aula 07 - equação da conservação da massa na forma integral

7/22/2019 Aula 07 - Equação da conservação da massa na forma integral

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Lnhébjho aes `mujaes J Vre`. Xtreinm

Lnhébjho aes `mujaes J Vïgjbo ? an 0

Lnhébjho aes @mujaes J

Ynmoçþns Jbtngrojs poro ul Pemuln an Hebtremn

Hebsnrvoçèe ao losso

Ver

Hcrjstjob Xtreinm

" Nu bèe inie ïguo… Es pnjxns trobsol bnmo..."

- Celnr Xjlpseb

?. Eidntjve

O hebsnrvoçèe ao losso n o hebsnrvoçèe ao nbnrgjo sèe obïmjsns ùbaolnbtojs poro e

nstuae ae helpertolnbte an sjstnlos. O portjr anstos obïmjsns pean-sn quobtj`jhor hel prnhjsèe

preprjnaoans ae sjstnlo n prnvnr snu helpertolnbte, suo n`jhjäbhjo n ulo sêrjn an hebajçþns anùbhjebolnbte. Hele e `mujae ê òhjmlnbtn anèrlïvnm, be snu nstoae ê helul an`jbjrles ulo

rngjèe ae nspoçe, qun anbeljboles vemul an hebtremn, n eisnrvoles es `muxes an losso qun

eherrnl bos `rebtnjros. Hel jsse peanles òhjmlnbtn nstoinmnhnr o vorjoçèe an losso anbtre

anstn vemuln. O hebsnrvoçèe ao losso ê o iosn poro e nbtnbajlnbte ao hebsnrvoçèe ao nbnrgjo n

o suo opmjhoçèe bèe sn rnstrjbgn nxhmusjvolnbtn o nbgnbcorjo.

9. @erlumoçèe lotnlïtjho

Hele vjste obtnrjerlnbtn, o èrlumoçèe lotnlïtjho poro quojsqunr grobanzos `ìsjhos nl

ul vemuln an hebtremn bo èrlo jbtngrom ê aoao pnme tnernlo ae trobspertn an Ynybemas4

)

E prjlnjre prjbhìpje `ìsjhe oe quom opmjho-sn o rnmoçèe jbtngrom poro ul vemuln an

hebtremn ê o hebsnrvoçèe ao losso. Ê jbtujtjve qun o losso bnl pean snr hrjoao bnl anstrujao; sn

o vozèe nl losso poro anbtre an ul vemuln an hebtremn nxhnanr oqunmo qun soj, o losso

ohulumor-sn-ï anbtre ae vemuln an hebtremn.




Lnhébjho aes `mujaes J Vïgjbo 9 an 0

Xoinbae nbtèe qun o hebsnrvoçèe ao losso anhmoro qun o losso nl ul sjstnlo ê

hebstobtn,

)

Eban

Opmjhobae o nquoçèe iïsjho vjste be jbìhje4

)

N hcolobae B < l n η < ?, tnles4

)

Ossjl,

9.?. Hoses Nspnhjojs

9.?.?. Yngjln pnrlobnbtn

Voro sjstnlo epnrobae nl rngjln pnrlobnbtn4

Pjste os preprjnaoans bèe sn omtnrornl hel e tnlpe.





9.?.9. Nsheolnbte ubjajlnbsjebom seirn ulo pmoho pmobo

Voro ul `muxe seirn ulo pmoho pmobo an morguro M hel pnr`jm an vnmehjaoans n anbsjaoan

vorjobae hel y, hcngo-sn o4

9.?.8. Nsheolnbte jbhelprnssìvnm

Hose o anbsjaoan pnrlobnço hebstobtn, hcngo-sn os sngujbtns nxprnssþns, qun bes mnvol

oe hebhnjte an vozèe vemulêtrjho4

Voro ul vemuln an hebtremn bèe anèrlïvnm eban ê `jxe, tnl-sn4

∫ (O vozèe vemulêtrjho an soìao anvn snr jguom o an nbtroao)

∫ (Pozèe vemulêtrjho nl ulo snçèe)

Betobae qun bèe èj `njto o supesjçèe ae nsheolnbte snr nl rngjln pnrlobnbtn, n sjl o

rnstrjçèe ae nsheolnbte snr jbhelprnssjvnm nl ul vemuln an hebtremn bèe anèrlïvnm.

8. Nxnrhìhjes

?. ^sobae es opebtolnbtes an oumo, lestrn hele surgn e sjbom pesjtjve poro o vozèe

lïssjho an nbtroao n e sjbom bngotjve poro o vozèe lïssjho an soìao.

9. Hele sn pean an`jbjr o vozèe vemulêtrjho bo èrlo jbtngrom5

8. _uom o vozèe lïssjho nbtrn os pmohos5 Aoaes4 Morguro aos pmohos<16hl, ajstébhjo nbtrn os

pmohos < 86hl;

8 l/s





1. _uom o lïxjlo vnmehjaoan bo soìao ae nsheolnbte nbtrn auos pmohos ajstobtns 16hl,

soinbae qun e pnr`jm an vnmehjaoans bo nbtroao ê ubjèrln, hel u < 9l/s, n bo soìao

poroiømjhe, n qun o pmoho supnrjer levn-sn hel vnmehjaoan an ? l/s.

>. Auos herrnjos an morguro >6hl levnl-sn hel vnmehjaoans an ?l/s (supnrjer) n 9l/s

(jb`nrjer) jlnrsos oe or hel anbsjaoan jguom o ?,9 kg/l8. O ajstébhjo nbtrn os herrnjos ê an

?6hl n e pnr`jm an vnmehjaoans nbtrn os herrnjos ê mjbnor. Antnrljbn o pesjçèe qun sn anvn

hemehor ulo pmoho ajvjsero an `muxe, nbtrn os herrnjos, poro qun o vozèe lïssjho nbtrn o

pmoho ajvjsero n herrnjos sndo jaäbtjho.

0. E tobqun oinrte ao `jguro hebtêl ïguo o 96¶H n pessuj

ulo teloao an ïguo bo snçèe ?. Ossulo

helpertolnbte jbhelprnssìvnm. Vrjlnjrolnbtn, hcngun

o ulo nxprnssèe obomìtjho poro o vorjoçèe ae bìvnm an

ïguo, ac/at nl tnrles aes `muxes vemulêtrjhes an ïguo

(_?, _9 n _8) n e ajélntre ae tobqun a. Opøs jste, sn o

omturo c ao hemubo an ïguo èr lobtjao hebstobtn,

antnrljbn o vnmehjaoan an soìao P9 poro es aoaes

èrbnhjaes. P? < 8l/s n _8<6,6? l8/s.

7. O ielio an dote jmustroae jbdnto ïguo o ^? < 16 l/s

per ulo pnqunbo tuiumoçèe an 8“ an ajélntre n sn

ljsturo hel ul `muxe an ïguo snhubaïrje o ^9 < 8

l/s nxjstnbtn bo rngjèe obumor ae pnqunbe tuie. Es

aejs `muxes sn terbol tetomlnbtn ljsturoaes, eban ^8

ê protjholnbtn hebstobtn. Voro nsheolnbte jbhelprnssìvnm n nl rngjln pnrlobnbtn,

homhumn ^8, nl l/s.

3. ^l tobqun rìgjae hel vemuln an 6,6> l8 hebtêl or o 366 kVo (oisemutes) n ?>¶H. Nl

t < 6, e or nshopo ae tobqun otrovês an ulo vïmvumo hel ulo ïrno an nsheolnbte an 0>

ll9. E or qun posso pnmo vïmvumo tnl ulo vnmehjaoan an 8?? l/s n ulo anbsjaoan an




Lnhébjho aes `mujaes J Vïgjbo > an 0

0,?8 kg/l8. Os preprjnaoans be rnste ae tobqun peanl snr hebsjanroaos ubjèrlns o hoao

jbstobtn. Antnrljbn o toxo jbstobtébno an vorjoçèe an anbsjaoan ae or be tobqun, nl t<6.

:. ^lo `jbo holoao an mìqujae, arnboao nl ul pmobe jbhmjboae,

hebèrln jmustroae, pessuj ul pnr`jm an vnmehjaoan (

, eban ^6 ê o vnmehjaoan bo supnr`ìhjn. Xn e

pmobe pessujr ulo morguro i (poro anbtre ae popnm), antnrljbn

o nxprnssèe poro o vozèe vemulêtrjho be `jmln. Xupebco qun c

< 6,>“ n qun o vozèe per lntre an morguro ê 6,30 l8/c. Nstjln o vnmehjaoan supnr`jhjom ^6

nl l/s.

?6. Ømne, hel anbsjaoan Ϗ < 3:6 kg/l8 nbtro nl ul hebaute n

nsheo an èrlo jbhelprnssìvnm n nl rngjln pnrlobnbtn hel

vnmehjaoan ubjèrln, u < ^6 < 3 hl/s, nbquobte qun oe mebge

ae aute e nsheolnbte sn ansnbvemvn an èrlo poroiømjho hel pnr`jm an vnmehjaoans u <

o.z.(z6-z), eban o ê ulo hebstobtn. Xn z6 < 1hl, quom e vomer ao vnmehjaoan lïxjlo, u lïx,

nl hl/s5

??. Ømne, hel Ϗ < 3:6 kg/l8 nbtro pnmo snçèe ? hebèrln jmustroae

hel ulo vozèe lïssjho an 9>,> kg/c poro muirj`jhoçèe an ullobhom. E ømne soj nl rngjln pnrlobnbtn roajomlnbtn bo èmgo

nbtrn os pmohos. Antnrljbn o vozèe vemulêtrjho an soìao, nl lM/s

n o vnmehjaoan lêajo an soìao, nl hl/s.

?9. ^l `mujae jbhelprnssìvnm nsheo seirn ulo pmoho

pmobo, hele jmustroae, hel ul pnr`jm an vnmehjaoans

ubjèrln bo nbtroao n ul pnr`jm bo soìao aoae pnmo

nxprnssèe

(

(

. Xoinbae qun Ϗ<?,91 kg/l8, i < 6,0 l, ^6 < 86 l/s n α <

>ll, antnrljbn o vozèe lïssjho bo rngjèe supnrjer ae vemuln an hebtremn.





?8. ^lo snrjbgo cjpeaêrljho hebtêl ul

lnajholnbte mìqujae hel Ϗ<?666 kg/l8. Xn nstn `mujae ê

jbdntoae hel ulo vozèe hebstobtn an 0 hl8/s, (o) quom o

vnmehjaoan ae älieme sn bèe ceuvnr vozolnbte nbtrn e

nlieme n o snrjbgo n (i) sn ceuvnr ul vozolnbte an ?6% nbtrn e nlieme n o snrjbgo5

?1. Mìqujae ê arnboae an ul tobqun hjmìbarjhe, an ajélntre A < >66 ll, per ulo

oinrturo, a < ?6 ll, be ùbae. O vnmehjaoan ae mìqujae soìbae ae tobqun ê an oprexjloaolnbtn

∔ , eban c ê o ajstébhjo vnrtjhom ae ùbae ae tobqun æ supnr`ìhjn mjvrn. Xn e tobqun nstjvnr

jbjhjomlnbtn hcnje an ïguo otê ulo ajstébhjo an 6,> l ae ùbae ae tobqun, (o) antnrljbn o

preùbajaoan be jbstobtn t < 96 sngubaes, (i) e tnlpe bnhnssïrje poro e nsvozjolnbte helpmnte

ae tobqun n (h) quom e beve tnlpe sn e ajélntre ae arnbe èr aupmjhoae.

?>. ^l rnsnrvotørje hñbjhe, hel ébgume ao gnrotrjz (lnje hebn) an γ¶, anjxo e mìqujae

nshopor per ul erj`ìhje an ajélntre a < ?6 ll be snu vêrtjhn. O vnmehjaoan ae mìqujae soìbae ae

tobqun ê an oprexjloaolnbtn ∔ , eban c ê o ajstébhjo vnrtjhom ae ùbae ae tobqun æ

supnr`ìhjn mjvrn. Xn c < 166 ll, antnrljbn e tnlpe an nsvozjolnbte ae tobqun sn (o) γ < 86¶; (i)

γ < 1>¶ n (h) γ < 06¶.

?0.

^l rnsnrvotørje hel èrlote an ul trebhe an hebn, hel ébgume ao gnrotrjz (lnjehebn) an γ¶, anjxo e mìqujae nshopor per ul erj`ìhje an ajélntre a < ?6 ll be ùbae. O

vnmehjaoan ae mìqujae soìbae ae tobqun ê an oprexjloaolnbtn ∔ , eban c ê o ajstébhjo

vnrtjhom ae ùbae ae tobqun æ supnr`ìhjn mjvrn. Xn c < 166 ll, antnrljbn e tnlpe an

nsvozjolnbte ae tobqun sn (o) γ < 86¶; (i) γ < 1>¶ n (h) γ < 06¶.

aula 07 - equação da conservação da massa na forma integral

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