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Rrj`iglfs mg Lge½fkaef fkaef mg Ciuamjs (Efp. 3) Figxf Fig xfkm kmgr gr Hal½ gkgz gkg z Geufea½ jk jk mgi ljlgk ljlgktj tj iakgfi iakgfi Rrj`i Rrj`iglf glf 3-00 Ug usf uk ejmj mg 12 pfrf maraoar nfeaf frra`f uk ffuhj mg fouf qug vagkg pjr uk tu`j njrazjktfi f rfz½jk jk mg 07 do/s. Gi ma½flgtrj flgtrj mgi ejmj gk tjmf su ijkoatum gs mg 62 el. Maenj ejmj mgsefrof gi fouf nfeaf if ftl½jscgrf jscgrf y, pjr ij tfktj, if prgsa½jk jk f if sfiamf gs if prgsa½jjk k ftljsc½graef graef ijefi. If macgrgkeaf mg gigvfea½jk jk gktrg ijs egktrjs mg if sfiamf y mg if gktrfmf mgi ejmj gs mg 57 el. Ug ejksamgrf qug gi pgsj mg gstg ejmj y mgi fouf qug gst½f gk ½gi gi gs mgsprgeaf`ig. Mgtgrlakg f) f ) if prgsa½jk jk lfkjl½ lfk jl½gtraef gtr aef gk gi egktrj mg if gktrfmf mgi ejmj y `) if cugrzf mg fkeifhg kgegsfraf pfrf sjstgkgr f maenj ejmj gk su iuofr. ]jlg gi cfetjr mg ejrrgeea½jk jk mgi ffuhj mg if efktamfm mg ljvalagktj ejlj 66,,25. ◣ Nap½ jtgsas 6 Gi ffuhj gs gstfeajkfraj g akejlprgsa`ig. 0 Ug mgsprgeaf gi pgsj mgi ejmj y mgi fouf gk ½gi. 5 Ug mgsprgeafk pgrmamfs pjr craeea½jk. jk. Fk½ fiasas sa s f) Ejlgkzfljs f pfrtar mg if geufea½jk jk mg @grkjuiia pfrf gkejktrfr if prgsa½jk jk lfk½jlgtraef jlgtraef gk if gktrfmf mgi tu`j. Ug tjlf if gktrfmf ejlj puktj 6 y if sfiamf ejlj puktj 0. S 60 S 00 R6 + φ + φoz 6 < R 0 + φ + φoz 0 0 0 mg fn½Ķ R6 < φo φozz0 dRff < (6222 (6222 do/ do/l5 )(1 )(1,,>6 l/s0 )(2 )(2,,57l) < 5, 5 ,=5 dR `) Rfrf gkejktrfr if cugrzf mg fkeifhg kgegsfraf pifktgfljs if geufea½jk mg ejksgrvfea½jk jk mgi ljlgktj iakgfi, gstf gs8 eugrpj + sup < ∐ C C ΰl ˑS ΰl ˑ S gkt sfi sustatuygkmj, j`tgkgljs Px + R6 F6 < ∐ Py < ΰ lS ˑ 0 6 ΰ lS ˑ 6 ∐ mjkmg ς (2 (2,,6 l)0 ςM 0 22?>7 >7 l0 < 2, 2 ,22? < = = 07do//s 07do l ˑ < 5, 5 ,6> l/s < S < (6 (6222 222 do/ do/l5 )(2 )(2,,22? 22?>7 >7 l0 ) φF F< pjr tfktj 6211 K Px < (5 (5 =5 =522 K/l0 )(2 )(2,,22?>7 22?>7 l0 ) + (6, (6,25)( 25)(07 07 do do//s)(5 s)(5,,6> l/s) < 62 Py < (6 (6,,25)( 25)(07 07 do do//s)(5 s)(5,,6> l/s) < >6, >6 ,1 K pjr uitalj u ½italj P < P + P < 653 653 K P 0 0 x ξ < 6>2 ◣ ∐ y tfk ∐ y 6 < 6=5 Px ◣ Rrj`iglf Rrj`i glf 3-0=A Wk enjrrj mg fouf njrazjktfi enjef ejktrf ukf pifef pifkf vgrtaefi f 52 ct/s y sg maspgrsf nfeaf ijs ifmjs gk gi pifkj vgrtaefi. Ua sg kgegsatf ukf cugrzf mg 572 i`c pfrf lfktgkgr if pifef ejktrf gi enjrrj mg fouf, mgtgrlakg gi ffuhj vjiul½ gtraej gtraej mg gstf uitalf. u ½ italf. 6 Gi ffuh ffuhjj gs gstf`ig gstf`ig g akejlprgsa`i akejlprgsa`ig. g. 0 Ug aokjrf if feea½jk jk mg if prgsa½jk jk ftljsc½ ftl jsc½graef gra ef yf qug fet½ uf uf gk tjmfs pfrtgs mgi vjiulgk vjiulgk mg ejktrji. 5 ]rfs enjefr tjmf gi fouf sg maspgrsf pgrpgkmaeuifr fi pfkj mg if pifef. jk jk mgi ljlgktj iakgfi, gstf gs8 Fk½ fiasas sa s Rifktgfljs if geufea½ Nap½ jtgsas jtgsas C < ΰlˑ S ΰlˑ S ∐ gkt sfi mg fn½Ķ, Ķ, tgkglj tgk gljss ∐ Cx < ΰ lS ˑ ∐ ∐← l ˑ < Cx S mjkmg sg ejksamgr½j ΰ < 6. Gi ffuhj vjiul½gtraej gtraej gs8 572 i`c i`c ˑ S < (30 (30,,=i`l =i`l//ct5 )( )(52 52 ct ct//s) Rrj`iglf Rrj`i glf 3-07 50 50,,0i`l ¿ ct ct//s0 6i`c 5 < 33,,20ct /s Ug usf uk ejmj rgmuetjr pfrf mgsvafr nfeaf frra`f gk uk ½ffkouij kouij ξ < =7 , rgspgetj mg su margeea½jk jk jraoakfi, uk ffuhj mg fouf qug vagkg pjr uk tu`j njrazjktfi f rfz½jk jk mg 52 do/s, qug fegigrf fi laslj taglpj. Gi ejmj mgsefrof gi fouf nfeaf if ftl½jscgrf. jscgrf. Gi frgf ½frgf mg if sgeea½jk jk trfksvgrsfi mgi ejmj gs mg 0 0 672el f if gk gktrf trfmf mf y mg 07 el f if sfiamf. If macgrgkeaf mg gigvfea½jk jk gktrg ijs egktrjs mg if sfiamf y mg if gk gktrfm trfmff gs mg =2 el. If lfsf mgi ejmj y mgi fouf gk ½gi gi gs mg 72 do. Mgtgrla Mgtgrlakg kg if cugrzf cugrzf mg fkeifhg kgegsfraf pfrf sjstgkgr gi ejmj gk su iuofr. ]jlg gi cfetjr mg ejrrgeea½jk j k mgi ffuhj mg if efktamfm mg ljvalagktj ejlj 6.25. ◣ Nap½ jtgsas 6 Gi ffuhj gs gstfeajkfraj g akejlprgsa`ig. 0 Ug mgsefrtf tjmf pgrmamf arrgvgrsa`ig. Fk½ fiasas sa s Rifktgljs if geufea½ jk jk mgi ljlgktj iakgfi C < ΰlˑ S ΰlˑ S ∐ gkt sfi 0 mg fn½Ķ Px + R6 F6 < ΰ lS ˑ 0 ejs(=7 ) ∐ ΰ lS ˑ 6 ◣ Py ∐ _ < ΰ lS ˑ 0 sak(=7 ) ◣ Rfrf rgsjivgr gstfs geufeajkgs mg`gljs gkejktrfr f R 6 , S 6 y S 0 . l ˑ 52do//s 52do < 00,,2 l/s < φF6 (6222 (62 22 do do//l5 )(2 )(2,,267l0 ) l ˑ 52do//s 52do S0 < 60,,2 l/s < < 60 φF0 (6222 (62 22 do/ do/l5 )(2 )(2,,2207l0 ) S6 < Rfrf R 6 pifktgfljs if geufea½jk jk mg @grkjuiia R6 + φ S 60 S0 < φ 0 + φoz 0 0 0 mg fn½Ķ R6 < φ S00 ∐ S60 0 + φoz 0 0 5 < (6222 (6222 do/ do/l ) (60 (60,,2 l/s) ∐ (0 (0,,2 l/s)0 0 0 + (1, (1,>6 l/s )(2 )(2,,= l) 10== Rf < ?5 10 Rjr tfktj, ◣ Px ∐ 0 ∐ 0 < (6 (6,,25)( 25)(52 52 do do/ /s)T(60 s)T(60,,2 l/s) ejs(=7 ejs(=7 ) 0,2 l/s\ (?510=K (?510=K//l )(2 )(2,,267l ) < Py < (1 (1,,>6 l/s0 )(7 )(722 do) + (6, (6,25)( 25)(52 52 do do//s)(60 s)(60,,2 l/s) sak(=7 sak(=7 ) < ?75 ?75 K ◣ ∐ 12>K Rjr uitalj u ½ italj P < P + P < 6 6>2 K P 0 0 x ξ < 6>2 ◣ ∐ y tfk ∐ 6 y Px < 6=2 ◣ Rrj`iglf Rrj`i glf 3-0? Ug fegigrf fouf pjr ukf `jquaiif nfstf 67 l/s y enjef ejktrf if supgrsteag pjstgrajr vgrtaefi mg uk efrrgt½jk jk qug sg gst½f ljvagkmj njrazjktfilgktg f ukf vgijeamfm ejkstfktg mg 7 l/s gk if margeea½jk jk mgi ffuhj. Gi ffuhjgkmggilfsf gs mg 07 pjstgrajr. do/s. Mgspu½ gMgtgrlakg s mgi enjqug, gi enjrrj f ouf sg gspfreg gk tjmfs margeeajkgs pifkjmgi mgfouf if supgrsteag f) gs if cugrzf qugmggsfouf kgegsfraf fpiaefr sj`rg ijs crgkjs mgi efrrgt½ jk jk pfrf alpgmar qug sg fegigrg. `) Ua sg usfrf gstf cugrzf pfrf ogkgrfr pjtgkeaf, gk vgz mg mgspgrmaeafrif gk ijs crgkjs, mgtgrlakg if efktamfm l½fxalf fxalf mg pjtgkeaf qug pugmg ogkgrfrsg. 5 Nap½ gssasRifktgfljs 6 Gi ffuhjifgs gstfeajkfraj g akejlprgsa`ig. geufea½ jk jk mgi ljlgktj iakgfi Fk½ fjiatsas sa C < ΰlˑ S ΰlˑ S r ∐ mjkmg Sr < S ∐ r gkt sfi UE , gstj gs S r < 67 S 67 l/s ∐ 7 l/s < 62 62 l/s C < ∐ΰ lS ˑ r ∐ 0722 K < (07do/ (07do/s) s)(6 (622 l/s) < 07 `) Gi trf`fhj gs8 ˑ < C ms < (072 (072 K)(7 K)(7 l/s) < 6, 6 ,07d_ _ mt Rrj`iglf Rrj`i glf 3-01A Wk enjrr enjrrjj mg fouf mg 622 ct5 /s sg gst½f ljvagkmj gk if margeea½jk jk x pjsatavf f 02 ct/s. Gi enjrrj enjef ejktrf uk `acurefmjr `acurefmjr gk rgpjsj, gk tfi lfkgrf qug if latfm mgi ffuhj sg mgsv½ mgsv½Ķf nfeaf frra`f gk =7 y if jtrf latfm sg maraog nfeaf f`fhj, y ijs mjs ffuhjs tagkgk ukf vgijeamfm stkfi mg 02 ct/s. Mgsefrtg ijs gcgetjs mg if orfvatfea½jk, jk, mgtgrlakg ifs ejlpjkgktgs x y z mg if cugrzf kgegsfraf pfrf lfktgkgr gi `acurefmjr gk su iuofr ejktrf if cugrzf mgi fouf. ◣ Nap½ jtgsas jk. jk. 5 6 Gi ffuhj gs gstfeajkfraj g akejlprgsa`ig. 0 Ug mgsefrtfk ijs gcgetjs mg if orfvatfea½ Gi ffuhj gst½f gxpugstj f if ftl½jscgrf jscgrf y if prgsa½jk jk mgi ffuamj gs if ftljsc½graef. graef. Fk½ fiasas sa s Rifktgfljs if geufea½ jk jk mgi ljlgktj iakgfi C < ΰlˑ S ΰlˑ S ∐ gkt sfi sustatuygkmj8 ˑ S ejs ξ ∐ ΰ lS ˑ Px < 0ΰ l 0 Pz < ΰ lS ˑ sak ξ ∐ ΰ lS ˑ sak ξ = 0=22 i` i`l l/s. Rjr tfktj8 mjkm mjkmgg l ˑ < φ Sˑ < (30, (30,=i`l =i`l/ /ct5 )( )(622 622 ct5 /s) < 3 0= Px < (30=2 i`l i`l/s) s)(0 (022 ct ct//s)(ejs(=7 ) ∐ 6) ◣ 6i`c 50, 50,0i`l ¿ ct ct//s0 < ∐6657i`c Rrj`iglf Rrj`i glf 3-56 Wk enjrrj mg fouf njrazjktfi mg 7 el mg ma½flgtrj flgtrj ejk vgijeamfm mg 6> l/s enjef kjrlfilgktg ejktrf ejkt rf ukf pifef vgrtaefi vgrtaefi euyf lfsf gs mg 6 222 do. Gstf pifef sg sjstagkg gk ukf v½ v½Ķf efsa sak craeea½ jk jk y gst½f akaeafilgk akaeafilgktg tg gk rgpjsj. Eufkmj gi enjrrj enjrrj enjef ejktrf if pifef, ½gstf gstf glpagzf f ljvgrsg ljvgrsg gk if margeea½ jk jk mgi enjrrj. Gi fouf saglprg sg maspgrsf gk gi pifkj mg if pifef qug sg rgtrjegmg. Mgtgrlakg f) if fegigrfea½jjk k mg if pifef eufkmj gi enjrrj enjef pjr pralgrf vgz ejktrf giif (taglpj < 2), `) gi taglpj qug pfsfr½f pfrf qug if pifef fiefkeg ukf vgijeamfm mg 1 l/s y e) if vgijeamfm mg gsf pifef 02 s mgspu½ mgspu½gs gs qug gi enjrrj enjef pjr pralgrf pralgrf vgz ejktrf ejktrf giif. Uupjkof qug if vgijeamfm vgijeamfm mgi enjrrj enjrrj gk rgifea½jk jk ejk if pifef sg lfktagkg ejkstfktg. gcgetjs mg if prgsa½ jjk k fi sgr sg r ½ggstf st f Nap½ jtgsas 6 Gi ffuhj gs gstfeajkfraj g akejlprgsa`ig. 0 Ug aokjrfk ijs gcgetjs if ftljsc½graef graef qug fet½uf uf gk tjmj gi vjiulgk mg ejktrji. 5 Gi fouf sg maspgrsf gk margeeajkgs kjrlfigs fi pifkj mg akeamgkeaf. jjk k mgi ljlgktj iakgfi, if eufi kjs frrjhf8 Fk½ fiasas sa s Fpiaefljs if geufea½ ∐ Px < ∐ lS ˑ mjkmg 0 l ˑ < φS F < (6222 (6222 do/ do/s) s)(6> (6> l/s) ς(2,(2,27l) = do//s < 57, 57 ,5 do f) Rjr tfktj, tgkgljs qug if cugrzf y if fegigrfea½jk jk sjk8 3577 K < lfx Px < (57, (57,5 do/ do/s) s)(6 (6>> l/s) < 35 3577 do ¿ l/s0 35 357l//s0 < 22,,357l fx < 6222do `) Uf`gljs qug f x < ∃S /∃t, pjr ij qug ∃t < e) Mg cjrlf salaifr 1 l/s < 6= 6=,,0 s 2,357l 357l//s0 ∃S < (2 (2,,357l 357l//s0 )( )(02 02 s) < 60, 60 ,? l/s Rrj`iglf Rrj`i glf 3-55 Orfkmgs tur`akfs mg vagktj qug sg ejksaougk gk gi lgrefmj tagkgk ma½flgtrjs flgtr js mgi e½Ķreuij qug mgsera`gk ifs puktfs mg ijs ½fif`gs fif`gs tfk orfkmgs ejlj 622 l y ogkgrfk l½fs fs mg 5 L_ mg pjtgkea p jtgkeaff gi½getraef getrae f gk ifs ejkmaeajkgs mg puktj mg masgk̇j. masg˙ kj. Ejksamgrg ukf tur`akf mg vagktj ejk uk ma½flgtrj flg trj mgi e½Ķreuij Ķre uij qug mgsera`gk ifs puktfs mg ifs fspfs mg 12 l suhgtf f vagktjs gk rgpjsj mg 07 dl/n. Ua if gsteagkeaf ejl`akfmf mgi tur`jogkgrfmjr mg if tur`akf mg vagktj gs mg 50 pjr eagktj, mgtgrlakg f) if pjtgkeaf ogkgrfmf pjr if tur`akf y `) if cugrzf njrazjktfi ghgreamf pjr gi vagktj sj`rg gi l½fstai fstai mg sjpjrtg mg if tur`akf. ]jlg if mgksamfm mgi farg ejlj 6.07 do/l5 y mgsefrtg ijs gcgetjs mg if craeea½jk. Nap½ jtgsas 6 Gi ffuhj gs gstfeajkfraj g akejlprgsa`ig. 0 Ug mgsprgeafk pgrmamfs kj rgifeajkfmfs ejk gi tur`jogkgrfmjr. tur`jogkgrfmjr. 7 gkgr groo½Ķf l½fxalf fxalf maspjka`ig maspj ka`ig gs if gkgro½Ķf Ķf eak½gtaef gtaef mgi vagktj Fk½ fiasas sa s If gk 0 ς(12l) 6222l 6 n 77005do//s l ˑ < φS F < (6 (6,,07do 07do/ /l )( )(07 07 dl/ dl/n) < 77005do = 6 dl 5322s S (3 (3, , 1= l / s) ˑ 5 0 _g < l ˑ 0 0 < (77005do/ (77005do/s) 0 < 6, 6 ,55L_ f) Fs½Ķ, Ķ, if pjtgkeaf ogkgrfmf pjr p jr if tur`akf gs8 ˑ < ο tur _ ˑ g < =03 _ =03 d_ `) Rfrf gkejktrfr if cugrzf ghgreamf sj`rg gi l½fstai fstai pifktgfljs if geufea½jk jk mgi ljlgktj iakgfi C < ΰlˑ S ΰlˑ S ∐ gkt sfi mg mjkmg sg tagkg Px < lS ˑ 0 ∐ lS ˑ 6 ∐ ∐← Px < l ˑ (S6 ∐ S0 ) mjkmg S 0 sg gkeugktrf pjr p jr `fifkeg mg gkgro½ gkgro½Ķf ˑ _ < 63 63,,= l0 /s0 g0 < g6 ∐ l ˑ S0 < 0(63 0(63,,= l0 /s0) < 7, 7 ,?5 l/s fs½Ķ Px < (77 (77 005 005 do do//s)(3 s)(3,,1= l/s ∐ 7,?5 l/s) < 33, 33 ,> dK Rrj`iglf Rrj`i glf 3-51A Wk vgktaifmjr ejk fspfs mg 0= ak mg ma½flgtrj flgtrj lugvg 0 222 ecl (pags e½ u`aejs u`aejs pjr lakutj, eu`ae cggt pgr lakutg) mg farg f ?2 C, f kavgi mgi lfr. Mgtgrlakg f) if cugrzf kgegsfraf pfrf sjstgkgr gi vgktaifmjr y `) if gktrfmf mg pjtgkeaf p jtgkeaf l½Ķkalf Ķkalf kgegsfraf pfrf gstg u uitalj. ½ italj. Giahf gi vjiulgk mg ejktrji susteagktglgktg orfkmg pfrf ejktgkgr gi vgktaifmjr y qug if prgsa½jk jk lfkjl½ lf kjl½gtraef gtraef y if vgijeamfm vgijea mfm mgi mg i farg far g gk gi ifmj mg if gktrfmf gktrfmf sgfk egrj. Uupjkof qug gi farg sg fprjxalf fprjxalf fi vgktaifmjr vgktaifmjr f trfv½ trfv½gs gs mg uk ½ffrgf rgf orfkmg, ejk vgijeamfm mgsprgeaf`ig, y qug gi farg sfig mg gsg vgktaifmjr ejk ukf vgijeamfm ukacjrlg, f if prgsa½jk jk ftljsc½graef, graef, f trfv½ gs gs mg uk eaiakmrj alfoakfraj euyj ma½flgtrj flgtrj gs gi ma½flgtrj flgtrj mg ifs fspfs mgi prjpaj vgktaifmjr. ◣ 6 Gi ffuhj gs gstfeajkfraj g akejlprgsa`ig. 0 Ug tjlf uk vjiulgk mg ejktrji mg lfkgrf tfi qug ifs prgsajkgs f if gktr gktrfmf fmf y sfiamf sgfk if ftljsc½ ftljsc½graef graef y if vgijeamfm f if gktrfmf gktrfmf sgf egrj. 5 Nap½ jtgsas Ug aokjrfk tjmfs pgrmamfs arrgvgrsa`igs. 3 Rrjpagmfmgs If mgksamfm mgi farg f 6 ftl y ?2 C gs 2, 2,2?=> 2?=>11 i`l i`l//ct5 . Fk½ fiasas sa s f) Rfrf gkejktrfr gkejktrfr if cugrzf ghgreamf ghgreamf sj`rg gi l½ fstai fstai pifktgljs if geufea½jk jk mgi ljlgktj iakgfi ◣ C < ΰlˑ S ΰlˑ S ∐ gkt sfi mg mjkmg Px < lS ˑ 0 ∐ lS ˑ 6 ∐← S Px < l ˑ (S0 ∐ 6) mjkmg Sˑ =Sˑ =(0222 ct5 /lak) =(0222 < < S0 < F ςM 0 ς (0=/ (0=/60ct)0 6lak ct//s < 62, 62 ,3 ct 32 s 6lak l ˑ < φ Sˑ < (2 (2,,2?=> 2?=>11 i`l/ i`l/ct5 )(0 )(0222 222 ct5/lak) 32 s < 00,,72i`l 72i`l//s pjr tfktj 6i`c Px < (0 (0,,72i`l 72i`l//s)(62 s)(62,,3 ct ct//s) 50 50,,0i`l ¿ ct ct//s0 < 22,,>05 i` i`cc `) Rfrf gkejktrfr if pjtgkeaf l½Ķkalf kgegsfraf pifktgfljs if geufea½ jjk k mg gkgro gkgro½½Ķf, mg mjkmg sg tagkg S00 6 ˑ (0,,72i`l 72i`l//s)(62 s)(62,,3 ct ct//s)0 _vgkt < l ˑ < (0 0 0 6@tu 6@tu//i`l 0725?ct0/s0 ? < 2,2273 227366 @tu/ @tu/s < 77,,10 _