Informe Caida de Presion de Tuberias Con Accesorios

July 6, 2022 | Author: Anonymous | Category: N/A
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XGJRH[QJEME EH AM[UMOHGM ^[LO[MDM EH JGOHGJH[ÄM ]XÄDJAM FMKL[MUL[JL EH L^H[MAJLGHQ XGJUM[JMQ J JGBL[DH ^[ÍAUJAM # = AMJEM EH ^[HQJÑG HG XGM UXKH[JM ALG MAAHQL[JLQ Mvjfês @mjrl=, Kustmdmgth Qhrojl=, Alrths Dmräm=, Olgzífhz Fjgmurys=, [hyhs Dmräm=, ^cE. Ígohf Olgzífhz;. = Hstuejmgth eh RJJ Qhdhstrh eh Jgohgjhräm ]uädjam, ;Elahgth eh fm Xgjvhrsjeme eh Amrtmohgm. [hajkjel0 >2 eh dmyl ehf ;>=:

[HQXDHG Qh puheh ehajr quh fm amäem eh prhsjñg hs fm ejsdjguajñg eh fm prhsjñg hg ug bfujel quh ajraufm plr ug algeuatl l tukhräm, hstl ehphgehg ehf tjpl eh bfujel, hf dmthrjmf eh fm tukhräm y hf usl eh ajhrtls maahslrjls aldl alels y vífvufms. Hstm príatjam eh fmklrmtlrjl sh hgblam hg hf hstuejl eh fms pêrejems amusmems plr fls maahslrjls, ejacls maahslrjls slg pmrth bugemdhgtmf ehf ejshýl eh ug sjsthdm alg tukhräms, msä aldl tmdkjêg slg pmrajmfdhgth rhsplgsmkfhs rhsplgsm kfhs eh fls alstls eh lphrm lphrmajñg ajñg ehf prla prlahsl hsl elgeh sh hdpfhmg. hdpfhmg. Qh rhmfjzñ rhmfjzñ ugm aldpmrmajñg eh fls vmflrhs eh amäem eh prhsjñg lkthgjels dhejmgth ug dmgñdhtrl ejojtmf y mgmfñojal, alg hf amfaufmel dhejmgth fms haumajlghs sudjgjstrmems plr fm fjthrmturm y fls alhbjajhgths eh pêrejem eh fls maahslrjls. ^mfmkrms afmvhs0 Amäem eh prhsjñg, maahslrjls, tukhräm, alhbjajhgths, Dmgñdhtrls.

MKQU[MAU Jt amg kh smje tcmt tch prhssurh erlp js tch eharhmsh jg prhssurh jg m bfuje tcmt ajraufmths tcrluoc m pjph, tcjs ehphges lg tch typh lb bfuje, tch dmthrjmf lb tch pjph mge tch ush lb  ahrtmjg maahsslrjhs suac ms hfklws mge vmfvhs. Ucjs fmklrmtlry prmatjah blaushs lg tch stuey lb tch flsshs amushe ky tch maahsslrjhs, smje maahsslrjhs mrh m bugemdhgtmf pmrt lb tch ehsjog lb m systhd wjtc pjphs, mge mrh pmrtjmffy rhsplgsjkfh blr tch lphrmtjgo alsts lb tch  prlahss wchrh tchy mrh ushe ushe.. M aldpmrjslg wms dmeh lb tch prhssurh erlp vmfuhs lktmjghe  ky dhmgs lb m ejojtmf mge mgmflo dmgldhthr, wjtc tcmt amfaufmthe ky tch hqumtjlgs prlvjehe  ky tch fjthrmturh mge tch flss alhbbjajhgts lb tch maahsslrjhs. maahs slrjhs.

Ihywlres0 ^rhssurh erlp, maahsslrjhs, pjph, alhbbjajhgts, dmgldhthrs.  \\\\\\\\\\\\\\\\\\\\\\\\\\  \\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\  \\\  =. JGU[ U[LE LEX XAA AAJÑ JÑG G

 

Fm dhaígjam eh bfujel sh jgthrhsm plr hstuejmr fms jgthrmaajlghs hgtrh hf bfujel y hf algtlrgl quh fl fjdj fjdjtm. tm. Hg ug sjsthdm eh tukhrä tukhräms ms hs aldðg hgalgtr hgalgtrmr mr ejvhrsms vífvufms y maahslr maahslrjls jls quh ohghrmg fm phrejem eh amrom, l amäem eh prhsjñg, mugquh hstms slg algsjehrmems dhglrhs hg aldpmrmajñg aldpmrmajñg m fms ohghrmems plr fm brjaajñg brjaajñg hg fls euatls, hg sudm, puhehg rhsuftmr tmg sjogjbjamtjvms quh algffhvhg hf omstl eh ejghrl hg hfhdhgtls pmrm jdpufsmr hf bfujel. Eh mauhrel m fm ohldhträm eh fm vífvufm l maahslrjl sh ehbjghg alhbjajhgths eh pêrejems quh jgbfuyhg ejrhatmdhgth hg fm amäem eh prhsjñg. Hg fms lphrmajlghs ugjtmrjms fls bfujels `uhomg ug pmphf prjgajpmf plr fl quh hsth bhgñdhgl hg hf trmgsplrth eh fäqujels y omshs sh prhshgtm aldl ugm vmrjmkfh eh dhejajñg jgeustrjmf, alg fm aumf fls jgohgjhrls quädjals hg hf h`hrajajl eh su prlbhsjñg sh hgbrhgtmg, y ehkhg hvmfumr fm amäem eh prhsjñg eh fls maahslrjls, mehdís, sj hs sjogjbjamtjvm fm phrejem, algsjehrmr fm mfthrgmtjvm dhgls alstlsm, hgtrh hsms amdkjmr maahslrjls l usmr ug hqujpl jdpufsmelr (kldkm). Hg hsth shgtjel, hs jgejsphgsmkfh hstuejmr fms amäems eh prhsjñg eh vífvufms y maahslrjls ehseh hf pugtl eh vjstm hxphrjdhgtmf y thñrjal plr su mdpfjm utjfjeme hg sjsthdms eh jgohgjhräm. ;. [email protected] ;.=. [email protected] OHGH[MF Mgmfjzmr eh prhsjñghg y fms phrejems amusmem plr fls maahslrjls, msä aldl hf bugajlgmdjhgtl eh hstls yfmfmsamäem jdpfjamajlghs hf sjsthdm.

;.;. [email protected] HQ^HA HQ^HAÄBJALQ ÄBJALQ   [hmfjzmr ug hstuejl eh fms jdpfjamajlghs eh fls maahslrjls hg fm amäem eh prhsjñg.  Hstmkfhahr ugm rhfmajñg hgtrh rhmfjzmr ugm aldpmrmajñg hgtrh fm amrom eh prhsjñg thñrjam y fm hxphrjdhgtmf.  Alglahr hf bugajlgmdjhgtl eh amem maahslrjl y hfhdhgtl eh fm tukhräm. 1. DM[A [AL LU UH HÑ[ Ñ[JJAL 1.=. [email protected] HG UXKH[JMQ0 1.=.=.. Bfuj 1.=.= Bfujel el fmdjgmr0 Hs ug bfujel auyl dlvjdjhgtl hs jgthgsmdhgth lrehgmel, amrmathrjzmel plr  ampms gl-mfthrmems. Y=T

1.=.;. Bfujel turkufhgtl0 Hs ug bfujel auyl dlvjdjhgtl hs jgthgsmdhgth ehslrehgmel, quh hs aldðg sh prhshgth m vhflajemehs mftms y sh amrmathrjzm plr bfuatumajlghs hg fm vhflajeme. Y;T

1.=.1. Gðdhrl eh [hyglfes0 Hf gðdhrl eh [hyglfes phrdjth amrmathrjzmr fm gmturmfhzm ehf bfu`l, hs ehajr, sj sh trmtm eh ug bfu`l fmdjgmr, bfu`l trmgsjajlgmf l eh ug bfu`l turkufhgtl, mehdís jgejam fm jdplrtmgajm rhfmtjvm eh fm thgehgajm ehf bfu`l cmajm ug rêojdhg turkufhgtl rhsphatl eh ugl fmdjgmr y fm plsjajñg eh hsth hstmel ehgtrl eh ugm flgojtue ehthrdjgmem. Y1T

№4

buhrzms jghrajmfhs jghrajmfhs  ύRE  4  (Ha. =) buhrzms buhrz ms vjsalsms vjsalsms  ζ

Elgeh  ύ  hs fm ehgsjeme ehf bfujel, R fm vhflajeme,  ζ  su vjsalsjeme y E hf ejídhtrl eh fm tukhräm.

 

Gldhgafmturm* h dha 

Hghroäm dhaígjam (@)

α  

^hsl hsphaäbjal ( G/d1) 

 ^

^rhsjñg (^m) 

R

Rhflajeme (d/s)

 o

Mahfhrmajñg eh fm ormvheme (:.3= d/s ;)

 z  

Mfturm hg ug pugtl eh rhbhrhgajm eh fm tukhräm (d)

c kldkm 

Amrom eh fm kldkm ðtjf hgtrhomem mf bfujel (d)

cturkjgm 

Amrom eh turkjgm hxtrmäem ehf bfujel (d)

c F  b  

^hrejem eh amrom jrrhvhrsjkfh (d)

Bmatlr eh brjaajñg  Gudhrl eh [hyglfes

E

Ejídhtrl eh fm tukhräm (d)

θ 

[uolsjeme rhfmtjvm (d)

 I  F 

Alhbjajhgth eh phrejem

 F 

Flgojtue eh fm tukhräm

 M  

Írhm trmgsvhrsmf eh fm tukhräm (d;)

]

Bfu`l vlfudêtrjal (d1/s)

RU

Rmflr thñrjal

DE

Rmflr dmgñdhtrl ejojtmf

Qj hf Gðdhrl eh [hyglfes hs ;>>> l dhglr hf bfu`l shrí fmdjgmr. Xg gðdhrl eh [hyglfes dmylr eh 5>>> jgejamg quh fms buhrzms vjsalsms jgbfuyhg plal hg fm pêrejem eh hghroäm y hf bfu`l hs turkufhgtl. Bjgmfdhgth, sj hf gðdhrl eh [hyglfes ffhom m hstmr hgtrh fls vmflrhs joumf l dmylr m ;>>> h joumf l dhglr m 5>>> sh algsjehrm quh hf bfu`l eh hsh bfujel hs trmgsjajlgmf. Y1T

1.;. HAXMAJÑG EH HGH[OÄM HG XG BFXJEL XGJEJDHGQJLGM XGJEJDHGQJLGMF F Fm hghroäm dhaígjam sh puheh ehbjgjr aldl fm blrdm eh hghroäm quh sh puheh algvhrtjr aldpfhtm y ejrhatmdhgth m trmkm`l dhaígjal plr dhejl eh ug ejsplsjtjvl dhaígjal jehmf aldl fl hs ugm turkjgm. Qh mslajm hgtlgahs m fm hghroäm dhaígjam alg fm prhsjñg eh ug bfujel bfuyhgth ehkjel m quh ugm kldkm trmgsbjhrh hghroäm dhaígjam m ug bfujel mudhgtmgel su prhsjñg y ugm turkjgm hxtrmh fm hghroäm ehf bfujel mf km`mr su prhsjñg. Fm buhrzm eh prhsjñg quh matðm slkrh ug bfujel m fl fmrol eh

 

ugm ejstmgajm prleuah trmkm`l ehf bfu`l l hghroäm eh bfu`l y quh sh hxprhsm hg bugajñg eh fms  prlpjhemehs ehf bfujel. Hgtlgahs fm hghroäm dhaígjam eh ug bfujel sh puheh hxprhsmr plr ugjeme eh dmsm aldl0 Y=T

ℓ wR ; h dha 4  +   + wz  (Ha. ;) α 

;o

Hg bfu`l eh tukhräms sh tjhghg hg auhgtm fls 1 tjpls eh hghroäm prhshgtmels hg fm haumajñg =0 hghroäm ;

ℓ ajgêtjam wR   , hghroäm plthgajmf wz  y hghroäm eh bfu`l . Y;T α  ;o

Elgeh, R0 vhflajeme, o0 ormvheme, z0 mfturm, ^0 ^rhsjñg, α0 ^hsl hsphaäbjal. Uhgjhgel hg auhgtm hgtlgahs quh fm hghroäm gl sh arhm gj sh ehstruyh, sjgl quh sh trmgsblrdm hg ltrm sj algsjehrmdls quh hf bfujel sh duhvh eh fm shaajñg = m fm ; hgtlgahs fm hghroäm pmrm hf bfujel hg = shräm Y;T0

ℓ= w R =; H= 4   +   + w z = (Ha. ;m) α 

;o

Z hg ;0 ;

w ^ ; wR ; H; 4  +   + w z; (Ha. ;k) α  ;o

Hgtlgahs sj gl cmy hghroäm quh sh morhouh l pjhrem hg hf bfujel hgtrh fms shaajlghs = y ;, hgtlgahs hf  prjgajpjl eh algshrvmajñg algshrvmajñg eh fm hghroäm rhqujhrh rhqujhrh quh Y;T0 ; ℓ= w R =;  ^ ; wR ;  +   + w z =  4   +   + w z ;  (Ha. 1)

α 

;o

;o

α 

Umdkjêg sh puheh hxprhsmr aldl0 ;

;

 ^ R   ^ R  = ; = ; =  z α   + ; o +   4 α   + ; o + z ;  (Ha. 5)

Hg hf amsl eh quh fm hxjstmg phrejems eh hghroäm hg hf sjsthdm, fm haumajñg ohghrmf sh hxprhsm eh fm sjoujhgth dmghrm0 ;

;

 ^ R   ^ = R =  + + z =+ ckldkm4 ;  + ; + z ; + cturkjgm + c F(Ha. 8) α  ; o α  ; o

Elgeh c kldkm hs fm amrom eh kldkm ðtjf hgtrhomem mf bfujel, cturkjgm hs fm amrom eh turkjgm hxtrmäem ehf bfujel y c Fhs fm phrejem eh amrom jrrhvhrsjkfh hgtrh = y ;. Y=T

1.1. ^H[EJEMQ HG XG QJQUHDM EH UXKH[ÄMQ

 

Hg ug sjsthdm eh tukhräms cmy ; tjpls eh pêrejems0 fms dmylrhs quh hs fm phrejem eh amrom plr  brjaajñg hg fls tukls y fms phrejems dhglrhs quh slg mquhffms prlvlamems plr fls maahslrjls quh jgthrrudphg hf sumvh bfu`l ehf bfujel y prlvlamg pêrejems mejajlgmfhs ehkjel mf bhgñdhgl eh shpmrmajñg y dhzafm ehf bfu`l quh prleuahg. Qlg h`hdpfls eh hstls maahslrjls0 ugjlghs, vífvufms, bfh bfhxj xjlgh lghs, s, ale alels, ls, rmd rmdjbj jbjama amajlg jlghs hs hg blr blrdm dm eh fht fhtrm rm U (al (alghx ghxjlg jlghs hs hg U), hgtrm hgtrmems ems,, smf smfjem jems, s, hgsmgacmdjhgtls y algtrmaajlghs. Y=T Fms pêrejems pêrejems dmylrhs sh hxpr hxprhsmg hsmg hg têrdj têrdjgls gls ehf bmatlr eh brja brjaajñg ajñg b  quh ehphgeh ehf tjpl eh tukhräm, su ruolsjeme ( θ ), ejídhtrl (E) y hf gðdhrl eh [hyglfes. Hsth bmatlr sh puheh cmffmr hg hf ejmormdm eh Dlley l amfaufmr alg fms sjoujhgths haumajlghs ehphgejhgel eh fm gmturmfhzm ehf bfujel0 Y=T b 4

25

№   (Ha. 2)

Bmatlr eh brjaajñg pmrm bfu`l fmdjgmr  

b 4

>,;8 ;

  θ flo + 8,?5 >.: 1,? E

Y (

  (Ha. ?)

)T



Haumajñg eh [email protected] pmrm hf aífaufl ehf bmatlr eh brjaajñg pmrm bfu`l turkufhgtl Uhgjhgel hf bmatlr eh brjaajñg sh puheh amfaufmr fm pêrejem m trmvês eh fm haumajñg0 ;

  F R    (Ha. 3) c F, dmylr4 b   E ; o

Fms pêrejems pêrejems dhgl dhglrhs rhs sh hxprh hxprhsmg smg hg têrdj têrdjgls gls ehf alhbjajh alhbjajhgth gth eh pêre pêrejem jem  I  F(tmdkjêg ffmdmel alhbjajhgth eh rhsjsthgajm), quh fls bmkrjamgths ehthrdjgmg eh dmghrm hxphrjdhgtmf y hstíg tmkufmels hg fm fjthrmturm Y=T. Fm haumajñg pmrm amfaufmrfms hs0  ;

c F, dhglr4 I   FF R    (Ha. :) ;o

Hgtlgahs fm pêrejem tltmf ehf sjsthdm shräm fm sudm eh fms phrejems dmylrhs y dhglrhs0 c F 4c F, dmylr+ c F ,dhglr  (Ha. =>m)  ;

;

  F R  R  c F 4b  + I   FF  (Ha. =>k)  E ; o ;o

^mrm sjsthdms eh dís eh ugm tukhräm alg ejbhrhgths ejídhtrls y dís eh ug maahslrjl sh amfaufm alg0 ❝

c F 4∝ b  j j

 Fj R j  E j

;

;o



+ ∝  I  F, `  `

R   ``

;

;o

 (Ha. =>a)

 

1.1.=. Ujpls eh maahslrjls 

Rífvufms Rífvu fms00 Qh usm usmgg hg fls sjsth sjsthdms dms eh tuk tukhrä hrämm pmr pmrmm alg algtrl trlfmr fmr fms rmzlg rmzlghs hs eh bfu bfu`l `l mf sjdpfhdhgth mfthrmr fm pêrejem eh amrom cmstm quh sh florm fm rmzñg eh bfu`l ehshmem Y=T. Hxjsthg vmrjls tjpls, hgtrh fls dís aldughs hstíg0  Rífvufm eh aldpuhrtm  Rífvufm eh oflkl Rífvufm Rífvufm eh eh ígoufl rhthgajñg Alels l bfhxjlghs y alghxjlghs hg U0 Xsmels pmrm fls amdkjls hg fm ejrhaajñg sjg ug amdkjl hg hf ejídhtrl eh fm tukhräm. Fms pêrejems hg hstls maahslrjls sh ehkhg m fm shpmrmajñg ehf bfu`l hg hf fmel jgthrjlr y hg fls bfu`ls mrrhdlfjgmels shaugemrjls quh sh  prlvlamg plr ejbhrhgths ejbhrhgths flgojtuehs eh trmyhatlrjm. trmyhatlrjm. Y=T Hgsmgacmdjhgtls y algtrmaajlghs0 Qjrvhg pmrm m`ustmr fls amdkjls hg fms rmzlghs eh bfu`l l  prlpjhemehs aldl fm ehgsjeme y fm vhflajeme. Fms pêrejems usumfdhgth slg duacl dís ormgehs hg hf amsl eh fls hgsmgacmdjhgtls y algtrmaajlghs rhphgtjgls (l hgsmgacmdjhgtls eh ormg ígoufl) ehkjel m fm shpmrmajñg ehf bfu`l Y=T . Hf alhbjajhgth eh pêrejems pmrm hgsmgacmdjhgtls sh puheh m mprlxjdmr alg0  

 

 

;

 M phquhým  I  F4 =∛ (Ha. ==)  M

(

ormgeh

)

Fm haumajñg ohghrmf eh fm hghroäm (Ha. 8) hxprhsmem hg fm ejrhaajñg eh bfu`l, hs ehajr, ehseh hf pugtl eh rhbhrhgajm = hg hf fmel jzqujhrel eh fm haumajñg cmajm hf pugtl eh rhbhrhgajm ; hg hf fmel ehrhacl0 ;

;

 ^ = R =  ^ R   + + z =+ ckldkm∛ cturkjgm∛c F4 ;  + ; + z ; α  ; o α  ; o

Uhgjhgel hg auhgtm fls trmdls eh bfu`l m hstuejmr hg hf hqujpl eh ejgídjam eh bfujels y kldkms, sh amrmathrjzmg plr0 

 

Urmdl eh bfu`l clrjzlgtmf, plr fl aumf gl cmy amdkjls eh mfturm  z ;∛ z =4>.  Gl prhshgtmg ejsplsjtjvls ejsplsjtjvls dhaígjals qu quhh omghg l rhduhvmg hghroäm c kldkm4c turkjgm4> Írhm eh shaajñg trmgsvhrsmf algstmgth, eh mauhrel m fm haumajñg eh algtjgujeme pmrm fäqujels R = M 4R ; M , hgtlgahs R =4R ;

^lr fl aumf fm haumajñg ohghrmf eh fm hghroäm (Ha. 8) sh rheuah m0 = α 

∛c F 4  ( ^;∛ ^= ) 

(Ha. =;)

^mrm fm amäem eh prhsjñg hg fls trmdls eh tukhräm, eh fm Ha.=;0 ∂ ^ 4c F α 4c F o ύ 

(Ha. =1)

b rjaajñg hg Fms pêrejems eh hghroäm c F, hstíg algblrdmems plr fm sudm eh fms pêrejems eh amroms plr brjaajñg fls tukls (c F, dmylr) y fms pêrejems eh amroms hg fls maahslrjls ( c F, dhglr). Hg hsth mgífjsjs sh

 

ehsprhajmg fms phrejems dmylrhs ehkjel m quh hg hf trmdl m hstuejmr fls maahslrjls audpfhg ug  pmphf eldjgmgth. Eh fm Ha.=>m y =>k sh trmgsblrdm pmrm guhstrl sjsthdm0 c F 4c F, dhglr  ;

c F 4 I   FF R   (Ha. =5) ;o

Alhbjajhgths eh pêrejem  I  F(tmdkjêg ffmdmel alhbjajhgth eh rhsjsthgajm), sh tldmrmg eh vmflrhs tmkufmels hg fm fjthrmturm pmrm fls tjpls eh maahslrjls usmels. ^mrm hf aífaufl eh fm vhflajeme R , R 4

]  (Ha. =2)  M ;

Elgeh, ]0 amuemf vlfudêtrjal y M0 Írhm eh shaajñg trmgsvhrsmf  M 4 ώ E  ( Ha .=? ) 5 Bjgmfdhgth sh amfaufm hf plrahgtm`h eh hrrlr hgtrh hf amdkjl eh prhsjñg amfaufmel (vmflr thñrjal) y eh fms dhejajlghs tldmems hg fm h`hauajñg eh fm príatjam (vmflr hxphrjdhgtmf)0

|

% Hrrlr4

  |

v.thlrjal ∛ v . hxphrjd hxphrjdhgt hgtmf mf ∟=>>  ( Ha .=3 ) v . thlr thlrja jal l

5. DHU HULE LELF LFLO LOÄM ÄM 5.=. DMUH[JMFHQ Fm príatjam shrí rhmfjzmem hg hf hqujpl pmrm hf hstuejl eh ejgídjam eh bfujels y kldkms. Qh hstuejmríg fls sjoujhgths maahslrjls0     

Rífvufm eh oflkl. Rífvufm eh klfm. Alels eh 58¾ y eh :>¾. Alghxjlghs hg U pmrm bfu`l hg fäghm y bfu`l ehrjvmel. Urjburamajlghs m 58¾ pmrm bfu`l hg fäghm y bfu`l ehrjvmel.

5.;. ^[LAHEJDJHGUL HS^H[JDHGUMF ^rjdhrl, sh prlaheh m alghatmr, hgahgehr hf hqujpl y mkrjr tlems fms vífvufms ehf sjsthdm, alg hf bjg eh rhmfjzmr fm purom ehf moum rhdmghgth hg hqujpl eh hxphrjhgajms prhvjms, sh ehkh hsphrmr m quh fms kurku`ms eh mjrh smfomg eh fms tukhräms mgths eh prlahehr m rhmfjzmr fms dhejajlghs.

 

 

 

 

Fuhol, sh prlaheh m shfhaajlgmr fm algbjourmajñg eh tukhräms ehshmem y sh ajhrrmg fms vífvufms phrthghajhgths m algbjo alg bjourm urmajl ajlghs ghs quh gl sh hstmr hstmríg íg usmge usmgel, l, thg thgjhg jhgel el hg auh auhgtm gtm quh hf sjsthdm ehkh thghr, plr fl dhgls, ugm vífvufm mkjhrtm quh phrdjtm hf bfu`l ehf moum. ^lst ^lsthr hrjl jlrd rdhg hgth th,, sh sh shfh fhaa aajl jlgm gm hf maahslrjl eh hstu maahslrjl hstuejl, ejl, sh algha alghatmg tmg fms dmgouhrms ehf hqujpl pmrm fm dhejajñg eh fm prhsjñg ejbhrhgajmf hg fls pugtls eh hgtrmem y smfjem ehf maahslrjl, shoðg alrrhsplgem. Qh tldm tldmgg vmfl vmflrh rhss eh fm amäe amäemm eh  prhsjñg, alg 8 amuemfhs ejbhrhgths y sh pms pmsmm mf sjo sjoujh ujhgth gth maa maahsl hslrjl rjl,, msä suah suahsj sjvm vmdh dhgt gthh cm cmst stmm rhmf rhmfjz jzmr mr fm dhejajñg hg tlels fls maahslrjls eh fm fäghm shfhaajlgmem.

 Bjo. =0 Ejmormdm eh eh kflquhs ehf prlahsl hxphrjdhgtmf

5.1. [email protected] HS^H[JDHGUMF

Hg hstm príatjam hxphrjdhgtmf sh trmkm`ñ hg sjsthdm eh tukhräms eh · eh pufomem eh ^RA aheufm 3>, alg ejbhrhgths maahslrjls (kjburamajlghs, alels, U, vífvufms) Hf sjsthdm eh tukhräm hstí alghatmel m els kldkms9 quh hstíg hg pmrmfhfl, fms aumfhs hstíg alghatmem m ug tmgquh eh mfdmahgmdjhgtl eh moum.

 Bjo. ;0 [hprhshgtmajñg oríbjam ehf dlgtm`h hxphrjdhgtmf.

 

8. EM EMUL ULQ Q Z [H [HQX QXFU FUME MELQ LQ

Eurmgth fm príatjam hxphrjdhgtmf sh rhojstrmrlg fls emtls eh amäem eh prhsjñg pmrm amem maahslrjl lkthgjems eh ug dmgñdhtrl ejojtmf y mgmfñojal, vmrjmgel hf vmflr eh fls amuemfhs aldl sh duhstrm hg hf Mghxl M-5. Fm amäem eh prhsjñg thñrjam sh ehthrdjgñ alg fm haumajñg =1, hg fm aumf fms prlpjhemehs ehf moum (ehgsjeme y vjsalsjeme ejgídjam) sh tldmrlg eh fls c

mgh mghxl xls s gM-; pm ug ugm m mrlg th thdp dphr urm eh ls1> 1>¾A ¾A.. alhbjajh Fms Fms ajhgth phr phrej ejem ems s dhglr dh hsm  I  F Feh mauhrelehm fm haumajñ haum ajñg =5,pmrm shrm amf amfauf aufmrl g hrmt hgmturm têr têrdjg djgls ehf alhbj gth eh pêreje pêrglrhs ejem lkthgjels fm fjthrmturm, Mghxls M-1. Mehdís, sh rhmfjzñ hf aífaufl eh hstls alhbjajhgths eh mauhrel mf  prlahejdjhgtl hstjpufmel hg hf fjkrl eh Dhaígjam eh Bfujels eh [lkhrtl Dltt alg hf bmatlr  eh brjaajñg eh bfu`l turkufhgtl, haumajñg ?, ehthrdjgmel alg hf gðdhrl eh [hyglfes, haumajñg =, y fm flgojtue hqujvmfhgth hg ejídhtrls eh tukhräms tmkufmels hg Mghxls M-8, lkthgj lkt hgjhge hgell rhsp rhspuhst uhstms ms sjd sjdjfm jfmrhs rhs pmrm hf alhb alhbjaj jajhgt hgthh eh phre phrejem jem m fms tmkufm tmkufmems ems plr fm fjthrmturm, vhr Mghxls M-2. ^mrm amfaufmr fm vhflajeme vhflajeme fjghmf buh ghahsmrjl rhaurrjr mf Mghxl M-=, hsphajbjamajlghs têagjams eh tukhräms ^RA Aheufm 3>, eh hsth tldmdls hf ejídhtrl jgth jgthrj rjlr lr eh ugm tu tukh khrä rämm eh ej ejíd ídht htrl rl gl gldj djgm gmff eh ·—, ·—, prlah prlahehd ehdls ls m am amfa fauf ufmr mr hf írhm írhm trmgsvhrsmf y alg hsth fm vhflajeme pmrm amem bfu`l vlfudêtrjal aldl sh lkshrvm hg Mghxls M-5. sh lktuvl rhsuftmel pmrm =1, fm amäem prhsjñg thñrjam (Rhr Mghxl M-5), fuholBjgmfdhgth eh rhhdpfmzmr vmflrhshfhg fm haumajñg y susehrhsphatjvls plrahgtm`hs eh hrrlr eh mauhrel m fls emtls eh amäem eh prhsjñg lkthgjels eh dmghrm hxphrjdhgtmf. Alg hf rhsuftmel eh fm jgblrdmajñg rhojstrmem hg fms tmkfms eh Mghxl M-5 sh ormbjañ0  Bjo. m0 Ormbjam eh amjem eh prhsjlg vs amuemf hg vmfvufm eh oflkl =;.>>>     T    m    ^     i     Y      g     ñ    j    s    h    r    ^    h     e    m     e     ä    m    A

Rífvufm eh Oflkl

=>.>>>

Ε^ Uhlrjal 3.>>>

 Ε^ DE  Ε^ DM

2.>>> 5.>>> ;.>>> >.>>>

2

3

=>

=;

=5

=2

=3

;>

Amuemf YF/djgT

 Bjo. k0 Ormbjam eh amjem eh prhsjlg vs amuemf hg vmfvufm eh klfm

;;

;5

;2

 

    T    m    ^     i     Y      g     ñ    j    s    h    r    ^    h     e    m     e     ä    m    A

8.>>> 5.8>> 5.>>> 1.8>> 1.>>>

Rífvufm eh Klfm Ε^ Uhlrjal  Ε^ DE  Ε^ DM

;.8>> ;.>>> =.8>> =.>>> >.8>> >.>>>

2

3

=>

=;

=5

=2

=3

;>

;;

;5

;2

Amuemf YF/djgT

 Bjo. a0 Ormbjam eh amjem eh prhsjlg vs amuemf hg hg fmel rhatl eh U  =.5>>     T    m    ^     i     Y      g     ñ    j    s    h    r    ^    h     e    m     e     ä    m    A

Alghxjñg hg U :>¾ (bu`l (b u`l hg fjghm)

=.;>>

Ε^ Uhlrjal Ε^ DE Ε^ DM

=.>>> >.3>> >.2>> >.5>> >.;>> >.>>>

2

3

=>

=;

=5

=2

=3

;>

;;

;5

;2

Amuemf YF/djgT

 Bjo. e0 Ormbjam eh amjem eh prhsjlg vs amuemf hg U :>¾ ;.8>>     T    m    ^     i     Y      g     ñ    j    s    h    r    ^    h     e    m     e     ä    m    A

Alghxjñg hg U :>¾ (bu`l ehrjvmel)

;.>>>

Ε^ Uhlrjal  Ε^ DE  Ε^ DM

=.8>> =.>>> >.8>> >.>>>

2

3

=>

=;

=5

=2

Amuemf YF/djgT

=3

 Bjo. h0 Ormbjam eh amjem eh prhsjlg vs amuemf hg alel eh 58¾

;>

;;

;5

;2

 

>.:>>

Alel 58¾

>.3>>     T    m    ^     i     Y      g     ñ    j    s    h    r    ^    h     e    m     e     ä    m    A

Ε^ Uhlrjal  Ε^ DE  Ε^ DM

>.?>> >.2>> >.8>> >.5>> >.1>> >.;>> >.=>> >.>>>

2

3

=>

=;

=5

=2

Amuemf YF/djgT

=3

;>

;;

;5

;2

;>

;;

;5

;2

;5

;2

 Bjo. b0 Ormbjam eh amjem eh prhsjlg vs amuemf hg alel eh :>¾ =.2>>     T    m    ^     i     Y      g     ñ    j    s    h    r    ^    h     e    m     e     ä    m    A

Alel :>¾

=.5>>

Ε^ Uhlrjal  Ε^ DE  Ε^ DM

=.;>> =.>>> >.3>> >.2>> >.5>> >.;>> >.>>>

2

3

=>

=;

=5

=2

Amuemf YF/djgT

=3

 Bjo. o0 Ormbjam eh amjem eh prhsjlg vs amuemf hg kjburamajlg eh 58¾ fjghmf >.2>>     T    m    ^     i     Y      g     ñ    j    s    h    r    ^    h     e    m     e     ä    m    A

Kjuramajlg Kjuramajl g eh 58¾ (bu`l hg fjghm)

>.8>>

Ε^ Uhlrjal  Ε^ DE  Ε^ DM

>.5>> >.1>> >.;>> >.=>> >.>>>

2

3

=>

=;

=5

=2

=3

;>

;;

Amuemf YF/djgT

 Bjo. c0 Ormbjam eh amjem eh prhsjlg vs amuemf hg kjburamajlg eh 58¾ ehrjvmel

 

=.;>>     T    m    ^     i     Y      g     ñ    j    s    h    r    ^    h     e    m     e     ä    m    A

Kjuramajlg Kjuramajl g eh 58 58¾¾ (b (bu`l u`l ehrjvmel ehrjvmel))

=.>>>

Ε^ Uhlrjal  Ε^ DE  Ε^ DM

>.3>> >.2>> >.5>> >.;>> >.>>>

2

3

=>

=;

=5

=2

Amuemf YF/djgT

=3

;>

;;

;5

;2

 Bjo. 10 Ormbjams eh rhsuftmels eh amäem eh prhsjñg thñrjals y hxphrjhdtgmfhs lkthgjels pmrm amem maahslrjl (m, k, a, e, h, b, o, c)     T    m =;.>>>    ^     i =>.>>>     Y      g     ñ    j    s    h    r    ^    h     e    m     e    j    m    A

3.>>> 2.>>> 5.>>> ;.>>> >.>>>

Amäem eh prhsjñg eh mauhrel m fls maahslrjls3 F/djg =; F/djg =2 F/djg ;> F/djg ;5 F/djg Rífvufm eh Alghxjñg hg Alghxjñg hg OflklU :>¾ (bu`l U :>¾ (bu`l Mkjhrtm plr hg fjghm) ehrjvmel) aldpfhtl

Alel 58 58¾

Alel :> :>¾

Rífvufm eh Klfm Mkjhrtm plr aldpfhtl

Kjuramajlg ZH eh 58¾ (bu`l hg fjghm)

Kjuramajlg ZH eh 58¾ (bu`l ehrjvmel)

Maahslrjls  Bjo. 5 0 Ormbjam eh amjem eh prhsjlg hg fls ejbhrhgths maahslrjls alg amem amuemf

2. MG MGÍF ÍFJQJ JQJQ QE EH H [H [HQX QXFU FUME MELQ LQ Fms oríbjams m, k, a, e, h, b, o, c, eh fm Bjo.1, duhstrmg fm vmrjmajñg quh hxphrjdhgtm fm amäem eh prhsjñg emem hg amem ugl eh fls maahslrjls trmkm`mels m dhejem quh sh vmräm hf amuemf ehf bfujel, hg hsth amsl pmrm 3, =;, =2, ;> y ;5 F^D. Hg amem oríbjam cmy 1 fäghms quh rhprhshgtmg fm amäem eh prhsjñg dmramem plr hf jgstrudhgtl mgíflol, fm emem plr hf ejojtmf y mehdís hf vmflr thñrjal eh hsms amäems eh prhsjñg. Hg fm Bjo.5 sh puheh lkshrvmr quh m dhejem quh mudhgtm hf amuemf ehf bfujel (moum), tmdkjêg fl cmah fm amäem eh prhsjñg, fl quh sh puheh algbjrdmr m pmrtjr eh fms haumajlghs : y =1 hg elgeh fm amäem eh prhsjñg hs ejrhatmdhgth prlplrajlgmf m fm vhflajeme ehf bfujel, quh m su vhz hs ejrhatmdhgth prlplrajlgmf mf bfu`l vlfudêtrjal y ehkjel m quh gl sh vmräm hf ejídhtrl eh fm tukhräm hgtlgahs mf mudhgtmr hf amuemf ehf bfujel jgarhdhgtm fm amäem eh  prhsjñg. Umdkjêg sh puheh lkshrvmr quh fls maahslrjls quh dís pêrejem eh prhsjñg

 

 prleuahg slg fms vífvufms, hgtrh >,8>> y =; i^m, hstl sh ehkh m quh plr su tmdmýl y blrdm rhprhshgtmg ugm dmylr rhstrjaajñg pmrm hf bfujel y plr fl tmgtl, ohghrm dís turkufhgajm flamf, mehdís quh hstms hstíg aldpfhtmdhgth mkjhrtms plr fl quh su I F hs duacl dmylr quh hf phrthghajhgth m fls ehdís maahslrjls y auyms pêrejems gl suphrmg fls ; i^m. Hg hf amsl eh fms kjburamajlghs eh 58¾ y :>¾ fms amäems eh prhsjñg slg dhglrhs hg mdkls amsls sh tldm hf bfujel hg fäghm (hgtrh =,; i^m), mf gl auhgtmaumgel fm ehrjvmajñg ehfhgbfu`l hstls matumrämg aldl >,= ugm ytukhräm fjsm ym plrquh fl quh fm thghr amäem hg eh  prhsjñg gl shrí duy mftm. Hg fm oríbjam h, b, o y c sh puheh mprhajmr qquh uh fms amäems eh prhsjñg hg fms kjburamajlghs eh bfu`l ehrjvmels (>,= m ;,1 i^m) m slg sjdjfmrhs m fms eh fls alels (>,= m =,1 i^m) ym quh hstms hstmrämg slfmdhgth amdkjmgel fm ejrhaajñg ehf bfu`l plr fl quh matumrämg aldl alels. Qjg hdkmrol, fls ∂ ^  eh fms kjburamajlghs slg ug plal dmylrhs m fms eh fls alels ehkjel m quh hstls prhshgtmg ugm aurvmturm quh ohghrm dhglr turkufhgajm hg hf bfu`l quh hf alrth rhatl eh fms kjburamajlghs, fl quh rhprhshgtmräm ugm pêrejem dhglr eh  prhsjñg. ?. ALG LGAF AFXQ XQJJLG LGHQ HQ

Mf usmr maahslrjls y mudhgtmr fm amäem eh prhsjñg sh mudhgtm ghahsmrjm pmrm dmgthghr ugm prhsjñg ghahsmrjm. Ehkhdls rheuajrfm mfamgtjeme díxjdlehhfhghroäm usl eh vífvufms fms aumfhs ohghrmg ugm ormg amäem eh prhsjñg. M fm clrm eh hfhojr hgtrh alels l  kjburamajlghs, hs dh`lr usmr alels ale ls quh ohghrmg ugm dhglr phrejem ph rejem eh prhsjñg. 3. KJK JKFJ FJLO LO[ [MBJ BJM M Y=T Z. hgohf, @. Ajdkmfm, R. Amdpls Lfouäg mge Q. Bmehhvm Qigmrjgm,  Dhaígjam eh bfujels bfujels, =st he. Dêxjal E.B. YhtaT0 DaOrmw Cjff, ;>>2, pp. 15=-125. Y;T [. Dltt, Dhaígjam eh bfujels (2m. he.) , 2tc he. Gmuamfpmg eh @uírhz0 ^hmrslg Heuamajñg, ;>>2,  pp. =22-=23.

Mghxls Mghxls M-=. Hsphajbjamajlghs têagjams eh tukhräm eh ^RA Aheufm 3>

 

 Buhgth0 HDDQM Qjsthdms eh Uukhräms.

Mghxls M-;. ^rlpjhemehs ehf moum m = mtd

 Buhgth0 Dhaígjam eh Bfujels. [lkhrt Dltt, ;>>2.

Mghxls M-1. Alhbjajhgths eh pêrejem plr maahslrjls

 

 Buhgth0 Dhaígjam eh Bfujels. Ahgohf, ;>>2 

 Buhgth0 Cjeríufjam eh Uukhräms. @umg O. Qmfemrrjmom.

Emtlstldmels rhojstrmels amuemf y amäems prhsjñgehdhejmgth ug gmgñdhtrl Mghxls ejojtmf yM-5. mgmfñojal hg eh fm h`hauajñg eh fm eh príatjam fmklrmtlrjl pmrm amem

 

maahslrjl. Aífaufls eh fm amäem eh prhsjñg thñrjam y plrahgtm`hs eh hrrlr rhsphatl m fls vmflrhs hxphrjdhgtmfhs. Rífvufm eh Oflkl- Mkjhrtm plr aldpfhtl DE

#

Amuemf YF YF/djgT

Amuemf Yd YdW1/sT

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Rh Rhfflaje ajeme Yd/ Yd/sT sT

cf YYd dT

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#

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 Ε^ Yi^mT Ε^ Yi^mT

Alel 58¾ DE

#

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Rífvufm eh Klfm - Mkjhrtm plr aldpfhtl DE DM Amuemf Yd YdW1/sT Rhfla hflaje jeme me Yd/ Yd/sT  Ε^ Yi^mT Ε^ Yi^mT

Ε^ Yi^mT % Hrrlr % Hrrlr

If cf YYd dT

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