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Exemplo 1

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Resolução Exemplo 1 V&'(#& R T"6(# "6(#"/ "/ TL

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Exemplo 2 2&$/.'(,( & (/8&"0($+& '( :"-&, 'M<=4" $40 6&8"#B C :"-&, ($+," $& 6&8"# " @ ( :(#&8.'"'( '( B W -,(//A& '& :"-&, $" /"?'" '& 6&8"# ; B W'0.+.$'& H4( & (/8&"0($+& /(P" "'."6<+.8&@ ,(:(,/?:(# ( (0 ,(=.0( -(,0"$($+(@ '(+(,0.$( " :(#&8.'"'( '& :"-&, $" /(%A& '( /"?'" '& 6&8"#B

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Resolução Exemplo 2 V&'(#& R T"6(#"/ TL

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Exemplo 3 Z0 .$:($+&, "#(=" +(, 8&$/+,4?'& 40 8&0-,(//&, 3,.=&,?3.8& "'."6<+.8& H4( ,(8(6( :"-&, /"+4,"'& '( G[ Q\]" " ( '(/8",,(=" & :"-&, ( B *//( -,&8(//& :.&#" " /(=4$'" #(. '" +(,0&'.$^0.8"B

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Resolução Exemplo 3 */+"'& Q D($+,"'"E R GQ\]["1 :"-B /"+B R & { R &

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. “ 7 . 7 . 7 m m m m m >m ? > * ‡{‘ š› . 0“š› 7 * F | ‡{‘ š› . * ?“š› 7 | š› . * ‡{‘ š› 7m Ÿ . 7 .m * 7 C¡— 0"/@ “ * ‡Y‘ ? ‡{‘ * d ? _ m  q * ‡ ‡ {‘ {‘ . 7m . 7m Ÿ Ÿ 7Ÿ a 7 Ÿ m  Ÿ . a 7 Ÿ * a 7Ÿ Ÿ * ˜)6B  œ a 7 œ * * q a7 X&=&@ m * m m m * Ÿ a 7m 7m . a 7

Exemplo 4 *0 40 8&0-,(//&, '( 40 -&/+& '( ="/&#.$"@ ", ; 8&0-,.0.'& '" 8&$'.%A& "06.($+( ( @ "+; " -,(//A& '( B W'0.+.$'& H4( & -,&8(//& /(P" "'."6<+.8&@ ,(:(,/?:(# ( H4( "/ :",."%>(/ '"/ ($(,=."/ 8.$;+.8" ( -&+($8."# /(P"0 '(/-,(O?:(./@ 8"#84#( & +,"6"#J& (/-(8?3.8& $& -,&8(//& '( 8&0-,(//A& ( " +(0-(,"+4," '& ", $" /(%A& '( '(/8",=" '& 8&0-,(//&,B

_ à3

e~F y _FF da3

Resolução Exemplo 4 7(( '( 2&$+,&#( R 2&0-,(//&, */+"'& Q D($+,"'"E R W,1 R R

-, * F " *F j‡ * ja * F D- * D- * D-

e~F y _FF da3

*/+"'& U D/"?'"E R W,1 R

_ à3

W-#.8"$'& " Q" X(. '" TL -"," 721

F,&8(//& R G(=.0( -(,0"$($+(

_ -,BC 0+D-& l& 0_e fm& 0 An * o 0+Dl 0 & BC # # e fm# 0 An#

F

L."=,"0"

F F

F

o DB C D- l& & * oBC 0 D-#l# | D-D-& l& * D- 0 D-# l# q p * l& ? l#

Q

-o$…

V&'(#& DU 0&'&/ '( ,(/&#:(,E R i
U

W-#.8"$'& " U" X(. '" TL -"," 721

># * >& 0 >1&2

q> *>

F

Resolução Exemplo 4 – 7(( '( 2&$+,&#( R 2&0-,(//&, */+"'& Q D($+,"'"E R W,1 R R

e~F y _FF da3

2&$/.'(,"$'& =
.m * .

*/+"'& U D/"?'"E R W,1 R

_ à3

F,&8(//& R G(=.0( -(,0"$($+( L."=,"0" Q

‡ constante

Ÿ am Ÿ | .m a

Ÿ * . aam Ÿ

| .m * e~F _FF q .m * bb~h~ y p * l ? lm * ‡Y‘ . ? .m | p * _hFF}€ e~F?bb~h~ q p * ?euFh~~ dxcdA

-o$… U

h¢ _FFF h¢

Resolução Exemplo 4 – Tabelas de Ar 7(( '( 2&$+,&#( R 2&0-,(//&,

Z+.#.O"$'& " T"6(#" '( ",

*/+"'& Q D($+,"'"E R W,1 R R

e~F y _FF da3

*/+"'& U D/"?'"E R W,1 R

_ à3

F,&8(//& R G(=.0( -(,0"$($+( L."=,"0" Q

-o$… U

*/+"'& Q D($+,"'"E

l * e~Fh}] dxcdA */+"'& U D/"?'"E >m ? > * >R‘ ? >R‘– ?“š› aam * F | >R‘ * >R‘– 0“š› aam ‘ * uh}~•Fb dxcdAy q > >R‘ * •hv]be_0Fhevuš› _FFF R _FF

Resolução Exemplo 4 – Tabelas de Ar */+"'& U D/"?'"E

>R‘ * uh}~•Fb dxcdAy

Z+.#.O"$'& " T"6(#" '( ", -"," ($8&$+,", "

Y$+(,-&#"$'&BBB

.m ?b}F * uh}~•Fb?uh}••}e q .m * bbbh•v y b•F?b}F uhbF}ee?uh}••}e lm ?b}}h•~ * uh}~•Fb?uh}••}e q lm* b•Fh~v dxcdA b•bh}u?b}}h•~ uhbF}ee?uh}••}e

. ^‚ b•F .m b}F

2<#84#& '& +,"6"#J& (/-(8?3.8&BBB

p * l ? lm * e~F}] ? b•F~v q p * ?euFbb dxcdA

.m ( lm

l dxcdA‚ b•bh}u lm b}}h•~ dx > dAy

Resolução Exemplo 4 – Comparação 7(( '( 2&$+,&#( R 2&0-,(//&,

.m * .

*/+"'& Q D($+,"'"E R W,1 R R

e~F y _FF da3

£

LA! 1&."M 0'N 0'4!#"4#.

Ÿ am Ÿ a

q .m * bb~h~ y p * l ? lm * ‡Y‘ . ? .m

*/+"'& U D/"?'"E R W,1 R

_ à3

F,&8(//& R G(=.0( -(,0"$($+( L."=,"0" Q

-o$… U

q p * ?euFh~~ dxcdA

F"O.M"! &. P%

>R‘ * >R‘– 0“š› aam q >R‘ * uh}~•Fb dxcdAy q .m * bbbh•v y q lm* b•Fh~v dxcdA

p * l ? lm q p * ?euFhbb dxcdA

Exemplo 5 C/ '(/4-(,"H4(8('&,(/ /A& 4+.#.O"'&/ -"," -,&'4O., :"-&, /"+4,"'& " -",+., '" 0./+4," '( :"-&, /4-(,"H4(8.'& 8&0 <=4" $& (/+"'& #?H4.'&B W 3.=4," "$(5" 0&/+," & (/6&%& '( 40 (H4.-"0($+& '(//( +.-& H4( ; "#.0($+"'& 8&0 '( :"-&, 'M<=4" " ( ( 8&0 <=4" #?H4.'" " L(+(,0.$( " :"OA& 0
eFF ^ ]FF da3

e rtc¤

eF ^¥ ]FF da3

Resolução Exemplo 5 7(( '( 2&$+,&#( R L(/4-(,"H4(8('&,

V&'(#& DU 0&'&/ '( ,(/&#:(,E R T"6(#"/ '( :"-&, 'M<=4"

*/+"'& Q D($+,"'"E R S=4"1 :"-&, /4-(,"HB R  R ( */+"'& U D($+,"'"E R S=4"1 #?H4.'& 8&0-B R */+"'& \ D/"?'"E R S=4"1 :"-&, /"+B R F,&8(//& R G(=.0( -(,0"$($+(

W$<#./( R BC R

D- * e dAc> eFF ^ ]FF da3 eF ^

]FF da3

L."=,"0"

- , * oBC * F j‡ * ja * F W-#.8"$'& " *HB 2&$+.$4.'"'(1

D-  0 D-m * D-„ W-#.8"$'& " Q" X(. '" TL -"," 721

_ -,BC 0+D-& l& 0_e fm& 0 An * o 0+Dl 0 & BC # # e fm# 0 An#

F

F F

F

F F

D- l 0 D-mlm * D-„l„ q D- l 0 D-mlm * D- 0 D-m‚l„ W-#.8"$'& " U" X(. '" TL -"," 721

+"# * +" & 0 "1&2 q D- „>„ * D-> 0 D- m>m 0 "1&2

Resolução Exemplo 5 */+"'& Q D($+,"'"E R S=4"1 :"-&, /4-(,"HB R  R  R  R  R 

D- * e dAc> . * eFF ^ a * ]FF da3 l * ev•bhb} dxcdA > * uh]__b dxcdAy

*/+"'& U D($+,"'"E R S=4"1 #?H4.'& 8&0-B R R m R m R m

eF ^ a * ]FF da3 l * v]h~} dxcdA > * Fhe~•• dxcdAy

Resolução Exemplo 5 */+"'& \ D/"?'"E R S=4"1 :"-&, /"+B R R „ R „ R „

]FF da3 . * _]]hbb ^ l * euebh]F dxcdA > * •h~~_v dxcdAy

Resolução Exemplo 5 G(/40.$'&BBB

W-#.8"$'& " Q" X(. '" TL -"," 721

*/+"'& Q D($+,"'"E R S=4"1 :"-&, /4-(,"HB R  R ( R  R 

D- l 0 D-mlm * D- 0 D-m‚l„ | D- l 0 D-mlm * D-l„ 0 D-ml„ D- * e dAc> l ? l  eFF ^ ]FF da3 q D- m * D- l„ ? l„m | D-m * e ev•bhb}?euebh]F euebh]F?v]h~} l * ev•bhb} dxcdA > * uh]__b dxcdAy D- m * Fh_F•e dAc>

*/+"'& U D($+,"'"E R S=4"1 #?H4.'& 8&0-B R R m R m R m

W-#.8"$'& " *HB 2&$+.$4.'"'(1

eF ^ D- „ * D- 0 D-m | D- „ * e0Fh_F•e D-„ * eh_F•e dAc> a * ]FF da3 l * v]h~} dxcdA > * Fhe~•• dxcdAy W-#.8"$'& " U X(. '" TL -"," 721 */+"'& \ D/"?'"E | " * D> ? D> ? D> D> * D> 0 D> 0 " 1 &2 „ „   m m „ „   m m 1 &2 R S=4"1 :"-&, /"+B -"1&2 * eh_F•e€•h~~_v?e€uh]__b?Fh_F•e€Fhe~•• R ]FF da3 R .„ * _]]hbb ^ -"1&2 * FhFue docy R l„ * euebh]F dxcdA * •h~~_v dxcdAy "

Escoamento Simples em PRPR* *0 -,&8(//&/ '( ,(=.0( -(,0"$($+( ( ,(:(,/?:(# D jFGFGE '( (/8&"0($+& /.0-#(/ Df$.8" ($+,"'" ( /"?'"E " "-#.8"%A& '"/ #(./ '" +(,0&'.$^0.8" ,(/4#+" (01

_ _ m , 0+Dl 0 f 0 An * o 0+Dl 0 L" X(. '" TL -"," 721 BC & & e & & BC # # e fm# 0 An# \ 0 l& 0_e fm& 0 An& * p 0 l# 0_e fm# 0 An# q p * \ 0 l& ? l# 0_e fm& ? fm# 0 A n& ? n# †, | ># * >& 0 >1&2 G †\ L" U X(. '" TL -"," 721 +"# * +"& 0 "1&2 0 G . . Q"

"

†\ !> * . 0 †>1&2 | †\ * .!> ?.†>1&2 *H4"%A& '( i.66/1 .!> * !l ?7!a # # # q †\ * !l ?7!a ?.†>1&2 Y$+(=,"$'&BBB \ * G& !l ? G& 7!a ? G& .†>1&2 # # \ * l# ? l&‚ ? G& 7!a ?G& .†>1&2

Escoamento Simples em PRPR* *0 -,&8(//&/ '( ,(=.0( -(,0"$($+( ( ,(:(,/?:(# D jFGFGE '( (/8&"0($+& /.0-#(/ Df$.8" ($+,"'" ( /"?'"E " "-#.8"%A& '"/ #(./ '" +(,0&'.$^0.8" ,(/4#+" (01

_ p * \ 0 l& ? l# 0e fm& ? fm# 0 A n& ? n# (

# # p * l# ? l& ‚ ? G& 7!a ?G& .†>1&2 # p * ?G& 7!a 0_e fm& 7"0&/ "$"#./", (/+" (H4"%A&BBB

# # \ * l# ? l& ‚?G& 7!a ? G& .†>1&2

_ 0 l& ? l# 0e fm& ? fm# 0 A n& ? n#

# ? fm# 0 A n& ? n# ?G& .†>1&2

Escoamento Simples em PRPR* # p * ?G& 7!a 0_e fm&

# ? fm# 0 A n& ? n# ?G& .†>1&2

2&0($+<,.&/1

¦&# .†>1&2 ; /(0-,( 40" /46+,"%A& '( 40 :"#&, [ F ( " 0".&, -,&'4%A& '( o &8&,,( -"," & 8"/& '& -,&8(//& ,(:(,/?:(#B UB *0 40 -,&8(//& ,(:(,/?:(#@ & o '( (.5& ; "//&8."'& 8&0 :",."%>(/ '( a@ j‡ &4 ja '( .$'.:.'4"# &4 8&06.$"'&B k4"$'& " a § D6&06" &4 8&0-,(//&,E & o +($'( /(, ?@ &4 /(P"@ o ($+," $& 72@ ( H4"$'& " a ¨ D+4,6.$"E@ & o +($'( /(, 0B # \B I( $A& J< o '( (.5& $& 72@ ($+A& & +(,0& ¦& 7!a '(:( /(, $4#&B _(//( 8"/&@ & QB C +(,0&

"40($+& '( :"#&, '( 40 '&/ +(,0&/ '(:( /(, 8&0-($/"'& -(#" '.0.$4.%A& '( &4+,&@ ( '(:(0&/ &6/(,:", ".$'" H4( & f#+.0& +(,0& /(0-,( /46+,".B 2&0& (5(0-#&@ +&0(0&/ & 8"/& '( 40 (/8&"0($+& ,(:(,/?:(# /(0 :",."%A& '( ( B *$+A&@ 8&0& & f#+.0& +(,0& ; $4#&@ " ; 8&$/+"$+( $& (/8&"0($+&B _& 8"/& ,("#@ & (/8&"0($+& +(0 /(0-,( "#=40 "+,.+&@ /($'&@ -&,+"$+& .,,(:(,/?:(#@ (5.=.$'& H4( & -,.0(.,& +(,0& /(P" -&/.+.:& D" '(/8,(/8(EB

ja

a a

j‡

Escoamento Simples em PRPR # p * ?G& 7!a 0_e fm&

# ? fm# 0 A n& ? n# ?G& .†>1&2

*/+" (5-,(//A& ; "-#.8"'" " -,&8(//&/ '( (/8&"0($+&@ +"./ 8&0& (0 +4,6.$"/@ 8&0-,(//&,(/ ( 6&06"/B

# _ p * ?G& 7!a 0e fm&

# ? fm# 0 A n& ? n# ?G& .†>1&2

F

# q p * ?G& 7!a

F

F

l .0-&,+"$+( '(/+"8", H4( (//( ,(/4#+"'& "-#.8"[ /( /&0($+( N /.+4"%A& '( 40 './-&/.+.:& 8&0 (/8&"0($+& '( 40 3#4?'& (

# ?G& 7!a

*.5&

m © G a!7

m,&$+(.,"

Escoamento Simples em PRP # p * ?G& 7!a 0_e fm&

# ? fm# 0 A n& ? n# ?G& .†>1&2

7 * ˜)6¥‚ # _ m m p * ?7a# ? a&‚ 0 e f& ? f# 0 A n& ? n# ?G& .†>1&2 I( 3&, %.,.%!Q,.M "1&2 * F ”
Exemplo 6 2"#84#( & +,"6"#J& ./($+,&-.8"0($+( '(

(/-(8?3.8& -"," ( "+;

6&06(", B

_FF da3 ]F ^ b à3

Bomba d’água Repare que na saída há o pequeno efeito de difusor, que reduz a velocidade para recuperar mais pressão. A entrada é no centro da parte traseira. O motor elétrico esta na direção da camara de bombeamento.

<=4"

Exemplo 7 2&$/.'(,( 40 6&8"# 4+.#.O"'& -"," $(64#.O", <=4" #?H4.'"B I( " -,(//A& '" #.$J" 3&, ( " +(0-(,"+4," '" <=4" @ H4"# " :(#&8.'"'( '& (/8&"0($+& $" /(%A& '( /"?'"@ "'0.+.$'& 6&8"# .'("#n

]FF da3

Nebulizador Repare que na saída há estreitamento da tubulação provocando o aumento da velocidade.

eF ^

Exemplo 8

b^ FhFv dAc> ] do •b ^ ] à3 ]F ^

7"-&, /"+4,"'& '( G[]QoW " ($+," (0 40 8&0-,(//&, $A& ./&#"'& '( 40" 8($+,"# '( ", 8&$'.8.&$"'& '&0;/+.8"B W :"OA& '( 3#4?'& ,(3,.=(,"$+( ; ( " -&+9$8." 3&,$(8.'" "& 8&0-,(//&, ; '( B C (/+"'& '( /"?'" '& 3#4?'& '& 8&0-,(//&, ; '( ( B W +,"$/3(,9$8." '( 8"#&, &8&,,( -"," "06.($+( " B L(+(,0.$( " +"5" '( =(,"%A& '( ($+,&-." $& -,&8(//&B

Aplicações de Engenharia m"O(, 40 ,(/40& '"/ "-#.8"%>(/ '( ($=($J",."@ :(,.3.8"$'& " '.3(,($%" ($+,( "/ 0
A diffuser reduces velocity. A jet engine nozzle.

Nozzles with lift fans for the F35B

A water nozzle

Diffuser on a Ford GT

A plate heat exchanger. The black lines are seals (gaskets). Alternate layers are used, one fluid is red the other fluid flow is blue. Flow is between the two holes not covered by a gasket around it.

A storage rack with the plates for heat exchangers.

© C. Borgnakke

A counter-flow heat exchanger

A nitrogen compressor with an intercooler driven by a hydraulic motor. The intercooler sketch is on the left and the real thing is the pipe shown on the right in the red box.

Aula 8 - 2a Lei Da TD - Volume de Controle

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