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  • 7/21/2019 Fluid Mechanics Theory_E

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    \ARZBJZ

    "dfibsagudfrpaysbjs.bi" 6

    @M^BC DNJAFIBJZ

    CN@ BIB SBKI K@ @M^BCSan tnrd `mubc rn`nrs tk f suestfijn taft jfi `mkw fic ckns ikt afvn f safpn k` bts kwi. @kr

    nxfdpmn mbqubc fic hfsns.

    @mubc bijmucns prkpnrty (F) Cnisbty (E) Pbsjksbty (J) Eumg dkcumus k` nmfstbjbty (C) prnssurn(N) spnjb`bj hrfvbty

    \UNZZ^UN BI @M^BCSan prnssurn p bs cn`binc fs tan dfhibtucn k` tan ikrdfm ` krjn fjtbih ki f uibt sur`fjn frnf.

    \ 4F

    @

    @ 4 ikrdfm `krjn ki f sur`fjn frnf F.

    San prnssurn bs f sjfmfr qufitbty. Sabs bs enjfusn aycrkstftbj prnssurn bs trfisdbttnc nqufmmy bi

    fmm cbrnjtbkis wani `krjn bs fppmbnc, wabja sakws taft f cn`bibtn cbrnjtbki bs ikt fsskjbftnc wbta

    prnssurn.

    Sarust.San tktfm `krjn nxnrtnc ey f mbqubc ki fiy sur`fjn bi jkitfjt wbta bt bs jfmmnc tarust k` tan mbqubc.

    JKIZNV^NIJNZ K@ \UNZZ^UN(b) Ufbmwfy trfjgs frn mfbc ki mfrhn sbznc wkkcni kr brki smnnpnrs. Sabs bs enjfusn tan wnbhat (`krjn)

    k` tan trfbi bs sprnfc kvnr f mfrhn frnf k` tan smnnpnr. Sabs rncujns tan prnssurn fjtbih ki tan

    hrkuic fic anijn prnvnits tan ybnmcbih k` hrkuic uicnr tan wnbhat k` tan trfbi.

    (bb) F safrp gib`n bs dkrn n``njtbvn bi juttbih tan keonjts tafi f emuit gib`n.

    San prnssurn nxnrtnc 4 @krjn/frnf. San safrp gib`n trfisdbts `krjn kvnr f sdfmm frnf fs

    jkdpfrnc tk tan emuit gib`n. Anijn tan prnssurn nxnrtnc bi jfsn k` safrp gib`n bs dkrn tafi bi

    jfsn k` emuit gib`n.

    (bbb) F jfdnm wfmgs nfsbmy ki sfic eut f dfi jfiikt bispbtn k` tan `fjt taft f jfdnm bs duja anfvbnr

    tafi dfi.

    Sabs bs enjfusn tan frnf k` jfdnms `nnt bs mfrhn fs jkdpfrnc tk dfis `nnt. Zk tan prnssurn

    nxnrtnc ey jfdnm ki tan sfic bs vnry sdfmm fs jkdpfrnc tk tan prnssurn nxnrtnc ey dfi. Cun tk

    mfrhn prnssurn, sfic uicnr tan `nnt k` dfi ybnmcs fic anijn an jfiikt wfmg nfsbmy ki sfic.

    P UB SBKI K@ \UNZZ^UN XBSA ANBHASFs su dp tbki s ? (b ) uifj jn mnrftn c mbqu bc (b b) uib` kr d cnis bty k` mbqubc (b bb ) uib`kr d hr fv bty

    Xnbhat k` tan sdfmm nmndnit ca bs efmfijnc ey tan nxjnss prnssurn. Bt dnfisca

    cp4h.

    \

    \f

    hcp a

    < I bs fppmbnc ki tan wftnr bi tan tabjgnr frd. Xaft `krjn

    sakumc en fppmbnc ki tan wftnr bi tan tabiinr frd sk taft tan wftnr dfy rndfbi bi

    nqubmberbud;

    Zkmutbki ? Bi nqubmberbud, tan prnssurns ft tan twk sur`fjns sakumc en nqufm fs tany mbn bi tan sfdn

    akrbzkitfm mnvnm. B` tan ftdkspanrbj prnssurn bs \ fic f `krjn @ bs fppmbnc tk dfbitfbi tan

    nqubmberbud, tan prnssurns frn

    \ h jd: , fic ft snf mnvnm, h 4 212> 21

  • 7/21/2019 Fluid Mechanics Theory_E

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    \ARZBJZ

    "dfibsagudfrpaysbjs.bi" 3

    \ \f

    4 h (y5

    y6) 4 hy

    \ 4 feskmutn prnssurn, \ \f

    4 hfuhn prnssurn.

    Saus, gikwbih y fic (cnisbty k` mbqubc), wn jfi dnfsurn tan hfuhn prnssurn.

    Nxfdpmn 5. S a n d f i k d n t nr s a k w i e n m k w b s u s n c t k d n f s u r n t a n c b ` `n r n i jn b i w f tn r m n v n m

    entwnni tan twk tfigs. Jfmjumftn tabs cb``nrnijn `kr tan jkicbtbkis bicbjftnc.

    Zkmutbki ? \f

    + a6h 3

  • 7/21/2019 Fluid Mechanics Theory_E

    5/17

    \ARZBJZ

    "dfibsagudfrpaysbjs.bi" >

    y c5 \

    x

    c6

    \f

    F F

    Bi J.H.Z.\

    f+ 6:.0 5 5> h + 6:.0 50 h 4 \

    \f

    + 6:.0 h W>< + 50T 4 \

    5\f

    4 \ W\f

    4 6:.0 h 80T

    Nxfdpmn 3. @bic kut prnssurn ft pkbits F fic E. Fmsk `bic fihmn .

    Zkmutbki ? \ rnssurn ft F \F

    4 \ftd

    6

    hm sbi\rnssurn ft E \

    E4 \

    ftd+

    5 ha

    Eut \E

    bs fmsk nqufm tk \E

    4 \F

    +:

    hm sbi Anijn - \

    ftd+

    5ha 4 \

    F+

    :hm sbi

    \ftd

    +5

    ha 4 \ftd

    6

    hm sbi + :

    hm sbi

    sb i 4)(

    a

    6:

    5

    .

    Nxfdpmn >. Bi tan hbvni `bhurn, tan jkitfbinr smbcns ckwi wbta fjjnmnrftbki

    f ki fi bijmbin k` fihmn . Mbqubc bs stftbkifry wbta rnspnjttk jkitfbinr. @bic kut -

    (b) Fihmn dfcn ey sur`fjn k` mbqubc wbta akrbzkitfm pmfin.

    (bb) Fihmn b` f 4 h sbi .

    Zkmutbki ? Jkisbcnr f `mubc pfrtbjmn ki sur`fjn. San `krjns fjtbih ki bt frn sakwi bi `bhurn.

    4

    Unsumtfit `krjn fjtbih ki mbqubc sur`fjn, wbmm fmwfys ikrdfm tk bt

    tfi 4

    sbidfdh

    jksdf4

    )sbifh(

    jksf

    Saus fihmn k` mbqubc sur`fjn wbta tan akrbzkitfm bs nqufm tk 4 tfi6)sbifh(

    jksf

    (bb) B` f 4 h sbi , tani 4 tfi6

    5sbihh

    jksf 4 tfi6 5jkshjkssbih

    4 tfi6 (tfi ) 4

  • 7/21/2019 Fluid Mechanics Theory_E

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    \ARZBJZ

    "dfibsagudfrpaysbjs.bi" 0

    Nxfdpmn 0. Xftnr fic mbqubc bs `bmmnc up enabic f squfrn wfmm k` sbcn. @bic kut

    (f) \rnssurns ft F, E fic J (e) @krjns bi pfrt FE fic EJ

    (j) Sktfm `krjn fic pkbit k` fppmbjftbki k` `krjn. (inhmnjt ftdkspanrn prnssurn bi nvnry

    jfmjumftbki)

    Zkmutbki ? (f) Fs tanrn bs ik mbqubc fekvn F,

    Zk prnssurn ft F, \F

    4 + 5.>T + 6 +:

    6 8.> 6.05 6< 0 4

    :

    8>.661 6< 0

    Sktfm tkrqun 4:

    6.66 8+

    :

    6.6 84

    :

    6.6: 8

    Sktfm tkrqun 4 tktfm `krjn cbstfijn k` pkbit k` fppmbjftbki k` `krjn `rkd tkp 4 @ . xp

    0.5> 6 :

    Sktfm tkrqun 431

    h62 3+

    53

    h 34

    31

    h56 3

    Eut @ xp

    431

    h56 3 p

    1

    h> :

    4

    31

    h56 3

    xp

    4: