w|l cg ie`il`xtgijù` j`jijgc hl G &I G2* ? 7;7;< O Yjl`he z G2 ? 4%9 ? 2.1111# lc rgtçolxte θ? /7> ζD? ¿ ζI?2

∸

                                 \yg`he lc rtektgog Reczogxf# yl cclkù g w|l cg ie`qltyjù` l` lw|jcjdtje ly 2<89;# z y|re`jl`he w|l yl tlw|jltl edxl`lt lc 62, hl ie`qltyjù` l` lc rteilye# l`xe`ily V ly jk|gc g 289< e 89<, a &v* ? &&&7;7;< - &&7 % 4* - v** % &&7 . &/2111 - v**** % &&&7;7;< - &7 / v** % &7 . &/2111 - v*** P 4 &&7;7;< - &7 % 4 / &7 % 4 - v*** % &7 . &/2111 - v***** / n v&ogv* ? 2::::::::: v&oj`* ? 222222227

n ? 2;6:;

Hjyre`jdjcjhgh hl tlgixjqey Cg hjyre`jdjcjhgh hl tlgixjqey rgtg cg rteh|iijù` ly d|l`g l` Oêvjie# zg w|l yl rgtxl hlc kgy `gx|tgc rgtg lc tlaetoghe G ie`xj`|gijù` yl rtlyl`xg |`g xgdcg hl cg rteh|iijù` hl kgy `gx|tgc l` olxtey iýdjiey

Dgyl hl hjyl÷e Cg ie`qltyjù` oçvjog w|l yl r|lhl cektgt ly cg ie`qltyjù` l` lc lw|jcjdtje v l ? <8, Gc erltgt g 722 gxo z 422 ²I &8;9 ²N* z |`g gcjol`xgijù` lw|joecgt l` |` tlgixet RAT Y|re`jl`he w|l yl w|jltl edxl`lt |`g ie`qltyjù` hl 62,# l`xe`ily v? 26vl Ret xg`xe cg ie`qltyjù` yltç hl 289< Y|re`jl`he w|l yl w|jltl` rteh|ijt <2 xe`lcghgy hl OlEF ret hïg# ce w|l ly jk|gc g= <2 xe`% hïg ? 76268 oec%y

                   ∮ 

Cg li|gijù` hl hjyl÷e rgtg |` RAT ly

Xltilt gqg`il‡

R ? 722 gxo X ? 422 ½I

F4 OlEF 4F4 . IE  IF9EF

IE Vl ? 2<8

Qgtjgdcly Hlrl`hjl`xly

J`hlrl`hjl`xly

n NI NR

X R x L T A m2  G //// //// //// //// //// ////

  

Z G2 I m t  m Q V Ir F²

Li|gije`ly |xjcj}ghgy Li|gijù` hl hjyl÷e RAT 

   ∮ 

Li|gijù` hl qlceijhgh 

          

Ie`yxg`xl hl lw|jcjdtje 

Ie`il`xtgijù` j`jijgc 

                             

Qlceijhgh hl ac|me qec|oêxtjie qgtjgdcl 

Hlcxg &θ*

Êryjce` &μ*

Lyrgije xjlore 

Gttfl`j|y 

Dgcg`il hl oecly / Tlgixet x|d|cgt RAT

Rgtxjl`he hlc dgcg`il kl`ltgc hl oecly



  ∮   Yj` qgtjgije`ly lyrgijgcly l` qlceijhgh hl`xte hl ∁Q



 ∮   ∸            .  ∸    

Ret g`gcekïg ie` cg hlaj`jijù` hl hltjqghg

Yj ∁Q ? 2

Rgtg cg lyrlijg G

Hlyrlmg`he hQ

  J`xlktg`he q?q7> A G ? A G2 z A G ? A G7

       ∮  ∮  Rgtg lvrtlygt cg li|gijù` l` xêtoj`ey hl cg ie`qltyjù`= 

Rgtxjl`he hl=

              Yj

Hltjqg`he tlyrlixe gc qec|ol`

O|cxjrcjig`he ret /7

    

Xgdcg lyxlw|jeoêxtjig Rgtg cg tlgiijù`= 4F4 . IE  IF9EF 4G . D  I Lyrlijl

Qlceijhgh Gcjol`xgijù`

 G

A G2

D

AD2

I

AI2

Igodje hl`xte hlc tlgixet

Qlceijhgh hlc Lac|l`xl

Ie`il`xtgijù`

                                              

Rgtg xltoj`gt hl ie`yxt|jt cg xgdcg# ly `lilygtje tliethgt gck|`ey rgtçolxtey igci|cghey hl gi|lthe g cgy ie`hjije`ly hlc rteilye

     Cg gcjol`xgijù` ly lyxlw|jeoêxtjig# ret ce xg`xe= z G2 ? 4%9 μ? &4%9*-&/7* ? /4%9 ζD ? ¿ ζI ? 2

I G2 ? 7;7;<

Zg yl r|lhl ie`yxt|jt cg xgdcg lyxlw|jeoêxtjig y|yxjx|zl`he qgcetly Lyrlijl

 G D

Qlceijhgh Gcjol`xgijù`

   

I

2

Igodje hl`xte hlc tlgixet

Qlceijhgh hlc Lac|l`xl

Ie`il`xtgijù`

                                               

Içci|ce hl ce`kjx|h &qec|ol`* z lyrgije / xjlore hlc tlgixet Hgxey= NI ? 2;6:; &C%oec*P4 n G ? 2<< &&C%oec*P4*- y/7 V ? 26Vl ? 289<

                             

Cg li|gijù` hl hjyl÷e hlc tlgixet x|d|cgt ly=

   ∮ 

Olhjg`xl lc rtektgog Reczogxf# yl lqgcýg cg j`xlktgc# |yg`he lc yjk|jl`xl iùhjke h&v*%h&q* ? &/tg* % &ag2* v&2* ? 2 ag2 ? 87<; q&2* ? 2 q&a * ? <2 ig2 ? 7;7;< d?7 g?4 i?7 xlxgd ? 2< xlxgi ? 2 lry ? /4 % 9 ig ? &ig2 - &7 / v** % &7 . &lry - v** id ? &ig2 - &xlxgd / &&d % g* - &v**** % &7 . &lry - v** ii ? &ig2 - &xlxgi . &&i % g* - &v**** % &7 . &lry - v** tg ? /&n* - &&&ig P 4* - &id** / &ii % ni** ni ? 2;6:; n ? 2<<

Rgtg |`g ie`qltyjù` hl 289< lc qec|ol` hlc tlgixet ly hl grtevjoghgol`xl 49 C Lyrgije xjlore 

                     Dgcg`il hl l`ltkïg 

W

Aj2

Aj

Fj2

Fj

Lc dgcg`il hl l`ltkïg rgtg |` yjyxlog gdjltxe ly=

Qlceijhgh hl

Ac|me hl igcet

Ac|me hl

gi|o|cgijù`

fgijg lc

xtgdgme

hl l`ltkïg l`

?

yjyxlog

/

tlgcj}ghe ret

lc j`xltjet hlc

rteilhl`xl

lc yjyxlog

yjyxlog

hl cey

yedtl cey

gctlhlhetly

gctlhlhetly

    

.

L`ltkïg

L`ltkïg w|l

gktlkghg gc

ygcl hlc

yjyxlog ret

/

yjyxlog ret

lc ac|me hl

ac|me hl ogyg

ogyg fgijg lc

w|l ygcl hlc

j`xltjet hlc

yjyxlog

Rgtg |` yjyxlog l` lyxghe `e lyxgije`gtje ie` ` lyrlijly

  ∗   ∗ 

Tliethg`he cg li|gijù` hl |`g tlgiijù` kl`ltgc

    

gG . dD . iI . hH

Y|yxjx|zl`he l` cg li|gijù` g`xltjet 

∗   ∗   ∗  &     *                        ∗  ∗     ∗                     ∗ 

Tlxeog`he

    ∗        ∮         ∮  ∮ ∮  

Ie`yjhltg`he Ir ? ie`yxg`xl z y|yxjx|zl`he l` cg li|gijù` lc dgcg`il hl l`ltkïg w|lhg hl cg yjk|jl`xl og`ltg

     ∗     Lyxg li|gijù` hl dgcg`il hl l`ltkïg# r|lhl grcjigtyl g i|gcw|jlt tlgixet.

I|gtxe gqg`il Hghe w|l lc tlgixet w|l yl |xjcj}g ly |` RAT jyexêtojie# edxl`lt cg ojyog ie`qltyjù` olhjg`xl exte gttlkce ieoe rehtïg ylt re`lt 4 e 9 RAT‚y l` yltjl

w|l y|ol` lc qec|ol` `lilygtje rgtg cg ie`qltyjù` hl 26V l yece jorcjigtïg fgilt oçy kgyxe# zg w|l cg ie`qltyjù` yltïg cg ojyog w|l rgtg |` yece RAT ie` |` qec|ol` hl grtevjoghgol`xl 49 Cjxtey Yj` lodgtke rgtg hlmgt lyxe oçy icgte yl rtlyl`xgtç |`g ktçajig hl clql`yrjlc lcgdetghg ie` reczogxf z gck|`ey içci|cey w|l hloeyxtgtg` ce w|l zg yl ol`ije`ù Ghloçy# fgijl`he cg y|reyjijù` hl w|l yl r|lhl |ygt |` IYXT# rgtg cektgt cg ojyog ie`qltyjù` w|l |` RAT yltïg `lilygtje |` ogzet  qec|ol` Ly ret lye w|l yl tlieojl`hg l` lyxl igye# lc |ye hlc RAT jyexêtojie# ieoe yl og`lmù hlyhl |` rtj`ijrje Ktçajig hl clql`yrjlc 

Ieoe yl edyltqg l` cg ktçajig# hghe w|l cg ie`qltyjù` gc lw|jcjdtje ly grtevjoghgol`xl 2<8# rgtg cektgtce yl `lilyjxgtïg |` tlgixet hl qec|ol` j`aj`jxe

Yl rtere`l |` gttlkce hl |` IYXT ylk|jhe hl |` RAT Ie` lc tlgixet IYXT yl rtere`l cclkgt g cg ie`qltyjù` hl 29 z aj`gcol`xl ie` lc RAT cclkgt g cg ie`qltyjù` hl 289< &V?Vl*

Qec|ol` hl IYXT Cg li|gijù` hlc hjyl÷e hlc IYXT ly

I|g`he V?29

 

A G2%/t  G ? <61 ylký` cg ktçajig hl clql`yrjlc Ie` cg li|gijù` hl hjyl÷e

       Qec|ol` hlc RAT Cg li|gijù` hl hjyl÷e hlc RAT ly

    ∮ 

Z lqgc|ç`hecg |yg`he Reczogxf hlyhl cg ie`qltyjù` hl 29 fgyxg 289<# lc qec|ol` edxl`jhe ly hl 72;6 C Lc iùhjke ly lc yjk|jl`xl= h&Q*%h&v* ? AG2 % &/tG* Q&2* ? 2 v&2* ? 29 v&a * ? 2894 tG ? /&n* - &&&iG P 4* - &iD** / &iI % ni** AG2 ? 87<; ) oec%y g?4 d?7 i?7 xlxgd ? 2< xlxgi ? 2 lry ? /4 % 9 iG2 ? 7;7;< ) oec%C

iG ? &iG2 - &7 / v** % &7 . &lry - v** iD ? &iG2 - &xlxgd / &&d % g* - &v**** % &7 . &lry - v** iI ? &iG2 - &xlxgi . &&i % g* - &v**** % &7 . &lry - v** n ? 2<< ni ? 2;6:;

Qec|ol` xexgc ? 7;<6 C . 72;6 C ? 4691 C

Xgc ieoe lyxgdg rtlqjyxe# lyxl xjre hl gttlkce `e yjtql hl o|ife   Gfetg yl re`htç rtjolte lc tlgixet RAT ylk|jhe hlc IYXT rgtg lqgc|gt w|l qec|ol` xexgc hl edxl`htïg hl |ygt lyxl gttlkce L` lyxl igye yl rtlxl`hl cektgt cg ie`qltyjù` hl 29 l` lc RAT z cclkgt fgyxg 289< ie` lc IYXT

Qec|ol` hlc RAT @|lqgol`xl yl |ygtç lc iùhjke hl Reczogxf rgtg lqgc|gt açijcol`xl cg j`xlktgc Cey cïojxly hl V ye` hl 2 g 29

v&2* ? 2 v&a * ? 29 tG ? /&n* - &&&iG P 4* - &iD** / &iI % ni** AG2 ? 87<; ) oec%y g?4 d?7 i?7 xlxgd ? 2< xlxgi ? 2 lry ? /4 % 9 iG2 ? 7;7;< ) oec%C iG ? &iG2 - &7 / v** % &7 . &lry - v** iD ? &iG2 - &xlxgd / &&d % g* - &v**** % &7 . &lry - v** iI ? &iG2 - &xlxgi . &&i % g* - &v**** % &7 . &lry - v** n ? 2<< ni ? 2;6:;

Lc qec|ol` rgtg cclkgt g cg ie`qltyjù` hl 29 ly hl 7479 C

Qec|ol` hl IYXT Cg li|gijù` hl hjyl÷e hlc IYXT gtg lyxl igye w|lhg hl cg yjk|jl`xl og`ltg=

  

Yjl`he V7 ? 29 z V4 ? 289< I|g`he V ? 289< cg ktçajig ogtig w|l lc qgcet hl A G2%/t  G ? 748 &grtevjoghgol`xl* Lqgc|g`he l` cg li|gijù` hl hjyl÷e

      Lc qec|ol` xexgc ly 7479 . 71;8 C ? 466; C

Yjl`he lyxl |` gttlkce gý` ol`ey ie`ql`jl`xl w|l lc g`xltjet.

Ie`ic|yje`ly z tlieol`hgije`ly Ieoe zg yl fgdïg ol`ije`ghe ie` g`xltjetjhgh# cgy ie`hjije`ly ùrxjogy rgtg lc rteilye ly xtgdgmgt g |`g xlorltgx|tg hl 422 ²I z 722 gxoùyaltgy hl rtlyjù` Gc xtgxgtyl hl |`g tlgiijù` gcxgol`xl lvexêtojig# i|gcw|jlt g|ol`xe hl cg xlorltgx|tg rteqeig w|l cg qlceijhgh z cg ie`qltyjù` hjyoj`|zg` htgoçxjigol`xl L` cg djdcjektgaïg yl y|kjltl xtgdgmgt hl 422 g 922 ²I# l` lyxl igye yl hlijhjù xtgdgmgt g 422 ²I @e yl xtgdgmg l` |` tlgixet ghjgdçxjie zg w|l lyxl `e rltojxjtïg cg cjdltgijù` hl igcet# z gc ylt o|z lvexêtojig cg tlgiijù`# cg xlorltgx|tg g|ol`xgtïg tçrjhgol`xl rteqeig`he cg aetogijù` hl y|drteh|ixey gyï ieoe |`g dgmg ie`qltyjù` Tlyrlixe gc gttlkce hl tlgixetly# zg yl ieol`xgdg cï`lgy g`xly# w|l lc tlgixet  gc ylt jyexêtojie z xtgxgtyl hl |` RAT# `e qgchtïg hl `ghg hjqjhjtce l` extey tlgixetly oçy rlw|l÷ey zg w|l lc qec|ol` rgtg gcig`}gt cg ie`qltyjù` hlylghg yltïg lvgixgol`xl lc ojyoe w|l |` yece RAT –ktg`hl‟. \ygt IYXT‚y xgoreie ly ie`ql`jl`xl r|ly ieoe zg yl hloeyxtù |yg`he cg ktçajig hl clql`yrjlc z olhjg`xl içci|cey# lc |ye hl lccey yece rteqeigtïg g|ol`xgt lc qec|ol` rgtg edxl`lt cg ojyog ie`qltyjù` Tlyrlixe gc jorgixe godjl`xgc> ieoe l` cg ogzetïg hl cey rteilyey l` cg j`h|yxtjg# ly j`lqjxgdcl ie`xgoj`gt lc godjl`xl# ce w|l yï yl r|lhl fgilt ly |` lya|lt}e rgtg xtgxgt hl oj`joj}gt ce oçy reyjdcl lyxl jorgixe O|ifg hl cg ie`xgoj`gijù` l` lyxl rteilye yl hldl gc |ye hl igchltgy z lw|jre w|l ei|rg ieod|yxjdcly aùyjcly# gyï ieoe lc |ye hl l`ltkïg lcêixtjig# w|l yl rehtïg rl`ygt `e rteqeig `j`k|`g ie`xgoj`gijù` hjtlixgol`xl# rlte yj ce fgil j`hjtlixgol`xl# zg w|l ie`xtjd|zl g cg lvrcexgijù` hl tli|tyey `gx|tgcly ieoe

r|lhl` ylt ieod|yxjdcly aùyjcly rgtg re`lt l` ogtifg cey kl`ltghetly lcêixtjiey# e lc jorgixe godjl`xgc w|l rteqeig cg ie`yxt|iijù` hl |`g rtlyg fjhtelcêixtjig Il`xtç`heyl ý`jigol`xl l` lc rteilye# cg ogzet ie`xgoj`gijù` yl hg gc edxl`lt lc kgy yl yï`xlyjy# w|l yl edxjl`l ret tlaetoghe e ret  evjhgijù` rgtijgc hl kgy `gx|tgc Lyxl kgy ie`xjl`l rlw|l÷gy rgtxïi|cgy hl g}|atl# ret ce xg`xe g`xly hl rgygt gc tlaetoghe# lc kgy `gx|tgc hldl rgygt ret  |` rteilye hl gdyetijù` rgtg w|jxgt lyxgy rgtxïi|cgy hl g}|atl# hl `e ylt gyï# lyxgy rgtxïi|cgy yltjg` lvrlhjhgy gc olhje godjl`xl# rteqeig`he |`g ktg` ie`xgoj`gijù`

Djdcjektgaïg  W|ïojig JJ 

Ygtg Gchgdl# Rlhte Gtgol`hjg Lhjxetjgc= Iecjf|l Rçkj`g= 7<7 Tlqjyxg –L`ltkïg g hldgxl‟

 G÷e 8# xeoe 7# @e 44 Ylrxjlodtl%Eix|dtl hl 422; Olxg`ec= ieod|yxjdcl hlc a|x|te  G|xet= Lh|gthe Dgttlxg ]l`xl`e Rçkj`gy= <4# <9 Og`|gc hl w|ïojig etkç`jig 

Fg`y Dlzlt# Meyê Dgtc|l`kg O|t# [ecakg`k [gcxlt  Lhjxetjgc Tlqltxê Hlijoe`eql`g lhjijù` Rçkj`gy= 74<# 741 W|ïojig y|yxl`xgdcl 

Meyê C|j} Ae`xly Oe`xljte Lhjxetjgc= \@C Rçkj`g= 18 Tlqjyxg –j`aetogijù` xli`ecùkjig‟ Xtg`yaetogijù` igxgcïxjig hlc kgy `gx|tgc. JJJ. Hltjqghey ie`ql`ije`gcly hlc kgy hl yï`xlyjy= goe`jgie z  olxg`ec.

Meyê J K|xjêttl} Etxj} Ojk|lc G Cgdethl 7::8 Rçkj`gy= 9<# 91# 96 Cey djeieod|yxjdcly 

Ogtiey Ogtxj` Lhjxetjgc= O|`hj/ Rtl`yg Ylk|`hg lhjijù` Rçkj`g= 989

Oêxehey hl cg j`h|yxtjg w|ïojig l` lyw|logy hl ac|me l` iecetly C|h{jk Ogzlt  Lhjxetjgc= Tlqltxê Rçkj`g= 6:# :2 W|ïojig etkç`jig dçyjig z grcjighg= hl cg oecêi|cg g cg j`h|yxtjg# Qec|ol` 7 Lh|gthe Rtjoe Zýaltg Lhjxetjgc Tlqltxê Rçkj`gy= 99;# 996

W|ïojig etkç`jig j`h|yxtjgc Ncg|y [ljyyltolc# Fg`y/Mótkl` Gtrl Lhjxetjgc= Tlqltxê Rçkj`gy= 92# 97# 94# 99 Olxfg`ec= Y|rrcz g`h hlog`h fxxr=%%{{{olxfg`ecetk%Olxfg`ec/Dgyjiy%Tlye|tily%OOYG/Kcedgc/Olxfg`ec/ Y|rrcz/g`h/Hlog`hgyrv

Xfl Olxfg`ec J`h|yxtz fxxr=%%{{{olxfg`ecetk%Olxfg`ec/Dgyjiy%Xfl/Olxfg`ec/J`h|yxtzgyrv Dgcg`}g ieoltijgc hl Oêvjie J@LKJ &dgcg`}g ieoltijgc hl rteh|ixey rlxtecltey# rçkj`g :* fxxr=%%{{{j`lkjkedov%rtehUyltq%ie`xl`jhey%lyrg`ec%dqj`lkj%rteh|ixey %ie`xj`|gy%lie`eojigy%lvxltjet%ol`y|gc%dio%diorha Edxl`ijù` hl Olxg`ec fxxr=%%{{{xlvxeyijl`xjajieyieo%w|jojig%olxg`ec%edxl`ije` Hgxey hl rteh|iijù` hl kgy `gx|tgc fxxry=%%{{{ijgkeq%cjdtgtz%r|dcjigxje`y%xfl/{etch/agixdeen% G nj`lxji yx|hz ea olxfg`ec j` g yc|ttz tlgixet |yj`k g I|E%]`E%Gc4E9 igxgczyx Xlyjy hl Fgogh Gdh|gc{gfgd Gc/ Gh{g`j Ogze 7::4 Lclol`xey hl J`kl`jgtïg hl cgy tlgiije`ly w|ïojigy F Yiexx Aekclt  I|gtxg z xltiltg Lhjijù` Lhjxetjgc Rlgtye` Rtl`xjil Fgcc Rtj`ijrjey lclol`xgcly hl cey rteilyey w|ïojiey Tjifgth O Alchlt  Xltiltg lhjijù` Lhjxetjgc Cjo|yg