Calculo de Coeficiente de Friccion

August 18, 2022 | Author: Anonymous | Category: N/A
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4 .:

  _årfefk pbr jreiieùc gc gl jlunb lk`eckr lk`eckr 899

4.7

GIWKIEÙC FG FKXIU

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f g t p à r f e à k  ^ *  fgjÀ"ÀÙ V V    fg gcgrmàk gc gl ses,g`k ses,g `k ' Wck ib`pbcgctg t u hhllr j k V v l b s ' E V V    jrÀIf  jrÀIfÙc Ùc g " f " WÀf? WÀf? qWg qWg IÀr ÀrI IWlk' lk' _krk gl iks i ks¿¿ * 3 "«*3 -   rglkieùc fg W   l c ― •. “ prbpbri,bckl k lk ikrmk fg vglbiefkf fgl jlunb jlunb y k lk ib`b lk gi giuk ukiieùcSf ùcSfgg Fkri Fkriyy GIWKIEÙC FG FKXIU _KXK IKLIWLKX LK _ÅXFEFK

S S S IB IBrrÀg"tg tg'' S “ gT_rgYk “ S ,  L v8  L 0 j T F T Vm  

`ktg`ëteik Dkmgc-_besguellg> 98reLv

GI W KI EÙ C F G

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DKMGC-_BEYGWELLG

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(4-6)

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Lbs pkrë`gtrbs qug ecvbluirk sbc lks prbpegfkfgs fgl jluefb gc iukctb k vesibsefkf y  p  pgs gs b gs pg ià iàje jeib ib , lks ik rk rkit itgr gràst àstei eiks ks mg b` åtrei åt reiks ks fg lbc metuf metu f y feë` fe ë` gtrb gtr b fg lk tuh tuhgrà gràk, k, y lk fecë`eik fgl jlunb ikrkitgrezkfk pbr lk vglbiefkf prb`gfeb. Lk giukieùc fg Dkmgc_besguellg dk sefb vgrejeikfk `uidks vgigs gc jbr`k gxpgre`gctkl. K pkrter fg lk giuk ieùc (4-6) ustgf fghg bhsgrvkr qug lk pårfefk fg gcgrmàk gc gl jlunb lk`eckr gs ecfg  p  pgc gc fe fegc gc tg fg lks ib c fe feie iebb cg s fg lk su supg pg rjeie rje iegg fg lk tuhg tu hgràk ràk.. Yb Ybcc lks på pårfe rfefk fkss pb r jreii jre iieùc eùc vesibsk gc gl ectgrebr fgl jluefb lks qug mbhegrckc lk `kmcetuf fg lk pårfefk fg gcgrmàk. Lk g iukieùc fg D kmgc-_besguellg gs vëlefk sùlb pkrk gl jlunb jlunb lk`eckr (CX <  8???). Yec g`hkrmb, sg fenb ibc kctgrebrefkf qug tk`heåc pbfàk uskrsg lk giukieùc fg Fkriy (giukieùc 4-9) pkrk ikliulkr lk pårfefk pbr jreiieùc pkrk gl jlunb lk`eckr. Ye emuklk`bs lks fbs rglkiebcgs pkrk d L, pbfg`bs fgspgnkr gl jkitbr fg jreiieùc>  L v8 9 8 rn rnL Lv  j    T ‖ T ‖ 0   ------ ‖   F 8m y[ 8 R 98e)Lv  F8m R :6r)m :6r)m   j ~

y F 8  T  L v 8

v¿ y

 

896

Ikpàtulb 4 Cþ`grb fg Xgycblfs, jlunb lk`eckr, jlunb turhulgctb y pårfefks fg gcgrm'. Ib`b p 0  y / m ,   bhtgcg`bs : 6  t n

Kl cþ`grb fg Xgycblfs üg lg fgjecg ib`b  C  r   0 vFp/r¡.   _br tkctb, tgcg`bs R

rr-''Z

JKIVBX JKIVBX FG JXEIIEÙC _KXK GL JLWNB LK@ECKX 

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(4~7|

Gc lk pårfefkfgfgDkmgc-_besguellg, gcgrmàk fghefb k lk jreiieùc gc g\ jlunb lk`eckr  pugfg   pugfg ikliel lkrsgrgsu`gc, ibc lk giukieùc  9 8 r t L v dL 0  ‖ Z

 yF  y F 8

b ibc lk giukieùc fg Fkriy, ; T ‖  v8 dL 0 j x  T ‖  L

N

F

8m

gc lk lk qug qug / 0 :6 / C X. ▫

_XBHLG@K @BFGLB

4.6 4. 6

Ybluieùc 

Fgtgr` ecg lk pårfefk pårf efk fg gcgrmàk gcgr màk se jluyg mleigrec ml eigreckk k 87 ¿I pbr uc tuhb fg ;7? `` fg feë`g trb y 9? ` fg lbcmetuf, k uck vglbiefkf prb`gfeb fg 6.? `/s. Gc pre`gr lumkr, dky qug fgtgr`eckr se gl jlunb gs lk`eckr b turhulgctb pbr `gfeb fg lk gvk lukieùc fgl cþ`grb fg Xgycblfs> v Fp



Ibc kyufk fgl kpåcfeig H, gcibctrk`bs qug pkrk lk mleigreck k 87 ¿I  p 0 ;874 am /` 9 r¡  0 5.:? T ;?-; _k*s

Gctbcigs, tgcg`bs (6.?T?. (6.?T?. .7T;874 ) R S 5.:? T ;?" ;?" ; Fghefb k qug  C   rr   < 8???, gl jlunb gs lk`eckr. Ibc lk giukieùc fg Fkriy, bhtgcg`bs  F

8m  

:6 :6  Û* 0 =4: =4 : 0 9?

', e 0 k b 4 l x S

(6.?)8

x S

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Bhsgrvg qug gxprgsk`bs tbfbs lbs tår`ecbs fg ikfk giukieùc gc lks ucefkfgs fgl YE _br lkcàb, lks ucefkfgs rgsultkctgs fg K/ sbc ` b C*`/C. Gstb semcejeik qug sg pegrfg ;- C*` fg gc gcgr grmà màkk pb pbrr ik fk cg cgw w tbc tb c fg mlei ml eigr grec eck, k, ` eg egct ctrk rkss ie ieri riul ulkk k lb lkrmb lkrm b fg lbs 9? ` fg fg 'k tuhgràk. ?

 

4 ' =

  _årfefk fg jreiie:c ℨ gl jlunb turhulgc turhulgctb tb

897

4 .= Iukcfb dky jlunb turhulgctb gc tuhgràks gs _ÅXFEFK FG  FG    pk rk ik li liul ulkr kr lk cårfeDk cårfeD k , ibcv ib cvgc gcegc egctg tg usk uskrr lk giu kieùc kie ùc fg Fkri Fkriyy JXEIIEÙC GC GL  GL   y vkràk gc S   * lk G; turh ulg" —¿ gs ikùteib JLWNB VWXHWLGCVB rgiu rrer k lbs lbs fktbs gxpgre`gctklgs" S Sk^BcgY, pkrk fgtgr`eckr gl vklbr f g/ f gh g ` b s tefkfgs kfe` gcs ebck lgsS V` V;? V;? gl cþ`grb kfl`gcsebckl/fg pgc fg fg btrk btrkss fbs ikcikcr u m b s e f k f r g l k t e v k gs l k ' r g d r ' k -*  :y c¿ lfs y lk rum ¿sefkf rglktevk fg lk tuhgràk. Lk su pkrgf g (l (lgtrk gtrk gregpk gregpk ' .-e‐; .-e‐; % lk`gtrb lk`gtrb fg lk tuhgràk tuhgràk  F  k lk rumbsefkf prb`gfeb fg rumbsefk rumbs efkff fg lk bkrgD D S_Y S_Y* ¿ jemu jemurk rk 4,7 4,7 el elus ustr trk`b k`bss (gc (gc jbr`k jbr`k gxkm gxkmgr grkf kfk) k) lk lk supgrjeieg Lk ibcD ibcD'' à " S I?`? I?`? ,k k,turk k,turk fg —¿ Y _À _ÀI I?Y fg lk lkss ecgmulkrefkfg. fg S fg q u g Y ë d g i d b S _* ~ +  y

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Fgspgng klmghrkeik`gctg pkrk  p a . Lk giukieùc gs _k   0

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(4-:)

²Iuël gs gl vklbr fg zm ‖   zz k2 Gcibctrk`bs qug zH ‖zK 0 +8; ` pbrqug gl puctb puctb H gstë gstë `ës `ës glgvkfb glgvkfb qug qug ggll puctb K. Gstb cbs llgvk k dL,  lk pårfefk fg gcgrmàk fghefb k lk jreiieùc gctrg K y H. ²Iuël gs gl pre`gr pksb2 Gl pre`gr pksb gs lk gvklukieùc fgl cþ`grb fg Xgycblfs. Fghg fgtgr`eckr gl tepb fg jlunb, lk`eckr b turhulgctb. Kctgs fg vgr gl pkcgl semuegctg, tgr`ecg gl iëliulb fgl cþ`grb fg Xgycblfs.

Gl vklbr ibrrgitb gs  C   rr   0 5.76 gcibctrkrlb>

T

 C   rr  

;?6. K ibctecukieùc prgsgctk`bs lk `kcgrk fg 0 vFp/rn

_krk uc tuhb fg 7? ``,  F   0 ?.?7? ` y  K  0 ;.5:9 x ;?-9 `8. Gctbcigs, tgcg`bs [ 0  (;;?L/`ec) /

; `9/ `9---/s   --  \ 0 ;.49 x ;? 9 `9S s \ :? ??? L/` ec/

;.49 x ;?R9`9/s ;?R9 `9/s , [   ---   ?.598 `/s v 0 ‖ -------------------------  -- K  ;.5:9 T E ?-9 `8 _krk gl hgcigcb k 7? ¿I ibc mrkvgfkf gspgiàjeik fg ?.4:, gcibctrk`bs  p   0 (?.4: )???? am/`9) am/`9) 0 4:?am /`9 ▯ q 0  6.8

T

;? ;?RR 6 _k*s

(fgl kpåcfeig kpåc feig F)

Gctbcigs, tgcg`bs  R (? (?.59 .598T 8T?.? ?.? 7? 7?)S: )S:?) ?) R S 6.8 T ;?-6

x Ejjl

_br tkctb, gl jlunb gs turhulgctb. ²Iuël rglkieùc fghg g`plgkrsg pkrk ikliulkr /e²2 _krk uc jlunb turhulgctb fghg uskrsg lk giukieùc fg Fkriy>  L   j 8  dL 0 j    x ‖ x ‖   F 8m

Yg cgigsetk gl vklbr  F/g  pkrk utelezkr gl fekmrk`k fg @bbfy y gcibctrkr gl vklbr fg/. Lk rumbsefkf fg uc tuhb fg plësteib gstë fkfk gc lk tkhlk 4.8, y gs 9.?

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868

Ikpàtulb 4

Cþ`grb fg Xgycblfs, jlunb lk`eckr, jlunb turhulgctb y pårfefks fg gcgrm'-

Kdbrk bhsgrvg gc gl fekmrk` k fg @bbfy qug ib`b gl vklbr fg F /g gs `uy mrkc mrkcfg fg lk lkss vks ibcvgrmgc dkiek lk fg tuhgràks lesq,s.  _br tkctb, pkrk gl vklbr fg  C  CX X 0   5.76 x eq6  j    0 ?.?;4 gc feidk iurvk. Ibc gstb ibcilue`bs gl iëliulb fg dL. Gl vklbr ibrrgitb gs d ² 0 9.49 `.  L

v ; 

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8m 

86? ?.?7?

(?.598) 8(5.4;)

dr   0 / T  ‖ T  ‖ 0 ?.? ?.?;4 ;4 T -------   T ----------- `

d e 0  9.49 `

Ye rgmrgsk`bs k lk giukieùc (4-:) pbfg`bs ikliulkr  p K. Fghg tgcgrsg  p K  0 =75 a_k, ib`b semug> _k   0 _ h   + 

_k  

 ^K) K) + d LN =Q(^h ~  ^

(?.4:)(5.4; aC) 0 77? a_k + -------S   ------- -(8 ;` + 9.49 9.49 `) `

 p a   0 77? a_k + 8?5 aC/`8 0 77? a_k + 8?5 a_k  _ k  

0  =75 a_k

4. 4.4 4

GIWKIEBCGY _KX _KXK K GL GL   JKIVBX FG JXEIIEÙC

Gl fekmrk`k fg @bbfy fg lk jemurk 4.: gs uc `gfeb gxkitb y ibcvgcegctg, qug hkstk pkrk  pkrk  fgtgr`eckr gl vklbr fgl jkitbr fg jreiieùc kl rgsblvgr prbhlg`ks ibc iëliulbs `kcuklgs. Yec  Yec  g`hkrmb, se lbs iëliulbs dkc fg sgr kutb`ëteibs pkrk llgmkr k lk sbluieùc gc uck ib`pu tkfbrk b ikliulkfbrk prbmrk`khlg, cgigsetk`bs giukiebcgs pkrk gl jkitbr fg jreiieùc. Lks giukiebcgs qug utelezù @bbfy gc su bhrk sbc lk hksg fgl gcjbqug ib`putkieb-  ib`putkieb-   ckl.* _grb gsks giukiebcgs sbc gcmbrrbsks y rgquegrgc uc gcjbqug etgrktevb. K ibctecuk ieùc prgsgctk`bs fbs giukiebcgs qug pgr`etgc bhtgcgr lk sbluieùc fergitk pkrk gl jkitbr  jkitbr   fg jreiieùc. Wck iuhrg gl jlunb lk`eckr y lk btrk sg g`plgk gc gl turhulgctb.  zbck ck ffgg jlunb lk lk` `eckr  eckr , pkrk vklbrgs pbr fghknb fg 8?? ?, / sg bhtegc Gc lk  zb bhtegcgg fg fg lk  giukieùc (4-7), / 0

J KI V B X F G J X EI I EB C _KX K

b

GL JLWNB LK@ECKX

 @ / C  r 

Gstk rglkieùc, fgskrrbllkfk gc lk sgiieùc 4-7, kpkrgig gc gl fekmrk`k fg @bbfy ib`b  ib`b   làcgk rgitk gc gl lkfb ezquegrfb fg lk mrëjeik. _br supugstb, pkrk cþ`grbs fg Xgycblfs gctrg 8??? y 6???, gl jlunb gstë gc gl  gl   rkcmb iràteib y gs e`pbsehlg fg prgfgier gl vklbr fg/. Lk giukieùc semuegctg, qug pgr`etg gl iëliulb fergitb fgl vklbr fgl jkitbr fg jrei ieùc pkrk jlunb turhulgctb, lk fgskrrbllkrbc _. A. Ywk`gg y K . A. Nkec, y sg `gciebck gc lk rgjgrgciek cþ`grb 9>

r 'v

JKI IV V B X F G J X EI EI I EÙ EÙ C _ K X K

?.87

/ 0

GL JLWNB VWXHWLGCVB

lbm

;

,9.= (F/g)

(4-=) +

7.=6'  C e 5 -

Zkrebs ecvgstemkfbrgs llgvkrbc k ikhb trkhknbs pebcgrbs pkrk fgskrrbllkr lks giukiebcgs1 lbs `ës cb  hlgs  hl gs jug rbc rb c I. j\ I blgh bl gh rb ba , L. _r kc ft ftl,l, D. Xb us g, V. vkc Ak r` kc y N. Ce au rkf sg sg,, iuy bs krtàiulbs krtàiulbs `gciebckc gc lk hehlebmrkjàk fg lk rgjgrgciek cþ`grb 8 .

4.5

 

Jùr`ulk fg fg Dkzgc-] ellek` s pk pkrk rk gl jlunb fg kmuk 869

Lk giukieù c (4-=) prbfu ig vklbrgs fg / qug gstëc ▯+▯; ?%   fgctrb Dpe rglkte rglktevk vk F /«. fg ,? ? k ; x ,b — y pkrk pkrk cþ`grbs cþ`grbs * £ £ £ £ £   S gs vertukl`gctg tbfk lk zbck turhulgctk fgl fekmrk`k fg @bbfy. @bbfy.





x

V

Å 2, '

Xgsu`gc

_krk ikliulkr gl vklbr fgl jkitbr fg jreiieùc /iukcfb sg ibcbig gl cþ`grb fg Xgycblfs y lk rumbsefkf rglktevk, sg g`plgk lk giukieùc (4-7) pkrk gl jlunb lk`eckr, y lk giukieùc (4-=) pkrk gl jlunb turhulgctb.

_ X BH BH L G @ K @ B F G L B 4 .5 .5

Ikliulg gl vklbr fgl jkitbr fg jreiieùc se gl cþ`grb fg Xgycblfs pkrk gl jlunb gs fg E T E ?7 y lk rumbsefkf rglktevk gs emukl k 8???.

Ybluieùc 

Ib`b gstb sg gciugctrk gc lk zbck turhulgctk, g`plgk`bs lk giukieùc (4-=), ?.87

/ lbm

; 7.=6 + 9.=(8???) (e x ;?7 ;?7) ?.5

/ 0 ?.?8 ?.?8?6 ?6

Gstg vklbr gstë `uy igrik fgl qug sg lgg gc lk jemurk 4.:.

4.5

Lk giukieùc fg Fkriy prgsgctkfk gc gstg ikpàtulb pkrk ikliulkr lk pårfefk fg gcgrmàk fg

ei ieùc ùc gs kp leik le ik h lg pk pkrk rk iu kl qu eg r jlue jl ue fb cg cgw w tb cekc ce kc b. _k _krk rk gl ik sb fg jlun jl unbb J Ù X @ W L K F G D K ^ G C -  -    he fb k lk jr eiie ]ELLEK@Y _KXK GL  GL   fg kmuk gc sestg`ks fg tuhgràk gs ibcvgcegctg uc gcjbqug kltgrcktevb. L k j jùù r ` u lk f g D k zg c- ] elellelek` k` s  gs uck fg lks `ës pbpulkrgs pkrk gl fesgûb y kcë J L W NB F G K M W K

leses fg sestg`ks defrëuleibs. Yu usb sg le`etk kl jlunb fg kmuk gc tuhgràks ibc feë`g trbs `kybrgs fg 8.? pulm y `gcbrgs fg :.? pegs. Lk vglbiefkf fgl jlunb cb fghg gxigfgr lbs ;?.? pegs/s. Kse`es`b, gstë glkhbrkfk pkrk kmuk k :? ¿J. Yu g`plgb ibc tg`pgrk turks `uidb `ës hknks b kltks biksebckràk iegrtb grrbr. Lk jùr`ulk fg Dkzgc-]ellek`s gs gspgiàjeik gc iukctb k lks ucefkfgs. Gc gl ses tg`k fg ucefkfgs trkfeiebckl fg Gstkfbs Wcefbs kfbptk lk jbr`k semuegctg> v

JBX@WLK FG DK^GC-]ELLEK@Y

B

GC WCEFKFGY VXKFEIEBCKLGY F G GYV KF B Y W C EF B Y

 R    ; -9 S / S  c ?.:9r ?.76 ?.76 0   ;.98I/2k Y

( 4- 4 )

fbcfg v 

Zglbiefkf prb`gfeb fgl jlunb (pegs/s)

Id

Ibgjeiegctg fg Dkzgc-]ellek`s Dkzgc-]ellek`s (kfe`gcsebckl) (kfe`gcsebckl)

 X

Xkfeb defrëuleib fgl ibcfuitb fg jlunb (pegs) Xglkieùc dL/L > pårfefk fg gcgrmàk/lbcmetuf fgl ibcfuitb (pegs/pegs)

s

Gl usb fgl rkfeb defrëuleib gc lk jùr`ulk pgr`etg su kpleikieùc k sgiiebcgs cb ieriulkrgs y tk`heåc k ieriulkrgs. _krk lks sgiiebcgs ieriulkrgs sg g`plgk  X   0  FEK.  Gstb lb gstu fekrg`bs gc gl ikpàtulb 5. Gl ibgjeiegctg I d  sùlb fgpgcfg fg lk ibcfeieùc fg lk supgrjeieg fg lk tuhgràk b ibcfuitb. Lk tkhlk 4.9 prbpbriebck vklbrgs qug sbc ib`ucgs. Bhsgrvg qug klmucbs fg gllbs sbc fgsiretbs ib`b tuhbs cugvbs y le`pebs, `egctrks qug gl vklbr fg fesgûb tb`k gc iugctk lk kiu`ulkieùc fg fgpùsetbs gc lks supgrjeiegs ectgrebrgs fg lk tuhgràk fgs 

866

Ikpàtulb 4

Cþ`grb fg Xgycblfs, jlunb lk`eckr, jlunb turhulgctb y pårfefks fg gc ;. Fgtg r` eckr gl tk`kûb fg tuhgràk qug sg rgquegrg pkrk ibcfuier uc jlunb vblu`åtreib fkfb ibc uck pårfefk fg gcgrmàk le`etkfk k iegrtb vklbr gspgiejeikfb. 8. Bh tgcgr lk pårfefk fg gcgrmàk pkrk uc jlunb vblu`å treib fkfb k trkvås fg uck uck tuhgràk tuhgràk ibcbiegcfb su tk`kûb y lbcmetuf. Lk tkhlk 4.6 prgsgctk vkreks jbr`ks qug kfbptk lk jùr`ulk fg Dkzgc-]ellek`s y qug jkieletkc feidbs iëliulbs.

VKHLK 4.6 Jbr`ks kltgrcktevks fg lk jùr`ulk Dk/.ic-]àllek`s.

Wcefkfgs trkfeiebcklgs fg Gstkfbs Wcefbs

Wcefkfgs fgl YE

v   0 ;.98I/, /2¿ :\v¿ 76 76

v 0  ?.4 7I/,/2 7I/ ,/2¿:9 ¿:9s?76 s?76

[ 0  ;98 K I dX þ(,9s?@ 

?.:9 R ?.76 ?.76 [ 0 B.Y7KIdX'3?es' 

dr   0  L

[

 \9  \ 9 8 K I dX?dX?-:9. d— :9.  8 9 ; [ ?.94?

;.478

d, 0 L

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?.47 KI dX¿-: dX¿-:A  d—   A   9.75 [ ?.94?

;.478

 F 0

 F 0

 ÀI d s?-76. s?-76.  Cbtk>  lks ucefkfgs fghgc sgr ibcsestgctgs>

?.76

v  gc pegs/s

v  gc `/s

[  gc pegs9/s

[ gc crZs  K  gc `8

 K  gc pegs8

4.;;

L

de, L, X y F  gc pegs

dy L, X y F  gc `

s  gc pegs/pegs (kfe`gcsebckl)

s  gc `/` (kfe`gcsebckl)

Gl cb`bmrk`k qug prgsgctk`bs gc lk jemurk 4.5 pgr`etg rgsblvgr lk jùr`ulk fg Dk zgc-]ellek`s ibc sùlb klecgkr ikctefkfgs ibcbiefks pbr `gfeb fg uck rgitk y lggr lks eciùmcetks gc lk ectgrsgiieùc fg åstk ibc gl gng vgrteikl kprbpekfb. Bhsgcg qug gl cb `bmrk`k gstë ibcstruefb pkrk gl vklbr fgl ibgjeiegctg fg Dkzgc-]ellek`s ibc   I/, 0 ;??. Ye lks ibcfeiebcgs rgklgs fg lk tuhgràk mkrkctezkc gl g`plgb fg uc vklbr fejgrgc tg fg I/– sg g`plgkc lks jùr`ulks semuegctgs pkrk knustkr lbs rgsultkfbs. Gl suhàcfeig ;?? sg rgjegrg kl vklbr qug sg lgg gc gc gl cb` bmrk ` k pkrk I I/, /, 0 ;??. ;??. Gl suhàcfeig i sg

C B @ B M X K @ K _ K X K  K  XGYBLZGX LK JÙX@WLK   FG DK^GC-]ELLEK@Y

rgjegrg kl vklbr pkrk gl I/, fkfb. v i 0   BanbÀ[ /EBB ) [ i  ‖  M ebb ([ e/;?? )

0 FebbIlBB/I/,)? FebbIlBB/I/,)?94 94 s i  0 àebbàlB B /I,,);47

Qvglbiefk QvglbiefkfP fP

(4-;?)

Qjlunb Qjlunb vblu`åtre vblu`åtreibP ibP

(4-;;)

Qfeë` gtrb fg lk tuhgràkP

(4-;8 )

Qpårfefk fg ikrmk/ ikrmk/lbcmet lbcmetufP ufP

(4-;9)

Lk làcgk puctgkfk fg lk mrëjeik `ugstrk gl g`plgb fgl cb`bmrk`k pkrk lbs fktbs fgl prbhlg` k ` bfglb 4.;?. pkrk gl iksb fg I/, I/, 0 ;??. ;??. Wc usb jrgiugctg fg uc cb`bmrk`k ib`b gl fg lk jemurk 4.5 ibcsestg gc fgtgr `eckr gl tk`kûb fg tuhgràk qug sg rgquegrg pkrk ibcfuier uc jlunb vblu`åtreib fkfb, kl `es`b teg`pb qug sg le`etk lk pårfefk fg gcgrmàk k iegrtb vklbr gspgiejeikfb. _br gstb ibcstetuyg uck dgrrk`egctk ibcvgcegctg fg fesgûb. (Ibcsultg lk rgjgrgciek 6.)  

Ikpàtulb 4  Cþ`grb fg Xgycblfs, Xgycbl fs, jlunb lk`eckr, jlunb turhulgctb turhulg ctb y pårfefks fg gc gcgrmj. rmj.

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