UNIVERSIDAD NACIONAL MAYOR SAN MARCOS
DE
(Universidad del Perú, DECANA AMÉRICA)
DE
FACULTAD DE QUÍMICA, INGENIERÍA QUÍMICA E INGENIERÍA AGROINDUSTRIAL
E.A.P INGENIERÍA QUÍMICA
DEPART DEPAR TAMENTO DE OPERACIONES O PERACIONES UNITARIAS
CURSO:
Laboraorio de In!enier"a #$"%i&a I
PR'CICA: PR'CIC A:
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CONTENIDO 1. RESUMEN 2. INTRODUCCIÓN 3. HISTORIA 4. PRINCIPIOS TEÓRICOS 5. DETALLES EXPERIMENTALES . TA!ULACIÓN DE DATOS DATOS Y RESUL RESU LTADOS ". DISCUSIÓN DE RESULTADOS #. CONCLUSIONES $. RECOMENDACIONES 1%. !I!LIOGRAFÍA 11. AP&NDICE 12. GR'FICOS
INTRODUCCIÓN P()( *+ -*- -*-*) *)/ / 0 0/ / +( *6 *6- * +/7 8/7 8/7 *7 9/):(9/):(-:* :* 9()( 9/*) 9/*) /-:) /-:)/+( /+()) +/7 ((+ ((+*7 *7 * +/7 ;*) ;*)*-: *-:*7 *7 8/7 8/7 :+< :+<(- (-/ / =*)7 =*)7(7 (7 ;/)(7 * -7:)*-:/7 * *6-, :(+*7 // *+ :>/ * 9:/:.
CONTENIDO 1. RESUMEN 2. INTRODUCCIÓN 3. HISTORIA 4. PRINCIPIOS TEÓRICOS 5. DETALLES EXPERIMENTALES . TA!ULACIÓN DE DATOS DATOS Y RESUL RESU LTADOS ". DISCUSIÓN DE RESULTADOS #. CONCLUSIONES $. RECOMENDACIONES 1%. !I!LIOGRAFÍA 11. AP&NDICE 12. GR'FICOS
INTRODUCCIÓN P()( *+ -*- -*-*) *)/ / 0 0/ / +( *6 *6- * +/7 8/7 8/7 *7 9/):(9/):(-:* :* 9()( 9/*) 9/*) /-:) /-:)/+( /+()) +/7 ((+ ((+*7 *7 * +/7 ;*) ;*)*-: *-:*7 *7 8/7 8/7 :+< :+<(- (-/ / =*)7 =*)7(7 (7 ;/)(7 * -7:)*-:/7 * *6-, :(+*7 // *+ :>/ * 9:/:.
P/) *++/ *7 * )(- 9/):(-( *) +( =*+/( /- +( (+ - 8/ )+( ( :)(=?7 * -( :>*)( /:)( /-6- (+0*)(, 9()( /-/*) *+ ( ( (+ (+,, 7*7*-/ / *7:* -( =()(> =()(>+* +* * 9)/ 9)/*7 *7/ / @( 0* +/7 +/7 ( (:* :*) )(+ (+*7 *7 7* :)(-79/):(- *- ;/)( * 8/ @ *7:/7 )+(- (7 7*9)* 9/) *+ -:*)/) * /-/-*7 *))((7, /- ;)**-( * 7*6- )+(). N/)(+*-:*, +/7 8/7 *>*- 7*) (9:(/7, >/>*(/7, /-/7 @ 7:)>/7. P/) :(-:/, *>*- 7*) 7:)>/7 *- (-:(, )*+()( @ /-(>+( (*(/7. P*7 P*7:/ :/ 0* 0* +( * * ( ( * ( ( (+ (+ =/+ =/+? ?:) :) / / *- +( - -7: 7:) )( ( 7* )*( *(+ +<( <(,, *-*)(+*-:*, /- -7:)*-:/7 0* (- +() ( -( 9)*76- ;*)*-(+ (+ 9(7/ *+ 8/, 8/, 9()( -*7:)/ -*7:)/ *7:/ *7:/ 7()*/7 7()*/7 *+ :>/ * 9:/: 0* *7 */) * 8B/ 7(/ 9()( *:*)-() =*+/(*7 9-:(+*7 ( 7:-:/7 )(/7 *- -( 7*6- :)(-7=*)7(+ (+ 8/. L(7 */-*7 0* )*(+<( 7/- * +( 9)*76- -(, 0* *9*-* 9)-9(+*-:* * +( *-*)( -?:( 0* 9/7*( *+ 8/ @ +( 9)*76- *7::(, 0* =()( * (*)/ /- *+ ((+. L( *( * =*+/( 7* +/)( *(-:* +( ;*)*-( * +( 9)*76- *7::( @ -( (++(( *- -( +-*( * /))*-:*.
RESUMEN
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
HISTORIA E+ :>/ * P:/:, -=*-:(/ 9/) *+ -*-*)/ @ ;7/ ;)(-?7 ;)(-?7 H*-) H*-) P:/: P:/: **- *+ *+ (/ (/ * 1"$3 1"$3 H*-) H*-) P:/: P:/: ;* *+ 9)*)/ 9)*)/ *- *) +( )(9*< )(9*< *+ (( *- *+ )/ S*-( S*-( :+ :+<(<(-/ / *+ :>/ :>/ P:/ P:/:, :, / /(/ (/ ( -( ;/)( 7 /*)-( *- 1#%% 9/) *+ *-:/ ;)(-?7 H*-)/ D()@. H*-)@ P:/: -(* *- A)(/- F)(-( *+ 3 * (@/ * 1$5 -* -*- -*) *)/ / ;)(;)(-?7 *79* 79*(+ (+<(/ <(/ *) )+ +( ( .*- 1"24 ;* ;* -/>)(/ -/>)(/ *> *>)/ )/ * +( ((*( * *-(7 * F)(-(. U:+<6 *+ )/ S*-( 9()( 77:*-:() =()(7 * 77 :*/)(7 * -7:)*-:/7 ;* -/>)( -/>)(/ / 79*)-:* 79*)-:*-* -*-:* -:* *+ (-(+ (-(+ * M M @ )*79/)*79/-7(> 7(>+* +* *+ (*:/ 0* (7*)(>( *+ (>(7:**-:/ * (( ( M/-:9*++*). M/-:9*++*). D* *-7* *-7*( ( P:/: P:/: /*-<6 /*-<6 ( -:*)*7 -:*)*7()7* ()7* 9/) +/7 +/7 9)/>+* 9)/>+*(7 (7 * +/7 8/7 8/7 7*-/ 7*-/ @ ):(/ ):(/ 77 (-+77 (-+77 @ :*/)(7 :*/)(7 * *7( ?9/( 9/) /-7*)()+(7 -;-((7. E- *+ 7+/ XX 7* /*-<6 ( (*) 7/ * +/7 :>/7 * P:/: 9()( )*(+<() */-* */-*77 * +( =*+/( =*+/( *+ ()*. ()*. L( (7( * (*-:*7 (*-:*7 * =*+/ =*+/ *7:=/ )*+(/-(( )*+(/-(( /- *79*);*:/7 *79*);*:/7 *- *+ */) @ /- />7:)/-*7 * *+/ *- +( >/0++(. E+ :>/ :>/ /) /)-(+ (+ * P:/: :/: 9)*7 9)*7**-:( :(>( >( :)*7 :)*7 -/ -/-= -=**-* *-: -:* *7 9()( 9()( 7 (9+(6- 9):( 1K R*0*)* * /7 *(7, -( +( 9)*76- *7::( *+ 8/, +( /:)( +( 9)*76- :/:(+ / * )*(-7/ J*7::( -(K, 9()( * (++ *)=() +( 9)*76- -( 9/) ;*)*-(. 2K E9+*( // +0/ (-/?:)/ *+ ((, 0* 9/) 7 >(B/ 9*7/ *79* *7 9* / / )*0 )*0* *)* )* +/- +/-: : *7 *7 * :>/ :>/77 ** **7 7=/ =/77 9()( 9()( * * )) +(7 +(7 9)*7 9)*7/-* /-*77 7(+ 7(+*-: *-:* * *-/-: *-/-:)( )((7 (7 *- +( 9): 9):( ( JP:/ JP:/:: 76 *- 77 *9*)*-:/7 :>/7 * (+)**/) * 1.#% * +()/K. 3K S* (9+( 7/+(*-:* ( +0/7 *- +( ?9/( * P:/: (- -/ 7* /-:*9+(>(- (9+(/-*7 ( +( *6- * /))*-:*7 * (7*7 **-*)(+ @ * ()*, *- 9():+() 9( ):+() J(*)/-(K. E7:/7 E7:/7 -/-= -/-=*- *-*-: *-:*7 *7 ;*)/;*)/- 79*)( 79*)(/7 /7 9/) *+ ;7/ ;7/ (+* (+*- L L P)(-:+ J1#"51$53K, *(-:* *+ 7*/ *+ :>/ 0* ++*=( 7 -/>)*. E+ :>/ * P)(-:+ />-( *- - 7/ -7:)*-:/ (>(7 *(7 * 9)*76-. E7:(7 *(7 7/- /9()((7 *- *+ :>/ *9+*(-/ - +0/ (-/?:)/ // *+ *))/ 0* 9/7** - 9*7/ *79*/ 13, =**7
(@/) 0* *+ *+ ((, +/ 0* )** 7*-7>+**-:* +(7 *-7/-*7 *+ -7:)*-:/. U- *70*( *+ :>/ 7* *7:)( *- +( 7*-:* )(
PRINCIPIOS
TEÓRICOS
CONCEPTO DE FLUIDO D*7* *+ 9-:/ * =7:( * +( *-( * 8/7, +( (:*)( 76+/ 9** 9)*7*-:()7* *- /7 *7:(/7 76+/ @ 8/ .L( 7:-6- *-:)* *7:/7 /7 *7:(/7 )(( *- 7 )*(6- ;)*-:* ( - *7;*) /):(-:*. U- 76+/ 9** )*77:) - *7;*) /):(-:*, - 8/ -/, *- /:)(7 9(+(>)(7 (+0*) *7;*) /):(-:* (9+(/ ( - 8/, 7- 9/):() 9*0*/ 7*( *-*)() *+ /=*-:/ *+ 7/. E7:*- /7 +(7*7 * 8/ L0/7 @ (7*7. L( ;*)*-( *-:)* *7:/7 +:/7 )(( *- +(7 ;*)<(7 /*7=(7 .U- +0/7 (+ *7:() /9*7:/ 9/) ()9(/-*7 * /+?+(7 @ *)(-(7 /- )(-*7 ;*)<(7 /*7=(7 :*-* ( /-7*)=() 7 =/+*- @ ;/)() -( 79*)* +>)* *- - (9/ )(=:(:/)/ 7 -/ *7: +:(/ 9/) ())>(. E- *+ (7/ * +/7 (7*7 77 /+?+(7 *7:- @ 7*9()((7 *-:)* 7, /- ;*)<(7 /*7=(7 *79)*(>+*7. P/) +/ 0* 7*) +>)* * *9(-7/-()7* (7:( 0* *-*-:)* 9()**7 0* +/ /--*PRESIÓN EST'TICA L( *7::( * +/7 8/7 7* )*+(/-( /- +(7 9)/9*(*7 * +/7 +0/7 *- )*9/7/. U- +0/ *- *0+>)/ )*>* 76+/ ;*)<(7 * /9)*76-, (7, +( -:*-7( * *7:( ;*)<( )*>* *+ -/>)* * 9)*76- *7::( @ * +( 9)*76- 0* :*-* - 8/ *- -( +-*( / )*9*-:*. E7:( 9)*76- 7* * (*-/ - 9*0*/ (B*)/ 9*)9*-+() ( +( 79*)*. PRESIÓN DIN'MICA L( 9)*76- -( *7 (0*++( 0* * +( *-*)( -?:( *- +( (+ 7* *79+(<( *+ 8/. E7:( 9)*76- 7* ( *;*:(-/ +( ;*)*-( *-:)* +( 9)*76- * *7:(-(*-:/ @ +( 9)*76- *7::(. S* :)(:( * -( 9)*76-7:(-:-*( 0* -/)(+*-:* 7* +* (7/( ( - 9(:/ / /0*. N?)(*-:* +( 9)*76- -( *7 +( *-*)( -?:( 9/) -( * =/+*- * -( 9():+( * 8/. L( 9)*76- -( *7 * */ -/ * +/7 :?)-/7 * +( *(6- * !*)-/++, 0* 7* 9** *)=() * +( /-7*)=(6- * +( *-*)( 9()( - 8/ *- /=*-:/. E- +/7 (7/7 79+(/7, +( 9)*76- -( *7 (+ ( +( ;*)*-( *-:)* +( 9)*76* *7:(-(*-:/ @ +( 9)*76- *7::(.
TEMPERATURA DE !UL!O HMEDO E+ /-*9:/ * :*9*)(:)( * >+>/ */ 7* 9** />7*)=() /- *B*9+/ 79/-( 0* 7* 9/7** - :*)6*:)/ (+ (+ 7* +* ( (/-(/ - :)(9/ */ *- *+ >+>/, (+ 9(7() *+ ()* 9/) *7:* +:/, +* ** (+/) (+ >+>/ */ *=(9/)(-/ *+ (( 0* /-:*-*, *+ (( *=(9/)(( 7* -/)9/)( (+ ()* */, *>/ ( 0* *7:* +:/ *6 (+/) +( :*9*)(:)( *+ ()* 7-@*, 7*-/ *7:( +( :*9*)(:)( * >+>/ */. P/) +/ :(-:/ 7* 9** /-+) 0* +( :*9*)(:)( * >+>/ */ *7 -( *( * (- 7(:)(/ *7: *+ ()*. L(7 :*9*)(:)(7 * >+>/ 7*/ JT>7K @ >+>/ */ JT>K * - (7 */ 7* 9**- *:*)-() *9*)*-:(+*-:* 9/) */ * 97)6*:)/ 0* *7 - -7:)*-:/ 0* /-:*-* /7 :*)6*:)/7 * *))/ ?-:/7, -/ /- *+ >+>/ *7>*):/ 9()( *) +( :*9*)(:)( *+ ()* @ /:)/ /- *+ >+>/ >*):/ /- -( (7( **(. E+ 97)6*:)/ 7* (* )() / 7* +* -* -( /))*-:* * ()*, *7:/ 9)/=/( - *-;)(*-:/ @ +( :*9*)(:)( *+ :*)6*:)/ >*):/ *7*-* 9)*)/ )9(*-:* @ *79?7 7 +*-:(*-:* (7:( (+(-<() - =(+/) *7:(/-()/. L( +*:)( )*7:)(( *- *7:* 9-:/ *7 +( :*9*)(:)( * >+>/ */, +( (+ )*9)*7*-:( +( :*9*)(:)( * *0+>)/ +/7 8B/7 * (+/) *-:)* *+ ()* @ +( (7( 9/) (+/) 7*-7>+* @ +(7 9?)(7 * (+/) 9)/(7 9/) +( *=(9/)(6- *+ +0/ *- *+ (7. E-:)* 7 *( /-:*-(, +( ;*)*-( 7*) *-/), @ */-/-*7 * 7(:)(6-, +( :*9*)(:)( * >+>/ 7*/ 7*) (+ ( +( * >+>/ */. C/- *+ /-/*-:/ * *7:(7 /7 :*9*)(:)(7 *7 9/7>+* (++() *+ =(+/) * +( *( )*+(:=(. TE%PERATURA &U'&O TE%PERATURA &U'&O
Diferencia de temperaturas proporciona informacin de cu!nta agua "a# en e$ aire
Gasa empapada
Aire no saturado
(igura ) temperatura de *u$*o "+medo
TU!O DE PITOT E7 - */) * 8B/ 0* 7* ()(:*)<( 9/) 7*) - :>/ *7>*+:/ 0* *7: (+-*(/ /- *+ 8B/. P** *) +( =*+/( ( 9():) * +(7 ;*)*-(7 * 9)*76-. S* ()(:*)<( 9/) 7*) - */) * ((+ -)*:/ *>/ @( 0* )*7:)( ;*)*-(+*7 * 9)*76-. P/) -/7 /)/7 +(:*)(+*7 7* * +( 9)*76- *7::( P*7: * +( /))*-:* @ ( :)(=?7 *+ /)/ ;)/-:(+ 7* * +( 9)*76- * )*(-7/ JP/K / 9)*76- :/:(+ +( (+ *7 />:*-( (+ *7(*+*)() +( /))*-:* -*-:* (7:( *+ )*9/7/. E+ /)/ ;)/-:(+ :(>?- 7* /-/* // /)/ * 9(:/ @( 0* *- *7:* (:( -( ()( -?:( (*7 * +( *7::(. E- =*< * *) +( 9)*76- :/:(+ @ +( 9)*76- *7::( 9/) 7*9()(/ 7* 7*+* *) 7 ;*)*-( )*:(*-:*.
L/7 8/7 0* :*-*- ,-*)/ * R*@-/+7 (@/) (igura distri*ucin de presiones en e$ ( 1%%% 9/7**- tu*o de Pitot* :>/ * P:/: @ 9/*/7 /9/):(*-:/ -/ =7/7/ (+)**/)
(9+() +( *(6- * !*)-/++ /- )(- 9)*76-, 9():/7 * >(+(-* * *-*)( Ec-Ep-U./entrante0/sa$iente -1entrante01sa$iente -Emasaentrante0 Emasasa$iente 2334I5 E+ 77:*( *7 *+ 8/, *7:* +:/ -/ *-*)( :)(>(B/ 7/>)* 77 (+)**/)*7 J*7 *) 7/>)* *+ :(-0* @ (*7/)/7K 9/) +/ :(-:/ 7(+*-:*%, (*7 7* /-7*)( 7/:?)/ JQ7(+%K T*-*-/ *- *-:( 0* E(7( P= 2
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p v + + z γ 2 g 1
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(igura 7 puntos esta*$ecidos para rea$i8ar *a$ance de energ9a # manometr9a
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P2 = h1 ρ aire + P 3 P1 = P4 + h2 ρ aire
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1
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E+ 9)-9(+ -/-=*-*-:* * *7:* 79/7:=/ *7 0* *+ :>/ *>* *7:() 1! (+-*(/ /- +( /))*-:* @( )*6-/ 9** 7*) /-/(. P()( -+/7 * *7(+-*(*-:/ (@/)*7 ( 5 7* #rror 9)/* *))/)*7 77:(-(+*7 *- +( *( * +(7 9)*7/-*7 :/:(+ @ -( "1! Jvéase fgura 4K P/) *+ 9*0*/ :((/ *+ :>/ +( $ngulo de gui%ada *( *7 9-:(+ @ 9** 7()7* -+7/ 9()( *) 8B/ 7(--*/ *- ():*)(7 @ =*-(7 Figura 4 #&ecto del 'ngulo de
W7:(6- *+ 9*)+ * =*+/(*7 F+B/ +(-() L( 9():+( * 8/ 7* *=* ( +/ +()/ * :)(@*:/)(7 -;/)*7 *(9(7 / +-(7, *7+<-/7* -( (9( 7/>)* +( (@(*-:*.
Figura N° 5 distribución de velocidades en ujo laminar
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ur:a)
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Figura P*)+ erfles * de velocidad ara di&erente
=*+/(*7 @ 8B/ *7())/++(/ E+ 9*)+ * =*+/(*7 :*-* ( (-:*-*)7* -(+:*)(/ ( :)(=?7 *+ :*9/, -*9*-*-:**-:* * 9*0*(7 =()(/-*7 * *:)/ *-:)/ * +( :>*)(, 7*9)* 0* +( 7*6- :)(-7=*)7(+ *7:? +>)* * -:*);*)*-(7 9)/=/((7 9/) (*7/)/7 // //7 , )*/-*7 >)7(7 * -+7/ /:)/7 */)*7 * 8B/ * /)/. P/) *7( )(<6- *7 -**7()( -( +/-: +-*(+ 9)*-(+ (-:*7 0* *+ 8/ ++** (+ :>/ * P:/:.
A+ -)*7() - 8/ *- - /-:/ *+ 8B/ /*-<( ( =()() 9()( ((9:()7* (+ /-:/, *- *7:( 9():* *+ /-:/ *+ 9*)+ * =*+/(*7 *+ 8B/ =()( *- +( )*6- *+ 8B/, @ *7:* 7* *-/-( 8B/ * *-:)((. S* * 0* *+ 8/ *7 /9+*:(*-:* *7())/++(/ (-/ *+ 9*)+ * =*+/(*7 *+ 8B/ *B( * (>() *- +( )*6*+ 8B/. S *(+<(/7 *7:* 8B/ 9/)*/7 />7*)=() 0* ( +( *-:)(( *+ 8B/ 7* /9/):( // - 8B/ -;/)*, +*/ (9()** -( (9( * 9()* =7/7( *- +(7 -*(/-*7 * +( 9()* *+ :>/ 0* )** ( +/ +()/ * +( +/-: *+ :>/, (7:( 0* +/7 *7;*)7 =7/7/7 /-(:/( +( 7*6- *+ :>/, *79?7 *+ 9*)+ 7* (>(-/ 9/) *;*:/ * +/7 *7;*)7 =7/7/7 (7:( />:*-*) - 8B/ /9+*:(*-:* *7())/++(/ J=*) )( "K
E- *+ (7/ * 8B/7 :)>+*-:/7 />:*-* - 8B/ *7())/++(/ (-/ Figura * ujo 7* desarrollado :/(7 +*7 ()(:*)7:(7 * 8B/ *B(- * (>() *- +( )*6- *+ 8B/. E7:/ 9+( 0* *79?7 * +( )*6- * -+*/ -/ =7/7/ 0* :*)-( *- L, =*-* +( )*6- * *7())/++/ * 9*)+ 0* :*)-( *- *7:* (7/ *- -( +/-: L, @ -(+*-:* 7* )*0*)* -( 7:(-( (/-(+ 9()( 0* 7* *7())/++* +( *7:):)( *:(++(( *+ 8B/ :)>+*-:/ 0* :*)-( *- LE. E- *+ (7/ * 8B/7 *- :>*)(7 /- R* 1%5 +(7 9)*>(7 ( (/
P*)/ *7:(7 +/-:*7 (>(- / *- ;-6- *+ -*)/ * R*@-/+7, *7 (7 0* 9()( *+ (7/ * R*4%%% *7:(7 +/-:*7 9**7*) (7:( 5 =**7 (@/)*7 ( +(7 *-/-((7. L/7 *9*)*-:/7 (- */7:)(/ 0* *+ 8B/ *7 :/:(+*-:* *7())/++(/ J*- - 8B/ @ :)>+*-:/K (-/ +( +/-: :/:(+ *7 * 25 ( 4% =**7 *+ *:)/ * +( :>*)(.
M&TODOS PARA DETERMINAR EL CAUDAL DE FLUWO CON UN TU!O DE PITOT M&TODO DE LAS 'REAS EQUIVALENTES U- ?:// 9()( />:*-*) *+ ((+ * 8B/ ( 9():) * +(7 *:*)-(/-*7 * +( =*+/(, /-77:* *- =) +( 7*6- * :>/ * /):* :)(-7=*)7(+, *- - -*)/ (+ * )*(7 (-+()*7 @ *;*:() +( *6- * +(7 =*+/(*7 ( :)(=?7 * *7:(7 )*(7 /+/(-/ *+ (9()(:/ / -7:)*-:/ 9()( +(7 *:*)-(/-*7 * +( =*+/( *- +/7 9-:/7 /-* *7:- +/7 9)/*/7 * *7:(7 =*+/(*7. E7:/7 9-:/7 7* /-7*)(- // +/7 9-:/7 */7 * +(7 )*(7, *7 *), *- +/7 9-:/7 /-* +/7 )+/7 =*- ( *7:(7 )*(7 9/) +( :(. E+ />B*:=/ -(+ *7 />:*-*) +( =*+/( *( 0* (/9:()*/7 9()( (( -/ * +/7 --:/7 9-:/7 0* /9/-*- - *:)/ (+0*)( * +( 7*6- :)(-7=*)7(+. E- +( )( # 7* />7*)=( +( )=( )*(+ * -( 7:)>6- * =*+/(*7 @ ( +( 0* )*9)*7*-:( ( +( =*+/( *(
Figura + distribución real de velocidades (1) , velocidad media (-) A+ :+<() *+ ?:// * +(7 )*(7 *0=(+*-:*7 7* />:*-*- +(7 =*+/(*7 *(7 * (( -/ * +/7 (-++/7 * )*(7 (+*7, 9/) +/ 0* 7* />:*-* *+ =(+/) 7 *)(-/ 9/7>+* ( *7:(7 =*+/(*7. P(7/7 ( 7*) 1. D=) *+ )*( -:*)-( * +( 7*6- :)(-7=*)7(+ *- N 9():*7 (+*7, ( +(7 )-;*)*-(7 0* 7*9()(- /7 )*(7 (+*7 7* +*7 ++(() (-++/7. 2. D=) ( (( -( * *7:(7 )*(7 (+*7 *-:)* 2, />:*-*-/ (7 2N )*(7 (+*7.
3. E7:(7 -*=(7 )-;*)*-(7 7/- +/7 )(/7 */7 * +/7 (-++/7 * )*(7 (+*7. T*6)(*-:* *7 9/7>+* />:*-*) +/7 )(/7 9)/*/7 * (( (-++/ * )*(7 (+*7. E7:( (( 9/) +( 7*-:* *9)*76- D/-* N *7 *+ -*)/ * 9():*7 *+(7 0* 7* =6 +( 7*6:)(-7=*)7(+ -(+*-:* @ (*7 Z[ *7 *+ \?7/ )(/ *+ (+ 7* /-:(>+<( * +( 9():* 7 *:*)/). R *7 *+ )(/ -:*)-/ * +( :>*)(
Fig. /. 0ivisión del 'rea de la sección transversal de una tubera en anillos de 'reas iguales M&TODO GRAFICO V PROMEDIO V M'XIMA E- *7:* ?:// 7* :/( +( =*+/( ( *- *+ *B* * +( :>*)(, @ /- +/7 =(+/)*7 * *-7(, =7/7( @ /- *+ *:)/ */ 7* />:*-* *+ -*)/ * R*@-/+7. P()( (++() *+ =(+/) * +( =*+/( 9)/*/ 7* -)*7( ( +( )( V 9)/*/ V (. C/-// *7:* =(+/) (7:( +:9+()+/ 9/) +( =*+/( ( 9()( />:*-*) +( =*+/( 9)/*/. P()( />:*-*) *+ ((+ 9)/*/ 7* +:9+( +( =*+/( 9)/*/ /- *+ )*( * +( 7*6- :)(-7=*)7(+ * :)(>(B/.
Fig. 12 rafca de Niuradse ara determinar la relación de velocidad romedio versus la velocidad m'ima. M&TODO INTEGRAL E- *7:* (7/ *+ ((+ 7* (++() 9/) -:*)(6- * =*+/(*7. E;*:(-/ +( *( * +( 7:)>6- * =*+/(*7 /- *+ :>/ * P:/:, 7*-/ *+ ((+ *+**-:(+ R
dQ = v ⋅ 2π r ⋅ dr → Q = 2π ⋅
∫ v ⋅ rdr 0
E+ =(+/) * +( -:*)(+ 7* 9** *:*)-() )(*-:* (++(-/ 9()( 7:-:/7 =(+/)*7 * = *+ 9)/:/ =r , )((-/ +( )=( =r > 5(r) @ +:9+(-/ *+ )*7+:(/ 9/) 2π . C(++/ *+ )*( 0* )*9)*7*-:( *+ C((+ *(-:* *+ ?:// *+ T)(9*/
Figura 112 6'lculo del caudal or integración de velocidades.
f ( a ) + f ( b ) 2
b
∫
A = f (r )d (r ) = ( b − a ) × a
D* /-* Q=2 × π × [ ∑ Áreasbajola curva]
F-(+*-:* 7* (++( +( =*+/( 9)/*/ /- +( 7*-:* ;6)+( V m
=
Q 2
π × r
D/-* Q *7 *+ ((+ (++(/ /- *+ ?:// -:*)(+ @ ) *7 *+ )(/ *+ :>/
DETA''ES E
U- :>/ * P:/: 1 =*-:+(/) *-:);/ /- 9(+*:(7 *+/(+*7 C(+>)(/) * ;)**-( M(-6*:)/ ;*)*-(+ -+-(/ J+0/ (-/?:)/ (*:*K M*/) * 9)*76- *7::( T>*)(7 * PVC /- :)(/ * :>/ ()+/ U- 97)6*:)/ / :*)6*:)/ )/:(:/)/ U-( -( U- (+>)(/) V*)-*)
PROCEDI%IENTO E
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DISCUSIÓN DE RESU'TADOS
•
L( 9)*76- *7::( 7* (-:=/ /-7:(-:* 9()( (+0*) )(/ /7 )*79*:=( ;)**-( *7:/ 7* *>* ( 0* +( 9)*76- *7::( -/ *9*-* * 7 =*+/(
•
• •
•
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
CONCLUSIONES •
•
•
•
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RECO%ENDACIONES •
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