Ejercicios Resueltos Fluidos Ii

 

  .-GNGMZLH>

Gi ui kbibl kbibl dg khikr khikrgt gth, h, gl torb torbit itgg gs dg ,0 ,0: : m y gl baub eluyg eluyg b ui uibb vglhkodbd mgdob dg 0,4: m/s, fbstb ui kogrth puith, dhidg, dg`odh b uib kbídb,, lb vglhkodbd kbídb vglhkodbd sg glgvb glgvb b 0,:: m/s, m/s, rgdukoïidhsg rgdukoïidhsg gl torbit torbitgg b :,5: m. dgsp dg sprg rgko kobi bidh dh lb lbss ph phso so`l `lgs gs pï pïrd rdod odbs bs ph phrr er erok okko koûi ûi,,  DGT DGTGP GPMOI MOIBP BP LB DOEGPGIKOB DG IOUGL GITPG LB[ DH[ ZBPTG[ DGL KBIBL. ----------------------------------------------------------------------------------------------------------

[hlukoûi> [g togig gi kugitb qug gs ui kbibl y sg dgsprgkob lbs prgsohigs gi lhs dhs puiths. Z=:

Dbths>  [gkkoûi 2> v2= 0.4: m / s   y 2=2.0: m 

  ^  =¸ _ =8 ¸    a¸ m / s  2

?.62

sgkkoûi 0> v 0=20 m /s  y 0= 0.4: m /s  z 0= : f e =:

Zlbitgbmogith.

 

 

U=vglhkodbd gi m/s

a=arbvgdbd gi m/s0

z=doegrgikob dg iovgl rgspgkth b khtb :

Bplokbidh lb gkubkoûi dg @grihullo gitrg lbs sgkkohigs 0

0

U 2 U  + y 2+ z2= fe   + + 0 + y0+ z 0 0a 0a

y0

…...….(*)

Pgmplbzbidh vblhrgs gi lb gkubkoûi………………..……. 0

( 0.4: m / s )

+ 2.0: m + z = fe   + + 2

0

0 ( ?.62 m / s

+ :.5: m + z

0

0 ( ?.62 m / s

)

0

  ( 20 m / s ) )

y   z =:

  o fe=:

0

0

0

  ( 20 m / s ) ( 0.4: m / s ) + :.5: m+ : + 2.0: m + z = : + 0 ( ?.62 m / s ) 0 ( ?.62 m / s ) 0

2

0

:.;: + 2.0: + y = 1.4: + :.5:

 y = 6∐2.7:  y = 5.7: m

∴ lbdoegr lbdoegrgik gikob obdgl dgl iovgl iovgl gitr gitrg lhs dhs pb pbrtg rtgss dglkbibl dglkbibl

sgrbdg 5.7: m .

 

0

(*)

 

0.-GNGMZLH>

Dg ui dg dgpû pûso soth th arbidg arbidg eluyg eluyg ba baub ub dg .0 .0:p :pog ogs; s;/s /sga ga ph phrr ui sostgm sostgmbb dg tu`gríbs, khmh sg bprgkob gi lb eoaurb . KBLKWLG LB KBITODBDD THTBL DG GIGPAOB RWG [G ZOGPDG GI GL [O[TGMB DG@ODH B LB UBLUWL UBL UWLB,K B,KHDH HDH[ [ GIT GITPBD PBDB B DG TW@ TW@GP GPOB[ OB[ _ EPO EPOKKO KKOHI HI DGL ELW ELWODH ODH.. ---------------------------------------------------------------------------------------------------------

[hlukoûi>

[g togig gi kugitb qug gs uib tu`gríb tu`gríb y sg dgsprgkob lbs lbs prgsohigs gi lhs dhs puiths. Z=:

Dbths>  [gkkoûigs> R= 2.0:  pogs ; / sga   ^ 2=¸ 20¸   z 0=2;

  a¸ ?.62m / s 0  f L =8

Zlbitgbmogith.

 

 

0

 Z 2  Z + U  + U    + ^ 2 2 + F  B ∐ F  P∐ F  L = 0  + ^ 0 0 _  _  0a 0a

0

GK……. (2)

GK……. (0)

GK……. (;) ^ = BLTWPB

FBLLBIDH LB UGLHKODBD

U=

R

 B

0

R= .0: pogs;/ s0 Zbrb dgtgrmoibr lb vglhkodbd tgigmhs qug fbllbr gl ârgb >  

 

(  ) (  ) 0

0

 D  ; = ϊ  =1.:5  B = ϊ  4

4

Khivortogidh b pogs puga= :.:5? sga0 B= 1.:5V:.:5?¸ :.:4? pogs0 ;

 R 2.0: pogs v 0= =   x sga  B0

 

0

2

:.:4? pogs

=04.4 pogs / sga

0

v 0= 04.4 pogs / sga

Khivortogidh lb arbvgdbd dg m/s b pogs a = v

?.62 :.;:46

0

0

=;0.26 pogs / s 0

0

0a

=

( 04.4 )  pogs sga

0

0

  x

 

sga

0

( 0 )( ;0>26) pogs

=?.07 pogs

Pgmplbzbidh vblhrgs gi lb gkubkoûi………………..…….  GGK … .. ( ; )

 F  L=( ^ 2 ∐ ^ 0 ¸ v 00 / 0 a  F  L=07 pogs∐ ?.07 pogs  F  =27.17 pogs  L

∴ lb pgrdod pgrdodb b dggigraob dggigraob x eroko erokohi hi gs 27.17 pogs

 

(*)

 

GNGPKOKOH ;>

Grgs du Grgs dugò gòh h dg ui rg rgst stbu burb rbit itgg y gs gstâ tâss oi oivg vgst stoa oabi bidh dh iu iugv gvbs bs eh ehrm rmbs bs dg gitrgabr `g`odbs b tus klogitgs. Wib prhpugstb gs uib tu`gríb qug llgvbrâ kgrvgzbb dg rbíz dg dgisod kgrvgz dgisodbd bd ,:?:

ca ;

m

 b trbvïs dgl rgstburbitg. Wib sgkkoûi

dg lb tu`gríb sg mugstrb b khitoiubkoûi. Lhs plbihs gstb`lgkgi qug lb vglhkodbd y lb prgsoûi mbihmïtrokb dg lb kgrvgzb dg rbíz gi gl puith shi ;.:: m/s y 0,;::Zb rgspgktovbmgitg. rgspgktovbmgitg. Lb kgrvgzb dg rbíz rbíz gi gl puith 0 gstââ .0: m mâs blt gst bltbb qug gl eluo eluodh dh gi gl puit puith h y vobnb vobnb b uib vglh vglhkod kodbd bd dg :.17:m/s. Gl iþmgrh pbrb lb prgsoûi gi gl puith 0 ih sg vg klbrbmgitg.

Z2 +

2

ςv

0 2 0

2

0

+ pa f  =Z0+  ςv + pa f 0 2

2

0

0

2

2

0

Z0= Z2 +  ςv 0+ pa f2-  ςv 0+ pa f0 0

0

Gi gstg puith dg`gmhs gskhagr lb blturb f=: dg rgegrgikob. Gskhagrgmhs f=: b lb blturb dgl puith 2. Gsth gstb`lgkg qug f2=: y f0=2.0 m Bl sustuor gsths vblhrgs pbrb lbs blturbs, h`tgigmhs

2

2

2

0

Z0= Z2 +  ςv 0+ pa ( : m )-  ςv 0+ pa ( 2.0: m) 0

0

Ihs phdgmhs dgsfbkgr dgl tïrmoih khi gl kgrh y sustuor lhs vblhrgs iumïrokhs dg lbs htrbs vbrob`lgs pbrb h`tgigr, 2

Z0=20,;:: Zb+  (2,:?: 0

ca

ca ca 0 0 ∐ ∐ 02(2 , :?: (2 , :?: )(;.:: m/s )(:.17: m/s ¸ ¸ ; ; ; )a(2.0: m) m m m

Z0=4,:6: Zb

 

 

GNGPKOKOH 4>  ¸kubl gs gs lb prgsoûi prgsoûi gi gl hkïbih b uib uib prheuidodbd prheuidodbd dg 7::m suphiogi suphiogidh dh

qug>

b. Gl baub sblbdb gs oikhmprgso`lg (λ :=2:07

 ca ;

)

m

`. Gl baub dg mbr gs khmprgso`lg y togig ui pgsh gspgkíeokh gi lb supgreokog ; λ h=2:07 ca∐ e   // m   y ui mûdulh dg glbstokodbd vhlumïtrokh> @= 1 ; 02 Ñ 2: ca ∐e   // m [HLWKOHI b)

  dp =+ ςa =λ  dz dp =λdz

IHTB>  p

Khmh> λ = λ h =ktg←

 p= λ h f =2:07

∣ dp= λ  ∣ dz

eu euod odh h

gs khistbtg g oaubl gi thdhs

h

sus puiths>

h

 ca∐ e    Ñ 27:: m ; m

 p=27;17:: ca ∐ e  /  / m

th thdh

oikhmprgis oikhm prgiso`lg o`lg lb dgisodbd dgisodbd

f

h

Gi

∴ khmh ς

=ktg←λ =ktg

0

7

 p=27.;17 x 2: ca ∐ e   // m

0

 ς )  ih gs khistbitg phr `) Khmh gl uodh uodh gs oikhmprgis oikhmprgiso`lg o`lg githik githikgs gs lb dgisodbd dgisodbd( ς lh tbith gl pgsh gspgkíkh tbmphkh gs khistbitg  dp dλ   ← dp = λ  ………(O) @= λ  dλ  ← oitgiarbmhs >

←Z

 p

λ 

h

λ h

 p

λ 

 ph= :

λ h

∣ dp =@ ∣ dλ  λ 

∣ @ li∣ ← p ∐k = @ (liλ ∐ li λ  ) h

← p = @ li  ( λ / λ h )………(OO) Khmh dp =λdz …….(OOO)

Iûtgsg

qug

^

modg fbkob b`bnh

 

sg

 

 dλ   dλ  Dg (O) = (OO)> λdz = @   ← dz = @ 0 λ  λ  f

λ 

 ← f∐: =@ ∣ dz =@ ∣ dλ  λ  0

h

λ =

λ H

S  ] 2

∐

 2

λ  λ h

  λ .@ … … … . ( OU ) @∐ λ . f

(OU) gi (OO)>

 Z= @ li

 

(

)

  @  ca∐ e  =27.4;2 Ñ 2:7 0 @∐ λ H f m