Hidráulica 3

 

MGDRNØLGIN Vrg`igpga dj J`jrkïn y In`tgdnd dj Oavgogj`ta O.Yi @ndgn Brgkgttj Brgkgttj Yn`nbrgn Yn`nbrgn Oç`djz Oç`djz @aobrj8 Eniultnd dj G`kj`gjrïn, G`kj`gjrïn Nkrïialn

www.usia.jdu.ia «Ugkglndn Og`jduinigù`³

 

Dgstrgbuigù` dj ln prjsgù` j` u`n sjiigù` dj in`nl Dgstrgbuigù` dj prjsga`js j` in`nljs rjitas y iurvas ia` pj`dgj`tjs bnhns u margza`tnljs j` ln sjiigù` bnha ia`sgdjrnigù`. m ? nlturn pgjzaoçtrgin3 ms ? nlturn mgdrastîtgin3 y I ? iarrjiigù` dj nlturn dj prjsgù` par iurvnturn. Jl nkun j` jstn ialuo`n djbj subgr mnstn ln lï`jn djl krnd krndgj gj`t `tjj mg mgdr drîu îulglgia ia a supj supjre regi gigj gj djl djl nkun nkun.. Ljy Ljy mgdrastîtgin dj ln dgstrgbuigù` dj prjsgù` pu`ta NB Egkurns. n) Eluha pnrnljla3 b) Eluha ia`vjxa3 i) Eluha iù`inva.

 

Jejita dj ln pj`dgj`tj j` ln dgstrgbuigù` dj prjsga`js

℀ ?    ℀ ? 

Da`dj  ? , ln praeu`dgdnd dj nkun ojdgdn pjrpj`dgiulnroj`t pjrpj`dgiulnroj`tjj djsdj ln supjregigj.

 

Jejita dj ln pj`dgj`tj j` ln dgstrgbuigù` dj prjsga`js Yg u` in`nl dj pj`dgj`tj nltn tgj`j u` pjregl la`kgtudg`nl ia` iurvnturn nprjignblj, ln nlturn dj prjsgù` djbj sjr iarrjkgdn par jl jejita dj ln iurvnturn dj lns lï`jns dj iarrgj`tj (egkurn). J` `atnigù` sgoplj, ln nlturn dj prjsgù` pujdj jxprjs jxp rjsnrsj nrsj iaoa iaoa    ′       da`dj    ′ js jl iajegigj`tj dj prjsgù`. Jstjj en Jst enita itarr dj iarr iarrjii jiigù` gù` (  ′ ) js gkunl n ln u`g u`gdnd dnd pnrn pnrunlo n loj` eluha eluj`tj hatjpnrnlj pnr laa), (eluha (el u`ge u`rgearo aroj eluh el uha a krnd krndun vnrg vnnljla rgnd nda) , uha oj`a oj`ar quj qujj lny u`gd u` gdnd nd pnr pnrn el eluh uha a ia` ia`vjx vjxa y onya onyarr quj quj ln u`gdnd pnrn eluha iù`inva

 

J`jrkïn djl eluha j` in`nljs nbgjrtas

 

J`jrkïn djl Eluha j` in`nljs nbgjrtas

  ?  +   +  2 Da`dj8  js ln jljvnigù` djl pu`ta N par j`igon djl `gvjl dj rjejrj`ign3    js ln praeu`dgdnd djl pu`ta N par djbnha dj ln supjregigj djl nkun ojdgdn n la lnrka dj ln sjiigù` djl in`nl3  js jl î`kula dj ln pj`dgj`tj djl in`nl

 

J`jrkïn J`jrk ïn djl eluha j` in`nljs nbgjrtas Lujka ln j`jrkïn djl in`nl js

  ?  +  +  2

Vnrnn in`nljs ia` pj`dgj`tjs bnhns  ≍ 6 ln j`jrkïn Vnr tatnl djl in`nl js8 

 ?++

2

Dj niujrda j` jl prg`igpga dj ln ia`sjrvnigù` dj ln j`jrkïn, ln nlturn dj ln j`jrkïn tatnl dj ln sjiigù` >, djbj sjr gkunl n ln nlturn dj ln j`jrkïn tatnl j` ln sjiigù` 2.

 +   + 



2

 ?  +   + 



2

 + ℀

 

J`jrkïn djl Eluha j` in`nljs nbgjrtas Çsttn ji Çs jiun unig igù` ù`u`jsin`nl np nplglgiidj nb nblj lj pn pnrrn eluh elpjqujþn, uhas as pn pnrrnl nljl jlas assjaia`vgjrtj krnd krndun unlo loj` j`tj tj vnrgndas. Vnrn pj`dgj`tj jsta j`8





2 +  + ℀ 2 ?  ?  +  +  2  +  +  2

Iunlqugjrn dj jstns das jiuniga`js sj ia`aij iaoa ln jiunigù` dj ln j`jrkïn. Iun`da ℀ ? 6 y  ? ? > ln øltgon jiunigù` qujdn8

     +  +  ?  +  + 2 2 Çstn øltgon js ln ouy ia`aigdn  jiunigù` dj j`jrkïn dj Bjr`aullg 

 

J`jrkïn J`jrk ïn djl eluha j` in`nljs nbgjrtas Ln j`jrkïn sjiigù` u` in`nl sj djeg`j ln j`jrkïn parjspjiïegin cglakrnoaj`djln nkun qujdjeluyj n trnvçs dj ln iaoa sjiigù`, ojdgdn ia` rjspjita nl ea`da djl in`nl. Dj la n`tjrgar, n`tjrgar, ln jiunigù` dj Bjr`aullg pnrn u` in`nl js8

  ?++ 2 Da`dj , X ? 6 (yn quj jl `gvjl dj rjejrj`ign js jl ea`da djl in`nl, abtj`gj`da ln jiunigù` dj ln j`jrkïn jspjiïegin iaoa8

  ?+ 2

 

J`jrkïn jspjiïegin Vnrnn u` in`nl dj pj`dgj`tj pjqujþn y ? > Vnr

   ?+ 2

La iunl g`dgin j`jrkïn jspjiïegin js gkunl n lnsuon dj ln praeu`dgdnd djl quj nkunlnoîs ln nlturn dj ln vjlaigdnd. Iaoa ? /

    ?  + 2

Inudnl Z`gtnrga (q), js ln rjlnigù` j`trj jl Inudnl y jl n`ima supjregignl djl In`nl

  ?

 

J`jrkïn Jspjiïegin

 

J`jrkïn jspjiïegin

 

Ej`ùoj`as lainljs J` las in`nljs nbgjrtas n oj`uda aiurrj` inobgas j` jl jstnda dj eluha subirïtgia n supjrirïtgia y vgijvjrsn, tnljs inobgas sj on`gegjstn` ia` u` iarrjspa`dgj`tj inobga j` inobga bga aiurrj aiurrj ia` rn rnpg pgdjz djz n la lnrka lnrka dj u` u`n n dgs dgstn` tn`ign ign ln praeu`dgdnd dj eluha.   Yg jl ino rjlntgvnoj`tj iartn, jl eluha js rîpgdnoj`tj vnrgnda y sj ia`aij iaoa ej`ùoj`a lainl.

Ln inïdn mgdrîulgin y jl rjsnlta mgdrîulgia sa` das tgpas dj ej`ùoj`a lainl. Inïdn mgdrîulgin8 Z` inobga rîpgda j` ln praeu`dgdnd djl eluha dj u` `gvjl nlta n u` `gvjl

bnha rjsultnrî j` u`n djprjsgù` nbruptn dj ln supjregigj djl nkun (inobga dj ln pj`dgj`tj djl in`nl a ln sjiigù` trnsvjrs trnsvjrsnl). nl). Jl eluha pnsn dj u` jstnda subirïtgia n supjrirïtgia. Rjsnlta mgdrîul mgdrîulgia8 gia8 Iun`da jl inobga rîpgda dj ln praeu`dgdnd djl eluha js djsdj u` `gvjl bnha n u` `gvjl nlta. N oj`uda js jl rjsultnda js u`n subgdn nbruptn dj ln supjregigj djl nkun. Aiurrj par djbnha dj u`n iaopujrtn djslgzn`tj dj rjkulnigù`, j` ln pnrtj dj nkuns djbnha dj u` vjrtjdjra a j` jl insa quj u` in`nl ia` nltn pj`dgj`tj sj vujlvj insg margza`tnl dj on`jrn søbgtn. Jl eluha pnsn dj u` jstnd supjrirïtgia n subirïtgia.

 

Jhjopla > Inliulnr jl inudnl quj pnsn par djbnha dj ln iaopujrtn djslgzn`tj, oastrndn j` ln egkurn, sg jl in`nl js margza`tnl.      ? 4 y      ? >  . Yj supa`j quj `a mny pçrdgdn dj j`jrkïn. Jl n`ima djl in`nl js dj : ojtras

 

Jhjopla > Yaluigù`8

 ?    ?        ?   ? ::∛∛4>

 ??2:6

Lujka

26  ? :  ?→→→→→→   ? 4 Jopljn`da ln ljy dj ln ia`sjrvnigù` dj ln j`jrkïn (Jiunigù` dj Bjr`aullg)

        ?  +  +   +  + 2 2

 

Jhjopla > Ia`tg`unigù`8

     +  +  ?  +  + 2 2

Iaoa lns sa` lns ogsons    ?   iatns a nlturns 

4 +   ? > +   Ia  Iaopnr opnrn`da n`da lns vjlaigdnd vjlaigdndjs js sj tgj`j` 4 +



 

 ? > +



  djspjhn`da djspjhn`da ln vjl vjlaigdnd aigdnd 



  ? 9 ≣↔→→→→    ? 

  ∛   

? >.7= >.7= / / par la tn`ta jl inudnl js8     ?    ? >.7=   26 ?  ? 97.52   ൛



 

Jhjopla 2 Var u` in`nl rjitn`kulnr eluyj` 46   Τ dj nkun, n u`n vjlaigdnd dj >.:   / Djbgda nl pnsa dj u`n tubjrïn ijrin djl jstjea`da sj jdjl ljvjin`nl ;6 js io`jijsnrga . Iunl jsquj ln prae pr aeu` u`dg dgdn dnd d rjs jsul ultn tn`t `tj j dj ln za za`n `n jljvndn1 Iunl js ln vjlaigdnd1 Jl n`ima supa`jdjlquin`nl j `ajs mdj ny>2pojtras. çrdgdn Yj dj j`jrkïn.

 

Jhjopla 2 Yaluigù`8

Inliuln`da ln inrkn dj ln j`jrkïn ig`çtgin j` jl pu`ta (>)    .  ? (. ) ? 

6.>>> . 6.>

 Nmarn sj inliuln ln praeu`dgdnd djl in`nl ia` jl inudnl

 ?    ?  ∛ ( ∛ T) Djspjhn`da  sj tgj`j   ?    ?

  .   ൛   ∛ 

 →→→   ? 2.2 2.222 .

Lujka ln j`jrkïn jspjiïegin js8

  ?

  +  →→→→   ?

2.22 + 6. 2.22 6.>> >> ? 22.9 .99 9.

 

Jhjopla 2 Ln krîegin dj ln j`jrkïn jspjiïegin pnrn jstj insa js8 Var la tn tn`t `ta a ln J` J`jr jrkï kïnn jsp jspji jiïeg ïegin in pnrn jl pu`ta 2 js8

   ?   ∅ ? 2.99  6.;   ? >. >.59  

 

Jhjopla 2 Inliuln`da ln inrkn dj ln j`jrkïn ig`çtgin    j` jl pu`ta (2)    ?  +  ?→→→→   ?  +   . 

Djspjhn`da      ?         ?    .   ?  +       

  

 ? ∛ . 

 ?  

Rjjoplnzn`da   ? 6.:55   ? → → → > . 5 9            ?   46   2∛7.=>∛>2

 

Jhjopla 2   >.5 >.59 + 6. 6.:5 :555 par oçtadas `uoçrgias sj djtjrog`n` lns rnïijs8   ? >.27 y   ? 6.=: Vnrn djtjrog`nr iunl js jl vnlar dj     sj djtjrog`n jl `uojra Eraudj j` lns das sjiiga`js, y jl eluha djbj djbj sjr gkunl j` lns das sjiiga`js. sjiiga`js.   46   ? >2 ∛ >.27 ? 2.: 2.:== /

 ?

   . ∛

 

Jhjopla 9 Z` in`nl dj sjiigù` s jiigù` rjitn`kulnr trn`spartn >6 Τ ia` u`n vjlaigdnd  dj :    . Jl n`ima djl in`nl quj g`gignloj`tj jrn 2 ojtras sj tgj`j quj rjduigr n >.= ojtras par rnza`js dj jspniga. Iunl sjrî ln vjlaigdnd dj ln `ujvn sjiigù`1

 

Jhjopla 9    ?     ?      ?    ? .      ?   >6  ? > :∛2 Vnrn djtjrog`nr jl tgpa dj eluha j` ln sjiigù` > sj inliuln jl `uojra dj Eraudj     ? ∛.  ?

   supjrirïtgi irïtgia a .∛? >.:7;0> Eluha supjr

 

Jhjopla 9 Nmarn sj djtjrog`n las inudnljs u`gtnrgas j` indn sjiigù`   ?   ?

    >6  ?   ? :   ൛  2

     >6  ?  ? :.::   ൛  >.=

Iaoa `a mny jljvnigù` djl ea`da djl in`nl

  ?    :   2 ?  ? > + (2∛7.=>∛> ) ? 2.2;   ?  + 2

 

Jhjopla 9 Iaoa `a mny jljvnigù` djl ea`da djl in`nl

   ?  +

  

?   ?           

  

2 2    .  ? 2.2;      ? . .  2.2;    ? ∛.   2.2; 2.2; + >.:; ? 6 , sj djbj rjsalvjr ln jiunigù` y iaoprabnr jl tgrn`t tgrn`tjj ia` Eraudj.   ?

   

?

     ൛  ? . ∛ ∛. . 

4.:2

>.29  Ln praeu`dgdnd   ? >.

 

 

Jhjopla 4 Var u` in`nl rjitn`kulnr eluyj nkun n u`n vjlaigdnd dj >o/s, ia` u`n praeu`dgdnd dj >.:o. ±Iuîl js jl inobga nbsaluta j` jl `gvjl dj ln supjregigj (ΔX‗), sg jl `gvjl djl ea`da sj jljvn 26 io1

 

Jhjopla 4

> ? 2 + ∅      ?  + 2 ∅ ? 6.2

 

  (>/) /   ? >. >.::    ? >. >.:  + 2 ∛ 7.=>/

→→→  ? >- ∅ →→   ? >.:: >.::  6.2 6.2     ? . 

          , ,  8 8   ?  + ,     2   ?   ?

 ? 

   ?   ? 

 ?

      ? 

 

Jhjopla 4          ?  +  →→   ?  + 2 2

   ? 

 

  ∛   →→   ? (

    >.: ?    (   )  

     ∛  ?



  

   ∛ 

   ? ,        2

  ∛ >.:o ? >.: o /s



>.9:     ∛  ? 6.>>:

7.=>    )    .    >.9: -  ? 6.>>:     >. >.9: 9: + 6.>> 6.>>:: ? 6     ? . (2 ∛

′

∅ ?   ( + ∅ ∅ )

′

∅ ? >.: >.:  (> (>.2 .2= = + 6. 6.2 2))

∅′ ? . .   

Tnllj nlljrr Ilnsj Ilnsj >.

Z` in`nl trnpjzagdnl ia` 4.: ojtras dj bnsj y î`kulas lntjrnljs dj 56¶ ia ia`d `dui uij j u` inudnl dj nkun dj 45 oP9/s ia` u`n vjlaigdnd dj 2.:4 o/s. ^uç tgpa dj eluha sj tg tgj j`j j` çstj stj in in` `nl1 ±Iu Iuî îl js su pr prae aeu u`dg dgd dnd dj elu eluha (y) y)1 1

2. Ln Egkurn oujstrn u` nuoj`ta dj pnsa j` jl ea`da djl in`nl. Yg jl n`ima djl in`nl js ia ia`s `sttn` n`tj tj y `a mny pçrd rdggdn dns, s, dj djtj tjrrog og`j `j Ln Vraeu raeu` `dgdn gdnd dj elu eluha y ln vj vjla laig igd dnd nkun uns s nbnh nb nha a dj ln tr trn` n`sg sgig igù` ù`..

 

Tnllj nlljrr Ilnsj Ilnsj 9. Z` in`nl trnpjzagdnl ia` bnsj dj 26 pgjs y tnlud dj 2 lljvn u` eluha dj 2666 pgjP9/s ia` u`n praeu`dgdnd dj = pgjs. Mny u`n trn`sgigù` sunvj n sjiigù` rjit n`kulnr dj 26 pgjs dj n`ima, niaopnþnda dj u` djsij`sa krndunl djl ea`da djl in`nl dj 2 pgjs. J`ia`trnr ln praeu`dgdnd djl nkun dj`tra dj ln sjiigù` rjitn`kulnr y jl inobga djl `gvjl dj ln supjregigj djl nkun.

 

Tnllj nlljrr Ilnsj Ilnsj 4. J` u` In`nl quj ia`duij u` inudnl dj 7 o9/s3 jxgstj u`n trn`sgigù` dj snlgdn, qujj sg qu sgrv rvjj pnr pnrn u`gr u`gr u`n u`n sjii sjiigù gù` ` rjit rjitn` n`ku kuln lnrr ia` ia` u`n u`n tr trnp npjz jzag agdn dnl, l, iuyns dg dgoj oj`s `sga ga` `js sj oujs oujstr trn` n` j` ln egku egkurrn. Djtjrog`nr iuîl js ln vjlaigdnd j` ln sjiigù` rjitn`kulnr, ia`sgdjrnr quj lns pçrdgdns j`trj ln sjiigù` > y 2 sa` sala djbgdns n ln trn`sgigù`, sgj`da ln eùrouln pnrn su iîliula ln sgkugj`tj8

      ℀−  ? 6.9   2 2

 

Tnllj nlljrr Ilnsj Ilnsj :. Jl nkun Eluyj ia` u`n vjlaigdnd dj 4.5 o/s y u`n praeu`dgdnd dj

6.5 o j` u` in`nl 6.5 n`nl dj sj sjii iigù gù` ` rjitn jitn`k `kul ulnr nr.. J` J`ia ia`t `trrnr jl ino nobg bga a nbsaluta j` jl `gvjl dj ln supjregigj (ΔX‗) praduigda par8 n) Z` jsinlù` sunv sunvjj mnign nrrgbn dj 6.>: o j` jl eea`da a`da djl in`nl b) Z` djsi djsij`sa j`sa sun sunvj vj dj 6.>: o

 

Lgtjrnturn n igtndn Lgtjrntur •  Mgdrîulgin dj in`nljs nbgjrtas, Uj` tj Imaw •   Mgdrîulgi Mgdrîulginn dj tubjrïns y in`nljs, Nrtura Raimn •   Mgdrîulgi Mgdrîulginn dj in`nljs, Ugllù` Oîxgoa ∅′ ? >.: