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ssrtçã♦ ♣rs♥t ♦ Pr♦r♠

Pósrçã♦ ♠ ♥♥r â♥ ♦

♥tr♦ ê♥s ♥♦ós ❯♥r

s ♦ st♦ ♥t tr♥ ♦♠♦

rqst♦ ♣r ♣r ♦t♥çã♦ ♦ ít♦

str ♠ ♥♥r â♥

r♥t♦r Pr♦ r ❱③ r

♦♦r♥t♦r Pr♦ r P♦ ér♦ r

♥ ❩♥s

❱

Ficha catalográfica elaborada pelo(a) autor(a), com auxílio do programa de geração automática da

Biblioteca Setorial do CCT/UDESC

Perão, Leandro Henrique Simulação numérica da transferência de calorconjugada de escoamentos turbulentos em canaisaletados / Leandro Henrique Perão. - Joinville ,2017. 156 p.

Orientador: Miguel Vaz Jr Co-orientador: Paulo Sérgio Berving Zdanski Dissertação (Mestrado) - Universidade do Estadode Santa Catarina, Centro de Ciências Tecnológicas, Programa de Pós-Graduação em Engenharia Mecânica,Joinville, 2017.

1. Troca térmica conjugada. 2. Escoamentoturbulento. 3. Canais de placas paralelas aletadas.I. Vaz Jr, Miguel. II. Zdanski, Paulo SérgioBerving. , .III. Universidade do Estado de SantaCatarina, Centro de Ciências Tecnológicas, Programade Pós-Graduação em Engenharia Mecânica. IV. Título.

♦s ♣r♦ss♦rs ♦ PP ♣♦r ♥trr ♠s ♦ q ♣rt ♦ ♦♥♠♥t♦

♣♦r s♥r♠ çã♦ ♦ ♣r♦ss♦♥s♠♦ rç♦ s♣♠♥t ♦ Pr♦

t♠é♠ ♦ Pr♦ ❩♥s ♣ ♦♣♦rt♥ ♣♦ t♠♣♦ ♦ ♣r s rçõs

st ♦tr♦s tr♦s

♦s q ♦r♠ ♣rr♦s ♥♥t♦rs ♦♦r♦rs ♦s r ♣

ss♦ ♠r ♥r ♦sé r♦s ♥r ♦♥③③ ♦s P♦♥ts ♦ã♦ ♦rt♦

♥③ ♦♠r ❲③② r ♦♠♣r♥

P ♦♦r♥çã♦ ♣rç♦♠♥t♦ Pss♦ í ♣r♦r ♣♦

♥♠♥t s♣♦rt ♥♥r♦ ♠♥t ♦s st♦s r♥t ♦ ♣r♦r♠

♦s ♥♦♥ár♦s ♦♥trt♦s ❯ ♣ ss♥ ♦♦rçã♦ ♣rtr s

rs♣ts ♥çõs srtr ♦t ♠♣③ â♥ t

rs tt rs tt ♦♥ tr

♦t② ♥ tt rs ssr rs ♥

s♦ ♦♥ t♦ s♦st②s r② rs♦♥

①st ♥tr ♦ês é♠ q s sá♦

♥t♥t P♦s ♥tã♦ q ♣r♦ ss♦ ♣♦

s ♦♠ ♦♠♣♦rt♠♥t♦ ♣s ss çõs

♣rts ♦♠ ♠ s♦r♦

❯

s♦♠♥t♦ tr♥t♦ ♣r♠♥♥t ♠é♦ ♠ ♦ ♥t♦♥♥♦ ♠ ♥s ♦

r③♦♥ts ♠♥s♦♥s ♦♠ ts ♣♥s tr♥srs♠♥t ♥♥s s♣♦sts

♦r♠ ♥ ♦ s♥ ♦ st♦ trés s♠çã♦ ♥♠ér ♥t♦ s

♣rs ♦s ♥s q♥t♦ s ts s qs ♦♠♣õ♠ ♦ ♦♠í♥♦ só♦ ♣♦ss♠ s♣s

sr sã♦ ♦♥t♦rs ♦r st ♦r♠ ♦s ♠ ♦♥srçã♦ tr♦ tér♠

♦♥ ♥tr ♦ só♦ ♦ ♦ s ♦t♦s ♣r♥♣s sã♦ ♦ st♦ ♥ê♥

rçã♦ ♣râ♠tr♦s ♦♠étr♦s r♦♥â♠♦s s♦r tr♥srê♥ ♦r

♣r r s rçõs ♦♠étrs ♦r♥♠s ♦s rr♥♦s ts

♥♦ s♥♦ ♥♦ â♥♦s ♥♥çã♦ s ts 90 té 0 ♥♦ s♥t♦

♦ s♦♠♥t♦ té três r③õs ♦q♦ t ♦s s♣ç♠♥t♦s ♥tr ts

t♦t s♦s ♦♠♥ s rçõs ♦♠étrs ♦♠ três r♥ts ♦♥çõs r♦♥â

♠s ♦♠♥t s♦r s ♣rs ♥ çã♦ é t trés ♦ ♦♥t

trt♦ s♣r Cfx ♦ ♥ú♠r♦ sst Nux çã♦ ♦ é r③

♦♠ s ♥♦ ♦♥t ♣rssã♦ Cp ♥♦ ♥ú♠r♦ sst ♠é♦ ♠♦♦ Nu

♦r♠çã♦ ♠ ♦♥srçã♦ ♦ ♦r tr♦♦ ♣s ts ♥s ♦r♠

r ♥ê♥ ♠s s♥t ♦s ♣râ♠tr♦s ♦♠étr♦s é r③ã♦ ♦q♦

t s ♣ ♥♥çã♦ ♣♦r ♠ ♣♦ s♣ç♠♥t♦ ♥tr s ts ♦r♦

♦♠ ♦s rst♦s tr♦ tér♠ ♦ é t ♣ ♦r♠çã♦ ③♦♥s rrçã♦

①♦s r♥ts t♠♣rtr ♣s rõs r♦♠♥t♦ t♦s r♥ts

t♠♣rtr s ♣rs ♦s ♥r ♦ s♦♠♥t♦ ♣r♥♣ ♦♦rr♠ ♣♦r s

♠♥t♦ ♦♠ ♦s órts Cfx ♥t♦ ♣♦r s♠♥t♦ ♦♠ s s♣rís s ♣rs

♦ ♥ Cfx ♣♦st♦ ♣r♥♣♠♥t s ♠♦rs rçõs ♦s s s♦r s

♣rs ♦ ♥ ♦♦rr♠ ♣r ♦ rr♥♦ s♥♦ ♦♥sr♥♦ ♠ ♠s♠ r③ã♦

♦q♦ ts ♦ rr♥♦ ♥♦ ♣rs♥t ♦rs s♣r♦rs ♣r s q♥ts

♦s ♥ás tr♦ tér♠ ♦♥ ♣r♠t ♥tr q tr♦ ♦r

trés s ts é r ♠♦r ♥♦ rr♥♦ ♥♦ ♦♠ s rçõs s ♦♥

çõs r♦♥â♠s ♥ ♥tr ♦ ♥ ♦ ♣♦ssí ♦tr ♠♥t♦ té ♣r ♦

sst ♦

Prs r♦ tér♠ ♦♥ s♦♠♥t♦ tr♥t♦ ♥s ♣s

♣rs ts

t♦♠♥s♦♥ st②stt ♦ ♥ ♣r♣t ♥♥s t tr♥srs ♣♥

♥s s ssss s♥ ♥♠r s♠t♦♥ t♠r qt♦♥s ♥ ♦♥♥t♦♥

t t s♦tr♦♣ tr♥t s♦st② ②♣♦tss r s♦ s♥ t s♦tr

t♦♦ CFX s♦ ♦♠♥ ♦♠♣rss t ♦♥t♥ ♥♥ s ♥ t♦ sts

♦ q②s♣ ♥s ♥ rs t♦ ♦♥t t tr♥sr ♣r♦♠ s ♦r

♥stts t ♥♥ ♦ sr ♦♠tr② ♦♠♥t♦♥s t r♥t ②r♦②♥♠

♦♣rt♥ ♦♥t♦♥s ♦♥ t ♠♥ ♥r② ♦ss ♥ t tr♥sr ♦♠tr

♠♦ ♦♥ts ♦r t♦ ♥ rr♥♠♥ts str ♥ ♥♥ ♥ ♥♥t♦♥s r♦♠

90 t♦ 0 str♠s ♣ t♦ tr ♥s ♦ rt♦ ♥ t♦ r♥t ♥ s♣♥

t♦t ♥♠r ♦ ss ♥s t ♦♠♥t♦♥ ♦ ♦♠tr stt♥s t tr

②r♦②♥♠ ♦♥t♦♥s tr r♥t ♥t ♦ts s♥ rt♦♥ Cfx ♥

♦ sst ♥♠r Nux r ♦♠♣t ♦r ♥♥ s ♠♦ sst ♥♠r

Nu ♥ t ♣rssr ♦♥t Cp r s s ♦ ♣r♦r♠♥ ♠srs s♦ tt

t t ♦ ♥s r s♦ t t s ♦♥ tt ♥ ♥r t ♠♦st s♥♥t

♥♥ ♦ t ♦♠tr ♣r♠trs s t ♥ ♦ rt♦ ♦♦ ② ♥♥t♦♥

♥ ♥ s♣♥ ♦r♥ t♦ t rsts t ♦ t tr♥sr s rt② t ②

rrt♥ ③♦♥s ♦ t♠♣rtr r♥ts ♥ ♦ rtt♠♥t t♠♣rtr

r♥ts ♦ r♥t ♠♥s♠s ♦ ♠♥ ♥r② ♦ss s ♣rt ② t s♥

rt♦♥ ♦♥t ♦rt① s♥ ♥t s ♦ Cfx ♦r sr strss ♣♦st

s ♦ Cfx ♠♥② str ♦♥rt♦♥ ♣rs♥t t st ♦st♦♥ ♦r

♦ q♥tts r ♦♠♣t ♦♥ t ♥♥ s ♦♥sr♥ ♥ q ♥

♦ rt♦ t rr s ♦r t ♦ q♥tts rst ♠♦st② ♦r t ♥♥

♦♥rt♦♥ rtss t st s ♦ sst Nu ♦r ♦r t str

♦♥rt♦♥ ♦♥t t tr♥sr s♦s tt t ♥♥ rr♥♠♥t ♣rs♥t

t rt♦♥ ♦ t ①♥ ② ♥s r t♥ t str ♦♥rt♦♥ ♦r

t r♥ ♦ ②r♦②♥♠ ♦♥t♦♥s ♥stt t s ♦♥ ♥ ♠♥tt♦♥ ♦r t

♦ sst ♣ t♦

②♦rs ♦♥t t tr♥sr r♥t ♦s ♥♥ ♣r♣t ♥♥s

❯Õ

①♠♣♦ ♣r♦♠ ♦♠ tr♦ ♦r ♦♥

strçã♦ ♥t♥s tr♥t ♥ rã♦ s♦♠♥t♦ ♣ró♦

❱rçã♦ ♦ ♥ú♠r♦ sst ♠é♦ ♦♠ ♦ ♥ú♠r♦ ②♥♦s ♣r

r♥ts r③õs tr ♥

t♦ tr t s♦r strçã♦ t♠♣rtr ♣r L/H = 4Pr = 0,71 Re = 200

❱t♦rs ♦ ♣r r♥ts r③õs ♦q♦ Pr

♥s ♦rr♥t ♣r r♥ts t♠♥♦s s♣ç♠♥t♦s ♥s

t ♠ ♥ã♦ strtr ♣r s♠çã♦ ♦ s♦♠♥t♦ tr

♥t♦ s♦r ♠ ♣ q ♦♠ ♥s sq♠át♦ ♦ ♦♠í♥♦

♦♠♣t♦♥

s♦s ♦ ♦♠í♥♦ ♦♠♣t♦♥ ♠♥s♦♥ r♣rs♥t♥♦ ♣rt s

♣r♦r ♦ t♦ tr♦♦r ♦r

sq♠ ♠♦str♥♦ s ♦♠trs ♦ ①♣r♠♥t♦ ♦ ♣r♠♥t♦ ♦

s♦♠♥t♦ s♥ár♦

♦♠tr ♦ ♥ ♦♠í♥♦ ♦♠♣t♦♥ ♦ s♦♠♥t♦ ♣ró♦

♥s ♦♠ ♦♠tr ♥♦ ♦r♠t♦

sq♠át♦ ♠ strtr í ♦ ♦♠í♥♦ ♦♠♣t♦♥ ♥♦ ♥

♣♥ê♥ t① tr♦ tér♠ ♠♥s♦♥ ♦♠ r③ã♦ s♣t♦

t ♦♠ r③ã♦ ♥tr s ♦♥ts tér♠s

♣r r♥ts ♥ú♠r♦s ②♥♦s

ú♠r♦ sst ♦ ♣r ♣r s♣r♦r ♥r♦r ♦ rr♥♦

s♥♦ ♣r ♦ rr♥♦ ♥♦

tí♣ rtrísts ♠♥s♦♥s t③s ♣r s ♦♠trs

♦♠ ①♣♥sã♦ r♣t

♥♣♥ê♥ ♠ ♣r ♦ s♦ ♦♠♣rt♦ ♦ ♣r ♦

♥tr três r♥ts ♠s

Pr ♦ ♠ x/d = 5,33 ♣r ♦♠tr ♥ ♦♠ r③ã♦

①♣♥sã♦ r♣t Hs/He

st♦ ♥♣♥ê♥ ♠ ♣r ♦ ♥ú♠r♦ t♥t♦♥ s♣rí

♥r♦r sçã♦ ①♣♥ ♦♠tr ♥ ♦♠ r③ã♦ ①♣♥sã♦

r♣t Hs/He

ú♠r♦ t♥t♦♥ ♦ ♣r s♣rí ♥r♦r sçã♦ ①♣♥

♦♠tr ♥ ♦♠ r③ã♦ ①♣♥sã♦ r♣t Hs/He

♦♠tr ♦♠ ts ♠ tí♣ t③ ♣r s♦çã♦ ♥r

♥ét tr♥t s♦

♥♣♥ê♥ ♠ ♣r ♦ ♣r ♥r ♥ét tr♥t ♥♠

sçã♦ ♥ ♣♥♦

❱rçã♦ ♦ ♣r ♥r ♥ét tr♥t ♥♠ sçã♦ ♥

♣♥♦

rtrísts ♠♥s♦♥s s ♦♠trs áss ♣r ♠♦s ♦s rr♥♦s

♥s t♦s ♥♦ s♣r♦r s♥♦ ♥r♦r

♦♠tr t ♦♠♦ ♥çã♦ ♦s r♥ts â♥♦s ♥♥çã♦ β ♣r

♠ ♠s♠ r③ã♦ ♦q♦

s ♦s s♣ç♠♥t♦s ♥tr ts b s rçõs r③ã♦ ♦q♦

t rba ♣r ♠♦s ♦s rr♥♦s ♥ t♦

①♠♣♦ ♠s ♣r♦③s r♥t ♦ st♦ ♥♣♥ê♥ ♠

t ♥♦ ♥t♦r♥♦ ♠ t ♦♠ β = 90

st♦ ♥♣♥ê♥ ♠ rst♦s ♣r s ♠s ♠♦strs

♥ r

♥s ♦rr♥t ♦♦rs ♦♠ ♦ ♣r r♥ts ♥♥çõs

t ♠♦s ♦s rr♥♦s ♥♦ ♦♥ sqr s♥♦ ♦

♥ rt ♥♦ s♦ ♦♠étr♦ b = 2H rba = 0,4 ♦♥çã♦ r♦♥â♠

ue = 9 m/s

♦♥t♦r♥♦s ♦ ♦♠ ♥s ♦rr♥t ♥ ♠t ♥r♦r ♦

♥ rst♥ts ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr

s♥♦ ♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 2H rba = 0,4

♦♥çã♦ r♦♥â♠ ue = 3 m/s

♦♥t♦r♥♦s ♦ ♦♠ ♥s ♦rr♥t ♥ ♠t ♥r♦r ♦

♥ rst♥ts ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr

s♥♦ ♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 3H rba = 0,4

♦♥çã♦ r♦♥â♠ ue = 3 m/s

❱rçã♦ ♦ ♦♥t trt♦ ♦ Cfx ♦♠ ♦ â♥♦ ♥♥çã♦

t β ♣r r③ã♦ ♦q♦ rba ♥s ♦♠trs ♦♠ s♣ç

♠♥t♦ ♥tr ts b = 2H

❱rçã♦ ♦ ♦♥t trt♦ ♦ Cfx ♦♠ ♦ â♥♦ ♥♥çã♦

t β ♣r r③ã♦ ♦q♦ rba ♥s ♦♠trs ♦♠ s♣ç

♠♥t♦ ♥tr ts b = 3H

♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦

rrê♥ ue ♣r ♥♥çã♦ β = 18 r③ã♦ ♦q♦ rba

s♣ç♠♥t♦ ♥tr ts b = 2H

♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦

rrê♥ ue ♣r ♥♥çã♦ β = 54 r③ã♦ ♦q♦ rba

s♣ç♠♥t♦ ♥tr ts b = 2H

♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦

rrê♥ ue ♣r ♥♥çã♦ β = 90 r③ã♦ ♦q♦ rba

s♣ç♠♥t♦ ♥tr ts b = 2H

strçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦

q♦ rba ♣r ♥♥çã♦ β = 18 s♣ç♠♥t♦ ♥tr ts b = 2H

♦ rrê♥ ue = 3 m/s

strçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦

q♦ rba ♣r ♥♥çã♦ β = 54 s♣ç♠♥t♦ ♥tr ts b = 2H

♦ rrê♥ ue = 3 m/s

❱rçã♦ ♦ ♣r ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦

♦q♦ rba ♣r ♥♥çã♦ β = 90 s♣ç♠♥t♦ ♥tr ts b = 2H

♦ rrê♥ ue = 3 m/s

❱rçã♦ ♦ Cp ♣r s r♥ts r③õs ♦q♦ s ♦♠trs

♥ ♦♠ b = 2H ♦ rr♥♦ ♥♦ b = 2H ♦ rr♥♦ s♥♦

b = 3H ♦ rr♥♦ ♥♦ b = 3H ♦ rr♥♦ s♥♦ ♥s

três ♦♥çõs r♦♥â♠s s♠s

♦♠♣rt♦ ♦ Cp ♥tr ♦s ♦s rr♥♦s r♥ts r③õs ♦q♦

s♣ç♠♥t♦ ♥tr ts b = 2H ♥s três ♦♥çõs r♦♥â♠s ue

❱♦rs Cp/Cp0 ♣r ♦ rr♥♦ s♥♦ r♥ts s♣ç♠♥t♦

♥tr ts ♥s três ♦♥çõs r♦♥â♠s ue

t rçã♦ ♦ s♦♠♥t♦ ♦ à rstrçã♦ ár rst♥t

♣r ♦ â♥♦ ♥♥çã♦ t β = 18 ♣r ♦♠tr ♦♠ rba = 0,6 b = 2a t♦♣♦♦ ♦ s♦♠♥t♦ ♥ ♣rt ♥r♦r ♦ ♥

♥s ♦rr♥t ♣r ♥r♦r ♦ ♥ ♦♥t♦r♥♦s t♠♣rtr

♣r ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s

♥♦ ♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 2H rba ♦♥çã♦

r♦♥â♠ ue = 3 m/s

♥s ♦rr♥t ♣r ♥r♦r ♦ ♥ ♦♥t♦r♥♦s t♠♣rtr

♣r ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s

♥♦ ♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 3H rba ♦♥çã♦

r♦♥â♠ ue = 3 m/s

♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♥♥çã♦

t rr♥♦ ♥♦ ♦♥ sqr rr♥♦ s♥♦ ♦♥

rt ♣r ♦♠trs ♦♠ b = 2H rba = 0,4 ♦ rrê♥

ue = 3 m/s

♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦

rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦

s♥ ♦♥ rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦

t rba = 0,4 ♥♥çã♦ β = 18

♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦

rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦

s♥ ♦♥ rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦

t rba = 0,4 ♥♥çã♦ β = 54

♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦

rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦

s♥ ♦♥ rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦

t rba = 0,4 ♥♥çã♦ β = 90

❱rçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦♠ ♦ â♥♦ ♥♥çã♦

t β r③ã♦ ♦q♦ rba = 0,4 ♣r ♠♦s ♦s rr♥♦s ♥s

♦♠trs ♦♠ s♣ç♠♥t♦ ♥tr ts b = 2H

❱rçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦♠ ♦ â♥♦ ♥♥çã♦

t β r③ã♦ ♦q♦ rba = 0,4 ♣r ♠♦s ♦s rr♥♦s ♥s

♦♠trs ♦♠ s♣ç♠♥t♦ ♥tr ts b = 3H

♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦

rrê♥ ue ♣r ♥♥çã♦ β = 18 r③ã♦ ♦q♦ rba = 0,4

s♣ç♠♥t♦ ♥tr ts b = 2H

♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦

rrê♥ ue ♣r ♥♥çã♦ β = 54 r③ã♦ ♦q♦ rba = 0,4

s♣ç♠♥t♦ ♥tr ts b = 2H

♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦

rrê♥ ue ♣r ♥♥çã♦ β = 90 r③ã♦ ♦q♦ rba = 0,4

s♣ç♠♥t♦ ♥tr ts b = 2H

strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦

q♦ rba ♣r ♥♥çã♦ β = 18 s♣ç♠♥t♦ ♥tr ts b = 2H

♦ rrê♥ ue = 9 m/s

strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦

q♦ rba ♣r ♥♥çã♦ β = 54 s♣ç♠♥t♦ ♥tr ts b = 2H

♦ rrê♥ ue = 9 m/s

strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦

q♦ rba ♣r ♥♥çã♦ β = 90 s♣ç♠♥t♦ ♥tr ts b = 2H

♦ rrê♥ ue = 9 m/s

ú♠r♦ sst ♦ ♠♦s ♦s rr♥♦s t ♣r s ♦♠trs

♦♠ s♣ç♠♥t♦ ♥tr ts b = 2H ♦♥ sqr b = 3H ♦♥

rt

r♥srê♥ ♦r ♥ ♥tr rçã♦ ♦ ①♦ ♦r t♦t

♠♥s♦♥ ♣r ♦ ♦r tr♦ trés s ts ♦♠ ♦ â♥♦

♥♥çã♦ t β ♣r ♦s r♥ts s♣ç♠♥t♦s t b = 2H♦♥ sqr b = 3H ♦♥ rt

❱rçã♦ rçã♦ ♦ ♦r tr♦♦ trés ♥tr ♦♠ ♦ â♥♦

♥♥çã♦ t β ♣r ♦s s♦s ♦ s♣ç♠♥t♦ t b = 2H

♦ rrê♥ ue = 9 m/s

♥ê♥ ♦ rrê♥ ue ♥ strçã♦ tr♦ tér

♠ trés ♥tr ♥♦ ♦r tr♥sr♦ t♦t ♠♥s♦♥ ♣r ♦s

rr♥♦s t s♥♦ s♣r♦r ♥♦ ♥r♦r

t♦ r③ã♦ ♦q♦ t rba s♦r ♣r ♦r tr♦

trés s ts s♦r ♦ ♦r tr♥sr♦ t♦t ♠♥s♦♥ ♣r ♠♦s

♦s rr♥♦s ♦♠trs ♦♠ b = 2H

s ♦♠étrs r♥ts ♣r ♦ CFX rs ♥ts ①

çã♦ ♦ ó♦ ♥♠ s♠çã♦ ♥♠ér

♦♥strçã♦ ♦ ♦♠ ♦♥tr♦ ❱ s♥♦ ♦r♠çã♦ ❱

r♥s♦r♠çã♦ ♥tr s ♦♦r♥s ♦s ♦ sst♠ s ♦♦r♥s

♦s t③s ♣s ♥çõs ♦r♠

Pr ♦ tí♣♦ ♠ ♠t tr♥t

❱rçõs ♦♠étrs ♦♥rçã♦ ts ♥s ♣r ♠ s♣

ç♠♥t♦ ♥tr ts b ♣r s r♥ts r③õs ♦q♦ t

rba ♦♥ ♦♥

❱rçõs ♦♠étrs ♦♥rçã♦ ts s♥s ♣r ♠ s

♣ç♠♥t♦ ♥tr ts b ♣r s r♥ts r③õs ♦q♦ t

rba ♦♥ ♦♥ ♦♥

♦♠♥çã♦ s rçõs ♦♠étrs b rba ♦♠ s rçõs s ♦♥

çõs ♦♥t♦r♥♦ r♦♥â♠s ue ♦ Re ♣r ♦ ♠ ♥♥çã♦

t β

st♦s r♥ts ♣rt♥♥ts ♣♥♦ té♥ ♥♠ér ♦ ①♣r

♠♥t

Pr♦♣rs íss t③s ♥ t♣ çã♦ rçã♦ ♦ ó♦

♥♠ér♦

♠♥sõs ♣r♠tr③s ♦♠tr t③ ♥♦ s♦ t♣

rçã♦ çã♦ ♦ ó♦ ♦♠♣t♦♥

♠♥sõs ♣r♠tr③s ♦♠tr t③ ♥ s♦çã♦ tér♠ s♦

t♣ rçã♦ çã♦ ♦ ó♦ ♦♠♣t♦♥

♦s s ♠s t③s ♣r ♦ st♦ r♥♦ ♠ ♣r

çã♦ rçã♦ ♥r ♥ét tr♥t κ

❱rçã♦ r③ã♦ ♥tr rr s t w s s♣ssr

t ♠ ♥çã♦ ♦ s â♥♦ ♥♥çã♦

Prâ♠tr♦s ♦♠étr♦s r♦s ♦♥rçã♦ ♣á r♥ts

s♣çã♦ ♦s ♣râ♠tr♦s ♦♠étr♦s ♥rss

Pr♦♣rs íss t③s ♣r rtr③çã♦ ♦s ♦♠í♥♦s ♦♠♣

t♦♥s ♦s s♦s st♦s

❱♦rs ♦ ♦♥t ♣rssã♦ ♣r ♦ ♥ s♠ ts

ú♠r♦ sst ♦ ♦ ♥ s♠ ts ♣r s três r♥ts ♦♥

çõs r♦♥â♠s

♥t ♦r tr♥sr ♣r ♦ ♦ ♥♦ ♥ s♠ ts ♣r s

três r♥ts ♦♥çõs r♦♥â♠s

③ã♦ ♦ ♦♥t ♣rssã♦ Cpdesalinhado/Cpalinhado r♥ç ♠é

♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 2H

③ã♦ ♦ ♦♥t ♣rssã♦ Cpdesalinhado/Cpalinhado r♥ç ♠é

♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 3H

③ã♦ ♦ ♥ú♠r♦ sst Nudesalinhado/Nualinhado r♥ç ♠é

♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 2H

③ã♦ ♦ ♥ú♠r♦ sst Nudesalinhado/Nualinhado r♥ç ♠é

♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 3H

❱❯

♦♠♣tçã♦ ssst ♣♦r ♦♠♣t♦r ♦ ♥ês ♦♠♣tr ♥♥r♥

♥â♠ ♦s ♦s ♦♠♣t♦♥ ♦ ♥ês ♦♠♣tt♦♥

②♥♠s

CFX ♣r♦r♠ ♦♠r

s♠çã♦ ♥♠ér rt ♦ ♥ês rt ♥♠r s♠t♦♥

❱ ♠ét♦♦ ♦♠s ♥t♦s s♦ ♠ ♠♥t♦s ♦ ♥ês

♠♥ts ♥t ♦♠ ♠t♦

♠ét♦♦ ♠♥t♦s ♥t♦s ♦ ♥ês ♥t ♠♥t ♠t♦

qçõs rt♦s ♦♠ ♠é ②♥♦s ♦ ♥ês

②♥♦s r rt♦s

♠é qrát ♦ ♥ês r♦♦t ♠♥ sqr

tr♥s♣♦rt s t♥sõs tr♥ts ♦ ♥ês sr strss

tr♥s♣♦rt

❱ ♦♠ ♦♥tr♦

❮

A ár

Ai t♦r ár ♥♦r♠

b s♣ç♠♥t♦ ♥tr ts ssss ♠ ♠s♠ ♣r

Bi ♦ rt♦ ♦ ♠tr③ ♦♥t♥♦ s♦çã♦ ♦ sst♠ ♥r s qçõs

srt③s

C ♦♥st♥t ♠♦♠ ♦ ♣ró①♠ à ♣r

c ♦r s♣í♦ ♣rssã♦ ♦♥st♥t

ci t♦r q ♦s ♥trós ♠♥t♦s ♥ts

cpi tr♠♦ ♦ ♦♠♣♠♥t♦ ♣rssã♦♦

Cfx ♦♥t trt♦ ♦

Cp ♦♥t ♣rssã♦

d tr ♦ r ♣r ♠ ♥ ♦♠ ①♣♥sã♦ r♣t ár

Dh â♠tr♦ rá♦

Dij t♥s♦r t① ♦r♠çã♦

D′

ij t♥s♦r t① ♦r♠çã♦ s♦r

dmin dmax stâ♥s t③s ♣♦ CFX♣r ♦ á♦ ♦ t♦r ①♣♥sã♦

♠

dpi tr♠♦ ♦ ♦♠♣♠♥t♦ ♣rssã♦♦

e s♣ssr ♣r ♦ ♥ t♦

F1 F2 ♥çõs ♦ ♠♦♦ trê♥

fi t♦r q ♦ ♥tró ♦ ♠♥t♦ ♦ ♥tró ♠ ss

s

FU ①♦ ♠♦♠♥t♦ ♥ rã♦ ♣r

fpi tr♠♦ ♦ ♦♠♣♠♥t♦ ♣rssã♦♦

h ♦♥t ♦♥t♦ tr♥srê♥ ♦r ♦

H tr ♠ sçã♦ ♦♠étr

Ha ♠á①♠ tr rt t

hx ♦♥t ♦♥t♦ tr♥srê♥ ♦r ♦

I ♥t♥s tr♥t

J ♠tr③ ♦♥

K ♦♥st♥t ♦♥ ár♠á♥

k ♦♥t tér♠ ♦ ♠♦

kt ♦♥t tér♠ tr♥t

L ♦♠♣r♠♥t♦ ♠ sçã♦ ♦♠étr

lt ♦♠♣r♠♥t♦ rtríst♦ s tr♥t

mpi ①♦ ♠áss♦ trés s♣rí ♠ ♦♠ ♦♥tr♦

M ♥ú♠r♦ ts ♥ ♠s♠ ♣r ♦ ♥

m ③ã♦ ♠áss

Ni ♥çõs ♦r♠

Nu ♥ú♠r♦ sst ♦

Nux ♥ú♠r♦ sst ♦

p ♣rssã♦ ♦

pi ♣♦♥t♦ ♥trçã♦

Pr ♥ú♠r♦ Pr♥t

q ①♦ ♦r

ri t♦r ♣rtr ♦ ♥ó ♠♦♥t♥t té ♦ ♣♦♥t♦ ♥trçã♦ ♦♥sr♦

rba r③ã♦ ♦q♦ t

Re ♥ú♠r♦ ②♥♦s

sij t♥s♦r t♥sã♦ s♦r

Stx ♥ú♠r♦ t♥t♦♥ ♦

T t♠♣rtr ♦

t t♠♣♦ ♦ s♣ssr t

T + t♠♣rtr ♠♥s♦♥ ♥ rã♦ ♣r

Tm t♠♣rtr ♠é ♦rít♠

ui ♦♠♣♦♥♥t ♦ rts♥

uτ ♦ trt♦

Uref ♦ ♠é rrê♥

vt ♦ rtríst s tr♥t

w rr s t

Wij t♥s♦r t① r♦tçã♦

xi, x, y ♦♦r♥ rts♥ ♦

y+ stâ♥ ♠♥s♦♥

trs rs

α α∗ ♦♥st♥ts ♦ ♠♦♦ trê♥

β â♥♦ ♥♥çã♦ t

Γ rá tér♠ ♣r

γ ♦♥st♥t ♦ ♠♦♦ trê♥

∆ rçã♦ ♣r♦♣r

δij ♦♣r♦r r♦♥r

ǫRMS ♠é qrát

ε t① ss♣çã♦ ♥r ♥ét tr♥t

ϑ tr♠♦ ♦rrçã♦ ♥♠ér t ♥♦ sq♠ t rs♦çã♦

κ ♥ ♥ét tr♥t

Λ rá ♥ér

µ s♦s ♥â♠ ♠♦r

µt s♦s ♥â♠ tr♥t

ν s♦s ♥♠át ♠♦r

νt s♦s ♥♠át tr♥t

ξ, η ♦♦r♥s ♦s t③s ♣s ♥çõs ♦r♠

ρ ♠ss s♣í

σκ σω σω2 ♦♥st♥ts ♦ ♠♦♦ trê♥

ς ς1 ς2 ♦♥st♥ts ♦ ♠♦♦ trê♥

τij t♥s♦r ②♥♦s

τint,x t♥sã♦ s♥t ♦ ♦ ♦ ♦♠ ♣r ♥ ♥ ♥tr só♦

♦

φ φ′ ♣rs ♠é t♥t ♦♠♣♦sçã♦ ②♥♦s

ψ rá tér♠ ♣r

Ω ♦rt

ω t① ss♣çã♦ s♣í

í♥s

0 rr♥t ♦ ♥ s♠ ts

a rr♥t às ts

e t q é♠ s♦♠ ♥tr s ♣rs ♦ ♦ ♠♦rs ♦

s♦♠♥t♦ tr♥ts

esp s♣♦

f ♦

i ♥ú♠r♦ q ♥t ♦ ♦♠ ♦♥tr♦ ♦ ♥ó ♦ qçõs ♦

sst♠ ♦♣♦ qçõs ssçã♦

i, j, k ♦♠♣♦♥♥ts r♦♥s ♥társ s♦r ♦s ①♦s ♦ sst♠ rts♥♦

int rr♥t à ♥tr só♦♦ ♥♦s ♥s t♦s

Λ rá ♥ér

max ♠á①♠

min ♠í♥♠

w ♣r

ref rrê♥

s só♦

t tr♥t

tan t♥♥

up ♠♦♥t♥t

x ♦ ♦ ♦♥♦ rçã♦ rts♥ x

♣rí♥s

∗ ♠♥s♦♥

o ♣ss♦ t♠♣♦ ♥tr♦r

e ♥tr

nb ③♥♦s

s sí

❯

❯

t♦s st tr♦

strtr st tr♦

❱ ❯

❯Õ Ó Õ

qçõs ♦♥srçã♦

♠♦♦ s qçõs ♦♥srçã♦

♦♠ trê♥

çã♦ ♣r r

çã♦ r♥srê♥ ♦r

❯ ❯Õ

❱rçã♦ çã♦ ♠♦♠ ♠t♠át s♦çã♦ ♥♠ér

♦ CFX

s♦ s♦çã♦ ♦

♦♠tr

♦♥çõs ♦♥t♦r♥♦

st♦s

s♦ s♦çã♦ tér♠

♦♠tr

♦♥çõs ♦♥t♦r♥♦

st♦s

s♦ s♦çã♦ ♥r ♥ét tr♥t

♦♠tr

♦♥çõs ♦♥t♦r♥♦

st♦s

Pr♦♠ ♦ s♦♠♥t♦ ♠ ♥s t♦s

♦♦ ♦♠étr♦ ♦ ♥ t♦

♣♦ st♦ r♥♦ ♠

♦♥çõs ♦♥t♦r♥♦ ♣r♦♣rs

Pr♥♣s rtrísts ♦ s♦♠♥t♦ ♥♦s s♦s ♦s ♥s t♦s

st♦s ♣r ♣r r

♥s ♦rr♥t t♦♣♦♦ ♦ s♦♠♥t♦

♦♥t trt♦ ♦ Cfx

r♥ç ♣rssã♦ ∆p ♦♥t ♣rssã♦ Cp

r♥srê♥ ♦r ♥tr ♦ ♦♠í♥♦ só♦ ♦ ♦♠í♥♦ ♦

strçã♦ t♠♣rtr t♦♣♦♦ ♦ s♦♠♥t♦

ú♠r♦ sst ♦ Nux

ú♠r♦ sst ♦ Nu

♦r t♦t ♠♥s♦♥ qtotal/q0 ♣r ♦r tr♦

♦ trés s ts

♦♠♣rt♦s s q♥ts ♦s

❯Õ PP❱ ❯❯

P

s♣t♦s ♥â♠ ♦s ♦♠♣t♦♥

rçã♦ ♠ ♥♠ér

ét♦♦ ♥♠ér♦ ♦r♠ ❱

♥çõs ♦r♠

r♠♦s s♦s

r♠♦s ♦♥t♦s

♦♣♠♥t♦ ♣rssã♦♦

sst♠ ♦♣♦ qçõs

♦♥çõs ♦♥t♦r♥♦

♦♦ trê♥

rt♠♥t♦ ♥t♦ à ♥tr só♦♦ ♥çõs ♣r s

ás ① ♦r♠çã♦ ①♦ ②♥♦s

①♦ ♠♦♠♥t♦ ♥ rã♦ ♣r

①♦ ♦r ♥ rã♦ ♣r

rr♥♦ ♥♦

rr♥♦ s♥♦

r♦r s♦s

❯

st♦ ♣r♦ss♦s ♥♦♥♦ tr♥srê♥ ♦r é r♥t ♠ ár♦s

s♠♥t♦s ♥strs ♣♦rt♥t♦ ♠ ♠♣ ♠ ♣sqss t♠ s♦ ♦♥t♥♠♥t

r③ s♥♦ ♠♦r ♥ ê♥ t♥t♦ ♥ t♣ ♣r♦t♦ q♥t♦ ♥ ♦♣r

çã♦ ♦s sst♠s tér♠♦s ♠♦r sts sst♠s ♦ à ♣rs♥ç ♦♥çã♦

♦rç ♦ r♠ s♦♠♥t♦ é ♦ tr♥t♦ é♠ ♦ r♠ s♦♠♥t♦ s

♣r♦♣rs íss ♦s ♦s ♦s ♠trs ♦♥strçã♦ ♦s ♦♠♣♦♥♥ts sts

sst♠s s rtrísts ♦♠étrs t♠é♠ ♥♥♠ rt♠♥t ♥♦ ♣r♦ss♦

tr♥srê♥ ♦r s ♣r♦ss♦s tr♥srê♥ ♦r ♣♦♠ sr st♦s

♦r♠ ①♣r♠♥t ♣♦ré♠ ♥s út♠s és s ♦sr ♠ ♦çã♦ ♥♦ s♦ r

r♠♥ts ♦♠♣t♦♥s ♦ts ♣r r③çã♦ ♣sqs s♥♦♠♥t♦

t♠s ♦♠♦ st

Pr s ♦tr ♠♦rs t①s tr♥srê♥ ♦r ♥tr ♠ s♣rí só

♠ ♦ ♦ s♦ ts stá ♥tr s té♥s ♠s t③s ♥tr♦çã♦ ts

é♠ ♣r♦♣♦r♦♥r ♠♥t♦ ár tr♦ tér♠ ♥tr ♣♦ tr ♦ ♣rã♦

s♦♠♥t♦ t tr♥srê♥ ♦r ♦♥ ♥ q

s♦çã♦ tér♠ ♦ só♦ ♦ ♦ é trt ♦r♠ ♦♣ ♣♦ sr t③ ♣r

str st t♣♦ ♣r♦♠ ss♠ s ♦♥srr ♥ê♥ s ♣r♦♣rs ♦

só♦ ♥ás ♣rã♦ ♥sts s♦s ♦♥sst ♥♦♥trr ♦♥rçã♦ q ♦rç

♦ ♠♦r ♥ç♦ ♥tr q ♣rssã♦ ♦ à ♦strçã♦ s ♣s ts ♦

♥♦ ♠ tr♥srê♥ ♦r q sts ♣r♦♣♦r♦♥♠ é♠ ♦ ♠♥t♦ ár

♥tr tr♦ tér♠ ♣rs♥ç s ts ♣♦ ♠♥tr ♦ ♥í trê♥ ♦

s♦♠♥t♦

♦s ♣r♦ss♦s ♥strs ♦♦rr ♦ ♣r♦♠í♥♦ s♦♠♥t♦s tr♥t♦s ♦s qs

♣rs♥t♠ s s♥ts rtrísts t♦s ♥ú♠r♦s ②♥♦s rrr ♦

t♦r s tçõs tr♠♥s♦♥s ♦rt ss♣çã♦ s

s♦♠♥t♦s tr♥t♦s sã♦ ♥ô♠♥♦s q ♦♦rr♠ ♥ s ♦ ♦♥tí♥♦ é ♠

rtríst ♦ s♦♠♥t♦ ♥ã♦ ♦ ♦ s♦ s♦♠♥t♦ ❯❨

♦♥sr♥♦s q á st ♣çã♦ st t♣♦ s♦♠♥t♦ ①st♠ qs q

♠♥♠ s♣ t♥çã♦ ♦♠♦ ♦s s♦♠♥t♦s tr♥t♦s ♦♠ s♣rçã♦ ♠

♠t t♦s sts ♦♦rr♠ ♦♠ ♣♦str♦r r♦♠♥t♦ ♠ ♠t ♥t♦ à ♠

s♣rí só st stçã♦ ♥ q á s♣rçã♦ r♦♠♥t♦ ♦ s♦♠♥t♦

♦r♥ ♥ ♠ ♠♦r ás ♥ q t♦rs ♠♦♦s trê♥ sã♦ tst♦s

♣♦ss♠♥t ♠♦r♦s t

s ♠♦♦s trê♥ q rs♥t♠ s♠♣çõs s♦r ís ♦s s♦

♠♥t♦s sr♠ ♦♠♦ tr♥t ♣r ③r ♦ s♦ rr♠♥ts ♥â♠

♦s ♦♠♣t♦♥ ♦ ♦ ♥ês ♦♠♣tt♦♥ ②♥♠s st s♥

t♦ ♠♦çã♦ s qçõs rt♦s ♦♠ ♠é ②♥♦s ♦ ♥ês

②♥♦sr rt♦s t♦r♥♦s ♦r♠ ♠s t③ ♣r

r s♦♠♥t♦s tr♥t♦s ♦ s♦ ♦s s♦♠♥t♦s tr♥t♦s st♦♥ár♦s ♦s qs

r♣rs♥t♠ ♠♦r s ♣çõs ♥♥r ♦♠♣♦sçã♦ ②♥♦s ♣r

s ♣r♦♣rs tr♥s♣♦rt é trt ♦r♠ sttíst ♦♠ ♠ ♠é ♥♦ t♠♣♦

❲❳ t

♦r♠ q ♦r♥ ♠♦r rá ♣r s♠çã♦ trê♥ ♣♦

ré♠ é q ♠ q s qçõs rt♦s sã♦ rs♦s s♠ ♦♥srr ♥♥♠

♣r♦♠♥t♦ ♠é ♦ ♣r♦①♠çã♦ é♠ ♦ ♣r♦ss♦ srt③çã♦ st t♣♦

s♠çã♦ é ♦♥ ♦♠♦ s♠çã♦ ♥♠ér rt ♦ ♥ês rt

♠r ♠t♦♥ ❩ P srs q ♦ s♦ s♠çõs

♠♣ ♣♦r ①♠♣♦ ♥♠ t♦ st♦ ♦♠♣t♦♥ é♠ rr ♠ q♥t

♦s s♥ssár ♣r ♣çõs ♥♥r ♥ ♣sr ♦s s♦rç♦s ♠ ♦

s s♦ ♠ s♦♠♥t♦s ♥trss rt♦ ♥ ♥♥r stá ♠ ♦♥♦ ♠♥♦ s

t♦r♥r ♣rát♦ ♠♦r q s ♣♦ ♥çr té ♥tã♦ sã♦ s♠çõs ♠♦r♦s ♥ú

♠r♦s ②♥♦s ♠ ♦♠trs ①tr♠♠♥t s♠♣s ♣♦r ①♠♣♦ ♦s ♣ró♦s

❱

♣rtr ♦ ①♣♦st♦ s♦r ♦ ♦♥t♦ ♦ s♦ s rr♠♥ts rts ♦

♥ês ♦♠♣t ♥♥r♥ ♥♦ ♥♠♥t♠♥t ♥á

s tér♠ ♦ s s♦ ♠♦r ③ ♠s rq♥t r♥t ♦ s♦ ♦s

♠♦s ♣r♦tót♣♦s rts P ❯ ♥sst ♦ ♦♠♣♠♥t♦

①♣r♠♥t ♦çã♦ ♠ ♣rt stá ♥ ♦ s♥♦♠♥t♦ ♦s

rrs♦s ♦♠♣t♦♥s ♣r♦ss♠♥t♦ r♠③♥♠♥t♦ ♦s ♣r♦r♠s ♦♠♣

t♦♥s ♦♠ rçã♦ ♦ s♥♦♠♥t♦ ♦s ♣r♦r♠s ①st♠ árs tr♥ts

s♥♦ q rsõs strís ♦r♠ ♦♠r sã♦ ♦♥srs ♦♠♦ s t♥♦♦s

♣♦♥t

♠♦r s rr♠♥ts ♦♠rs FLUENT CFX1 STAR −CD STAR −CCM+ s s ♥ ♦r♠ ♦ ♠ét♦♦ ♦s ♦♠s ♥t♦s ♣

♥♦ ♣r♦ss♦ srt③çã♦ s qçõs r♥s st ♠ét♦♦ s s ♥

♦r♠ ♥tr s qçõs ♦♥srçã♦ ♦♠♦ ♣♦♥t♦ ♣rt s♥♦ ♦ ♦♠í♥♦

s♦çã♦ s♦ ♠ ♠ ♥ú♠r♦ ♥t♦ ♦♠s ♦♥tr♦ ❱ trés ♠

♠❩ P ♦ ♠ét♦♦ ♦s ♦♠s ♥t♦s áss♦ ♦ ♦♠ ♦♥

tr♦ ♦♥ ♦♠ ♦ ♠♥t♦ ♠ s♥♦♦ ♠s r♥t♠♥t ♦ ♠ét♦♦ ♦s

♦♠s ♥t♦s s♦ ♠ ♠♥t♦s ♦ ♥ês ❱ ♠♥ts ♥t ❱♦♠

t♦ r ♠ ❱ q é ♦♠♣♦st♦ ♣♦r s♦♠s ♦r♥♦s ♦ ♣r♦ss♦ sã♦

Pr♦r♠ s♠çã♦ ♥â♠ ♦s ♦s ♦♠ tr♥srê♥ ♦r rçõs qí♠s ♦♠r③♦ ♣ ❨

Pr♦r♠ ♥ás ♦♥â♠ ♦♠♣t♦♥ ♦♠r③♦ ♣ ♣♦Pt♦r♠ ♠ts♣♥r ♣r s♠çã♦ ♦♠r③♦ ♣ ♠♥s

♦s ♠♥t♦s ♠ st♥t ♣r♦♣r♦ q♥♦ s t③ ♠s ♥ã♦strtrs

st t♣♦ ♠ t♠é♠ é q ♣r s t③r ♦♠ ♦tr ♦r♠çã♦ ♦

♠ét♦♦ ♦s ♠♥t♦s ♥t♦s ♦ ♦ ♥ês ♥t ♠♥t t♦

♦r♦ ♦♠ rs ♦ é ♥tr♠♥t ♣r♦♣r♦ ♣r ♠s

♥ã♦strtrs ♦r♠ ♣rtr ♣r ♦r♠çõs ss ♥♦s érts ♦s

♠♥t♦s ♠ ♥♦ ♦ ♠s♠♦ t♦r ♥ ♠ ♦s ♣ss♦s ♦ ♠ét♦♦

♦♥sst ♥r ♠ ♠♥t♦ ♠ ♠ r♣rs♥tçã♦ ♣r♠étr s rá

s ♣♥♥ts ♦♠ s ♥♠ ♠í ♥çõs ♦r♠ ss♦ à ♠♥t♦

srs q ♥♦ ♣r♦r♠ t③♦ ♥st tr♦ ♦ CFX stá ♠♣♠♥t♦ ♦

♠ét♦♦ ❱ q t♠é♠ t③ s ♥♦♠♥s ♥çõs ♦r♠ ♦s ♣ê♥s

st tr♦ ♥♦♥tr♠s ♥♦r♠çõs ♠s s♣ís s♦r ♦ ♣r♦r♠ ♥t♠♥t

♦♠ ♦tr♦s s♣t♦s

❱

♣r♥♣ ♦t♦ st tr♦ é ♦ st♦ ♥ê♥ ♦ ♣♦s♦♥♠♥t♦

ts ♦♥t♦rs tr♥srss ♦ s♦♠♥t♦ ♠ ♠ ♥ sçã♦ rt s♦r

tr♥srê♥ ♦r ♦♥ s♦r ♣r r ♣♦s♦♥♠♥t♦ s ts

trá s ♦♥rçõs áss ♥ s♥ ♦♥♦r♠ str♦ ♥ r

stçã♦ ♠♦♥str ♥st r t♥t♦ ♣r ♦ ♥ q♥t♦ s ts

♣♦ss♠ s♣ssr ♦♥③♠ ♥r st♦ rtr③ ♠ ♣r♦♠ ♥♦ q ♠s s

♦r♠s tr♦ ♦r ♠ sr trts ♠♥r ♦♥ ♦♥çã♦ ♥♦ só♦

♦♥çã♦ ♥♦ ♦ ♣♦r ♠♦ ♠ ♥tr só♦♦ q sr st

♥tr é ♦ t♣♦ ♦♥srt st♦ ♠♣ q t♦♦ ♦ ♦r q ① ♦ ♦♠í♥♦ só♦

é ♦♥t③♦ ♣r ♦ ♦♠í♥♦ ♦ ❨

♦♠tr ♦♥sr ♥ r ♣rs♥t árs ♣♦sss q♥t♦ ♦s

♣râ♠tr♦s ♦♠étr♦s st♦ Pr st tr♦ ♦r♠ s♦s rçã♦ ♦

â♥♦ ♥♥çã♦ s ts r③ã♦ ♦q♦ t ♦ s♣ç♠♥t♦ ♥tr ts

sts ♣râ♠tr♦s ♦r♠ ♦s ♠ ♠s s ♦♥rçõs r ♦♥

♠♥t ♣r ♠ ♥ás ♦ t♦ rçã♦ ♦ rrê♥ ♦ s♦♠♥t♦

♦r♠ rs♥ts três ♦♥çõs ♦♥t♦r♥♦ r♥ts ♦ st♦

Pr ♥çr ♦s ♦t♦s ♣r♥♣s ♦s s♥ts t♥s sã♦ ♦♥sr♦s

❼ ❱çã♦ rçã♦ ♦ ♣r♦r♠ ♦♠r CFX ♣r s♦s ♦♥t♥♦

íss s♠♥ts às q srã♦ ♥♦♥trs ♥st tr♦

❼ ♥tçã♦ s ♣rs ♦r tr♥srs ♣r ♦ ♦ ♣♦r ♠♦ s ts

♣♦r ♠♦ s ♣rs ♦ ♥

❼ çã♦ ♦ ♠♣♦ t♠♣rtrs ♦s ♦♠í♥♦s só♦ ♣rs ♦ ♥ ts

♦

❼ çã♦ t♦♣♦♦ ♦ s♦♠♥t♦ ♣r ♦s s♦s ♦ ♣r♦♠♦

❼ çã♦ ♣r r trés ♦ ♦♥t ♣rssã♦ t♠é♠ ♦ ♦♥t

trt♦ ♦♠♥t

❼ çã♦ tr♥srê♥ ♦r trés ♦ ♥ú♠r♦ sst ♦ ♦

t♠ ♣rt♥♥t ♦ ♦♥♥t♦ s♦s st♦s ♥st tr♦ srá ♦

q♥t♦ à ♥ê♥ ♦s ♣râ♠tr♦s ♦♠étr♦s r♦♥â♠♦s

r ①♠♣♦ ♣r♦♠ ♦♠ tr♦ ♦r ♦♥

20 H

b /2

b/2

♥ ♦♠ ts s♥s

H

l

β

b b/2 L

w

e

20 H

x

y

♥ ♦♠ ts ♥s

♦♥t ♣t♦ P t

❯❯

♣rs♥t ssrtçã♦ é strtr ♦ ♦♥♦ sçõs sss♠♥t ♥tr♦

çã♦ sã♦ trtr ♦r♠çõs órs ♦♥srçõs st♦s s

ssõs ♦♥sõs Prs♣ts trs

sã♦ trtr ♣rs♥t ♠ rs s♦s ♥♦♥♦ ♦ s♦

ts ss♠♦s ♣r ♥r♠♥t♦ tr♦ tér♠ rsst♥♦ ♦s ♣r♥♣s s♣t♦s

♦♥sr♦s ♦ ♦♥í♦s ♣♦s ss t♦rs sçã♦ s ♦r♠çõs órs

♦♥srçõs sã♦ ♣rs♥ts s s♠♣çõs ♣ótss ♦s ♠♦♦s ♠t♠át♦s

rst♥ts ♣r ♦ ♣r♦♠ ♦s ♥s t♦s s t♣s çã♦ rçã♦

♠ ♦♠♦ ♦ s♥♦♠♥t♦ ♣rs♥tçã♦ ♦s rst♦s s s♠çõs ♥♠érs ♦s

s♦s ♣r♦♣♦st♦s ♥♦ ♣rs♥t tr♦ ♦♠♣õ sçã♦ ♦s st♦s sssõs s

♦♥sõs Prs♣ts trs sã♦ rstr♦s ♦s stqs ♦s st♦s t♦s

♥♠♥t ♠s r♦♠♥çõs tr♦s tr♦s

❱ ❯

té♥ ♠♥t♦ tr♥srê♥ ♦r r é ♦♠♠♥t t③

♠ s♦♠♥t♦s ♠♦♥♦ás♦s ♣r ár♦s t♣♦s ♣çõs ♥strs ♣♦s♦♥♥♦s

ts ♦r♠ ♣ró ♠ ♥s q♠♥t♦ ♦ rsr♠♥t♦ ♥s ①♠♣♦s

♣♦s à ♥♥r sã♦ ♦s tr♦♦rs ♦r ♦ t♣♦ s♦t♦ ♦♠ ♥s s

♠♥ts ♦t♦rs s♦rs rsr♠♥t♦ ♥tr♥♦ ♣ás tr♥s ♥s t♣♦s ①♦

♦♠ r♥t♦ s♠ ♦r♠ ♣rtr ♦ s♦ ♣r♦♠♦t♦r trê♥ ♥♦ s♦

♠♥t♦ é st♥t ♦♠♠ ♦ ♦ ①♦ ♦♥t ♦♥t♦ tr♥srê♥ ♦r

♣rs♥t♦ ♣ ♠♦r ♦s ss sr ♣rs♥ts ♠ rs♠♦ árs ♣sqss

r tr♥srê♥ ♦r s qs ♣rs♥t♠ s♠♥ç ♦♠ s ♣r♦♣♦sts st

tr♦

st♦ ♦ s♦ ts ♣r ♣r♦♠♦r ♦ ♠♥t♦ ár tr♦ tér♠

♦ ♣r♦ss♦ ♠str t♠ s♦ r③♦ t♥t♦ ♠♥r ①♣r♠♥t q♥t♦

♠♥r ♥♠ér ♦♥sr♥♦ ♦ s♦ ♥♠ér♦ s s♠çõs tê♠ s♦ ♦♥③s

♠♣♠♥t ♣r s♦s ♠♥s♦♥s ♦ ♦♠ ♣r♦♣rs ♦♥st♥ts ♠ ♠t♦s

s♦s ♣♥♦s ♦♥çõs ♣r♦ ♥t♦ à ♦♠tr ♥♦ s♦ ♥s

♦♠ ts tr♥srss ♦ s♦♠♥t♦ á s ♣♦sss ♣r ♦ rr♥♦ s ts

t③s ♠ ♠s s ♣rs ♥♦ s♥♦ ♥tr ♠ ♠s♠♦ rr♥♦ é

♦♠♠ ♥çã♦ ♠♥sõs ♣r♠tr③s ♦r♠ q s stç♠ r③õs

s♣t♦ ♦♠étrs é♠ ss♦ s ♣rs ♦ ♥ sã♦ rq♥t♠♥t ssttís

♣♦r ♠ ♦♥çã♦ ♦♥t♦r♥♦ s q ♦ ♥trss ♠♦r s ♦ ♦♠í♥♦ ♦ ♦

♠♦str ♥s ♦s ①♠♣♦s ♦s tr♦s r③♦s ♣r ♥stçã♦

♦ s♦♠♥t♦ tr♥srê♥ ♦r ♠ ♥s t♦s

st♦s r♥ts ♣rt♥♥ts ♣♥♦ té♥ ♥♠ér ♦ ①♣r♠♥t

t♦rs ♠

t r♦ tér♠ ♦♥ s♦♠♥t♦ ♠♥r ♠

♥s ♦♠ ts ♥♥s

P t r♦ tér♠ ♦♥ s♦♠♥t♦ ♠♥r ♠

♥s ♦♠ ts ♥♥s

P ❲

s♦♠♥t♦ ♥tr s ♥s ♦♠ r♥ts ♦♠♣r

♠♥t♦s r♥ts s♣ç♠♥t♦s

❩ ❯

r♥srê♥ ♦r q ♣rssã♦ ♠ ♠ ♥

♠♥s♦♥ ♦♠ ♥s r♥ts trs

st♦s r♥ts ♣rt♥♥ts ♣♥♦ té♥ ♥♠ér ♦ ①♣r♠♥t

t♦rs ♠

t ♠çã♦ ♥♠ér tr♥srê♥ ♦r ♠ ♥

♦♠ ts ♦♥t♥s ♦♥sr♥♦ ♦♥çã♦ ♠st

♠ s♦ tr♥srê♥ ♦r ♦♥♦

❨ t st♦ ♥♠ér♦ ♦ rsr♠♥t♦ ♠ t tr♥s

rs ♠ ♠ ♥ ♣s ♣rs s♦ ♥ê♥

rçã♦ ♦ ♥ú♠r♦ r③ã♦ s ♦♥ts

tér♠s r③ã♦ s♣t♦ t

♠çã♦ tr♦ ♦r ♦ s♦♠♥t♦ tr♥t♦

♠ ♥ ♦♠ rr♥♦ s♥♦ ♣r♦trâ♥s r

♦ss r ♣ss ♣r r♥ts ♠♦♦s tr

ê♥

❱❯

♥stçã♦ ①♣r♠♥t tr♥srê♥ ♦r ♦♥

t ♠st ♠ ts ♦♥t♥s ♠ ♥ rt♥

r ♦r③♦♥t

❩ t st♦ ♥♠ér♦ ♦ s♦♠♥t♦ tr♥t♦ ♠ ♥

t♦ ♦♠♣rt♦ ♥tr ts rt♥rs ts tr

♣③♦s

PPP

P❱

♥ás ♥♠ér s♦♠♥t♦ ♠♥r ♣ró♦ ♠

♥ ♦♠ t ♠ ♦r♠t♦ ♠♥t

❯ t ♥ás ♥♠ér ♥ê♥ s♦r tr♥srê♥

♦r ♦rr♥t ♥srçã♦ ♠ t tr♥srs ♦

s♦♠♥t♦

❨❯ t st♦ ①♣r♠♥t ♥♠ér♦ ts ♥♥s ♦♥

t♥♠♥t ♦ s♦♠♥t♦ ♣r r♥ts â♥♦s

r♥ts t♠♥♦s ♥ ♠ ♠ ① tr♥t

♦ ♥ú♠r♦ ②♥♦s

♥stçã♦ ♥♠ér ♦ s♦♠♥t♦ ♠♥r ♠ ♥s

♦♠ ts ♣♦r♦ss

❯❱

♠çã♦ ♥♠ér tr♦ tér♠ ♦ s♦♠♥t♦

♠♥r r♥ts Pr ♦♥sr♥♦ rã♦ ♥tr

♠ ♥ ♦♠ ts s♥s ♣rs s♦tér♠s

st♦s r♥ts ♣rt♥♥ts ♣♥♦ té♥ ♥♠ér ♦ ①♣r♠♥t

t♦rs ♠

❨ ❲ tr♠♥çã♦ tr♦ tér♠ ♦ s♦♠♥t♦ tr

♥t♦ ♠ ♥ ♦♠ ts ♣♦r♦ss s♥s

t Prsõs ♥♠érs tr♥srê♥ ♦r ♦♥

♠ ♣ss♥s ♦♠ r♦s t③♥♦ ♦ FLUENT

çã♦ ♦ t♦ s ♦♥çõs ♦♥t♦r♥♦ tér♠s

♣r ♠ ♠ó♦ ♣ró♦ ♦ ♥

t ①♣r♠♥t♦s s♦r ♦ t♦ ♦ rr♥♦ ♣r♦trâ♥s

r♦ss s♦r tr♥srê♥ ♦r ♦♠♣♦rt♠♥t♦

♦ s♦♠♥t♦ ♠ ♣ss♥s rt♥rs rr♦♥

♣sss

❨❯ çã♦ ♥♠ér ♥ê♥ tr t ♣r

s♦♠♥t♦ tr♥t♦ ♠ ♥ ♦♠ rr♥♦ ♥♦

P❩ t ♠çã♦ ♥♠ér ♠ ♥ tr♠♥s♦♥ ♦♠

çã♦ tr♥srê♥ ♦r ♦ s♦♠♥t♦

t ①♣r♠♥t♦ tr♦ tér♠ s♦♠♥t♦ tr♥t♦

s♦r ♥s r♥ts trs

❲

❯

st♦ ♥♠ér♦ ♦♥çã♦ ♠♥r ♦rç ♠

♥s ♣s ♣rs ♦♠ ts tr♥srss r

çã♦ ♦ rr♥♦ ♥tr ♥♦ s♥♦ ♦♥sr♥♦

♣r♦

t ♥stçã♦ ①♣r♠♥t s ♣r♥♣s rtrísts

♦ s♦♠♥t♦ tr♥t♦ ♠ tr♦♦rs ♦r ♦ t♣♦

s♦t♦ ♣r r♥ts trs ♥s

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r♥r t ♣rs♥tr♠ s ♣r♥♣s rtrísts ♦ s♦♠♥t♦ tr

♥t♦ ♥♠ ♥ ♠♥s♦♥ ♦r♠ t③s r♥ts trs ♥s té

♥s s③çã♦ ♦♠ ♦ ♦t♦ ♥t♥r ♦ s♦♠♥t♦ ♠ tr♦♦rs ♦ t♣♦

s♦t♦ st tr♦ ♦ sr♦ q ♦ r♠ ♠♥r ♣r ♦s s♦s ♦s

♦♦rr ♣r Re ≤ 600 P♦r ♠♦ ♥♠♦♠tr sr♦♣♣r sr♦♣♣r ♥♠♦

♠tr② ♦s t♦rs ♠r♠ ♦s ♦rs s tçõs ♦s ♥ rçã♦

rt s♥♦ ♣♦ssí ss♠ tr♠♥r strçã♦ ♥t♥s tr♥t ♥tr

s ssss ♥s ♥ rã♦ s♦♠♥t♦ ♣ró♦ ♦♥♦r♠ r

r strçã♦ ♥t♥s tr♥t ♥ rã♦ s♦♠♥t♦ ♣ró♦

2

1

0 0,5 1x/s

chicana 7chicana 6

Res=9440

y/D0,280,430,510,580,660,73

2(v')

(Vs)

♦♥t ♣t♦ t

♦r♦ ♦♠ ♦s ①♣r♠♥t♦s t ♠ t♦ rt♥r ♦♠

ts s♥s ♣r r ♠♥t ♦♠ ♦ ♠♥t♦ tr s ts

é♠ ss♦ ♦s rst♦s ①♣r♠♥ts ♣♦♥t♠ q ♦s ♣râ♠tr♦s ♦ ♠é♦

tr♥srê♥ ♦r ♠♥t♠ ♦♠ ♦ ♠♥t♦ ♦ ♥ú♠r♦ ②♥♦s ♦♠ tr

s ts ♦♠♦ str r ♥ t ♦♥sttr♠ q ♣r

r ss♦ ♦ ♠t♦ ♠♦r ♦ q ♦ ♠♥t♦ ♥ tr♥srê♥ ♦r

❯♠ st♦ ♥♠ér♦ ♦ s♦♠♥t♦ tr♥t♦ ♣ró♦ ♥♠ ♥ ♦♠ rr♥♦

♥♦ ts t③♥♦ ♦ ♠♦♦ trê♥ κ− ǫ r♦ q ♣r ♠s♠ ♣♦

tê♥ ♦♠♠♥t♦ ♠♥♦r tr t t ♠♦r ♥ê♥ s♦r ♦ s♠♣

♥♦ tér♠♦ ❨❯ st ♦♠♣♦rt♠♥t♦ á s♦ r♦ ♣♦r ♥s♥

❲♥s♥ q♥♦ ♦ st♦ ♠ s♦♠♥t♦ ♠♥r ♥♠ ♥ ♣s

♣rs ts tr♥srss ♥sts ♣r r♥ts s♣ç♠♥t♦s st út♠♦

♦s t♦rs trír♠ ♥ê♥ ♦ rr♥♦ ♥♦ à r♥s rrçõs ♦r♠s

♥s rõs ♦ s♣ç♠♥t♦ ♥tr ts s ♦♥t♦r♥♦s t♠♣rtr ♦♠ tr s

ts ♣♦ sr s③♦ ♥ r

♦ s tr♦ ♦s ♦♦♠♥ s♠r♠ ♥♠r♠♥t ♦ s♦

♠♥t♦ ♠♥r ♦♥sr♥♦ rã♦ ♥tr ♥♠ ♥ ♦♠ ts s♥s

♣rs s♦tér♠s ♦♥stt♥♦ q tr♥srê♥ ♦r ♠♥t ♦♠ ♦ ♠♥t♦

tr s ts ♦♠ ♠♥çã♦ ♦ ♣ss♦ s ts ♦sã♦ ♦s t♦rs t♠é♠

r♠ ♥ê♥ ♦ ♥ú♠r♦ Pr♥t st s♥t♦ ♦srr♠ q ♦ s♦♠♥t♦

♣♦ s t♦r♥r ♣r♦♠♥t s♥♦♦ ♠t♦ ♥ts ♣r ♦s ♣rs ♦ ♦

q ♣r ♦s ♣rs t♠♣rtr tr♦ t♦r ♥trss ①♣♦r♦ ♣♦s t♦rs

r ❱rçã♦ ♦ ♥ú♠r♦ sst ♠é♦ ♦♠ ♦ ♥ú♠r♦ ②♥♦s ♣rr♥ts r③õs tr ♥

F/D duto liso0,7 madeira0,7 alumínio0,5 alumínio0,3 alumínio

200

160

120

80

40

0 4 8 12 16

Re x 10-3

Nu

Nu0

♦♥t ♣t♦ t

♦ ♥ê♥ tr s ts ♥ r♦♥â♠ ♦ s♦♠♥t♦ á ♠ ♠♥ç

s♥t ♥♦ ♣rã♦ ♦ s♦♠♥t♦ ♦♠♦ s ê ♥ r

Prr♥ ♦ r③r♠ ♠ st♦ ♥♠ér♦ ♣r ♦ s♦ s

♦♠♥t♦ ♥♦♠♣rssí tr♥t♦ ♠ ♠ ♥ rt♥r ♦♠ s ♥s s

rst♦s ♦r♠ ♦t♦s ♣r ♦♠♥çã♦ s s ♥s ♠♦♥ts ♥ ♠s♠ s

♣rí ♦♠ r♥ts ♦♠♣r♠♥t♦s r♥ts s♣ç♠♥t♦s s♣ç♠♥t♦ ♥tr

s ♥s ♦ r♦ ③s tr ♦ ♥ s t♦rs t③r♠ ♦ ♠♦♦

trê♥ ♦♥sttr♠ q ♦ ♦♠♣r♠♥t♦ r♦♠♥t♦ s♥t út♠

♥ ♦ ♣r♦①♠♥♠♥t ♦♥st♥t ♥♦ s♦ ♠ q st é ♠♥♦r q t ♥t

r t♦ tr t s♦r strçã♦ t♠♣rtr ♣r L/H = 4Pr = 0,71 Re = 200

(a) e/H=0,5 (b) e/H=0,3

(c) e/H=0,4 (d) e/H=0,2

♦♥t ♣t♦ ❲❯

r ❱t♦rs ♦ ♣r r♥ts r③õs ♦q♦ Pr

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0

0

0

0

0

0

y/H

y/H

y/H

x/H

x/H

x/H

♦♥t ♣t♦ ❯❱

r♦r ♥♦ ♦s t♦rs st♦ ♦♦rr ♣♦s út♠ ♥ s ♦③ ♠rs ♥ rã♦

rrçã♦ r ♣ ♥ ♥tr♦r r stã♦ strs s ♥s

♦rr♥t ♣r três s♦s ♣r♦③♦s ♣♦r sts t♦rs ts ♠s♠♦ ♦♠♣r♠♥t♦

♣r♠r t ♠♦r q s♥ ♣r♠r t ♠♥♦r q s♥

r ♥s ♦rr♥t ♣r r♥ts t♠♥♦s s♣ç♠♥t♦s ♥s

(a)

(b)

(c)

♦♥t ♣t♦ P ❲

st♦ ♦♠♥çã♦ rçã♦ tr ♥ t♠é♠ ♦ st♦ ♣♦r

❩ ❯ ♣r ♠ ♥ ♦♠ ♥s sq♥s ♠♦♥ts s♦r

♠ ♣ q r stá ♠ s♦ç♦ ♦ ♦♠í♥♦ ♦♠♣t♦♥ t♠é♠ ♦

t r♥♠♥t♦ ♠ t③♦ s t♦rs t③r♠ ♠ ♣r♦r♠ ♦♠r

FLUENT ♦ ♠♦♦ trê♥ κε s ♦♥ír♠ q ♦ s♦ ♠

♥ ♠♥♦r ♥ ♣r♠r ♣♦sçã♦ ♠ ♥ ♠♦r ♥ út♠ ♠♥ r♥ç

♥tr ♠á①♠ ♠í♥♠ t♠♣rtr ♣ q ♦r♥♦ t♠♣rtrs

♠s ♦♠♦ê♥s

♦♥r st♦ ♥♠r♠♥t ♦ t♦ ♣r♦trâ♥s r♦ss

sçã♦ rt rr♥♦ s♥♦ ♥ tr♥srê♥ ♦r ♠ s♦♠♥t♦ tr♥t♦ ♥♦

r t ♠ ♥ã♦ strtr ♣r s♠çã♦ ♦ s♦♠♥t♦ tr♥t♦s♦r ♠ ♣ q ♦♠ ♥s sq♠át♦ ♦ ♦♠í♥♦ ♦♠♣t♦♥

Seção de entrada

Placa aquecida

Seção de teste

yx

EntradaSaída

Chicanas

♦♥t ♣t♦ ❩ ❯

♥tr♦r ♠ ♥ t♦r t③♦ ár♦s ♠♦♦s trê♥ ♦♥stt♦ q

♣rçã♦ s♦r ♦ s♦♠♥t♦ ♦ ♠s r q tr♦ tér♠ ♥ ♦

♥st♦ ♦ t♦ ♦ ♥ú♠r♦ Pr♥t tr♥t♦ s♦r ♠ ① ♦♠

t♦ s♥♥t s♦r ♦s rst♦s s♦çã♦ tér♠

♠♦r ♥♦ ♣r♦ss♦ tr♥srê♥ ♦r trés ♥srçã♦ ♠ ú♥

t ♦ ♥st ♣♦r q t t♦ ♠♥sã♦ t t♠é♠

s ♦r♥tçã♦ ♦ st♦ ♠ ts trés s♠çã♦ ♥♠ér ♠ ♦♠í♥♦

♠♥s♦♥ ♦♥♦r♠ r s rst♦s ♣♦♥t♠ ♣r ♠ s♥♥t ♠♦

r ♥ tr♦ tér♠ ♦ q♣♠♥t♦ ♣♦r ♠♦ ♥tr♦çã♦ ♠ t ♥♥ ♥

rçã♦ ♦ s♦♠♥t♦ ♦♠ ♠♥♦r ♣r r

♥stçã♦ ①♣r♠♥t ♣ss♥s ♦♠ ♣r♦trâ♥s r♦ss ♥♥s

♦♠ rçã♦ ♦ s♦♠♥t♦ ♦ r③ ♣♦r ♠ t st st♦ ♦s t♦rs

s♠ r ♦s t♦s ♦ rr♥♦ ♦s ♠♥t♦s r♦s s♦r ♦ s♦♠♥t♦

tr♥srê♥ ♦r s♥♦ ♣çã♦ ♥♦ rr♠♥t♦ s ♣ás ♠ tr♥ ás

r stá ♠ sq♠ ♠♦str♥♦ ♠ ♥ô♠♥♦ q ♦♦rr ♦♠ rqê♥ ♥♦

s♦♠♥t♦ ♠ ♥s sçã♦ ♥ã♦rr ♦ s♦♠♥t♦ s♥ár♦

♠♦r s s♠çõs ♥♠érs ♥♦♥♦ ♦ tó♣♦ ♠ qstã♦ é r③

♣r ♦ s♦ ♠♥s♦♥ ♥trt♥t♦ ♦♥♦r♠ á ♠♥♦♥♦ trê♥ é ♠

♥ô♠♥♦ tr♠♥s♦♥ st s♠♣çã♦ ♠♣ ♥ ♣r ♥♦r♠çã♦ ♦ st♦

♥♦♠♥t ♥tr♦çã♦ ♦stá♦s ♥♦ s♦♠♥t♦ ♣♦ rstr ♠ t♦s tr

♠♥s♦♥s ♠s♠♦ ♣r ♦ s♦ ♠♥r ♦♣③ t str♠ tr♥srê♥

♦r ♠ ♠ ♥ tr♠♥s♦♥ ♦♠ ♥s ♠♦♥str♥♦ ♣rs♥ç ♦rts

t♦s tr♠♥s♦♥s P♦r ♠♦ ♦ ♦♠♣rt♦ ♦♠ ♠ s♦ ♠♥s♦♥ s

♠♦♥strr♠ q ♣rsã♦ ♦ t♦r trt♦ ♣r ♦ s♦ é s♠♣r ♠♦r ♣r qs

rtrísts ♦♠étrs

♣rsã♦ ♥♠ér ♣r tr♥srê♥ ♦r ♦♥ ♥♠ ♥ ♠♥

s♦♥ ♦♠ r♦s r ♣ss ♦ r③ ♥♦ ♠ ♦♥srçã♦ ♦s t♦s

r♥ts ♦♥çõs ♦♥t♦r♥♦ r♥♦ t ♦♠♣rr♠ ♦s rst♦s

♥tr tr♦ tér♠ ♦♥ ♦♠ ♦ s♦ ♠ ♣r ♦ ♥ ♦♠ ①♦ ♦r

r s♦s ♦ ♦♠í♥♦ ♦♠♣t♦♥ ♠♥s♦♥ r♣rs♥t♥♦ ♣rt s♣r♦r ♦ t♦ tr♦♦r ♦r

Parede

saídaentrada

Y

Xlinha de centro

h50 cm

D/2

(a)

saídaentrada

Y

X

50 cm

(b)

saídaentrada

Y

X

50 cm

(c)

saídaentrada

Y

X(d)

♦♥t ♣t♦ ❯ t

♦♥st♥t P♦r ♠♦ rst♦s ①♣r♠♥ts s ♣rsõs ♥♠érs ♦s t♦rs

♠♦strr♠ q ♣rsã♦ tr♥srê♥ ♦r é st♥t s♥sí ♦ t♣♦ ♦♥çã♦

♦♥t♦r♥♦ t③ ♥♦ ♠♦♦ ♥♠ér♦ st s♥s é ♠s ♥t q♥♦

é t ♣rsã♦ ♦ ♥ã♦ s♥♦ s♥t ♥ ♠é ♥ ♦ ♦♥stt♦ q

♠s sr♣â♥s ♥tr ♣rsã♦ ♥♠ér ♦ ①♣r♠♥t♦ ♣♦♠ sr ♠♥ís

♦♥sr♥♦ ♦♥çã♦ ♦r ♥s ♣r♦trâ♥s r♦ss rs st♦ é tr♥srê♥

♦r ♦♥

t♦ ♣♦r♦s ♠ ts t♠é♠ ♦ ♦t♦ st♦s ♥♠ér♦s P♦r

①♠♣♦ ♦ rr♥♦ s♥♦ ts sós ♣♦r♦ss ♦ ♥st♦ ♣r s♦♠♥t♦

tr♥t♦ ♠ ♠ ♥ rt♥r ❨ ❲ s t♦rs ♦♥sttr♠ q

tr♥srê♥ ♦r ♣r ♠s ♠♥t ♦♠ ♦ ♠♥t♦ tr s ts ♦ ♦

t♦ rçã♦ ♦ s♦♠♥t♦ ♦♠♦ ♣♦r♦s ♠♥ ♦ ♦q♦ ♦ s♦♠♥t♦

st t♣♦ ts ♣r♦♣♦r♦♥♦ ♠♥♦r ♣r r ♥t♦s ♠♦s t♠é♠

str♠ ♦ t♦ ts ♣♦r♦ss ♥ã♦ ♥♦♥tr♥♦ ♥t♥s ♥♦ s♦ ♠trs ♦♠

① ♣♦r♦s ♣r ♦ s♦♠♥t♦ ♠♥r ♥st♦

❱rçõs ♦♠étrs ts q ♦♠ ♦ ♦r♠t♦ ♣♥♦ áss♦ á ♦r♠

♦rs ♥♠r♠♥t r♣tt♥♣♣t Pr♦♠♦♥ ♥sr♠ ♦ s♦

♠♥t♦ ♠♥r ♣ró♦ ♠ ♠ ♥ sçã♦ rt ♦♠ ts ♠ ♦r♠t♦ ♠♥t

r ♦r♠ ♦ts ♠♦rs ♥ tr♥srê♥ ♦r ♦♠ rçã♦ às tr♦

r sq♠ ♠♦str♥♦ s ♦♠trs ♦ ①♣r♠♥t♦ ♦ ♣r♠♥t♦ ♦s♦♠♥t♦ s♥ár♦

Padrã

o de

esc

oam

ento

secu

ndár

io

Fundo Recolamento do

escoamento

45°Obstáculo

Separação do

escoamento

Lateral direita Linhas de

trajetória

Local da conexão do "obstáculo" com a parede superior

Topo

♦♥t ♣t♦ t

♥s ts ♣♥s ♣♦ré♠ ♦♥♦♥s ♠♥♦rs â♥♦s rtr tr♦ ①♠♣♦

♦ ♦ st♦ ♥③♥♥ t ♥♦ q ♦r♠ ♦♥③s s♠çõs ♥♠érs

♦ s♦♠♥t♦ tr♥t♦ ♠ ♥ ♣♥♦ ♣r ♦s ♦r♠t♦s ♥ ♦ rt♥r

áss♦ ♠ tr♣③♦ st s♦ ♦s t♦rs ♦♥sttr♠ ♠ ♦♥srá ♠♥t♦

♦s ♥♦ s♦ s ts tr♣③♦s ♦♠ rçã♦ ♦ ♦r♠t♦ tr♥r t♥♦

♦♠♦ ♦♥sqê♥ ♠ ♣rá ♠♥♦ ♦ ♦♥t trt♦ ♥♥ t

str♠ ♥♠r♠♥t ts ♦♠ ♦r♠t♦ ♠ ♦♥♦r♠ r s

t♦rs t③r♠ ♦ ó♦ ♦♠r FLUENT ♦♠ ♦ ♠♦♦ trê♥ s

♦♥sttr♠ q ♦ ♠♥t♦ ♥♦ ♥ú♠r♦ ②♥♦s ♣r♦♦ ♠ ♠♥t♦ sst♥ ♥♦

♥ú♠r♦ sst ♣♦ré♠ ♦♠ ♠♥t♦ ♥t♦ ♥ q ♣rssã♦

r ♦♠tr ♦ ♥ ♦♠í♥♦ ♦♠♣t♦♥ ♦ s♦♠♥t♦ ♣ró♦

H

b

s=H

L=2H

fronteiras periódicas

♦♥t ♣t♦ PPP P❱

r♥ts ♣♦s♦♥♠♥t♦s s ts ♥♦ ♥tr♦r ♦ s♦♠♥t♦ t♠é♠ ♦r♠

st♦s ❨♥ t str♠ ♦ t♦ ♥♥çã♦ s ts ♥♦ s♥t♦ ♦

s♦♠♥t♦ ❯♠ ♣r♦tót♣♦ rt ♦ s♠♦ ♥♠r♠♥t ♦ q stá str♦

♥ r

r ♥s ♦♠ ♦♠tr ♥♦ ♦r♠t♦

Le

s

chicanas em "L"

Lout

L

H

♦♥t ♣t♦ t

r sq♠át♦ ♠ strtr í ♦ ♦♠í♥♦ ♦♠♣t♦♥ ♥♦ ♥

30

6

h1

1parede

aleta inclinada

parede711,5

domínio

numérico

2H

fluido

y

x

♦♥t ♣t♦ ❨❯ t

ss♠ ♦♠♦ s rtrísts ♦♠étrs r③ã♦ ♥tr s ♣r♦♣rs ♦ só♦

♦ ♦ t rt♠♥t tr♥srê♥ ♦r ❨ t t

♦♠♣rt♦ ♥tr s r♥ts r③õs ♥tr s ♦♥ts tér♠s

♦ só♦ ♦ ♦ ♣♦ sr s③♦ ♥ r Prs ♣♦ ♦

♠á①♠ q ♠♥t♥♦ r③ã♦ ♠ ③s t① tr♥srê♥ ♦r

♠♥s♦♥ ♣rs♥t ♠ ♠♥t♦ ♣r♦①♠♠♥t qr♣♦

♠ét♦♦ ♦♠s ♥t♦s t♠é♠ é t③♦ ♣r ♦♠í♥♦s ♦♠♣t♦♥s q

r♣rs♥t♠ ♠ só♦ ♦ tr♦ r③♦ ♣♦r t ♦♥çã♦ ♠st

♠ s♦♠♥t♦ tr♥t♦ ♠ ♥ ♦r③♦♥t rt♥r ♦♠ ts ♦♥t♥s ♦

❯♠ ♦s s♦s t③♦s ♣♦s t♦rs ♥♦ çã♦ tr♦ ♦r

♦♥ ♥ q ♦ ♦♠í♥♦ só♦ ts ♦ ♠♥t srt③♦ trés ♦ ♠ét♦♦

♦s ♦♠s ♥t♦s

♥ê♥ ♥♥çã♦ ts tr♥srss s♦r tr♦ ♦r ♦♥

♠ ♥s sçã♦ rt ♦ r♥t♠♥t st ♣r s♦♠♥t♦ ♠♥r P t

t③♥♦ ♦ CFX ♦sã♦ ♦s t♦rs ♦♥ír♠ q ♦ ♠♥t♦

r ♣♥ê♥ t① tr♦ tér♠ ♠♥s♦♥ ♦♠ r③ã♦ s♣t♦ t ♦♠ r③ã♦ ♥tr s ♦♥ts tér♠s ♣r r♥ts♥ú♠r♦s ②♥♦s

K=10Pr=0,7

(a)(b)

40

30

20

10

00 2 4 6 8 10 12 14 16 18 20 22

Local de máximo

Re=2000Re=1500Re=1000Re= 700Re= 500Re= 200Re= 100

Q

80

60

40

20

0

100

0 2 4 6 8 10 12 14 16 18 20 22

Local de K=200Pr=0,7

Re=2000Re=1500Re=1000Re= 700Re= 500Re= 200Re= 100

máximo

Q

♦♥t ♣t♦ ❨ t

ár tr♦ tér♠ ♣♦r ♠♦ s ts ♥ã♦ ♦ s♥t ♣r ♦♠♣♥sr s rõs

① tr♦ tér♠ ♦ às ③♦♥s rrçã♦ ♦ ♦ ♥t♦ à s s ts

é♠ ss♦ ♦s t♦rs ♦♥sttr♠ q ♦ ♦♥trár♦ ♦ rr♥♦ s♥♦ ♦ rr♥♦

♥♦ ♣rs♥t♦ ♠♥çã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦ â♥♦

♥♥çã♦ s ts ♦♥♦r♠ s r ♥ r sts q ♦ st♦ ♦

r③♦ ♦♠♦ tr♦ ♣r♠♥r ♥ ♦rçã♦ ♦s s♦s ♣r♦♣♦st♦s ♣r ssrtçã♦

r ú♠r♦ sst ♦ ♣r ♣r s♣r♦r ♥r♦r ♦ rr♥♦s♥♦ ♣r ♦ rr♥♦ ♥♦

0,0

2,0

4,0

6,0

8,0

10,0

0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0

Nu

x

x*/a*

0° 23° 45° 68° 90° posição da aleta (a)

0,0

2,0

4,0

6,0

8,0

10,0

0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0

Nu

x

x*/a*

0° 23° 45° 68° 90° posição da aleta (b)

0,0

2,0

4,0

6,0

8,0

10,0

0,0 2,0 4,0 6,0 8,0 10,0

Nu

x

x*/a*

0° 23° 45° 68° 90° posição da aleta (c)

♦♥t ♣t♦ P t

❯Õ Ó Õ

st ♣ít♦ srã♦ ♣rs♥ts s ♦r♠çõs rst♥ts ♠♦♠ ♦ ♣r♦

♠ tr♥srê♥ ♦r ♦♥ ♦ s♦♠♥t♦ ♠ ♠ ♥ tr♥srs♠♥t

t♦ sçã♦ rt sts ♦r♠çõs ♦♥sr♠ ♠s s♠♣çõs ♥ q

♣óts ♠♥s♦♥ s ss♠ ♠♦♠ é ♣rs♥t ♣r ♦ s♦ tr♠♥

s♦♥ Pr♠r♠♥t sã♦ srts s qçõs ♦♥srçã♦ ásss ♣r ♠ss

q♥t ♠♦♠♥t♦ ♥r st út♠ t♠é♠ é ①♣rss ♣r ♦ s♦ ♦

só♦ sqê♥ s qçõs ♦♥srçã♦ ♦ ♦ sã♦ ♠♦s t③♥♦s

♠s♠ ♦r♠ q rst♠ s qçõs ♦♠ ♠é ♥♦ t♠♣♦ ♦ q á

♦r♠ ♦ ♣r♦♠ áss♦ ♦ ♠♥t♦ trê♥ sr ♣rs♥t♠s s

qçõs ♦♥srçã♦ ♠ tr♠♦s q♥ts ♠és q♥ts ts q

♥♠ ♦s t♦s ♦ ♦ r♠ s♦♠♥t♦ ♥♠♥t ♠ ③ q ♣óts

♦ss♥sq ♦ t③ ♣r ①♣rssr ♦ t♥s♦r ②♥♦s sts r♠♥t

♦r♠ ♣r s qçõs s♦s tr♥t ♣♦ ♠♦♦

♠ rtr③r rr♠♥t s♠çã♦ t③ ♥♦ ♣ê♥ stã♦

♣rs♥ts ♥♦r♠çõs r ♦ ♠ét♦♦ srt③çã♦ t♠é♠ s♦r strté

s♦çã♦ ♥♠ér

❯Õ ❱

r♦t♥ ♥♥r t♠é♠ r♥t r③çã♦ ♣sqss é ♦♠♠

♦çã♦ strtés ♠♦♦ rstr♥r ♦♠♣① ♦ t♠ ♠ qstã♦ st

st♦ ♦ ♣r♦♠♥t♦ é t♦ ♠♥t ♦♥srçã♦ s s♥ts s♠♣çõs

♦ t♦♥♥♦ Pr♦♣rs íss ♦♥st♥ts ss♣çã♦ s♦s ♦rçs

♦r♣♦ rçã♦ s♣r③ís ã♦ á rsstê♥ tér♠ ♦♥tt♦ ♥tr s ss s

ts s s♣rís ♥tr♥s s ♣rs ♦ ♥ ã♦ á ♦♥t rçã♦ ♥r

s♦♠♥t♦ ♥♦♠♣rssí ♠♥s♦♥ r♠ ♣r♠♥♥t ♦r♠

♠é ②♥♦s ♥♦ t♠♣♦ ♣r rs♦r s qçõs tr♥s♣♦rt

♦r♦ ♦♠ s s♠♣çõs ss♠s ♦r♠çã♦ ♦♥srt ♣r ís

♦ ♣r♦♠ ♥ ♦r♠ ♥ é r♣rs♥t ♣s qçõs q s♠

Pr ♦♥srçã♦ ♠ss

∂ρf

∂t+ ∂(ρui)

∂xi= 0, i = 1,2,3

♥ q ρf é ♠ss s♣í ♦ ♦ t r♣rs♥t ♦ t♠♣♦ xi sã♦ s ♦♦r♥s ♦

sst♠ ♦ ui sã♦ s ♦♠♣♦♥♥ts ♦

Pr ♦♥srçã♦ q♥t ♠♦♠♥t♦

∂(ρfui)∂t

+ ∂(ρfujui)∂xj

= − ∂p∂xi+ ∂sij∂xj

, i, j = 1,2,3

♥ q p é ♣rssã♦ ♦ sij é ♦ t♥s♦r t♥sã♦ s♦r

sij = 2µfD′

ij, i, j = 1,2,3

s♥♦ µ s♦s ♠♦r D′

ij ♦ t♥s♦r t① ♦r♠çã♦ s♦r

D′

ij =Dij − 1

3Dkkδij, i, j, k = 1,2,3

♥ q δij é ♦ ♦♣r♦r r♦♥r ♦ t♥s♦r t① ♦r♠çã♦ Dij é ♦t♦

♣rtr

Dij = 1

2(∂ui∂xj+ ∂uj∂xi) , i, j = 1,2,3

♦ts q ♣rtr ♣óts ♥♦♠♣rss ♣ qçã♦ ♦

s♥♦ tr♠♦ ♦ t♥s♦r t① ♦r♠çã♦ s♦r sr ♥♦ s qçõs

s t♦r♥♠ q♥ts

Pr ♦♥srçã♦ ♥r ♥♦ ♦

∂(ρfcfT )∂t

+ ∂(uiρfcfT )∂xi

= ∂

∂xi(kf ∂T

∂xi) , i = 1,2,3

♥ q T é t♠♣rtr cf é ♦ ♦r s♣í♦ ♣rssã♦ ♦♥st♥t ♦ ♦ kf é

♦♥t tér♠ ♠♦r ♦ ♦ Pr ♦♥srçã♦ ♥r ♥♦ só♦

∂(ρscsT )∂t

= ∂

∂xj(ks ∂T

∂xj) , j = 1,2,3

♥ q ρs é ♠ss s♣í ♦ só♦ cs é ♦ ♦r s♣í♦ ♣rssã♦ ♦♥st♥t ♦

só♦ ks é ♦♥t tér♠ ♦ só♦

❯Õ ❱

s ♠ét♦♦s ♥♠ér♦s ♦♠♣t♦♥s sã♦ t③♦s ♦♠♦ ♠ tr♥t ♣r

♣r♦①♠r s♦çã♦ s qçõs ♦♥srçã♦ ♦♥s ♦♠♦ qçõs r

t♦s ♦♠♦ tr♥t ♣r s♦çã♦ s♦♠♥t♦s ♦♠♣①♦s sã♦ ♣s ♦r♠

çõs sttísts ♦♠♦ t③ ♥st tr♦ ♦r♠ ②♥♦sr

r t♦s

♦r♠ ♦r♠ s á ♣♦r ♦t q♥♦ ②♥♦s ♣♦

s ♣sqs s♦r s♦♠♥t♦s tr♥t♦s ss♥♠♥t s qçõs rs

♣r♦♠çã♦ ②♥♦s sã♦ ss ♥ ♦♠♣♦sçã♦ ♠ q♥t ♠ ♠

♣r ♦r ♠é♦ φ ♠ ♣r ♦r t♥t φ′ ♦♠♦

φ = φ + φ′

♦♠♦ ♣rt t♥t é ♥tr③ tór ♠ trt♠♥t♦ sttíst♦ ♠é

♥♦ t♠♣♦ é ♣♦ st s♦ é ♣r♦♣r ♣r trê♥ st♦♥ár ♦ s

♣r ♠ s♦♠♥t♦ tr♥t♦ q ♥ ♠é ♥ã♦ r ♦♠ ♦ t♠♣♦ s ts

s♦r st ♣r♦♠♥t♦ ♣♦ sr ♥♦♥tr♦ ♠ ❲♦① t ♣ós ♣r st

♠t♦♦♦ às qçõs ♦♥srçã♦ ♦ ♦ t♠s qçã♦ ♦♥srçã♦

♠ss

∂ρf

∂t+ ∂(ρfui)

∂xi= 0, i = 1,2,3

s♥♦ q i = 1,2,3 r♣rs♥t♠ s rçõs ♦s ①♦s s ♦♦r♥s qçã♦

♦♥srçã♦ q♥t ♠♦♠♥t♦ s t♦r♥

∂(ρfui)∂t

+ ∂(ρfui uj)∂xj

= − ∂p∂xi+ ∂(sij − ρfu′iu′j)

∂xj, i, j = 1,2,3

♥ q ♦ tr♠♦ q ♥ tçã♦ s ♦s ♦ ♣♦ t♥s♦r ②♥♦s

τij = −ρfu′iu′j, i, j = 1,2,3

♥ q u′

i sã♦ s tçõs s ♦♠♣♦♥♥ts ♦ rçã♦ ♦♥sttt é

sij = 2µfD′

ij, i, j = 1,2,3

s♥♦

D′

ij =Dij − 1

3Dkkδij, i, j, k = 1,2,3

♦♠

Dij = 1

2(∂ui∂xj+ ∂uj∂xi) , i, j = 1,2,3

ssts q ♦ tr♠♦ τij á ♦r♠ ♠ t♥s♦r ♣r♥t ♦rrs♣♦♥♥♦ ♠

t① tr♥srê♥ q♥t ♠♦♠♥t♦ ♥♦s s tçõs ♦

♦ ♦ st tr♠♦ é ♦♥♦ ♦♠♦ t♥s♦r ②♥♦s ♥sst sr ①♣rss♦

♦r♦ ♦♠ ♠ ♠♦♦ trê♥ sr st♦ ♥♦ t♠ st ♣r♦♠ é

♦♥♦ ♦♠♦ ♦ ♣r♦♠ ♦ ♠♥t♦ trê♥ ♣r ♦r♠ st

♦r♠ q é ♣r♦♠♥♥t♠♥t t③ ♠ t t♠é♠ r♣rs♥tçã♦

ís ♦ ♣r♦♠

Pr qçã♦ ♥r t♠s t

∂(ρfcfT )∂t

+ ∂ρfcfuiT∂xi

= ∂

∂xi(kf ∂T

∂xi− ρfcfu′iT ′) , i = 1,2,3

♥ q ♦ tr♠♦ −ρfcfu′iT ′ rst ♦ ①♦ ♦r ♥♦ s tçõs tr♥ts

❯❯

♣r♦♠ ♥♠♥t ♦ á♦ s♦♠♥t♦s tr♥t♦s stá ♥ tr♠

♥çã♦ ♦s tr♠♦s ♦ t♥s♦r ②♥♦s qçã♦ s ①♣rssõs ♥♦♥♦ s

tçõs ♦ q sr♠ ♦♠♦ ♦♥sqê♥ ♦ ♣r♦ss♦ ♠é ②

♥♦s r♣rs♥t♠ ♥♦s ♥ó♥ts ♥çã♦ ♠♦♠ trê♥ é ♣♦rt♥t♦

s♥♦r ♣r♦①♠çõs ♣r sts ♦rrçõs s♦♥s ❲❳ t

①st♠ s ♦r♥s st♥ts ♣r ♠♦r ♦ t♥s♦r ②♥♦s ♦s ♠♦♦s

s♦s tr♥t ♦s ♠♦♦s t♥sõs ②♥♦s sts út♠♦s ♦♠♣t♠

t♦ ♦s t♥s♦rs ♣r♥ts ♦ t♥sõs ♣r♦③s ♣rtr ♦ t♥s♦r ②♥♦s

♥q♥t♦ q ♦s ♣r♠r♦s s s♠ ♥ ♣óts ♦ss♥sq sr s♠ s

♦♥srçõs ♣óts ♦ss♥sq

−ρfu′iu′j = µt (∂ui∂xj+ ∂uj∂xi) − 2

3ρfκδij, i, j = 1,2,3

♥ q µt é s♦s tr♥t δij é ♦ t r♦♥r κ é ♥r ♥ét

tr♥t ①♣rss ♣♦r

κ = 1

2u′

iu′

i, i = 1,2,3

stt♥♦ s qçõs ♥ qçã♦ t♠s

∂(ρfui)∂t

+ ∂(ρfui uj)∂xj

= −∂pe∂xi+ ∂

∂xj[µe (∂ui

∂xj+ ∂uj∂xi)] , i, j = 1,2,3

♥ q s♦s t µe é s♦♠ s ♣rs ♠♦r tr♥t

µe = µf + µt

pe é ♣rssã♦ t

pe = p + 2

3ρfκ .

♥♦♠♥t ♣r ♦♥srçã♦ ♥r t♠s

∂(ρfcfT )∂t

+ ∂(ρfcfuiT )∂xi

= ∂

∂xi(ke ∂T

∂xi) , i = 1,2,3

♥ q ♦ ①♦ ♦r s tçõs tr♥ts é ♠♦♦ ♣♦r

−ρfcfu′iT ′ = kt ∂T∂xi , i = 1,2,3

ke é ♦♥t tér♠ t ♦rrs♣♦♥ à s♦♠ ♥tr ♣r ♠♦r

♣r tr♥t

ke = kf + kt .

tr♠♥çã♦ ♦♥t tér♠ tr♥t s s ♥♦ ♥ú♠r♦

Pr♥t tr♥t♦

kt = cfµt

Prt

srs q ♦ ♥ú♠r♦ Pr♥t tr♥t♦ ♥ã♦ é ♣r♦♣r ♦ ♦ ♠s

ss♠ ♠ ♦r ♦♥st♥t ♦♠ s ♠ ①♣r♠♥t♦s ♥áss ♦♥stt♦s q Prts st ♣ró①♠♦ q é ♦ ♦r t③♦ ♥st ♦r♠çã♦ ❱ t

♥♠♥t é ♥ssár tr♠♥çã♦ q♥t µt q srá ♦t ♣♦r ♠♦

♠ ♠♦♦ trê♥

♦♥♦r♠ ♠♥♦♥♦ ♥ sçã♦ s♦r ♦ ♠♦♦ trê♥ ♦ à ís

♣rs♥t ♥♦ s♦♠♥t♦ ♦s s♦s st♦s ♥s ♦ s♦ ♦ ♠♦♦ ③♦♥

♥tr ♦r♦ ♦♠ ♣çã♦ ♦ t♦r t♠s qçã♦ ♣r ♥r

♥ét tr♥t κ

Dρfκ

Dt= τij ∂ui

∂xj− α∗ρfωκ + ∂

∂xj[(µf + σκµt) ∂κ

∂xj] , i, j = 1,2,3

❯♠ s♥ qçã♦ ♥♦ ♠♦♦ ♦r♥ t① ss♣çã♦ s♣í ω

Dρfω

Dt= γνtτij∂ui

∂xj−αρfω2+ ∂

∂xj[(µf + σωµt) ∂ω

∂xj]+2(1−F1)ρfσω2 1

ω

∂κ

∂xj

∂ω

∂xj, i, j = 1,2,3

s ♦rs s ♦♥st♥ts s qçõs tr♥s♣♦rt κ ω sã♦ tr♠♥s

trés ♠ ♦r♠çã♦ q ♠str ♦s ♦rs s rs♣ts ♦♥st♥ts ♥tr ♦rs

♦ ♠♦♦ ♣rt ♥tr♥ ♦ ♠♦♦ κ − ε ♣rã♦ ♣rt ①tr♥ ♦r♠çã♦

♠str é ♣♦r

ς = F1ς1 + (1 − F1)ς2

♥ q ♦s ♦rs s ♦♥st♥ts t③s ς1 ς2 ♣r ♦t♥çã♦ ♦ ♥♦♦ ♦♥♥t♦

♦♥st♥ts ♦ ♠♦♦ ♣♦♠ sr ♥♦♥trs ♠ ♥çã♦ ♠str

F1 é ♥ ♣♦ ♦♥♥t♦ qçõs q s

F1 = tanh(arg41),arg41 =min [max(

√κ

0,09ωy;500ν

y2ω) ; 4ρfσω2κCDκωy2

] ,CDκω =max(2ρfσω2 1

ω

∂κ

∂xj

∂ω

∂xj; 10−20) , j = 1,2,3

♥♦ q y é stâ♥ ♣r s♣rí ♠s ♣ró①♠ CDκω é ♣rt ♣♦st ♦ tr♠♦

sã♦ r③ qçã♦

♥çã♦ s♦s tr♥t é ♣♦r

µt = ρa1κ

max(a1ω;ΩF2) , Ω = √2WijWij e Wij = 1

2(∂ui∂xj− ∂uj∂xi) , i, j = 1,2,3

♥ q Ω é ♦ ♦r s♦t♦ ♦rt W é ♦ t♥s♦r t① r♦tçã♦ ♥çã♦ F2

é ♥ ♦♠♦

F2 = tanh(arg22),arg2 =max(2

√κ

0,09ωy;500ν

y2ω)

❱ P

❯♠ çã♦ ♠♣♦rt♥t ♥♦ ♣r♦t♦ q♣♠♥t♦s ♥♦♥♦ s♦♠♥t♦

♦rç♦ é ♣r r r♣rs♥t ♣ q ♣rssã♦ ∆p ❯♠ ♦s ♣r♥♣s

♠♦t♦s é ♦ st♦ ♦♣r♦♥ q s t♦r♥ ♠♦r q♥t♦ ♠♦r ♣r r

♦r♠ ♦ ♦ ♦ ♦ ♦♥t rçã♦ ♦ trt♦ s♣r Cfx

♦ ♦♥♦ s ♣rs ♦ ♥ ss♠ s rõs ♦♥srs ♥ çã♦ st ♦

♥t ♥ã♦ r♣rs♥t♠ ♦ trt♦ ♦ ♦ ♦♠ s ts ♠s s♦♠♥t ♦ trt♦ ♦ ♦ ♦♠

♥tr só♦♦ ♥s rõs ♣r ♠♦r ♥ã♦ ♦r♥ç ♠ ♠ rt

♦ t♦ ♦ rrst♦ s♦s♦ s♦r s ts ♦ ♦♠♣♦rt♠♥t♦ ♦ Cfx é ♥tr♥s♠♥t

tr♦ ♦s ♣râ♠tr♦s ♦♠étr♦s qs ♥ ♦ ♦♥t é ♠ ♣râ♠tr♦

♠ ♠t r♦♥â♠ st ♦r♠ é ♠ ♥♦r ♥♠♥t ♣r ♥t♥

r s rçõs ♥st rã♦ ♦ s♦♠♥t♦ ss♠ t♠s q ♦ ♦♥t trt♦

s♣r é ♦r♥♦ ♣♦r ❳ t

Cfx = τint,x∣y=±H/21

2ρfU

2

ref

♥ q τint,x é t♥sã♦ s♥t ♦ ♦ ♦ ♦♠ s s♣rís ♣r ♥ ♥tr

só♦♦ Uref é ♦ rrê♥ ss♠ ♦♠♦ ♦ ♥ ♥tr

♦ ♥

Pr ♠ çã♦ ♦ ♠ ♣r r ∆p é ♠♥s♦♥③

trés r③ã♦ ♦♠ ♣rssã♦ às ♦rçs ♥rs ♦ s♦♠♥t♦ ♥♠ sçã♦

rrê♥ ♥tr ♦ ♥ ♦♥♦r♠ qçã♦ ss♠ sã♦ ♦s ♠

♦♥srçã♦ ♦s t♦s ♦ trt♦ ♦ s♦♠♥t♦ ♦♠ s ♣rs ♦♠ s ts é♠

ss♣çã♦ ♥r ♠â♥ ♣♦s órts q sr♠ ♦ às ts ♦ trt♦

♥tr♥♦ q ♦♦rr ♥♦ ♦ st r③ã♦ é ♦♥ ♣♦r ♦♥t ♣rssã♦ Cp

♥ sr ❳ t

Cp = ∆p1

2ρfU

2

ref

♥ q ∆p é r♥ç ♣rssã♦ ♥tr ♣rssã♦ ♦ ♠é ♥♠ ♣♥♦ ♦③♦ ♠

x = 30H ♣rssã♦ ♠é ♥ sçã♦ ♥tr ♦ ♥ srs q ♣r

t♦♦s ♦s s♦s ♦ ♣♦♥t♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♣ós ♦ tr♦ t♦ ♥

♦♦rr ♠ ♣♦sçõs ♠♦t♥t x = 30H

❱

tr♥srê♥ ♦r ♥tr ♦s ♦♠í♥♦s s♠♦s ♦♦rr ♠♥r ♦♥

♥ ♣♦r ♠ ♥tr ♦♥srt st♦ é t♦♦ ♦ ♦r q trss ♦ ♦♠í♥♦ só♦

é ♦♠♣t♦ ♣r ♦ ♦♠í♥♦ ♦

♦r♠ ♦ tr♦ tér♠ ♦ trés ♦ ♥ú♠r♦ sst ♦ q

r♦♥ tr♥srê♥ ♦r ♦♥t ♦♠ tr♥srê♥ ♦r ♦♥t

Nux = hxDh

kf

♥ q Nux é ♦ ♥ú♠r♦ sst ♦ Dh é ♦ â♠tr♦ rá♦ hx r♣rs♥t

♦ ♦♥t ♦♥t♦ tr♥srê♥ ♦r ♦ kf ♦♥t tér♠ ♦

♦

♦♥t tr♥srê♥ ♦r ♦♥t♦ ♦ é ♥♦ ♣ ♦♠♥çã♦

♥tr q♥t ♦r tr♦ trés ♥tr ♠ r♥ç t♠♣rtrs

ss♠ t♠s

hx = qint,x∣y=±H/2Tint,x∣y=±H/2 − T e

s♥♦ qint,x Tint,x ♦ ①♦ ♦r t♠♣rtr ♦ ♦♥♦ ♥tr só♦♦

♥s ♣♦sçõs y = ±H/2 T e é t♠♣rtr rrê♥ ♥♦r♠ ♦♠♦ ♦♥çã♦

♦♥t♦r♥♦ ♥ ♥tr ♦ s♦♠♥t♦

srs q ♥çã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦♥♦r♠ qçã♦

r♣rs♥t s rõs ♥tr ♥tr ts ♦ s ♥ rã♦ s ♣rs ♦

♥ st♦ ♦♥t ♣♦s s rrê♥s t③s y = ±H/2 ♦♥♠ ♦♠ s ss

s ts ♥s ss rs♣ts ♣♦sçõs sts ♦s ♣♦rt♥t♦ ♥çã♦ ♦ ♥ú♠r♦

sst ♥ã♦ s ♣ ♠ ③ q ú♥ ♦r♠ tr♥srê♥ ♦r ♦♦rr ♣♦r

♦♥çã♦ ♥tr ♣r ♦ ♥ s t

♦ts t♠é♠ ♥ qçã♦ ♠s ♠♣çõs tr♦ ♦r ♦♥

♦ ♥♠r♦r t♠s ♠♦r ♥ê♥ ♦ s♦♠♥t♦ ♠ ③ q st ♣♦ rr

r♠ ♥ís ♥t♥s tr♥t s♥ q♥t ♥♦ ♥♦♠♥♦r

é ♠t ♣ ♣ ♦ só♦ tr♥srr ♦r s r♦♥tr ①tr♥ ♦♠

rás s♣s té ♥tr só♦♦

♣r ♦sr♦ ♦ ♥ú♠r♦ sst ♦ ♥ rã♦ ♥tr s ts rst

♦r♠çã♦ ③♦♥s rrçã♦ ♣ró①♠s s ts ♥s ♠♥r ①♣r♠♥

t ❱♦ t♦♥ str♠ ♦♠tr ♠ ♥ ♦♠ ①♣♥sã♦ r♣t ♦♥

s ♦r♠ ♠ ③♦♥ rrçã♦ s♥t ♦ r s t♦rs ♦srr♠ q ①st

♠ ① t① tr♥srê♥ ♦r ♥ ③♦♥ rrçã♦ s ♠ ♠♥t♦

♥t♦ té t♥r ♠á①♠ t① q ♦♦rr ♣ró①♠ ♦ ♣♦♥t♦ r♦♠♥t♦ st

srçã♦ ①♣ ♦ ♦♠♣♦rt♠♥t♦ ♣rst♦ ♣s s♠çõs ♥♠érs st tr♦

♥♦ q ♦ s♦♠♥t♦ ♦ s♦♠♥t♦ ♦♦rr ♣rtr ♣♦♥t s ts ♦♠♦ srá

st♦ sr

Pr ♦♥srr ♦ t♦ ♦ tr♦ tér♠ st♦ é s sçã♦ ♥tr

té stâ♥ rrê♥ x = 30H ♦ t③♦ ♠ ♥ú♠r♦ sst ♠é♦ ♦

♦ ♥çã♦ ♦ s ♥♦ tr♦ ♦ srs q st

tr♥t s ③ ♥ssár ♠ ③ q ♦ ♥ú♠r♦ sst ♠é♦ áss♦ Nu ♦t♦

♥trçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♥ã♦ ♠ ♦♥t ♦ t♦ s ts

s♦r tr♥srê♥ ♦r ss♠ ♦ ♥ú♠r♦ sst ♦ é ♦ ♣♦r

Nu = hDh

kf

♥ q

h = mcf(T e − T x=30H)2Lx=30H∆Tm

,

s♥♦

∆Tm = T e − T x=30H

ln( T x=30Hint − T e

T x=30Hint − T x=30H

)

T x=30Hint = T x=30H

int ∣y=H/2

+ T x=30Hint ∣

y=−H/2

2

s♥♦ h ♦ ♦♥t ♦♥t♦ tr♥srê♥ ♦r ♦ m ③ã♦ ♠áss ♦

♦ T x=30H Lx=30H sã♦ t♠♣rtr ♠é ♠str ♦ ♦♠♣r♠♥t♦

♦s ♥ ♣♦sçã♦ rr♥t x = 30H ∆Tm é r♥ç t♠♣rtr ♦rít♠

srs q ♠é rt♠ét s t♠♣rtrs ♠és ♥s ♥trs ♦ ♥ s

♥tr té stâ♥ rrê♥ x = 30H T x=30Hint ♦♥sr s♦♠♥t ♥tr

s rõs ♣r

♠♥r ♦♠♣♠♥tr ♦ ♥ú♠r♦ sst ♦ ♦ ♦r♠ r③s

♠s çõs tr♦ ♦r ♣r ♦ tr♦ s ♥tr té sçã♦ ♥ ♣♦sçã♦

x = 30H ♦r♠ tr♠♥r ♦ ♦r s ts st ♥ás s t♦r♥ ♠♣♦rt♥t

t♥♦ ♠ st ♦s ♦♠♣♦rt♠♥t♦s ♦♥trst♥ts ♣r ♦ ♥ú♠r♦ sst ♦ ♠é♦

♦♥♦r♠ ♣rs♥t♦ sr

♦r s ts qa ♦ q♥t♦ ♣♦ s♦♠tór♦ ♦ ♣r♦t♦ ♥tr ♦ ①♦

♦r trés s ts s ár s♣r

qa = 2N ∫Aa

qintdAa

♥ q 2N é ♦ ♥ú♠r♦ t♦t ts Aa r♣rs♥t ár s♣r ♠ ú♥

t

♦r t♦t qtotal tr♥sr♦ ♣r ♦ ♦ t♠é♠ ♦ q♥t♦ ♣r ♦

tr♦ ♥ s ♥tr té ♣♦sçã♦ x = 30H Pr ♦tr ss q♥t

rs♥ts ♦ ♦r tr♥sr♦ trés s ♣rs ♦ ♥ ♦ ♦r tr♦♦ trés s

ts qa

qtotal = ∫Aint

qintdAint

♥ q qint Aint ♦rrs♣♦♥♠ ♦ ♦r à ár t♦t ♥tr só♦♦ s

♥tr té ♣♦sçã♦ x = 30H

sr sã♦ ♣rs♥t♦s ♦s rst♦s st tr♦ s ♦♥srçõs s♦r

♦r♠ ♥♠ér ♣♦♠ sr ♦♥sts ♥♦s t♥s ♦ ♣ê♥ ♥♦ q sã♦

♦r♦s ♦s ♣r♥♣s s♣t♦s ♠

❯ ❯Õ

st ♣ít♦ é ♥♦ ♦♠ ♣rs♥tçã♦ s t♣s rçã♦ çã♦

♣r ♠s ♠s ♣rt♥♥ts ♦♠♦ ♦ ♥ú♠r♦ t♥t♦♥ ♥r ♥é

t tr♥t sts t♣s sã♦ ♠♣♦rt♥ts ♣♦s ♣r♠t♠ r ♣ ♦

♣r♦r♠ ♦♠r ♦rrt ♦♥strçã♦ ♦s s♦s ♣ss♥♦ ♣ ♦♠tr

♠ ♠ét♦♦ ♥♠ér♦

♣ós ♦s s♦s t♣ çã♦ rçã♦ stã♦ ♣rs♥t♦s ♦s t♥s q

♠♦tr♠ r③çã♦ st tr♦ st♦ é ♦ st♦ ♦ s♦♠♥t♦ tr♥t♦ ♥♦s

♥s t♦s ♥tr♦ sçã♦ sã♦ ♣rs♥ts s rçõs ♣r♦♣♦sts ♦♠étr

s r♦♥â♠s s t♣s ♦♥strçã♦ s ♠s s ♦♥çõs ♦♥t♦r♥♦

♣r♦♣rs íss sssã♦ ♦s rst♦s ♦t♦s

❱ ❱

❯ ❯ CFX

♠ rçã♦ çã♦ sã♦ ♦s ♦s ♣r♥♣s ♦♥t♦s ♠♣♠♥t

t③♦s ♣r rr ♦♥ rá s♦çã♦ ♠♥r rs♠

rçã♦ é çã♦ rá s♦çã♦ ♣r ♠ ♠♦♦ ♦♠♣t♦♥ P♦r

s ③ çã♦ stá r♦♥ à çã♦ rá ♠ s♠çã♦ trés

s ♦♠♣rçã♦ ♦♠ ♦s ①♣r♠♥ts ♦♦♦ ♠♦♦ r♥t rçã♦

é ♠ qstã♦ ♠t♠át ♥q♥t♦ q çã♦ é ♠ qstã♦ ís P

❯

s s♦çõs ♣r s qçõs ♦♥srçã♦ q♥t ♠♦♠♥t♦

♥r ♦r♠ rs ♣r ♦ s♦ ♠ ①♣♥sã♦ r♣t ♦♥♦r♠ rst♦s

♦t♦s ♣♦r ❩♥s t ♥s♦r t ♠ t ❱♦

t♦♥ Pr t♥t♦ ♦s s♦s ♦r♠ ♦r♥♦s stã♦ ♣rs♥t♦s ♥s ssçõs

s♦çã♦ ♦ s♦çã♦ tér♠ ♦♠tr ♣r s♦ é

rtr③ ♣♦s ♦♠♣r♠♥t♦s sçã♦ ♥tr sçã♦ ①♣♥ ♣ tr

♦ r q ♥ r③ã♦ ①♣♥sã♦

♦r♠ ♦♠♣♠♥tr s♦çã♦ qçã♦ tr♥s♣♦rt ♥r ♥ét

tr♥t κ ♦ ♦♠♣r ♦♠ ♣rsã♦ ♥♠ér ❩♥s t ♦♠

♦s ♦s ♥s♦r t st út♠♦ s♦ q stá ♣rs♥t♦ ♥

ssçã♦ s♦çã♦ ♥r ♥ét tr♥t ♦♠tr t③ ♦ ♠

♥ ♦r③♦♥t

♠ t♦♦s ♦s s♦s rçã♦ çã♦ t③♦s ♦ r t♠♦sér♦ ♦♠♦

♦ s s♠çõs ♥♠érs s ♣r♦♣rs íss ♣♦♠ sr ♦♥sts ♥

Pr♦♣rs íss t③s ♥ t♣ çã♦ rçã♦ ♦ ó♦♥♠ér♦

Pr♦♣r ❱♦r

❱s♦s ♥â♠ ♠♦r µf 1,831 × 10−5 Pa ⋅ sss s♣í ρf 1,185 kg/m3

♣ ♦rí ♣rssã♦ ♦♥st♥t cf 1004,4 J/kgK♦♥t tér♠ ♠♦r kf 0,0261 W /mK

♦♥t ♦t ♣r♦♣rs ♦ ♣r♦r♠ CFX

s♦ s♦çã♦ ♦

st st♣ rçã♦ çã♦ ♦ t③ ♦♠tr ♦rrs♣♦♥♥t

♠ ♥ ♦♠ ①♣♥sã♦ r♣t ❯♠ ♣r ♦s rtríst♦ ♦t♦ ♥ sçã♦

①♣♥ é ♦♠♣r♦ ♦♠ ♦s ①♣r♠♥ts ♦tr♦s ♠♦♦s ♦♠♣t♦♥s

♦♠tr

stã♦ ♣rs♥ts s ♠♥sõs ♣r♠tr③s ♦♠tr t

③ ♥♦ s♦ q ♣♦♠ sr s③s ♥ r

♠♥sõs ♣r♠tr③s ♦♠tr t③ ♥♦ s♦ t♣ rçã♦ çã♦ ♦ ó♦ ♦♠♣t♦♥

srçã♦ ♠♥sã♦

tr sçã♦ ♥tr He 2d

tr sçã♦ ①♣♥ Hs 3d

♦♠♣r♠♥t♦ sçã♦ ♥tr Le 3d

♦♠♣r♠♥t♦ sçã♦ ①♣♥ Ls 20d

tr ♦ r d (m)

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

♥♣♥ê♥ s♦çã♦ ♥♠ér ♦♠ rçã♦ à ♠ ♦ trés ♦

st♦ ♦ r♥♦ ♠ Pr t♥t♦ ♦ r③ ♠ sqê♥ s♦s ♦♠ rçã♦

♦ ♥ú♠r♦ ♦s ♠♥t♦s ♠♥t♦ ♦ r♥♦ ♠ t♣♦ ♠♥t♦ t③♦ ♥

rçã♦ s ♠s ♦ qrtr

r ♠♦str ♠ ♠ tí♣ t③ ♥st t♣ rçã♦

çã♦ ♣r s ♦♠trs ♦♠ ①♣♥sã♦ r♣t

r tí♣ rtrísts ♠♥s♦♥s t③s ♣r s ♦♠trs ♦♠①♣♥sã♦ r♣t

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

♦♥çõs ♦♥t♦r♥♦

♦ s♦ s♦çã♦ ♦ t③♦s s s♥ts ♦♥çõs ♦♥t♦r♥♦

❼ çã♦ ♥tr ♣r ♦s ♠ ♠t tr♥t ♣♥♠♥t

s♥♦ ♦♠ ♥t♥s tr♥t ♦ rrê♥ st

s♦ ♦ Uref = 18,2 m/s❼ ♣rís ♦rrs♣♦♥♥ts às trs ♦♠étrs ♦♥çã♦ ♣♥♦ s♠tr

❼ Prs ♦♥çã♦ ♥ã♦s③♠♥t♦ ♦ ♦ ③r♦ ♥ts q ♦

s♦ ♠ ♣r ♠♣ q ♥ã♦ á ①♦ ♠ss trés q r♦♥tr

♣♦rt♥t♦ é t♠é♠ ♦♥sr ♠♣r♠á

❼ çã♦ sí ♦♠tr ♣rssã♦ stát ③r♦

st♦s

♦♠♦ rst♦ ♣r ♦ st♦ r♥♦ ♠ ♣rs ♣r♦①♠

s s♦çõs ♦ts ♣r s três r♥ts ♠s ♠♥t♦s

♠♥t♦s ♠♥t♦s ♣rs♥ts ♥ r ♣r ♦s

♠♥s♦♥ ♦ ♦t♦ ♥♠ sçã♦ ♦③ x/d = 5,33 ♣r ♦♠tr ♥

♦♠ r③ã♦ ①♣♥sã♦ r♣t Hs/He s rst♦s ♣r r③ã♦ u/u∞

r ♥♣♥ê♥ ♠ ♣r ♦ s♦ ♦♠♣rt♦ ♦ ♣r ♦♥tr três r♥ts ♠s

−0,4 −0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,20,0

0,5

1,0

1,5

2,0

2,5

①♦rrs♦

u/Uref

(y+d)/d

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

♣rs♥tr♠ ♠ rçã♦ ♥♦ ♦r ♠á①♠♦ st r③ã♦ ♥♦ ♦r

♠í♥♠♦ st r③ã♦ ♥tr s ♠s

Pr ♥s rçã♦ çã♦ st s♦ t③♦s ♦♥♦r♠ ♣r

s♥t♦ ♥ r Prs q ♦s rst♦s r♦s ♥st tr♦ ♣rs♥tr♠

♠ ♦ ♣r♦①♠çã♦ ♠ rçã♦ ♦s ♦rs ①♣r♠♥ts trtr ①t♦ ♣ r

ã♦ ♣ró①♠ à ♣r st rã♦ ♦♥t♦ s ♠♥ts ♦srs ♦ ♦

①♦ rrs♦ r♠ ♥tr♦ ① rt ♣♦s t♦rs ♦ tr♦ ①♣r♠♥t

♦ rrê♥ 18,2 ms−1 srs ♥ q ♦ ♠♦♦

♣rs♥t rst♦ ♠s ♣ró①♠♦ ♦ ①♣r♠♥t q♥♦ ♦♠♣r♦ ♦♠ ♦s ♠♦♦s

κ − ε ♦♠ stq ♣r rã♦ ①♦ rrs♦

str ♥ q ♦♥çã♦ ♦♥t♦r♥♦ t③ ♥ sçã♦ ♥tr

♠♣♦ ♥ r③♦á r♥ç ♥tr ♦ ♠♦♦ κ − ε ❩ t ♦ ♠♦♦

♣rs♥t tr♦ ♠ ❩♥s t ♦s t♦rs t③r♠ ♠ ①♣rssã♦

♣r ♦ ♣r tr♥t♦ ♦s ♥ sçã♦ ♥tr P♦ré♠ ♥st tr♦

♦♥♦r♠ ♠♥♦♥♦ t③♦s ♠ ♣r tr♥t♦ ♣♥♠♥t s♥♦♦ ♦ q

♦ ①♣♦rt♦ ♣rtr sçã♦ sí ♠ ♥ sçã♦ rt ♠s♠ tr

♠ q ♦s sçã♦ ♥tr ♦♠tr srt ♥ r♥ç ♠

qstã♦ é q ♦sr ♣r rã♦ ♠s st ♣r (y + d)/d > 1,0 ♦♥

♦ ♠♦♦ ♣r ♦♠ ♠♦r rá ♦ q ♦ ♠♦♦ κ − ε ❩ t

♦ ♦r♠t♦ t♦ ♦ ♣r ♦s

r Pr ♦ ♠ x/d = 5,33 ♣r ♦♠tr ♥ ♦♠ r③ã♦ ①♣♥sã♦ r♣t Hs/He

−0,4 −0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,20,0

0,5

1,0

1,5

2,0

2,5

①♦rrs♦

u/Uref

(y+d)/d

❱♦rs ①♣r♠♥ts t ♦♦ κ − ε ♣rã♦ ❯ t ♦♦ κ − ε ❩ t ♦♦ SST st tr♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

s♦ s♦çã♦ tér♠

st s♦ s♦çã♦ tér♠ ♦ ♣r ♠ ♦♠tr ♥ ♦♠ ①

♣♥sã♦ r♣t s rst♦s sã♦ ♦♠♣r♦s ♦s trtr s♥♦ ♦♥r♦♥t♦s ♦♠

♦s ①♣r♠♥ts ♠ ♦♠♦ ♦♠ ♣rsõs ♥♠érs ♦tr♦s t♦rs

♦♠tr

♦♠tr t③ ♥ s♦çã♦ st s♦ é s♠r àq ♦ s♦ ♠

♠ q ♠s ③♠ s♦ ♠ ①♣♥sã♦ r♣t ♠ ♥s ♣r♥♣ r♥ç é

r③ã♦ ①♣♥sã♦ Hs/He q ♥st s♦ é sã♦ ♣rs♥ts s

♠♥sõs ♦♠étrs ♣r st s♦

♠♥sõs ♣r♠tr③s ♦♠tr t③ ♥ s♦çã♦ tér♠ s♦ t♣ rçã♦ çã♦ ♦ ó♦ ♦♠♣t♦♥

srçã♦ ♠♥sã♦

tr sçã♦ ♥tr He 4d

tr sçã♦ ①♣♥ Hs 5d

♦♠♣r♠♥t♦ sçã♦ ♥tr Le 3d

♦♠♣r♠♥t♦ sçã♦ ①♣♥ Ls 20d

tr ♦ r d (m)

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

rst♦ ♥stçã♦ ♥♣♥ê♥ s♦çã♦ ♣r r♥ts t♠

♥♦s ♠s ♦♠ ♠♥t♦s qrtrs ♣ ♠♥t♦s t

♠♥t♦s ♠♠ ♠♥t♦s stá ♣rs♥t♦ ♥ r ♥ q stá

♠♦str strçã♦ ♦ ♥ú♠r♦ t♥t♦♥ ♦ ♦♥♦ s♣rí ♥r♦r sçã♦

①♣♥ tr Hs ♦ ♥ strçã♦ ♦ ♥ú♠r♦ t♥t♦♥ é ♣♦r

Stx = hx

ρfUrefcf

♥ q ♦ ♦♥t ♦♥t♦ tr♦ tér♠ ♦ ♦ ♦t♦ ♦♥♦r♠ sr

hx = qesp

Tw,x − Tref

♦♠ t♠♣rtr rrê♥ Tref s♥♦ ♣ró♣r t♠♣rtr ♥♦r♠ t③

♦♠♦ ♦♥çã♦ ♦♥t♦r♥♦ ♥ sçã♦ ♥tr ♦ ♥ qesp ♦ ①♦ ♦r s♣

♦ ♥ s♣rí ♦♥sr

♦♥çõs ♦♥t♦r♥♦

çã♦ rçã♦ s♦çã♦ tér♠ ♦r♠ t③s s s♥ts ♦♥

çõs ♦♥t♦r♥♦

❼ çã♦ ♥tr ♣r ♥♦r♠ t♠♣rtr 300 K ♣r ♦

s ♠ ♠t tr♥t ♣♥♠♥t s♥♦ ♦♠ ♥t♥s

tr♥t srs q ♦ ♣r♦♠♥t♦ ♣r ♦tr ♦ ♣r ♦s ♦ ♦

♠s♠♦ ♣♦ ♥♦ s♦ ♦ rrê♥ st s♦ ♦ Uref = 16 m/s❼ ♣rí ♥r♦r sçã♦ ①♣♥ sçã♦ tr Hs ①♦ ♦r ♦♥st♥t

qesp = 270 W /m2

❼ ♣rís trs ♦♠tr ♦♥çã♦ ♣♥♦ s♠tr

r st♦ ♥♣♥ê♥ ♠ ♣r ♦ ♥ú♠r♦ t♥t♦♥ s♣rí♥r♦r sçã♦ ①♣♥ ♦♠tr ♥ ♦♠ r③ã♦ ①♣♥sã♦ r♣t Hs/He

0 2 4 6 8 10 12 14 16 18 200

0,5

1

1,5

2

2,5

3

3,5

4

x/d

St×10

3

♣

t

♠♠

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

❼ Prs ♦♥çã♦ ♥ã♦s③♠♥t♦

❼ çã♦ sí ♦♠tr ♣rssã♦ stát ③r♦

st♦s

Pr ♦ st♦ ♥♣♥ê♥ s ♠s ♣rs♥ts ♥ r r♥ç

♥tr ♦ ♠á①♠♦ ♦r ♦ ♥ú♠r♦ t♥t♦♥ ♦ ♥tr s ♠s ♠♠ t

♥tr ♠ t ♠ ♣ ss♠ ♦ s♦ ♠ t

♣r s ③r ♦ ♦♠♣rt♦ ♦♠ ♦s ♦s ①♣r♠♥ts ♦♠ s s♦çõs ♥♠érs

trtr

r ♣rs♥t ♦ ♦♠♣rt♦ ♠ t ♦♠ s ♣rsõs ♥♠érs

t③♥♦ ♠♦♦ κ−ǫ ts ♣♦r ❩ t t③♥♦ ♦ ♠ét♦♦ s r♥çs

♥ts ♣♦r ❩ t t③♥♦ ♦ ♠ét♦♦ ♦s ♦♠s ♥t♦s ♦♠ ♦s

rst♦s ①♣r♠♥ts ❱

r ♦srs q ♥q♥t♦ s s♠çõs ♥♠érs ♦♠ ♠♦♦ κ−ǫ♣rs♥t♠ ♦rs ♠♦rs q ♦s ①♣r♠♥ts ♠ ♣rt♠♥t t♦♦s ♦s ♣♦♥t♦s é♠

♠ s♦♠♥t♦ ♦r③♦♥t ♥♦ ♣♦ ♦ ♥ú♠r♦ t♥t♦♥ ♦ ♠♦♦ é ♣③

r ú♠r♦ t♥t♦♥ ♦ ♣r s♣rí ♥r♦r sçã♦ ①♣♥ ♦♠tr ♥ ♦♠ r③ã♦ ①♣♥sã♦ r♣t Hs/He

0 2 4 6 8 10 12 14 16 18 200

0,5

1

1,5

2

2,5

3

3,5

4

♦sçõs ♦ ♦sórts ♥t♦

x/d

St×10

3

❱♦rs ①♣r♠♥ts ❱ ♦♦ κ − ε ❩ t ♦♦ κ − ε ❩ t ♦♦ SST t

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

♣rr ♦③çã♦ st ♣♦ ♠ ♦♥tr♣rt ♣r st út♠♦ ♠♦♦ á ♠

q ♠s ♥t ♣r ♦ ♥ú♠r♦ t♥t♦♥ ♥ rã♦ ♣ós ③♦♥ rrçã♦

♦ ♣ós ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♠s♠ r ♥ á ♠ ♦srçã♦

♣r s ♦sçõs ♦ ♥ú♠r♦ t♥t♦♥ ♥t♦ ♦ r q s rr à ♣rs♥ç ♦s

órts ♦♥trr♦tt♦s ❯♠ ③ q ♦ ♥í r♥♦ ♠ ①♦ ♣r ♦ ♠♦♦

é t♦ sts strtrs sã♦ ♣trs ♦♠♦ rtrísts ♦ s♦♠♥t♦ ♠é♦

s♦ s♦çã♦ ♥r ♥ét tr♥t

♦ s♦ s♦çã♦ ♥r ♥ét tr♥t ♦♠tr t③ ♦ ♠

♥ sçã♦ ♥♦r♠ rst♦ ♥♠ér♦ ♦t♦ ♣r ♥r ♥ét tr

♥t ♠♥s♦♥ ♥♠ sçã♦ ♥ t③♥♦s ♦ ♠♦♦ trê♥ ♦

♦♠♣r♦ ♦♠ ♦trs s ♣rsõs ♥♠érs

♦♠tr

♠♥r s♠r à ♦♠tr ♦s s♦s ♥tr♦rs r ♣rs♥t

♦♠tr t③ ♥♦ s♦ ♥t♠♥t ♦♠ ts ♠ ♦♥♠♥t

r ♣rs♥t s rtrísts ♦♠étrs ♠♥s♦♥s ♥çã♦ ♣♦sçã♦

sçã♦ ♦♥ ♦s rst♦s ♦r♠ ♠♦str♦s tr ♦ ♥ ♦ s♣ ♦♠♦

H = 0,011m

r ♦♠tr ♦♠ ts ♠ tí♣ t③ ♣r s♦çã♦ ♥r♥ét tr♥t s♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

s ♠s t③s ♥♦ st♦ r♥♦ stã♦ r♦♥s ♥ ♦s

s ♠s ♦r♠ ♦♥strís ♦♠ ♠♥t♦s qrtrs r stã♦ ♠♦str♦s

♦s rst♦s ♣r s três ♠s

♦s s ♠s t③s ♣r ♦ st♦ r♥♦ ♠ ♣r çã♦ rçã♦ ♥r ♥ét tr♥t κ

sõs ♠♥t♦s y+ κmax(Jkg−1) κ/u2τ ① ① ①

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♥♣♥ê♥ ♠ ♣r ♦ ♣r ♥r ♥ét tr♥t ♥♠sçã♦ ♥ ♣♥♦

0,0 0,5 1,0 1,5 2,0 2,5 3,00,0

0,2

0,4

0,6

0,8

1,0

κ/(u2τ)

y/(H/2)

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

srs q t♥t♦ ♦♠tr ♦ ♥ ♦♠ sçã♦ ①♣♥ r

q♥t♦ ♦♠tr ♦ ♥ ♦♠ sçã♦ ♦♥st♥t r ♦r♠ ♦ s♦ ♠

♦ t♣♦ strtr ♦ à t♦♣♦r sts ♦♠trs ♦r♠ r♦s ♣♥s

♠♥t♦s qrtrs ♣r t♦s s ♠s sts ♠♥t♦s ♠s stã♦ s♠♣r

♦rt♦♦♥s ♥s ♦♠ rçã♦ ♦s ♦tr♦s t♥♦ ♦ ♥♠♥t♦ ♠ ♦♠ rçã♦

♣r♥♣ ♦ s♦♠♥t♦

♦♥çõs ♦♥t♦r♥♦

Pr s♦çã♦ ♥r ♥ét tr♥t ♦r♠ t③s s ♦♥çõs

♦♥t♦r♥♦ sr

❼ çã♦ ♥tr ♣r ♥♦r♠ ♦ ue = 19,3 m/s ♥t♥s tr

♥t

❼ ♣rís trs ♦ ♥ sçã♦ ♦♥st♥t ♦♥çã♦ ♣♥♦ s♠tr

❼ Prs ♦♥çã♦ ♥ã♦s③♠♥t♦

❼ çã♦ sí ♦♠tr ♣rssã♦ stát ③r♦

st♦s

s ♣rs ♥r ♥ét tr♥t ♦ ♦♥♦ sçã♦ ♥ ♦r♠ ♠♦s

tr♦s ♠ ♠ stçã♦ ♦③ ♠ stâ♥ x/H = 45 q stá ♥ ♥ r

srs q st é ♠s♠ stâ♥ q ♦ t③ ♣♦r ❩♥s t

r ♠♦str q ♦s ♣rs ♦t♦s ♣rtr s ♠s rs r♠ st♥t

s♠♥ts ♥tr s st ♦r♠ ♠ ♥tr♠ár ♦ s♦ ♣r ♦ ♦♠♣rt♦

♦♠ ♦s ♦s trtr ♣rs♥t♦ ♥ r

r ❱rçã♦ ♦ ♣r ♥r ♥ét tr♥t ♥♠ sçã♦ ♥♣♥♦

0,0 1,0 2,0 3,0 4,0 5,00,0

0,2

0,4

0,6

0,8

1,0

κ/(u2τ)

y/(H/2)

❯ t ❩ t κ − ε st tr♦ SST

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

❯♠ ③ q ♦ ♠♦♦ trê♥ ♦t♦ é ♠ ♠♦♦ ♠♦ ①♦

②♥♦s ♦ ♥ s♦ ♠ ω ♥♦ts q é ♣♦ssí ♦tr s♦çã♦ ♣r κ s

♣r y = 0 ♠♦♦ trê♥ κ − ε t③♦ ♥ ♦♠♣rçã♦ ♦r♥ ♠

♠♦r ♣rsã♦ ♣r ♣r♦♣r ♦♥t♦ ♣♦r sr ♠ ♠♦♦ t♦ ②♥♦s

♥ã♦ é ♣③ ♦r♥r ♣rsã♦ ♥ rã♦ ♦rrs♣♦♥♥t à ③♦♥ ♠s ♥tr♥

♠ ♠t s rõs ♣ró①♠s à ♣r ♦ ♠♦♦ trê♥ t③♦s ♥s

s♠çõs ♦ ♣rs♥t tr♦ ♣rs♥t ♦ rá ♥ ♦♠♣rçã♦ ♦♠ s♠çã♦

rt

P ❱

st sçã♦ srã♦ ♣rs♥t♦s st♦s ♦s s♦s ♣r♦③♦s ♥st tr♦

♦♥sr♥♦ rs♦s s♣t♦s ♦♠étr♦s r♥ts ♦♥çõs r♦♥â♠s

sqê♥ ♠ sts t♥s é ♣rs♥t♦ st♦ ♠♥r ♣ré ♦s rst♦s

♦t♦s

♦♦ ♦♠étr♦ ♦ ♥ t♦

s ♦♠trs áss ♦ ♥ st♦ ♦♠ ♦s ♣r♥♣s ♣râ♠tr♦s ♣♦♠

sr sts ♥ r ♦♥rçã♦ ts s♥s é ♦t trés ♦ s

♦♠♥t♦ r ts ♦③s ♥ ♣r s♣r♦r ♦ ♥ ♦♥rçã♦

♥ ♠♦♦ q ♣r♠r t s♣r♦r st ♦③ ♥ stâ♥ ♦r③♦♥t

♦rrs♣♦♥♥t à ♣♦sçã♦ ♠é ♥tr s s ♣r♠rs ts r ♥r♦r st

trçã♦ ③ ♦♠ q ♦ t♠♥♦ ♦ ♥ ♣r s ts s♥s s ♠♦r ♣♦s

stâ♥ ♠í♥♠ s♣ s♥t út♠ t ♣r♠♥ ③s

tr ♦ ♥ Ls = 20H â♥♦ β ♥♥çã♦ s ts ♦ r♦ ♥tr 0

90 s♥♦ q ♦ ♣r♠r♦ ♦rrs♣♦♥ ♠ ♥ s♠ ts ♦ s♥♦ é ♦♥sr♦

♦ s♦ áss♦

s rtrísts ♠♥s♦♥s t sã♦ ♥s ♠ ♥çã♦ três s♣

çõs s♣ssr t ♦ â♥♦ ♥♥çã♦ s ts β r③ã♦ ♦q♦

t rba s s út♠s ♦r♠ rs r♥t ♦ st♦ ♥q♥t♦ q s♣ssr

s♣ t ♦ ♠♥t ♠s♠ ♣r t♦♦s ♦s s♦s srs q ♥♥çã♦

t ♠♣ ♥♠ rr s rá s rçõs q ♥♠ r③ã♦ ♦

q♦ t rba rr s t w sã♦ s ♥s qçõs

rs♣t♠♥t s ♦rs s t st st♦ s ♥♦♥tr♠ ♥

♦♠♣♠♥tr♠♥t ♦ t♦ ♦ ♠♥t♦ s ♦♠ ♠♥çã♦ ♦ â♥♦ ♥♥

çã♦ ♣♦♠ sr st♦s ♦r♠ qtt s♠ s ♥ r ss♠ r③ã♦

♦q♦ é

rba = Ha

H,

♥ q Ha é ♠á①♠ tr rt t H é tr ♦ ♥ t♠♥♦

s t é

w = t

sen(β) ,

r rtrísts ♠♥s♦♥s s ♦♠trs áss ♣r ♠♦s ♦s rr♥♦s ♥s t♦s ♥♦ s♣r♦r s♥♦ ♥r♦r

L

LsLe

Ha t

b

H

e

e

w

L

LsLe b

H

e

e

y

x

y

x

aletas:

direção do escoamento

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

s♥♦ t β s♣ssr ♦ â♥♦ ♥♥çã♦ t rs♣t♠♥t

tr♦ ♣râ♠tr♦ ♦♠étr♦ r♦ r♥t ♦ st♦ ♦ ♦ s♣ç♠♥t♦ ♥tr

ts b ♦s r♥ts ♦rs ♦r♠ ♥st♦s ♦ ♦r♦ ♦ tr♣♦ rtr

♦ ♥ b = 2H b = 3H st rçã♦ ♦ t③ ♠ ♠s s ♦♥rçõs

t ♥ s♥ Pr strr st rtríst r ♣rs♥t

♦♠♣rçã♦ s♠ s ♥tr ♦s ♦s s♣ç♠♥t♦s ♥tr ts st ♠s♠ r

stã♦ ♣rs♥ts s r③õs ♦q♦ t rba rs ♣r ♦♥rçã♦

♥ t♦ ♦♥♦r♠ s ♦sr ♥♦s s♦s r♦s ♦ rr♥♦ ♥♦ s♦♠♥t

s r③õs ♦q♦ t ♦r♠ ♣s ♥q♥t♦ q três r③õs

♦q♦ ♦r♠ ♣s ♣r ♦ rr♥♦ s♥♦

s ♦♠trs q r♠ ♠ ♠s♠♦ s♣ç♠♥t♦ ♥tr ts b ♣♦♠

sr sts s♠ s ♥s rs ♦s ♣ê♥s sts strçõs stã♦

♠♦♥str♦s ♦s tr♦s s♠♦s ♥ s ♥tr té s♥ t s♣r♦r

❱rçã♦ r③ã♦ ♥tr rr s t w s s♣ssr t♠ ♥çã♦ ♦ s â♥♦ ♥♥çã♦

β w/t90 72 54 36 18

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♦♠tr t ♦♠♦ ♥çã♦ ♦s r♥ts â♥♦s ♥♥çã♦ β ♣r♠ ♠s♠ r③ã♦ ♦q♦

72°

54°

36°

18°

Ha

90°

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

rú♥ ♦s ♣râ♠tr♦s ♦♠étr♦s q ♦r♠ r♦s ♥st st♦

♠ ♦♠♦ q♥t rçõs ♦♥rçã♦ t à q sts s ♣♠

ss♠ ♦s ♣râ♠tr♦s q sr♠ s ♠s rtrísts ♦♠étrs ♦ ♦r♠

s♣♦s ♦♠♦ ♦♥st♥ts ♦ sã♦ r♦s qs ♠♦str♦s ♥st t s

♣r♠r♦s á♦s ♣r t♦s s s♠çõs ①ts ♣♦r ss♦ ♥♦♠♦s ♥rss

♣♦♠ sr ♥♦♥tr♦s ♥

♣♦ st♦ r♥♦ ♠

Pr ♦ s♦ ♦♠trs ♦♠♣①s é ♣r♦♠♥♥t ♦ s♦ ♠s ♦ t♣♦

♥ã♦ strtrs s ♠s ♦s s♦s ♣r♦③♦s ♥st tr♦ ♦r♠ rs ♦♠

♠♥t♦s ♦ t♣♦ ①r♦s ♦♠ r♥♠♥t♦ ♥s rõs ♣ró①♠s às s♣rís ♦

♥ ts r♥♠♥t♦ ♦ ♣♦ ♦r♠ ♦r ♦ rqst♦ ♦ ♠♦♦

trê♥ y+ < 1 r stã♦ ♣rs♥t♦s ts qtr♦ ♠s

t③s ♥♦ st♦ ♦♥rê♥ ♠ ♣r ♠ ♦s s♦s st tr♦

r s ♦s s♣ç♠♥t♦s ♥tr ts b s rçõs r③ã♦ ♦q♦ t rba ♣r ♠♦s ♦s rr♥♦s ♥ t♦

b=3H

H

H

b=2H

0,20,4

0,6rba

0,2

rba0,4

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

Prâ♠tr♦s ♦♠étr♦s r♦s ♦♥rçã♦ ♣á r♥ts

Prâ♠tr♦ ♦♥rçã♦ ♣á ❱r♥ts

b ♠s 2H 3H

rba ts ♥s 0,2 0,4

rba ts s♥s 0,2 0,4 0,6

β ♠s 0 18 36 54 72 90

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

s ♣râ♠tr♦s s♦s t③♦s ♣r ♦ st♦ ♥♣♥ê♥ ♠ ♦♠♦

s r ♦r♠ ♦s ♦rs t♠♣rtr ♣rssã♦ s♥♦ q ♦ ♦r y+

t♠é♠ ♦ ♠♦♥t♦r♦ s ♠çõs s rás st♦ ♦r♠ ♦ts s♥t

út♠ t ♣ós ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ x = 30H ♦ q s ♦ ♦ ♦r

♠é♦ ♣r ♠s ♦ s♦ ♦ y+ ♦ t③♦ ♦ ♠á①♠♦ ♦r tr♠♥♦ ♣r st

q♥t ♠ t♦♦ ♦ ♦♠í♥♦ ♦

r ♠♦str ♦s rst♦s ♦ st♦ ♦ r♥♦ ♠ ♣r ♦ s♦

â♥♦ ♥♥çã♦ t β = 90 r③ã♦ ♦q♦ t rba = 0,2

s♣ç♠♥t♦ ♥tr ts b = 2H ♥ú♠r♦ ②♥♦s ue = 9 m/s ♣r ♦♥rçã♦ ♥ ts ♠s♠♦ ♣r♦♠♥t♦ ♦ s♥♦♦ ♣r

♠♦çã♦ r③ ♥ ♦♠tr ♦ ♥ ♦♥çã♦ ♥tr ♦ rrê♥

♦♥rçã♦ ♥ sr ♦s ♠s♠♦s ♣râ♠tr♦s ♦r♠ ♣♦s ♣r

♦♥rçã♦ s♥ ♦♠♦ ♣r♠r st♠t ♠

s♣çã♦ ♦s ♣râ♠tr♦s ♦♠étr♦s ♥rss

Prâ♠tr♦ srçã♦ s♣çã♦

M ♥ú♠r♦ ts ♥ ♠s♠ ♣r ♦ ♥ 5

t (mm) s♣ssr t 3H/20Le (mm) stâ♥ ♥tr ♥tr ♦ ♥ ♣r♠r t 2H

Ls (mm) stâ♥ ♥tr út♠ t sí ♦ ♥ 20H

e (mm) s♣ssr ♣r ♦ ♥ H/2H (mm) tr sçã♦ ♥tr ♦ ♥ 20

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ①♠♣♦ ♠s ♣r♦③s r♥t ♦ st♦ ♥♣♥ê♥ ♠t ♥♦ ♥t♦r♥♦ ♠ t ♦♠ β = 90

♠♥t♦s ♠♥t♦s

♠♥t♦s ♠♥t♦s

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

♦♥çõs ♦♥t♦r♥♦ ♣r♦♣rs

s♠♥t ♦s t♣♦s ♦♥çõs ♦♥t♦r♥♦ ♦r♠ t③s ♦ ♦♥♦ s

r♦♥trs ♠♦s ♦s ♦♠í♥♦s só♦ ♦ rt ♦ ♠♥♥

r st♦ ♥♣♥ê♥ ♠ rst♦s ♣r s ♠s ♠♦strs♥ r

3 4 5 6 7 80,50

0,55

0,60

0,65

0,70

0,75

y+

P

ú♠r♦ ♠♥t♦s × 105

y+P

Pa

319,0

319,2

319,4

319,6

319,8

320,0

T K

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

♦♥sr♥♦ r q ♣rs♥t s rtrísts áss ♣r s r

çõs ♦s s♦s ♠♦s ♦s rr♥♦s s ♥♦r♠çõs ♦ts ❨ s♠

s s♣çõs ♣r s ♦♥çõs ♦♥t♦r♥♦

❼ çã♦ ♥tr ♣rs ♥♦r♠s t♠♣rtr 298,15K ♦s r

ssçã♦ ♦♥♠♥t ♦ s♣♦ ♦ ♦r ♥t♥s tr♥t

I = 10%

❼ çã♦ sí ♣rssã♦ stát ③r♦ ♦s s ♠s q♥ts sã♦ ①

tr♣♦s ♣rtr ♦ ♥tr♦r st♦ é ♣r q♥ts srs ♦ ó♦ ♥♠ér♦

♠♣õ ♠ rstrçã♦ r♥t ♦♥st♥t ♥ r♦♥tr sí

❼ s s♣rí s ♣rs trs ♦ ♥ ♦♥çã♦ át sts s♣rís

sã♦ ♦♥srs s♦s ♣♦rt♥t♦ ♦ ①♦ ♦r trés s sr ♥♦

❼ ♣rí ①tr♦rs s ♣rs s♣r♦r ♥r♦r ♦ ♥ t♠♣rtr ♦♥st♥t

358,15K

❼ ♥tr ♦só♦ ♦♥çã♦ ♥ã♦s③♠♥t♦ ♣r ♦ ♦♥çã♦

♦♥srt ♣r ♥r ♥r q s ♦ ♦♠í♥♦ só♦ ♥r q ♥tr

♥♦ ♦♠í♥♦ ♦

❼ P♥♦s trs ♦ ♥ ♥♦r♠s ♦ ♣♥♦ s♦♠♥t♦ xy ♦♥çã♦ s♠

tr

❼ Pr ♦s s♦s ♥♦♥♦ ♦♥rçã♦ ♥ ts ♣♥s ♠t s♣

r♦r ♦ ♥ ♦ s♠ ♣♥♦s ♠ ♣♥♦ s♠tr ♦ ♦♥♦ ♦ ①♦ x ♠

y = 0s ♣r♦♣rs íss t③s ♣r ♦s s♦s st♦s ♥st tr♦ sã♦ ♣r

s♥ts ♥ sã♦ ♦rrs♣♦♥♥ts ♦ r

Pr♦♣rs íss t③s ♣r rtr③çã♦ ♦s ♦♠í♥♦s ♦♠♣t♦♥s ♦s s♦s st♦s

Pr♦♣r♦♠í♥♦

♦ ó♦

♦♥t tér♠ k Wm−1K−1 ♣ ♦rí c Jkg−1K−1 ss s♣í ρ kgm−3 ❱s♦s ♥â♠ µ Pas 1,846 × 10−5

♦♥t t

❱rçõs s ♦♥çõs ♦♥t♦r♥♦ r♦♥â♠s

Pr s♦ ♦♠étr♦ ♦♥♦r♠ srt♦ ♦ ♦♥♦ ssçã♦ ♦r♠

t③s três rçõs ♦♥çã♦ ♦♥t♦r♥♦ r♦♥â♠ ♦ rrê♥

♥ ♥tr ♦ ♥ st♦ ♣♦sst♦ ♦ st♦ ♥ê♥ ♠ ① ♦ ♥ú♠r♦

②♥♦s s♦r tr♦ tér♠ ♦♥ ♥♦s ♥s t♦s s r♥ts ♦♥çõs

♦♥t♦r♥♦ t③s ♣r s ♦s rrê♥ ♥ ♦r♠ ♣rs ♥♦r♠s

♦ ♦r♠ ue1= 1 m/s (Re1 = 2517) ue2 = 3 m/s (Re2 = 7550) ue3 = 9 m/s (Re3 =

22649) ♦ ♥ú♠r♦ ②♥♦s ♦ ♦ ♦♠ s ♥♦ â♠tr♦ rá♦ Dh =2H

♦♠♥çã♦ rst♥t s rs ♦♠étrs ♦♠ s rs ♦♥

çõs ♦♥t♦r♥♦ r♦♥â♠s ♣♦ sr ♠♦r s③ ♥ r ♦ ♣ê♥

srs q â♥♦ ♥♥çã♦ t β á ♦r♠ ♠ ①♦r♠ ♦♠♦

♦ ♣rs♥t♦ ♥st ♣ê♥

Pr♥♣s rtrísts ♦ s♦♠♥t♦ ♥♦s s♦s ♦s

♥s t♦s

r ♣rs♥t s ♠♦çõs ♦rr♥ts ♣rs♥ç s ts ♥

t♦♣♦♦ ♦ s♦♠♥t♦ r♣rs♥t ♣s ♥s ♦rr♥t ♦ s♦♠♥t♦ ♠é♦ ♥♦

t♠♣♦ s ♥t♦s str♦s ♣r três r♥ts â♥♦s ♥♥çã♦ ♣r ♠♦s ♦s

rr♥♦s t sã♦ r♣rs♥tt♦s t♦♦s ♦s ♠s s♦s ♥st♦s ♥st tr

♦ ♥♦ ss♠ s ♣r♥♣s rtrísts ♥♦♥trs ♥♦s s♦♠♥t♦s st♦s

♦♥t♥♦ ts tr♥srss sã♦ s rõs rrçã♦ r♦♠♥t♦ ♥♦ tr♦

♦♠♣r♥♦ ♥tr ♦s ♦stá♦s ts ♠s ♦♦rr♠ ♠ ♥çã♦ ♦ s♦♠♥t♦ ♦

s♦♠♥t♦ ♦ ♠ ♠t ♦ à ①stê♥ r♥ts ♣rssã♦ rs♦s

s ♠♣çõs s rrçõs ♦ r♦♠♥t♦ s♦r ♦ s♠♣♥♦ ♦s tr♦♦rs

♦r t♦s srã♦ st♦s sr ♥♦s tó♣♦s ♣rt♥♥ts

s rs ♦ rr♥♦ ♥♦ é ♣♦ssí ♦srr q ♣r

t♦s s ♥♥çõs ♦♦rr ♦r♠çã♦ rrçã♦ s♦r t♦♦ ♦ tr♦ ♥tr s

ts ♦♠♦ ♦♥sqê♥ ♦srs q r♥ç ♦s ♥♦ tr♦ t♦ é

s♥t ❯♠ ♦tr♦ s♣t♦ stq ♣r sts rs é s♠tr ①st♥t ♥♦

s♦♠♥t♦

s s♦s ♦ rr♥♦ s♥♦ ♣rs♥t♦s ♥s rs

♣rs♥t♠ s♠♥t s rõs st♥ts ♥♦ tr♦ ♥tr ts rrçã♦

♦ r♦♠♥t♦ ♠ ♠ q ♦ â♥♦ t ♠♥ β → 0 ♥♦ts ♦

♠♥t♦ ③♦♥ rrçã♦ st♦ ♦♥t♥ té q ♣r ♦ ♠♥♦r â♥♦ ts

β = 18 ③♦♥ rrçã♦ s♦ ♣♦sçã♦ rã♦ r♦♠♥t♦ ♣r

s♣rí t s♥t ♦♣♥♦ t♦♦ ♦ tr♦ ♥tr s ts

Pr ♠♦s ♦s rr♥♦s ♥t♦ às s s ts ♣♦♠ sr ♦sr♦s ♦s ♠

♦s órts ♥t♦ q ♥♦ s♦♠♥t♦ ♠é♦ ♦ ♣rs♥t st♦ sr♠ ♦♠♦ ♣q♥s

rrçõs srs q ♥ r s ♥s ♦rr♥t stã♦ ♦♦rs ♣

♦ ♦ s é ♣♦r

U∗ = U −Umin

Umax −Umin

,

s♥♦ U Umin Umax s ♦s ♦s ♠í♥♠ ♠á①♠ rs♣t♠♥t ♠s

q Umax = 66,6 m/s ♣ ♦♥çã♦ ♥ã♦s③♠♥t♦ Umin = 0 m/s st♦s ♣r ♣r r

ss♣çã♦ ♥r ♠â♥ ♦ ♦r♠ ♦ t♠é♠ ♦r♠

♦ s q♥ts t③s ♣r tr♠♥r sts ♠s ♦r♠ rs♣t♠♥t

♦ ♦♥t trt♦ Cfx ♦ ♦♥t ♣rssã♦ Cp sr ♣rs♥ts ♦s

♦♥t♦r♥♦s ♦ ♠♣♦ ♦s rst♥t ♠s rçõs ♦♠étrs ♣r

♠♦s ♦s rr♥♦s sts rst♦s qtt♦s s♠ r s♣♦rt ♣r s çõs

q♥ttts q ♦s s♠

r ♥s ♦rr♥t ♦♦rs ♦♠ ♦ ♣r r♥ts ♥♥çõs t ♠♦s ♦s rr♥♦s ♥♦ ♦♥ sqr s♥♦ ♦♥ rt ♥♦s♦ ♦♠étr♦ b = 2H rba = 0,4 ♦♥çã♦ r♦♥â♠ ue = 9 m/s

β = 18 β = 18

β = 54 β = 54

β = 90 β = 90

0,000

0,069

0,138

0,207

0,276

0,345

0,414

0,483

0,552

0,621

0,690

0,759

0,828

0,897

0,966

1,000

U*

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

♥s ♦rr♥t t♦♣♦♦ ♦ s♦♠♥t♦

s rs ♠♦str♠ ♦ t♦ rçã♦ ♦ â♥♦ ♥♥çã♦ β

s♦r ♦s ♠♣♦s ♦ t♦♣♦♦ ♦ s♦♠♥t♦ ♣r ♠ ♠s♠ r③ã♦

♦q♦ t rba ♠♦s ♦s rr♥♦s r ♦♥té♠ ♦s rs♣t♦s s♦s

♣r ♦ s♣ç♠♥t♦ ♥tr ts b = 2H r ♣rs♥t sts s♦s ♣r ♦

s♣ç♠♥t♦ b = 3H s ♦rs ♦rrs♣♦♥♥t ♦s ♦♥t♦r♥♦s ♦ ♠♣♦ ♦

s ①♦ r ♦ ♠♥s♦♥③ ♦r♦ ♦♠ qçã♦ Pr

♠♥s♦♥③çã♦ t♠s q Umax = 21,9 m/s ♣ ♦♥çã♦ ♥ã♦s③♠♥t♦

Umin = 0 m/s♦ ♦ t♦ rr♥♦ é ♣♦ssí ♥tr ③♦♥s rçã♦ s

rçã♦ ♦ s♦♠♥t♦ ♣r♥♣ ♣r ♦ rr♥♦ ♥♦ st♦ q á ♠ rçã♦

♦♦rçã♦ rã♦ ♥tr ♦ ♥ rstrçã♦ ár ♠♣♦st ♣ r③ã♦ ♦q♦

ts rba ♦rç à rçã♦ ♦ s♦♠♥t♦ ♥ sçã♦ ár ♥tr s ♣♦♥ts s

ts Pr st rr♥♦ ♣♦s ♥ ♥rr ♦♠ s ♥sts rs q s ♣rs

♥r ♠â♥ ♦ s♦♠♥t♦ ♣r♥♣ ♦♦rr♠ ♥ sçã♦ ár ♥tr s ♣♦♥ts s

ts ♥♦ s♠♥t♦ ♦♠ ♦s órts s♠♥t

♦s s♦s ♦ rr♥♦ s♥♦ ár s♦♠♥t♦ é r ♦♠ ♠s rqê♥

♦ ♦♥♦ ♦ ♥ sr♠ rõs rçã♦ s à ①ã♦ ♦ s♦♠♥t♦

♥s ♦r♠ s♣ ①ã♦ ss♠étr é rtríst ♠s ♥♥t

♣r rçã♦ ♦ s♦♠♥t♦ ♦♠ s ♥ t♦♣♦♦ ♦ s♦♠♥t♦ é ♣♦ssí ♥

rr q ♥r ♠â♥ é ss♣ ♦ s♦♠♥t♦ ♣r♥♣ ♥♦ rrst♦ trt♦ ♦♠

s ♣rs ts é♠ ♦ s♠♥t♦ ♦♠ ♦s órts ♦ trt♦ ♥tr♥♦ ♦ ♦

♦♥t trt♦ ♦ Cfx

s rs rst♥ts tr♠♥çã♦ ♦ ♦♥t trt♦ s♣r sã♦ ♣r

s♥ts ♣r ♠ tr♦ r♣rs♥tt♦ ♥ t♦ ♣r ♠♦s ♦s rr♥♦s sr

s q ♦ à s♠tr ♦♠étr s♦♠♥t ♦s rst♦s ♣rt♥♥ts ♦s tr♦s

♣r s♣r♦r srã♦ ♣rs♥t♦s ♣r ♦ rr♥♦ ♥♦ ts ♦♠ ss♦ ♦r♥r

s ♣r♥♣s rtrísts ♦s ♣rs Cfx rst♥ts ♦s s♦s ♦r♦s ♥ê♥

♦s ♣râ♠tr♦s ♦♠étr♦s r♦♥â♠♦s ♥s s♦r ts rtrísts é

st sr

♥ê♥ ♦ â♥♦ ♥♥çã♦ t

s rs str♠ s rtrísts ♦ ♣r Cfx rst♥ts ♣r

rçã♦ ♦ â♥♦ ♥♥çã♦ t β s s♦s ♦r♠ ♦♥strí♦s ♣r

♦ rrê♥ ue = 3 m/s ♣r ♠s♠ r③ã♦ ♦q♦ t rba

t♣♦ rr♥♦ ♦ts ♥ q á ♥çã♦ ♣♦sçã♦ sq♥ s ts

♦rrs♣♦♥♥ts ♦ s♦ β = 18 ♠ ♣r

s rs ♦♥rçã♦ s♥ ♠♦strs t♥ê♥

♦ ♠♥t♦ ♠♥t ♦ ♦♥t trt♦ ♦ ♦♠ ♦ â♥♦ ♥♥çã♦

t rçã♦ r♣t ár s♦♠♥t♦ ♣r ♥♥çã♦ ♦rt♦♦♥ rst ♠

♠♦r rçã♦ ♣♦rt♥t♦ ♠♦rs ♦s ♥ts à ♣r Pr ♦ ♠♥♦r

â♥♦ ♥♥çã♦ β = 18 ♥♦ q s ♣rs ♥tr ts ♠ ♠♥♦s ①♣♦sts ♦

s♦♠♥t♦ ♣r♥♣ ♥♦ts q ♦ s♦♠♥t♦ ♠é♦ ♣rs♥t ♠ r♥ rã♦

r♥ç ♦s ♠t♦ ♣ró①♠ ③r♦ ♥t♦ à ♣r

❯♠ r♥ç ♠r♥t ♥tr s rs é q ♣r st út♠

á ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ t♠é♠ ♣r ♦ s♦ ♦ ♠♥♦r â♥♦ ♥♥çã♦

t β = 18 t♦ ♦♥♦r♠ s ♣♦ ♦srr ♥ r ♥st ♥♥çã♦

①ã♦ ♦ s♦♠♥t♦ ♣r♥♣ rst ♥ s ♥ê♥ s♦r s s s ssss

ts ♣rs ♦♣♦sts ♦tr ♦r♠ ♥ t♦♣♦♦ ♦ s♦♠♥t♦ ♠♦str

q á ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♣r♥♣ ♥ rã♦ ♣r ♠ q

①ã♦ ♦ s♦♠♥t♦ ♠♥t β → 90 ♦ s♦♠♥t♦ ♣r♥♣ ♥ s♦r rã♦

♣r ♦♥♦r♠ s rs

♦♠ rçã♦ à ♥ê♥ ♥♥çã♦ ♥♦s ♦s r♥ts s♣ç♠♥t♦s ♥tr ts

♣r ♦ rr♥♦ s♥♦ ♥ ♦♦rr♠ stçõs ♦♥trst♥ts ♦ s♣ç♠♥t♦

♦rrs♣♦♥♥t b = 3H ♦sr♠s ♠♥♦rs ♠♥ts ♦ ♦♥t trt♦ ♣r ♦s

♦s ♠♦rs â♥♦s ♥♥çã♦ β = 72 β = 90 ♣♦ré♠ ♦♦rr ♠♥t♦ ♦ Cfx ♣r

♦s ♠s â♥♦s ♥st♦s P♦r ①♠♣♦ ♥♦ts q r ♣r ♦ â♥♦ β = 36 ♥♦ s♣ç♠♥t♦ b = 2H r rs q ♦t ♣r ♦ s♣ç♠♥t♦

b = 3H r st út♠♦ b = 3H ♣rs q á ♠ rã♦

r♦♠♥t♦ ♦ s♦♠♥t♦ ♥♦ tr♦ ♥tr ts ♠ ③ q r ♦ ♦♥t

trt♦ ♣rs♥t ♠ ♥rsã♦ ♠ ♥ s♥ r♦♠♥t♦ st s♦ ♣♦ sr

r♦ ♣ t♦♣♦♦ ♦ s♦♠♥t♦ ♦♥♦r♠ r

Pr ♦ rr♥♦ ♥♦ ♥s rs t♠é♠ ♦srs ♠

r♥ç s♥t ♥♦ ♣r ♦ ♦♥t trt♦ ♣r ♦ s♦ s ts ♠♥♦r

â♥♦ ♥♥çã♦ β = 18 st ♥♥çã♦ ①♠♣♦ ♦ q ♦♦rr ♥♦ rr♥♦

s♥♦ ♦ rrst♦ ♣♦r trt♦ ♥ rã♦ ♣r ♦♦rr ♦r♠ s♥t s♦♠♥t

♣r ♠ tr♦ rt♦ rã♦ ♥tr ts ♦③♦ ♣ró①♠♦ à s s ts r s

♣♦sçõs s ss t ♥s ♥ rs♣t r Pr ♠♦s ♦s s♣ç♠♥t♦s

♥tr ts b = 2H r b = 3H r ♣r♦♠♥♠ ♦s ♦rs

Cfx ♥t♦s ♣♦ssí ♦srr ♦ t♦ t♦♣♦♦ s♦r sts rst♦s ♥s

rs ♣r b = 2H b = 3H rs♣t♠♥t sts

rs ♠♦str♠ ①stê♥ rrçã♦ ♦ s♦♠♥t♦ ♠é♦ s♦r ♣rt♠♥t

t♦ rã♦ ♣r ♥tr ts

♦♠♦ rst♦ rçã♦ ♦ â♥♦ ♥♥çã♦ ♣r ♦ rr♥♦ s♥♦

t♠s q ♦ ♦r ♦ Cfx ♣r β = 90 é ③s ♠♦r q ♣r β = 18 b = 2H

③s ♠♦r ♥♦ s♦ b = 3H s rst♦s ♣r ♦ rr♥♦ ♥♦ ♦r♠ ♠s

♦♠♦ê♥♦s ♠ tr♠♦s ♠♥ts s♥♦ ♠♦r r♥ç rt ♥tr β = 90

β = 18 b = 2H ♦ b = 3H

♥ê♥ ♦ rrê♥

rs♣♦st ♦ ♦♥t trt♦ ♦ ♣r rçã♦ ♦ rrê♥

stá ①♠♣ ♥s rs ♥ê♥ ♦ ♠♥t♦ s ♦rçs

♥rs ♥ ♥tr ♦ ♥ é str ♣r três ♥♥çõs s♣ç♠♥t♦ ♥tr ts

b = 2H ♠♦s ♦s rr♥♦s t♥ê♥ ♦sr é ♠♥çã♦ ♠♣t s

rs ♦ ♦♥t trt♦ ♠ ♥çã♦ ♦ ♠♥t♦ s ♦rçs ♥rs ♥ ♥tr ♦

♥

♠é ♦♠ rçã♦ ♦ ♥tr 1 m/s ♣r 9m/s ♦s ♦rs ♣♦ ♦ Cfx sã♦ ♣♦r ♦t ③s ♠♥♦r ♠ ♠♥t ♣r ♠♦s ♦s rr♥♦s P♦r

♦tr♦ ♦ t♥sã♦ s♠♥t♦ ♥ ♣r t♠ ♠♥t♦ ♠é♦ s♥t♦ té

③s ♣r ♦ rr♥♦ ♥♦ té ③s ♣r ♦ rr♥♦ s♥♦ srs q

♦ ♠♥t♦ t♥sã♦ s♥t é ♦♥sqê♥ ♥t♥sçã♦ ♦ tr♥s♣♦rt ♦♥t♦

q♥t ♠♦♠♥t♦ ♦r♠ ♣r♦♠♥♥t ♥ rçã♦ x ♥t♥sçã♦

♦s tr♠♦s ♦♥t♦s ♦♦rr s ♦r♠s ♠♥r rt trés ♦ ♠♥t♦

♦ rrê♥ ♥ ♥tr ♦ ♥ ♦♠♦ ♦♥sqê♥ ♦ ♠♥t♦ ♦

tr♥s♣♦rt ♠♦♠♥t♦ ♦ às tçõs ♦s trê♥ ♦ts q ♦

♣r strçã♦ ♦ ♦♥t trt♦ s♣r é ♣rt♠♥t ♦♥sr♦

♥ê♥ r③ã♦ ♦q♦

Pr strr ♥ê♥ r③ã♦ ♦q♦ ♥♦ ♦♥t trt♦ ♦

t③♦s ♦s ♠s♠♦s s♦s ♦ t♠ ♥tr♦r P♦rt♥t♦ ♦ t♦ rçã♦ s três

r③õs ♦q♦ ♣r ♦ rr♥♦ s♥♦ s s ♦ rr♥♦ ♥♦ ♦r♠ ♥

sts ♣r s ♥♥çõs β = 18 β = 54 β = 90 ♦ rrê♥

ue = 3 m/s s rst♦s stã♦ ♣rs♥t♦s rs♣t♠♥t ♥s rs

t♥ê♥ ♦sr ♦ ♠♥t♦ ♦ ♦♥t trt♦ ♦♠ r③ã♦ ♦q♦

t é ♠ ♦♥sttçã♦ rt rstrçã♦ ár s♦♠♥t♦ s ♦strçõs

ss ♣ ♣rs♥ç s ts ♥♦ rs♦ ♦ s♦♠♥t♦ s♠ ♦ sr♠♥t♦ rõs

♦♠ rçõs ♦s ♦ q ③ ♠♥tr s ♦s ♥t♦ às ♣rs ♦♥sq♥

t♠♥t t① s♠♥t♦ τint,x

Pr ♦ rr♥♦ s♥♦ ♠é ♦ ♠♥t♦ ♦s ♦rs ♣♦ ♦ Cfx ♣♦

rr té ③s ♥tr rba = 0,6 rba = 0,2 β = 90 ♥q♥t♦ q ♣r ♦ rr♥♦

♥♦ s rçõs ♠és ♦♦rr♠ ♣♦r ♦t ③s ♥tr rba = 0,4 rba = 0,2♦♥sr♥♦ ♠s♠ rçã♦ r③ã♦ ♦q♦ ♣r ♦♥rçã♦ s♥

rba = 0,2 rba = 0,4 rçã♦ ♠é ♦s ♦rs ♣♦ Cfx r♠ ♥tr

③s

♥ê♥ ♦ rr♥♦ t

s r♥çs ♥♦♥trs ♥♦ ♣r s rs ♦ ♦♥t trt♦ s♣r

♣r ♠♦s ♦s rr♥♦s sã♦ ♠ s♥ts ♦♠♦ ♦♥sqê♥ ♦ ♥♠♥t♦ ♥tr

s ts ♥♦ rr♥♦ ♥♦ ♦ s♦♠♥t♦ ♣rs♥t ♦s ♥ts ♥t♦ à ♣r

♣r ♣rt♠♥t t♦ rã♦ ♥tr ♥tr s ts s ♦rs ♣♦st♦s ♦

♦♥t ♥st rr♥♦ ♦♦rr♠ ♣r ♥tr♦s ♠t♦ ♣q♥♦s ♥♦s tr♦s ♥tr ts

♦s s♦s ♦♥rçã♦ s♥ sã♦ ♦srs rõs s♥s ♦♣♦st♦s

♣r ♦ ♦♥t rçã♦ ♦ ♠ ♠s s ♣rs s♥t s ts r ♦

Cfx ♣rs♥t ♦rs ♥t♦s ♠ q ♦ s♦♠♥t♦ ♥ç ♣rs ♠

♥rsã♦ ♠ ♥ ♦ s♥ ♦ ♥t♦ à ♣r rã♦ ♥tr ts

♣♦sçã♦ ♦♥ ♦ ♦r Cfx ♣ss ♣♦ ③r♦ ♦ ♦♥♦ st ♥rsã♦ s♥s ♥t

rã♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♣r♥♣ s ③♥♥çs st ♣♦♥t♦ ♥♦

♥ r ♦ s♦♠♥t♦ s ♠ ♣rt rr ♥♦ ♦r♠ ♦s ♦rs

♥t♦s ♦ ♦♥t trt♦ s♥t ♦ r♦♠♥t♦ ♣♦rt♥t♦ ♦s ♦rs ♦

♦♥t trt♦ s t♦r♥♠ ♣♦st♦s

♦♠♦ ♦♥sqê♥ ♦ r♦♠♥t♦ ♥s rõs ♣r ♥tr ts s ♠♦

rs ♠♥ts ♣♦ ♦ Cfx sã♦ ♥♦♥trs ♠♥r ♣r♦♠♥♥t ♥♦ rr♥♦

s♥♦

r♥ç ♣rssã♦ ∆p ♦♥t ♣rssã♦ Cp

♦r♠ ♦ çã♦ ♣r r ♥s ♦♠trs ♣r♦♣♦sts ♦ r

③ ♣♦r ♠♦ ♦ ♦♥t ♣rssã♦ Cp t♠é♠ r♥ç ♣rssã♦ ∆p

ss♦ sts s q♥ts sã♦ r♦♥s ♦r♦ ♦♠ qçã♦ ♣r

s♥t ♥♦ ♥í♦ st sçã♦

r stã♦ ♣rs♥t♦s ♦s ♦♥ts ♣rssã♦ ♦t♦s ♣r t♦♦s ♦s

♥ár♦s rst♥ts ♦♠♥çã♦ ♥tr ♦s r♥ts s♣ç♠♥t♦s t s

r③õs ♦q♦ t ♦ s♦ ♦ rr♥♦ s♥♦ rs ♦

♥ú♠r♦ r③õs ♦q♦ é três s rst♦s stã♦ ♣rs♥t♦s ♥ ♦r♠

r③ã♦ s♥♦ q ♦s ♦rs t③♦s ♦♠♦ rrê♥ ♦r♠ ♦s rs♣t♦s ♦♥ts

♣rssã♦ ♦ ♥ s♠ ts ♠♥♦♥♦s ♥ st r ♥ ♥♦ts

①stê♥ r♥ts ♣t♠rs ♠r♦s ♣♦r sts sts ♣t♠rs ♦rrs♣♦♥♠

às rçõs s três ♦♥çõs ♦♥t♦r♥♦ r♦♥â♠ ue ♣r s st♥ts r③õs

♦q♦ t rba ♥s s♦r r

❱♦rs ♦ ♦♥t ♣rssã♦ ♣r ♦ ♥ s♠ ts

♦♠♣r♠♥t♦ ♥s♠ ts β = 0 ❱♦ rrê♥ ue ♦♥t ♣rssã♦ Cp0

①1,0 m/s 3,0 m/s 9,0 m/s

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

t♥ê♥ ♦sr ♣r ♣t♠r é ♠♥çã♦ ♦ ♦r Cp/Cp0♦♠ ♠♥çã♦ ♦ â♥♦ ♥♥çã♦ t β → 0 ♣r t♦s s r♥ts

♦s rrê♥ ♦♥t♦ é ♣r♣tí ♥s rs q st

t♥ê♥ ♥ã♦ s r ♥♦s s♦s ♦♠♣r♥♦s ♣ r③ã♦ ♦q♦ t rba = 0,6♦ rr♥♦ s♥♦ sts s♦s ♦ ♦r ♠é♦ ♦Cp ♣r ♦ ♠♥♦r â♥♦ 18 é

♣r♦①♠♠♥t 54% b = 2H 22% b = 3H ♦ ♦r ♦ Cp ♣r ♦ ♠á①♠♦ â♥♦

♥♥çã♦ 90 rts ♠ ①♣rss ♥rsã♦ ♥ t♥ê♥ q ♣♦s ③♥♦

♦ ♠s♠♦ ♦♠♣rt♦ ♣r ♦ â♥♦ 36 t♠é♠ ♦♠ rçã♦ ♦ ♠á①♠♦ â♥♦

♥♥çã♦ 90 ♦s ♦rs sã♦ 29% b = 2H 19% b = 3H rs♣t♠♥t s t♦rs

q ♦♦r♠ ♣r ♦ sr♠♥t♦ st ♥rsã♦ srã♦ ♠♦♥str♦s ♥ sqê♥ ♦

tr♦

sr ♦s r♥ts t♣♦s ♥ê♥ s♦r ♦s rst♦s ♦t♦s ♣r ♦ ♦

♥t ♣rssã♦ srã♦ st♦s ♦r♠ ♥ s t♦rs ♥ê♥ ♦♥sr♦s

♣♦♠ sr t♥t♦ ♥tr③ ♦♠étr q♥t♦ r♦♥â♠

♥ê♥ ♦ rr♥♦ t

♠ t♦♦s ♦s s♦s s♠♦s ♦ rr♥♦ ♥♦ ♦ ♦ q rst♦ ♥♦s ♠♦rs

♦rs Cp ♣r ♠ ♠s♠ r③ã♦ ♦q♦ t r ♠♦str r③ã♦

Cp/Cp0 ♣r ♠♦s ♦s rr♥♦s Pr str ♦ s♣t♦ ♦♠♣rçã♦ s♦♠♥t s

r③õs ♦q♦ rba = 0,2 rba = 0,4 sã♦ ♣rs♥ts Prs q ♠ ♠s♠

r③ã♦ ♦q♦ t rba ♦♥té♠ ♠ r♣♦ rs q r♣rs♥t♠ s r♥ts

♦♥çõs r♦♥â♠s ue sts r♣♦s rs r ♣♦ss♠ ss

♦rrs♣♦♥♥ts ♣t♠rs ♥ r

s rst♦s ♦t♦s ♠♦str♠ q ♠é ♦ ♦r r③ã♦ ♥tr ♦ ♦♥t

♣rssã♦ ♣r ♦♥rçã♦ ♥ ♦ ♦♥rçã♦ s♥ Cpalinhado/Cpdesalinhado rba = 0,2 b = 2H té rba = 0,4 b = 3H ♦ts q ♣♦r t♦

♦ rr♥♦ ♠♦r s ♠♦rs ♣rs r sã♦ ♦ts ♣r ♦♥rçã♦ ♥

s ♠♦rs rçõs ♣r ♠ ♠s♠ ♦♥çã♦ r♦♥â♠ ♦♦rr♠ ♥ ♦♥rçã♦

s♥ ♦♥♦r♠ r

♥ê♥ ♦ â♥♦ ♥♥çã♦ t

♦♥♦r♠ á ♦♠♥t♦ ♠♦str♦ ♥ r á ♠ t♥ê♥ ♠♥

çã♦ ♦ Cp ♦♠ ♦ â♥♦ ♥♥çã♦ s ts ♥♦ ♠ st q♥t ♥

ssçã♦ ♥tr♦r Cpalinhado/Cpdesalinhado é ♥trss♥t ♥♦tr q st r③ã♦ ♠♥t

♠♥r ♥rs ♦ â♥♦ ♥♥çã♦ ss♠ ♦ r r③ã♦ Cpalinhado/Cpdesalinhado♣rs q ♦♦rr ♠ ♠♥t♦ ♠é♦ s rba = 0,2 b = 3H té ♣r♦①♠

♠♥t rba = 0,4 b = 2H ♦ s♦♠♥t à rçã♦ ♦ â♥♦ ♥♥çã♦

β = 90 ♣r β = 18 st♦ é ♣r♣tí q♥♦ s ♦sr♠ ♦s ♦♠♣♦rt♠♥t♦s ♦

♦♥t ♣rssã♦ ♣r sts ♦s rr♥♦s t ♦♥♦r♠ r á

♠ ♠♦r rçã♦ ♥♦ Cp ♣r ♦ rr♥♦ s♥♦ ♠♥r ♠s ♥t ♣r

♠♦r r③ã♦ ♦q♦

♠♥t♦ ♦ â♥♦ t β → 90 ♣r♦♠♦ ♠♦r q ♣rssã♦ ∆p ♦

♦♥♦ ♦ tr♦ ♥ ♦ ss♠ ♠♦r q ♣rssã♦ ♦♦rr ♣r ♦s s♦s

♦♠ ♥♥çã♦ t 90 ♠♥♦r q ♣rssã♦ é ♥♦♥tr ♦♠ ♠♦r

rqê♥ ♣r ♥♥çã♦ 18 ♦♥rçã♦ ♥ r♥ç ∆p

♥♥çã♦ 90 é r ♠♦r ♦ q r♥ç ♥♥çã♦ 18 ♥♦s

s♦s ♦♠ s♣ç♠♥t♦ ♥tr ts b = 2H r ♠♦r ♥♦s s♦s ♦♠ s♣ç♠♥t♦

b = 3H ♦♥rçã♦ s♥ ♦ ∆p ♥♥çã♦ 90 é r

♠♦r b = 2H rba = 0,2 ♠♦r b = 3H rba = 0,4 ♦♠♣r♦s à ♥♥çã♦

18

♥ê♥ r③ã♦ ♦q♦

♦♥♦r♠ s ♦sr ♥ r ♦ ♣r♥♣ t♦ r③ã♦ ♦q♦

t rba s♦r q♥t Cp/Cp0 é ♣r♦♠♦r ♦ s ♠♥t♦ ♦♥t♦ ♠s

r♥çs sã♦ ♦srs ♣r rr♥♦ ❯♠ rtríst ♥trss♥t ♣r ♦

rr♥♦ s♥♦ é q ♠ ♠ q rba é ♠♥t ♥t♥ss rçã♦

Cp/Cp0 ♣r ♠ ♠s♠ ♦♥çã♦ r♦♥â♠ ue st t♦ ♥ã♦ é ♦sr♦ ♥♦

rr♥♦ ♥♦ s♠tr ♦♠étr

❯t③♥♦ s rs ♠s♠ ♦ r ♣♦s str ♠

t♦r ♣r♦♣♦r♦♥ ♣r r ♦ t♦ s s r③õs ♦q♦ t

♣rs♥ts s ♠ r③ã♦ ♥tr s q♥ts (Cp/Cp0)β rba=0,4 (Cp/Cp0)β rba=0,2♦♠♥♦ ♦s ♦s ①tr♠♦s ♣r ♦ â♥♦ ♥♥çã♦ t ♦ t♦r ♣r♦♣♦r♦

♥ é ♣r♦①♠♠♥t t♥t♦ ♣r β = 90 q♥t♦ ♣r β = 18 ♠

t♦s s ♦s ♦ rr♥♦ ♥♦ ♦ rr♥♦ s♥♦ ♦ ♣r♥♣♠♥t

à rçã♦ ♦sr ♣r rba = 0,4 ♦ t♦r ♣r♦♣♦r♦♥ é ♣ró①♠♦ q♥♦

β = 90 r③ ♦♥sr♠♥t ♣r ♥ ♥♥çã♦ β = 18 ♦♠ ♦ ♠♥t♦ ♦

s♣ç♠♥t♦ ts ♣r b = 3H ♦ t♦r ♣r♦♣♦r♦♥ ♠ t♦r♥♦

♣r ♠♦s ♦s â♥♦s β = 90 β = 18 ♦ rr♥♦ s♥♦ á ♠ t♦ ♠♦r

♦ s♣ç♠♥t♦ ♦ t♦r ♣r♦♣♦r♦♥ é r q♥♦ β = 90 ♥

♥♥çã♦ β = 18 r q ♣rs♥t r③ã♦ ♦ Cp/Cp0 ♣r t♦♦s ♦s s♦s ♦ rr♥♦

s♥♦ ♠♦str ♠ ♥rsã♦ ♥♦ ♦r Cp ♠♥r ♣r♦♣♦r♦♥ st♦ r♣r

s♥t q ∆p ♠♥t ♣r ♦ ♠♥♦r â♥♦ r♥t♠♥t ♦ ♥♦♥tr♦ ♥s ♠s

r③õs ♦q♦ t s rst♦s ♠♦str♠ ♠ ♠♥t♦ ♦ ∆p b = 2H

b = 3H ♣r ♦ â♥♦ 18 ♦♠ rçã♦ ♦ â♥♦ 36

r ♠♦str q ♣r st s♦ s♣í♦ rst♥t ♦♠♥çã♦ ♦

♠étr ♥tr β = 18 rba = 0,6 rstrçã♦ ár ♣ss♠ é ♠í♥♠ ♥tr ♣♦♥t

♠ t ♠♦♥t♥t t ssq♥t ♣r ♦♣♦st r é

♠♦str♦ ♥ ♦s ♦♥t♦r♥♦s ♦ ♣r ♠ rã♦ ♦ tr♦ t♦ ts

t♦♣♦♦ ♦ s♦♠♥t♦ ♠é♦ ♥t♦ à ♣r ♥r♦r s rõs ♦♥t♦r♥♦s ♠

r♠♦ r♣rs♥t♠ s ♠♦rs ♦s q ♦♦rr♠ ♦ ♦s t♦rs rs

trçã♦ ár s♦♠♥t♦ t♠é♠ ♦ à ♣rs♥ç rõs rrçã♦ q

♣r♦♦♠ ♦ s♦ ♦ s♦♠♥t♦ ♣r♥♣ ♦♥♠♥t ♦s r♥s órts ♦r♠

♦s s♥t s ts ♣r♦♠♦♠ ♦ ♠♥t♦ q ♣rssã♦ ♦♥sq♥t♠♥t

♦ ♦ t♥ ♦s qs ③s ♦ ♥tr ♥♦ ♥ ue

♥ê♥ ♦ rrê♥ ♥ú♠r♦ ②♥♦s

t♦ rçã♦ s ♦♥çõs ♦♥t♦r♥♦ r♦♥â♠s ♦ s♦♠♥t♦ ♦

♦ ♣r três r♥ts ♦s ♥tr ue = 1 m/s ue = 3 m/s ue =9 m/s ♦♠♦ ♦♥sqê♥ ♥♦♠♣rss ♦ ♦ ♣r♥♣♠♥t ♦♦rr ♦

s♠♣s s♦♠♥t♦ r ♦ Cp/Cp0 ♦♥♦r♠ ♠♦str♦ ♥s rs

sts rs s ♣r q ♦ ♣r Cp/Cp0 ♣r ♠ ♠s♠ ♦ ♥tr

ue s ♠♥té♠ ♣r♦①♠♠♥t ♥♣♥♥t r③ã♦ ♦q♦ ♣ ♦

s♦♠♥t♦ ♠♥t♦ ♦ rrê♥ ue = 1 m/s ♣r ue = 3 m/s rst♥♠ ♠♥t♦ ♦ ∆p ♣r♦①♠♠♥t ③s ♥♦ ♦ é ♠♥t

♣r ue = 9 m/s ♦ ♠♥t♦ ♦ ∆p é ♣r♦①♠♠♥t ③s rçã♦ qrát

q ♣rssã♦ ♦♠ ♦ ♦♦rr ♣r ♠s s ♦♥rçõs t ♦♠

rçã♦ ♠ t♦r♥♦ ♥tr rr♥♦s rba = 0,2 rba = 0,4 r♥srê♥ ♦r ♥tr ♦ ♦♠í♥♦ só♦ ♦ ♦♠í♥♦

♦

Pr ①r ♥s çõs s q♥ts ♦s ♦s sã♦ ♣rs♥t♦s ♥♦s

♣ró①♠♦s t♥s sr ♦s ♦♥t♦r♥♦s t♠♣rtrs ♣r ♠♦s ♦s ♦♠í♥♦s s ♥s

♦rr♥t ♣r rçã♦ ♦♠étr

strçã♦ t♠♣rtr t♦♣♦♦ ♦ s♦♠♥t♦

sts t♥s tr♥srê♥ ♦r é ♦r♠ qtt s♥♦ ♥r

qr ♥ás tr♥srê♥ ♦r ♣♦str♦r Pr t♥t♦ t③♠s strçã♦

t♠♣rtr ♥s ♦rr♥t ♠♦strs ♣♥s ♥t♦ à ♣r ♥r♦r ♦ ♥

strçã♦ t♠♣rtr ♥ ♦s t♦s tr♥srê♥ ♦r ♦♥

s ♥s ♦rr♥t ①♠ ♦ ♥t♥♠♥t♦ ♦s ♥ô♠♥♦s tr♥s♣♦rt ♥♦♦s

♥ê♥ ♥♥çã♦ t

s ♠♣♦s t♠♣rtr ♠ ♠♦s ♦s ♦♠í♥♦s só♦ ♦ rst♥ts ♦

t♦ ♥♥çã♦ stã♦ ♣rs♥t♦s ♥s rs srs q ♦ à

r③ã♦ ♦♥t tér♠ t③ ♥s s♠çõs ks/kf ♦ ♦♠í♥♦ só♦

♣rs ♦ ♥ ts ♥ s ♣ ♣r r ♥ã♦ ♣rs♥t rçã♦

♣r♣tí ♣r ♠♦r ♦s s♦s

sr s ♦rs ♦ ♠♥s♦♥③ s♥t ♦r♠

T ∗ = T − Tmin

Tmax − Tmin

s♥♦ T Tmin Tmax s t♠♣rtrs ♦s ♠í♥♠ Tmin = 298,15 K ♠á①♠ Tmax =358,15 K rs♣t♠♥t

♦s s♦s ♣rs♥t♦s t♦♣♦♦ ♦ s♦♠♥t♦ é s♣♠♥t ♥♥

♣ ♥♥çã♦ s ts ♣r ♦ rr♥♦ s♥♦ rs

♠ q ♦ â♥♦ ♥♥çã♦ ♠♥ β → 0 ①ã♦ s ♥s

♦rr♥t ♠♥ s♦♥♦ ♦ ♣♦♥t♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♦♠♦ ♦♥sqê♥

♣r tr♦ tér♠ st♦ t r♠♦çã♦ ♦r ♥ rã♦ ♣r ♥tr ts ♦t

s ♦ sr♠♥t♦ rõs qs s♦ s ts q♥t♦ ♠♥♦r ♦ â♥♦ ♥♥çã♦

β → 0 P♦r ♦tr♦ ♦ tr♦ tér♠ ♥ r♦♥t t ♠♥t ♦♠ s

♥♥çã♦ ♦ à ♣r♦①♠ ♦ s♦♠♥t♦ ♣r♥♣ s♣rí t ♦ q

♣r♦♠♦ ♠♦rs r♥ts t♠♣rtr

♦ rr♥♦ ♥♦ rs ①st ♦r♠çã♦

rrçã♦ rtríst ♣r t♦s s ♥♥çõs ♦ts q rã♦ rrçã♦

♥ç s♦r ♠♦♥t♥t s ts ♦♠ ♠♥çã♦ ♦ â♥♦ ♥♥çã♦

♦ às rrçõs ♦ s♦♠♥t♦ ♣r♥♣ é st♦ s ♣rs s♦ ♣rr♥

♠♥t ♣ ♣rt ♥tr ♦ ♥ ♣r♥♦ tr♦ tér♠ ♥ rã♦ s ♣rs

♥tr ts s rs ♠♦str♠ q ♦ ♦ ♠♦r s♣ç

♠♥t♦ ♥tr ts b = 3H ♦ s♦♠♥t♦ ♣r♥♣ s ♣r♦①♠ ♣r ♦ ♥ ♥

rã♦ ♥tr ts ♦ q ♠♥t tr♦ tér♠ ♦

♦♠ ♦s ♦♥t♦r♥♦s t♠♣rtr ♣♦s ♦r♠ rstrt ♦ só♦ ♣rs

ts ♥♦ts ♦ t♦ tr♦ tér♠ ♦♥ s rs

♠♦str♠ q ♣r ♦ rr♥♦ ♥♦ r♠♦çã♦ ♦ ♦r ♥ rã♦ ♣r é ♣r

♣ ①stê♥ rrçõs ♥t♦ à s♣rí ♣r P♦rt♥t♦ rçã♦

t♠♣rtr ♥s ♣rs ♦♦rr qs q ①s♠♥t ♥ rã♦ ♣ró①♠ s ss

s ts P♦r ♦tr♦ ♦ ♥♦ rr♥♦ s♥♦ rs é

♣♦ssí ♦tr ♠ ♠♦r r♠♦çã♦ ♦r s ♣rs ♦ só♦ st♦ ♦♦rr ♥♦ s♥t♦

♠♥t♦ ♦ â♥♦ ♥♥çã♦ s ts β → 90 ♦ s q♥t♦ ♠s ♦ s♦♠♥t♦

é t♦ ♣s ts ♠ rçã♦ às ♣rs st♦ t strçã♦ t♠♣rtrs

♦ ♦♥♦ s ♣rs ♦ tr♦ t♦ ♥ t♦r♥♥♦ ♠s ♦♠♦ê♥

srs q ♥ r s t♠♣rtrs t③ ♠s♠ ór♠

qçã♦ ♦♠ Tmin = 355,294 K Tmax = 358,15 K s ♦♠ st ①

♦rs ♦ ♦♥strí ♣r ♣rs s♦ ♠ ♦s s♦s st r st♦ é t③♥♦

s s ♦♦rrê♥s ♠í♥♠ ♠á①♠ t♠♣rtr ♥tr qs ♦♠trs ♣r

♦♥çã♦ ♦ rrê♥ ♥

♥ê♥ ♦ rrê♥

t♦ rst♥t ♦ rrê♥ ♥ ♦r♠ ♦♥t♦r♥♦s t♠♣

rtr srá str♦ ♣r ♦ ♦♠í♥♦ só♦ ♣rs ts ♣♥s Pr t♥t♦ ♦s

rst♦s s três ♦♥çõs ♦ rrê♥ sã♦ ♠♦strs ♣r três r♥

ts ♥♥çõs ♥s rs β = 18 β = 54 β = 90 sts rs

s t♠♣rtrs é ♠s♠ q t♠é♠ ♦ ♦♥strí s♦ ♠ ♣rtr

qçã♦ t③♥♦s Tmin = 351,79 K Tmax = 358,15 K

Pr sts três rs ♣rs ♠ ♠♦r rçã♦ ♦ ♠♣♦

t♠♣rtrs ♥♦ só♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ♦ q ♥

rs♥t tr♦ tér♠ ♥tr ♦s ♦♠í♥♦s ♦♠♣t♦♥s ♦ts q é♠ rstr

♠ ♠♥♦rs t♠♣rtrs ♥s ts ♦ ♠♥t♦ ♦ rrê♥ tr

♦r♠ ♦♥srá ♦ ♠♣♦ t♠♣rtrs s ♣rs ♦ ♥

s ♣ró①♠s sçõs stã♦ ♣rs♥ts s q♥tçõs tr♦ tér♠ sts

q♥tçõs ♦r♠ tr♠♥s ♦♠♥t s♦r s ♣rs ♦ ♥ trés ♦ Nux

♦r♠ ♦ ♣♦r ♠♦ ♦ Nu ♦ qtotal

ú♠r♦ sst ♦ Nux

sqê♥ srã♦ st♦s ♠♥r ♥ ♦r♠ ♦♠♦ ♦s ♣râ♠tr♦s

r♦s t♠ strçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦ q tr♠♥

q♥t ♦r tr♦ trés s ♣rs ♥

♥ê♥ ♦ â♥♦ ♥♥çã♦ t

Pr strr rçã♦ ♦ ♥ú♠r♦ sst ♦ ♥ rã♦ ♣r ♦♠ s

ts ♥♥s ♦r♠ s♦♥♦s ♦s ♠s♠♦s s♦s çã♦ ♦ Cfx st♦ é r③ã♦

♦q♦ t rba = 0,4 ♦ rrê♥ ♥tr♠ár ue = 3 m/s r ♣rs♥t s rtrísts rst♥ts ♣r ♦ ♥ú♠r♦ sst ♦

♦♠♦ ♦♥sqê♥ rçã♦ ♦ â♥♦ ♥♥çã♦ t ♥s ♦♠trs ♦♠

s♣ç♠♥t♦ ♥tr ts b = 2H Pr ♦ rr♥♦ ♥♦ r s♦♠♥t é

♠♦str♦ ♦ Nux ♥ ♣r s♣r♦r ♦ à s♠tr ♦♠étr ♦ts ♥ q

á ♥çã♦ ♣♦sçã♦ sq♥ s ts ♦rrs♣♦♥♥ts ♦ s♦ β = 18 ♠

♣r ♣r ♠♦s ♦s rr♥♦s st♦ ♥ q s rs ♣rs♥ts r♣rs♥t♠

s♦♠♥t ♦ ♥ú♠r♦ sst ♥s rõs ♣r st♦ é ♥trts ♦♥♦r♠ ♥çã♦

♦ Nux

s rtrísts rst♥ts ♣r s rs s ♦♠trs ♦♠ s♣ç♠♥t♦ b =3H sã♦ st♥t s♠♥ts às q ♦rrs♣♦♥♠ ♦ s♣ç♠♥t♦ ♣rs♥t♦ b = 2H

♦♥♦r♠ s ♦sr ♥ r st r ♠♦str q ♦s ♣rs ♣r strçã♦

♦ ♥ú♠r♦ sst ♦ sã♦ ♠t♦ s♠♥ts ♦s ♥♦♥tr♦s ♥s ♦♠trs

♠♥♦r s♣ç♠♥t♦ ♥tr ts

Prs ♥s rs q ♠♦str♠ ♦ rr♥♦ ♥♦ q

♠♦r r♥ç ♥♦ Nux é ♣r ♥♥çã♦ ♦ â♥♦ β = 18 ♣sr ♣rs♥tr

♦ ♠s♠♦ ♣r s ♠s rs ♦s ♦rs sst ♦ ♦♥♦ ♣r ♦r♠

♠♦♦ r ♦s ♠♥♦rs ♥tr t♦♦s ♦s s♦s ♠ ♦♠♣rçã♦ ♣r ♦ ♠á①♠♦ Nux

♥tr s ♥♥çõs β = 18 β = 90 st út♠ é s♣r♦r ♠ ♠♦s ♦s s♣ç♠♥t♦s

t ♠♦r ♣r b = 3H ♠♦r ♣r b = 2H srs q st♦ é

♠ ♦♥sqê♥ rt r♥ç ♦sr ♥♦s ♠♣♦s t♠♣rtrs ♦ ♦♠í♥♦

só♦ s rs ♥♠ q t♠♣rtr ♦ ♦♥♦ ♥tr

s ♣rs é ♠s ♦♠♦ê♥ t♠é♠ ♠s t ♣♦ s♦♠♥t♦ ♥♦ s♦ β = 90 s rs ♣r ♦ rr♥♦ s♥♦ r♥ç ♦Nux ♥tr

s ♥♥çõs é ♠s s♥t Prs q r♥ç ♥tr s ♥♥çõs ①tr♠s é

♦♥srá ♦ ♠♥♦r â♥♦ ♥♥çã♦ β = 18 ♦ sst rã♦ ♣r é

♥r♦r ♦s ♠s s♦s é♠ ♣♦ssr ♠ ♣r ♥♦t♠♥t st♥t♦ ♦s ♠s

â♥♦s β = 36 té β = 90 ♦ ♣r ♣r Nux é ♣rt♠♥t ♦ ♠s♠♦ ♦♠ ♠

♣q♥ r♥ç ♥s rõs ♣ró①♠s às ss t à ♣rs♥ç ♦s órts

♥t♦ ♦ ♥ês ♦r♥r s ♦r♠ q♥ttt ♦♦rr ♠♥çã♦ ♣r♦rss

♦ ♦r ♦ ♠á①♠♦ sst ♦ ♦♠ ♠♥çã♦ ♦ â♥♦ ♥♥çã♦ β → 18

rçã♦ ♦s ♦rs ♠á①♠♦s Nux ♥tr β = 90 β = 72 é r ♣ss

♣r q♥♦ s ♦♠♣r ♦s ♦rs rçã♦ ♥tr β = 90 β = 18 ♥ ♠é

♣r ♠s s ♣rs ♦ s♣ç♠♥t♦ ♥tr ts b = 2H Pr ♦s s♦s ♦ s♣ç♠♥t♦

b = 3H s rs♣ts rçõs sã♦ q♥ts

♥ê♥ ♦ rrê♥ ♦ ♥ú♠r♦ ②♥♦s

♠♥t♦ ♦ rrê♥ ue ♦ ♦ ♥ú♠r♦ ②♥♦s ♦ s♦

♠♥t♦ ReDh ♣r♦♠♦ ♥t♥sçã♦ ♦ tr♥s♣♦rt ♦♥t♦ ♥r ♦♥

♠♥t s ♣r♦♣rs ♦ s♦♠♥t♦ trê♥ ♦♠♦ ♦♥sqê♥ st ♠♥t♦

♣r♦♦ ♦ s♦♠♥t♦ rt ♥s rs ♦ ♥ú♠r♦ sst ♦ s♠ trçã♦ ♦

s ♣r s rs str♠ st t♦ ♣r três r♥ts ♥♥çõs

β = 18 β = 54 β = 90 ♠♦s ♦s rr♥♦s t s s♦s ♣rs♥t♠ s

♠s♠s rtrísts ♦♠étrs b = 2H rba = 0,4 ♥s três r♥ts ♦♥çõs

♦♥t♦r♥♦ r♦♥â♠s st tr♦

çã♦ ♦ Nux ♦ rr♥♦ ♥♦ ♠♦str ♦ ♠♥t♦ ♥♦ sst ♦ ♦

♦r ♣♦ rr r ③s ♦ s ♠♥tr ♦ rrê♥ ♣rtr

ue = 1m/s ♣r ue = 3m/s ue = 9m/s rs♣t♠♥t ♦ s♦ ♦ rr♥♦ s♥♦

♦ ♦r ♦ ♠á①♠♦ ♥ú♠r♦ sst ♦ é ♣r♦①♠♠♥t ue = 3 m/s

ue = 9 m/s ③s ♠♦r ♦ s ♠♥tr ♦ rrê♥ ♣rtr ue = 1 m/s♥ê♥ r③ã♦ ♦q♦ t

Pr strr st t♦ ♦r♠ ♠♥t♦s ♦s três â♥♦s ♥♥çã♦ t

♥ás ♣ré β = 18 β = 54 β = 90 ♣r ♦ s♣ç♠♥t♦ ♥tr ts b = 2H

♦♥çã♦ r♦♥â♠ ue = 9 m/s ♦ t③ s rst♦s ♣r ♠♦s ♦s

rr♥♦s sã♦ ♠♦str♦s ♠ sqê♥ ♣s rs

♥s♥♦ ♥♠♥t s rs ♣rs q ♥♣♥♥t ♦ â♥♦

♥♥çã♦ ♦♦rr ♦ ♠♥t♦ ♦ ♠á①♠♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦

♦q♦ t ♣r ♠♦s ♦s rr♥♦s ♦ts ♥ ♠ r♥ r♥ç ♥♦ ♣r

r strçã♦ ♦ Nux ♥ ♠♥♦r r③ã♦ ♦q♦ ♦ rr♥♦ s♥♦ ♣r

β = 18 r

Pr ♦ rr♥♦ ♥♦ ♦ ♠♥t♦ ♥♦ ♦r ♠á①♠♦ sst ♠ ♦rrê♥

rçã♦ ♥ r③ã♦ ♦q♦ é ♣ró①♠♦ Pr ♦ rr♥♦ s♥♦ st t♦r

é rá ♥s ♥♥çõs s s t♥ê♥ ♠♥r ♦ t♦r ♥♦ s♥t♦

♦ ♠♥♦r â♥♦ ♥♥çã♦ β → 18 ❱r♥♦s r③ã♦ ♦q♦ t

♣rtr ♣r ♦té♠s ♦ t♦r ♠♥t♦ ♦ ♦r ♦ sst ♦ ♠á①♠♦

♣r ♦s â♥♦s β = 90 β = 54 β = 18 rs♣t♠♥t s♦

s ♦♠♣r♦ ♦ t♦ ♦ ♠s♠♦ ♠♥t♦ r③ã♦ ♦q♦ q ♥♦ rr♥♦ ♥♦

st♦ é rba = 0,2 ♣r rba = 0,4 ♦ t♦r ♠♥t♦ ♦ ♦r ♣♦ ♦ Nux é ♠s

♦♠♦ê♥♦ s♥♦ ♣r ♦s â♥♦s β = 18 β = 54 β = 90 rs♣t♠♥t

♥ê♥ ♦ rr♥♦ t

♠ ♠♦s ♦s rr♥♦s ♦ ♣r ♦ sst ♦ ♣rs♥t rtrísts ♠♥t♦

s♥t ♠♥çã♦ ♠t♠♥t ♠♦♥t♥t s t ♦♥♦r♠ ♠♦str♦

♥ r ♣♦r ①♠♣♦ ♦r♦ ♦♠ ①♣r♠♥t♦s trtr ❱

♦ rés♠♦ é ♦♥sqê♥ ①stê♥ rrçã♦ ♥q♥t♦ q ♦ ♠♥t♦

sút♦ ♦♦rr ♦♠♦ ♦♥sqê♥ ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♣r♥♣

s rõs ♦ s♦♠♥t♦ ♥♦ q ①st♠ rrçõs s ♣r♦♣rs t♥♠

sr ♠s ♦♠♦ê♥s ♠♣♥♦ ♥♠ ① r♥ç t♠♣rtrs ♦ q t

rt♠♥t tr♥srê♥ ♦r P♦r ♦tr♦ ♦ q♥♦ ♦ s♦♠♥t♦ ♣r♥♣ r♦

♥ s♣rí ♦ ♥ ♦ r♥t tér♠♦ é ♣r♦♠♦♦ ♣♦r ss♦ ♦♦rr ♦ ♠♥t♦

tr♥srê♥ ♦r ♥♦ ♥t♦r♥♦ rã♦ r♦♠♥t♦

srs q á ♠ r♥ç ♠r♥t ♦ ♣r ♦ sst ♦ rst♥t

♦s ♦s rr♥♦s st♦s Pr ♦♥rçã♦ ♥ ♦ ♣r r Nux♣rs♥t ♠ s♣é ♣tô ♥ rã♦ ♠á①♠♦ Nux ♥q♥t♦ q ♥ ♦♥rçã♦

s♥ st rã♦ é ♠♦r srt ♣♦r ♠ ♣♦ ♦♥t♦ st♦ é r♦ ♥♦s

s♦s r③ã♦ ♦q♦ ♣r ♦ rr♥♦ s♥♦ s♦♠♥t sts s♦s

①ã♦ ♦ s♦♠♥t♦ é ♠s ♣r♦♥♥ q ♣r r③ã♦ ♦q♦ ♥♦ ♠s♠♦

rr♥♦ s ♠♦rs ①õs ♣r♦♦♠ ♦ s♦ ♦ s♦♠♥t♦ ♣r♥♣ ♣r rõs

♠s ♣ró①♠s ♣r ♦♣♦st rst♥♦ ♥♠ ♠♦r r♥t t♠♣rtrs ♠♦r

sst ♦

ú♠r♦ sst ♦ Nu

é♠ s ♦r♠çã♦ ♦ ♠ ♥ú♠r♦ sst ♦ t♠é♠ ♦ t③♦

♥s çõs r ♣rs♥t ♦s ♦rs sst ♦ ♣r t♦s s r③õs

♦q♦ ♦s rrê♥ â♥♦s ♥♥çã♦ ♠♦s ♦s rr♥♦s ♦t

s q ♦ sst ♦ Nu é ♣rs♥t♦ ♥ ♦r♠ r③ã♦ ♣r ♦ sst ♦ ♦

♥ s♠ ts Nu0 ♦s rs♣t♦s ♦rs stã♦ ♥

ú♠r♦ sst ♦ ♦ ♥ s♠ ts ♣r s três r♥ts ♦♥çõs r♦♥â♠s

♦♠♣r♠♥t♦ ♥s♠ ts β = 0 ❱♦ rrê♥ ue ú♠r♦ sst ♦ Nu0

①1 m/s 3 m/s 9 m/s

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

sqê♥ srã♦ st♦s ♠♥r ♥ q ♦r♠ ♦s ♦s r♥

ts ♣râ♠tr♦s ♦♠étr♦s s r♥ts ③õs ♥sts t♠ strçã♦ ♦

♥ú♠r♦ sst ♦

♥ê♥ ♦ â♥♦ ♥♥çã♦ t

♥ê♥ ♥♥çã♦ t s♦r ♦ sst ♦ é ♠s s♥t ♣r

♦ rr♥♦ s♥♦ rs st rr♥♦ rs ♠ t♥ê♥

q ♦ sst ♦ ♦♠ ♠♥çã♦ ♦ â♥♦ ♥♥çã♦ t β → 0 Pr

♦s s♦s ♦ rr♥♦ ♥♦ rs ♥♥çã♦ t ♥ã♦ ♣rs♥t♦

♥ê♥ ♥♦tá s♦r Nu

♠é ♣r ♠s s r③õs ♦q♦ ♦ rr♥♦ ♥♦ rçã♦ ♦

sst ♦ é ♠♥♦r ♦ q ♣r ♦ s♣ç♠♥t♦ ♥tr ts b = 2H ❯♠ r♦

♠♥t♦ ♦♦rr ♥♦ s♣ç♠♥t♦ b = 3H ♥♦ q rçã♦ ♠é ♠ t♦r♥♦

Pr ♦ rr♥♦ s♥♦ ♠♥♦r r③ã♦ ♦q♦ t ♣rs♥t rçã♦

♠é ♥tr b = 2H b = 3H Pr s ♦trs s r③õs ♦q♦

t rba = 0,4 rba = 0,6 s rçõs ♠és sã♦ t♦s ♠♦rs q ♥♦

rba = 0,6 b = 2H

♥ê♥ ♦ rrê♥

t♦ rçã♦ ♦ rrê♥ s♦r ♦ ♥ú♠r♦ sst ♠é♦

Nu é s♠r ♦ q ♦ ♦sr♦ ♣r ♦ ♥ú♠r♦ sst ♦ ♦ s ♦ ♠♥t♦

♦ rrê♥ ♠♣ ♥♦ ♠♥t♦ ♦ Nu ♠♥s♠♦ ♥t♥sçã♦ é

♦ ♠s♠♦ t♠é♠ á st♦

♠♥r r ♦ ♠♥t♦ ♠é♦ ♦ sst ♦ stá ♥tr ♦ s

♠♥tr ♦ rrê♥ ♣rtr 1 m/s ♣r 3 m/s ♠s♠♦ ♣r♥t

rés♠♦ é r♦ ♣r ♦ ♥r♠♥t♦ ♦ rrê♥ ♣rtr 3 m/s♣r 9 m/s♥ê♥ r③ã♦ ♦q♦ t

♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦ t á ♦ rés♠♦ ár tr♦

tér♠ é♠ ♦s t♦s q ♠♦r rstrçã♦ ár ♠♣õ à ♥â♠ ♦ s♦♠♥t♦

♦♥♦r♠ á ♦♠♥t♦ Pr ♠♦s ♦s rr♥♦s q♥t♦ ♠♦r r③ã♦ ♦q♦

t ♠♦r ♦ ♥ú♠r♦ sst ♠é♦ ♦ s rst♦s ♠♥♦♥♦s sr

sã♦ ♦♠♥s ♦s ♦s s♣ç♠♥t♦s ♥tr ts b = 2H b = 3H

Pr ♦ ♠♥t♦ r③ã♦ ♦q♦ t rba = 0,2 ♣r rba = 0,4 ♦ t♦r

♠♥t♦ ♠é♦ ♦ sst ♦ é r ♦♥sr♥♦ t♦s s ♥♥çõs st

t♦r ♠♥t♦ ♦ ♦ ♠ ♠♦s ♦s rr♥♦s t

♦r♠ s♣í ♣r ♦ rr♥♦ s♥♦ r③ã♦ ♦q♦ t é

♠♥t rba = 0,4 ♣r rba = 0,6 rst♥♦ ♠ ♠ t♦r ♠♥t♦ ♠é♦ ♠

t♦r♥♦

♥ê♥ ♦ rr♥♦ t

♦♠ s ♥♦s rst♦s ♣rs♥t♦s ♣ r t♠s q ♦ rr♥♦

ts ♥s rs ♥ã♦ ♣rs♥t ♥ê♥ ♦♥srá s♦r ♦

sst ♦ ♦ts q st♦ é á♦ ♣r s s r③õs ♦q♦ ♣rs♥ts

rr♥♦ ts s♥s rs ♣♦ tr ♦r♠

s♥t ♦ sst ♦ q♥t♦ ♠♦r r③ã♦ ♦q♦ é♠ ss♦ ♠♦str♦s

q ①♠♣♦ ♦ q ♦♦rr ♣r ♦ ♦♥t ♣rssã♦ ♥ ♠♦r r③ã♦ ♦q♦

rba = 0,6 ♦ sst ♦ ♣rs♥t ♠ ♦♠♣♦rt♠♥t♦ s♣ ♣r ♦ ♠♥♦r â♥♦

♥♥çã♦ β = 18 ♦ à rstrçã♦ ár ♣ss♠ ♦ s♦♠♥t♦ r

♦r t♦t ♠♥s♦♥ qtotal/q0 ♣r ♦r tr♦♦ tr

és s ts

♦♠♦ ♥t♠ ♦ st♦ tr♥srê♥ ♦r ♦♥ ♣♦s r ♦

♦r t♦t tr♥sr♦ ♣r ♦ ♦ ♠ s ♣rs ♠ ♦rrs♣♦♥♥t à tr♦ tér♠

q ♦♦rr trés s♣rí s ts ♦tr q ♦rrs♣♦♥ à tr♦ tér♠

trés s♣rí s ♣rs ♦ ♥ ♠♥r ♦♠♣♠♥tr às çõs ♦s

♥ú♠r♦s sst ♦ ♦ q♥t♦s sts ♣rs ♠ s♣r♦ ♥

♦s ♥ê♥ ♦s ♣r♥♣s ♣râ♠tr♦s st♦s s♦r ts ♣rs

♥ê♥ ♥♥çã♦ t

r ♦srs ♦ t♦ ♥♥çã♦ s♦r ♣r tr♥srê♥

♦r trés s♣rí s ts t♠é♠ s♦r q♥t ♠♥s♦♥ qtotal/q0q r♣rs♥t ♦ t♦r ♠♥t♦ tr♥srê♥ ♦r ♦ à ♣rs♥ç s ts

♦♠ rçã♦ ♦ rs♣t♦ s♦ ♦ ♥ s♠ ts ♣r ♦ tr♦ L = 30H s ♦rs

t③♦s ♦♠♦ rrê♥ ♣r q♥t qtotal/q0 sã♦ ♠♦str♦s ♥

srs q ♦s s♦s r r♣rs♥t♠ ♦s rst♦s ♣r ♦♥çã♦

♦♥t♦r♥♦ ue = 3 m/sPr ♦ rr♥♦ ♥♦ rs q♥t qtotal/q0 ♣rs♥t♦

rçã♦ ♠♥♦r q ♦♠ ♦ â♥♦ ♥♥çã♦ s ts rçã♦ st q♥t

♥♦ rr♥♦ s♥♦ ♦♥t♦ é s♥t ♠ b = 3H ♥ ♥♦ts

q ♣r ♠ ♠s♠♦ s♣ç♠♥t♦ ♥tr ts ♦ rr♥♦ ♥♦ ♣rs♥t ♦s ♠♦rs

t♦rs ♠♥t♦ ♥ tr♥srê♥ ♦r ♣r t♦s s ♥♥çõs t q♥♦

♥t ♦r tr♥sr ♣r ♦ ♦ ♥♦ ♥ s♠ ts ♣r strês r♥ts ♦♥çõs r♦♥â♠s

♦♠♣r♠♥t♦ ♥s♠ ts β = 0 ❱♦ rrê♥ ue q♥t ♦r q0

①1 m/s 0,5745 W

3 m/s 1,287 W

9 m/s 3,051 W

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

b = 3H r ① r P♦ré♠ ♣r ♦ ♠♥♦r s♣ç♠♥t♦ ♥tr

ts b = 2H st♦ só é r♦ ♣r s ♠♦rs ♥♥çõs r ① r

♥ssár♦ ♥♦tr rçã♦ ♦♠♣♠♥tr ♦s rst♦s r ♦♠

strçã♦ Nux r ♦♥♦r♠ ♦♥stt♦ ♣r ♥♥çã♦ β = 18 ♦♥ú♠r♦ sst ♦ ♥ rã♦ ♣r s st ♣♦r sr ♦♥sr♠♥t ♠♥♦r

q ♣r ♦s ♠s â♥♦s ♥♥♦ q tr♦ ♦r ♣r♦♠♥r ♥s ts

st s♣♦sçã♦ é r ♣♦s ♦s rst♦s ♣r ♥♥çã♦ β = 18 r♠ q

♠♦r ♣rt tr♦ ♦r ♦♦rr t♦ trés s♣rí s ts ♣r ♠♦s

♦s rr♥♦s ♣r♥t ♦r tr♦♦ trés s ts té ♦ t♦t

β = 18 rba = 0,6♥ ♦s rst♦s ♣rs♥t♦s ♣r ♦ sst ♦ r sr♠ q

tr♦ tér♠ ♠♥ ♥ rã♦ ♣r ♣r ♦s ♥s ♦♠ ts q ♣rs♥t♠

♠♥♦r â♥♦ ♥♥çã♦ β → 0 t♦ r ♠♦str ss t♥ê♥

♣♦s st q ♠♦rs ♥♥çõs t♥♠ ♣rs♥tr ♠♦rs tr♦s ♦r trés

s♣rí t r ♠♦str q á ♠s♠ t♥ê♥ ♣r ♠♦s ♦s

rr♥♦s ♥t♦ ♥ r q♥t♦ ♥ r ♦srs q ①st

♠ ♥♥çã♦ ♣rtr q s rçõs ♦r sã♦ trs ♥tr ♦s â♥♦s

♥st♦s ♣rs q ♣r s ♥♥çõs té β = 54 q♥t♦ ♠♥♦r ♦ â♥♦

♥♥çã♦ t ♠♦r rçã♦ ♦r tr♦ trés s ts Pr ♥♥çõs

t ♠ ♦ â♥♦ st♦ ♣♦ré♠ ♥ã♦ ♦♦rr rçã♦ ♦♥srá sts

q♥ts

♦r♠ ♦♠♣♠♥tr st♦ ♣♦ sr s③♦ ♥ r q ♠♦str s

rçõs ♦ ♠♣♦ t♠♣rtrs ♥♦ ♦♠í♥♦ só♦ ♣rs ts st r

♥♦ts q s ♠♦rs rçõs sã♦ ♦③s s♦r s ts ♠♦r ♥♥çã♦

♥ê♥ ♦ rrê♥

Pr r ♥ê♥ ♦ rrê♥ ue s♦r ♣r ♦ ♦r

tr♥sr♦ ♣r ♦ ♦ trés s ts ♦r♠ t③♦s ♦s ♠s♠♦s s♦s s rs

♦♠ st♦ ♥♦♠♥t é ♣♦ssí ③r ♦ ♦♠♣rt♦ ♥tr s ♣rsõs

♦ ♥ú♠r♦ sst ♦ tr♦ ♦r ♥tr ♥ s♣rí s ♣rs s

ts ❯♠ ③ q ♦ Nux ♠♥t ♦♠ ♦ rrê♥ ♠ ♠♦r ♣r

♦r é tr♥sr ♣r ♦ ♦ trés s ♣rs ♦ ♥ P♦rt♥t♦ ♠♥çã♦

♣r ♦ ♦r trés s ts ♠♦str ♥ r é ♦r♥t ♦♠ ♣rsã♦

♥♠ér ís ♦ s♦♠♥t♦ ♣r ♠♦s ♦s rr♥♦s ♦ts ♦♥t♦ q á ♦

♠♥t♦ ♥ tr♦ ♦r t♦t ♠♥s♦♥ qtotal/q0 ♦♠ ♦ rrê♥

♦s ♠♦t♦s á ♦r♠ ♣r♠♥t st♦s

♠á①♠ rçã♦ ♦ ♦r t♦t ♠♥s♦♥ ♦♦rr ♣r ♦ rr♥♦ s♥♦

♦♠ β = 90 r Pr st ♦♥rçã♦ ♦ ♠♥t♦ ♦ ♦r

t♦t ♠♥s♦♥ ♦ ♠♥tr ♦ rrê♥ ♣rtr ue = 1 m/s ♣r

ue = 9 m/s st ♠s♠ ① rçã♦ ♦ rrê♥ ♥ê♥ ♥

strçã♦ ♦ ♦r ♦ ♠♦r ♣r ♦ rr♥♦ ♥♦ ♦♠ β = 18 r ♥♦

q s ♦sr ♠ ♠♥çã♦ ♦ ♦r trés s ts

♠♥r ♦♠♣♠♥tr ♦s rst♦s ♣r ♥ê♥ ♦ s♦r ♦

♠♣♦ t♠♣rtrs ♥♦ ♦♠í♥♦ só♦ ♣♦♠ sr st♦s ♥s rs

♣r ♦s â♥♦s ♥♥çã♦ t β = 18 β = 54 β = 90 rs♣t♠♥t

r ♦♥t♦r♥♦s ♦ ♦♠ ♥s ♦rr♥t ♥ ♠t ♥r♦r ♦ ♥rst♥ts ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s♥♦♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 2H rba = 0,4 ♦♥çã♦ r♦♥â♠ue = 3 m/s

β = 18 β = 18

β = 36 β = 36

β = 54 β = 54

β = 72 β = 72

β = 90 β = 90

0,000

0,069

0,138

0,207

0,276

0,345

0,414

0,483

0,552

0,621

0,690

0,759

0,828

0,897

0,966

1,000

U*

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♦♥t♦r♥♦s ♦ ♦♠ ♥s ♦rr♥t ♥ ♠t ♥r♦r ♦ ♥rst♥ts ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s♥♦♦♥ rt ♣r ♦ s♦ ♦♠étr♦ b = 3H rba = 0,4 ♦♥çã♦ r♦♥â♠ue = 3 m/s

β = 18 β = 18

β = 36 β = 36

β = 54 β = 54

β = 72 β = 72

β = 90 β = 90

0,000

0,069

0,138

0,207

0,276

0,345

0,414

0,483

0,552

0,621

0,690

0,759

0,828

0,897

0,966

1,000

U*

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ❱rçã♦ ♦ ♦♥t trt♦ ♦ Cfx ♦♠ ♦ â♥♦ ♥♥çã♦ t β ♣r r③ã♦ ♦q♦ rba ♥s ♦♠trs ♦♠ s♣ç♠♥t♦ ♥tr tsb = 2H

-0.5

0.0

0.5

1.018° 36° 54° 72° 90°

-0.5

0.0

0.5

1.0

Parede superior

Parede inferior

Cf x

4 5 6 7 8 9 10

x/H

4 5 6 7 8 9 10

x/H

# posição das aletas para β=18°

#2 #3

Cf x

(β)

#2 #3 #4

recolamento do

escoamento

rr♥♦ s♥♦

-0.3

-0.1

0.1

0.318° 36° 54° 72° 90°Parede superior

Cf x

4 5 6 7 8 9 10

x/H

(β)

#3#2 #4

# posição das aletas para β=18°

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ❱rçã♦ ♦ ♦♥t trt♦ ♦ Cfx ♦♠ ♦ â♥♦ ♥♥çã♦ t β ♣r r③ã♦ ♦q♦ rba ♥s ♦♠trs ♦♠ s♣ç♠♥t♦ ♥tr tsb = 3H

-0.3

-0.1

0.1

0.318° 36° 54° 72° 90°

-0.3

-0.1

0.1

0.3

Parede superior

Parede inferior

Cf x

4 5 6 7 8 9 10

x/H

4 5 6 7 8 9 10

x/H

# posição das aletas para β=18°

Cf x

(β)

#2

#3

#2

recolamento do

escoamento

rr♥♦ s♥♦

-0.3

-0.1

0.1

0.318° 36° 54° 72° 90°Parede superior

Cf x

4 5 6 7 8 9 10

x/H

(β)

#3#2

# posição das aletas para β=18°

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 18 r③ã♦ ♦q♦ rba s♣ç♠♥t♦ ♥trts b = 2H

-0.2

-0.1

0.0

0.1

0.29 m/s 3 m/s 1 m/s

-0.2

-0.1

0.0

0.1

0.2

aleta n° 2

Parede superior

Parede inferior

4 5 6 7 8 9 10

x/H

Cf x

aleta n° 2 aleta n° 3

aleta n° 3

aleta n° 4

rr♥♦ s♥♦

-0.5

-0.3

0.0

0.3

0.59 m/s 3 m/s 1 m/sParede superior

Cf x

4 5 6 7 8 9 10

x/H

aleta n° 3aleta n° 2

aleta n° 4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 54 r③ã♦ ♦q♦ rba s♣ç♠♥t♦ ♥trts b = 2H

-0.5

-0.3

0.0

0.3

0.59 m/s 3 m/s 1 m/s

-0.5

-0.3

0.0

0.3

0.5

Parede superior

Parede inferior

4 5 6 7 8 9 10

x/H

Cf x

aleta n° 2 aleta n° 3 aleta n° 4

aleta n° 2 aleta n° 3 aleta n° 4

rr♥♦ s♥♦

-0.5

-0.3

0.0

0.3

0.59 m/s 3 m/s 1 m/sParede superior

Cf x

4 5 6 7 8 9 10

x/H

aleta n° 2 aleta n° 3 aleta n° 4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♥t♥sçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 90 r③ã♦ ♦q♦ rba s♣ç♠♥t♦ ♥trts b = 2H

-1.0

-0.5

0.0

0.5

1.09 m/s 3 m/s 1 m/s

-1.0

-0.5

0.0

0.5

1.0

Parede superior

Parede inferior

4 5 6 7 8 9 10

x/H

Cf x

aleta n° 2 aleta n° 3 aleta n° 4

aleta n° 2 aleta n° 3 aleta n° 4

rr♥♦ s♥♦

-0.5

-0.3

0.0

0.3

0.59 m/s 3 m/s 1 m/sParede superior

Cf x

4 5 6 7 8 9 10

x/H

aleta n° 2 aleta n° 3 aleta n° 4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r strçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦ rba ♣r ♥♥çã♦ β = 18 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ ue = 3 m/s

-0.2

-0.1

0.0

0.1

0.2Parede inferior

4 5 6 7 8 9 10

x/H

Cf x

aleta n° 3 aleta n° 4

aleta n° 2 aleta n° 3

aleta n° 2

-0.2

-0.1

0.0

0.1

0.2rba=0,6 rba=0,4 rba=0,2rba=0,6 rba=0,4 rba=0,2

aleta n° 2 aleta n° 3

Parede superior

rr♥♦ s♥♦

-0.2

-0.1

0.0

0.1

0.2rba=0,4 rba=0,2Parede superior

Cf x

4 5 6 7 8 9 10

x/H

aleta n° 3aleta n° 2

aleta n° 4

rba=0,4 rba=0,2

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r strçã♦ ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦ rba ♣r ♥♥çã♦ β = 54 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ ue = 3 m/s

-1.0

-0.5

0.0

0.5

1.0rba=0,6 rba=0,4 rba=0,2

-1.0

-0.5

0.0

0.5

1.0

Parede superior

Parede inferior

4 5 6 7 8 9 10

x/H

Cf x

aleta n° 2 aleta n° 3 aleta n° 4

aleta n° 2 aleta n° 3 aleta n° 4

rba=0,6 rba=0,4 rba=0,2

rr♥♦ s♥♦

-0.5

-0.3

-0.1

0.1

0.3

0.5rba=0,4 rba=0,2Parede superior

Cf x

4 5 6 7 8 9 10

x/H

aleta n° 4aleta n° 2 aleta n° 3

rba=0,4 rba=0,2

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ❱rçã♦ ♦ ♣r ♦ ♦♥t trt♦ ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦ rba ♣r ♥♥çã♦ β = 90 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ ue = 3 m/s

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0rba=0,6 rba=0,4 rba=0,2

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Parede superior

Parede inferior

4 5 6 7 8 9 10

x/H

Cf x

aleta n° 4aleta n° 3aleta n° 2

aleta n° 4aleta n° 3aleta n° 2

rba=0,6 rba=0,4 rba=0,2

rr♥♦ s♥♦

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3rba=0,4 rba=0,2Parede superior

Cf x

4 5 6 7 8 9 10

x/H

aleta n° 2aleta n° 3

aleta n° 4

rba=0,4 rba=0,2

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ❱rçã♦ ♦ Cp ♣r s r♥ts r③õs ♦q♦ s ♦♠trs ♥ ♦♠ b = 2H ♦ rr♥♦ ♥♦ b = 2H ♦ rr♥♦ s♥♦ b = 3H♦ rr♥♦ ♥♦ b = 3H ♦ rr♥♦ s♥♦ ♥s três ♦♥çõs r♦♥â♠ss♠s

18 36 54 72 90

1

10

100

1.000

rba = 0,2

rba = 0,4

β ( )ue (m/s)

Cp/Cp

0

18 36 54 72 90

1

10

100

1.000

rba = 0,2

rba = 0,4

rba = 0,6

β ( )ue (m/s)

Cp/Cp

0

18 36 54 72 90

1

10

100

1.000

rba = 0,2

rba = 0,4

β ( )ue (m/s)

Cp/Cp

0

18 36 54 72 90

1

10

100

1.000

rba = 0,2

rba = 0,4rba = 0,6

β ( )ue (m/s)

Cp/Cp

0

100 101 102 103Cp/Cp0

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♦♠♣rt♦ ♦ Cp ♥tr ♦s ♦s rr♥♦s r♥ts r③õs ♦q♦ s♣ç♠♥t♦ ♥tr ts b = 2H ♥s três ♦♥çõs r♦♥â♠s ue

ue = 1m/s ue = 3m/s ue = 9m/s

1

10

100

1.000

♥♦rba = 0,4

rba = 0,2

β( )

Cp/Cp

0

1

10

100

1.000

s♥♦

rba = 0,4

rba = 0,2

β( )

Cp/Cp

0

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ❱♦rs Cp/Cp0 ♣r ♦ rr♥♦ s♥♦ r♥ts s♣ç♠♥t♦♥tr ts ♥s três ♦♥çõs r♦♥â♠s ue

ue = 1m/s ue = 3m/s ue = 9m/s

1

10

100

1.000

b = 2H rba

β( )

Cp/Cp

0

1

10

100

1.000

b = 3H rba

β( )

Cp/Cp

0

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r t rçã♦ ♦ s♦♠♥t♦ ♦ à rstrçã♦ ár rst♥t♣r ♦ â♥♦ ♥♥çã♦ t β = 18 ♣r ♦♠tr ♦♠ rba = 0,6 b = 2a t♦♣♦♦ ♦ s♦♠♥t♦ ♥ ♣rt ♥r♦r ♦ ♥

A = 0,4 H

0,00,544

1,091,632,182,713,263,804,344,885,435,986,517,067,60

u/ue

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♥s ♦rr♥t ♣r ♥r♦r ♦ ♥ ♦♥t♦r♥♦s t♠♣rtr♣r ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s♥♦ ♦♥rt ♣r ♦ s♦ ♦♠étr♦ b = 2H rba ♦♥çã♦ r♦♥â♠ ue = 3 m/s

β = 18 β = 18

β = 36 β = 36

β = 54 β = 54

β = 72 β = 72

β = 90 β = 90

0,000

0,069

0,138

0,207

0,276

0,345

0,414

0,483

0,552

0,621

0,690

0,759

0,828

0,897

0,966

1,000

T*

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♥s ♦rr♥t ♣r ♥r♦r ♦ ♥ ♦♥t♦r♥♦s t♠♣rtr♣r ♦ t♦ ♥♥çã♦ t ♥♦ ♦♥ sqr s♥♦ ♦♥rt ♣r ♦ s♦ ♦♠étr♦ b = 3H rba ♦♥çã♦ r♦♥â♠ ue = 3 m/s

β = 18 β = 18

β = 36 β = 36

β = 54 β = 54

β = 72 β = 72

β = 90 β = 90

0,000

0,069

0,138

0,207

0,276

0,345

0,414

0,483

0,552

0,621

0,690

0,759

0,828

0,897

0,966

1,000

T*

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♥♥çã♦ t rr♥♦ ♥♦ ♦♥ sqr rr♥♦ s♥♦ ♦♥ rt ♣r♦♠trs ♦♠ b = 2H rba = 0,4 ♦ rrê♥ ue = 3 m/s

β = 18 β = 18

β = 36 β = 36

β = 54 β = 54

β = 72 β = 72

β = 90 β = 90

0,000

0,068

0,137

0,208

0,277

0,346

0,414

0,483

0,552

0,621

0,690

0,759

0,828

0,897

0,966

Ts*

1,000

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦ rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦ s♥ ♦♥rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦ t rba = 0,4 ♥♥çã♦ β = 18

ue = 1 m/s ue = 1 m/s

ue = 3 m/s ue = 3 m/s

ue = 9 m/s ue = 9 m/s

0,000

0,149

0,212

0,277

0,339

0,402

0,465

0,528

0,591

0,654

0,717

0,780

0,843

0,906

0,969

Ts*

1,000

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦ rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦ s♥ ♦♥rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦ t rba = 0,4 ♥♥çã♦ β = 54

ue = 1 m/s ue = 1 m/s

ue = 3 m/s ue = 3 m/s

ue = 9 m/s ue = 9 m/s

0,000

0,149

0,212

0,277

0,339

0,402

0,465

0,528

0,591

0,654

0,717

0,780

0,843

0,906

0,969

Ts*

1,000

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♦♥t♦r♥♦s t♠♣rtr ♥♦ ♦♠í♥♦ só♦ ♣r ♦ t♦ ♦ rrê♥ ue ♦♥rçã♦ ♥ ♦♥ sqr ♦♥rçã♦ s♥ ♦♥rt ♣r ♦♠trs ♦♠ b = 2H r③ã♦ ♦q♦ t rba = 0,4 ♥♥çã♦ β = 90

ue = 1 m/s ue = 1 m/s

ue = 3 m/s ue = 3 m/s

ue = 9 m/s ue = 9 m/s

0,000

0,149

0,212

0,277

0,339

0,402

0,465

0,528

0,591

0,654

0,717

0,780

0,843

0,906

0,969

Ts*

1,000

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ❱rçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦♠ ♦ â♥♦ ♥♥çã♦ t β r③ã♦ ♦q♦ rba = 0,4 ♣r ♠♦s ♦s rr♥♦s ♥s ♦♠trs ♦♠s♣ç♠♥t♦ ♥tr ts b = 2H

0

100

200

300

0.08 0.10 0.12 0.14 0.16 0.18 0.20

18° 36° 54° 72° 90°

0

100

200

300

0.08 0.10 0.12 0.14 0.16 0.18 0.20

Parede superior

Parede inferior

Nu

x

4 5 6 7 8 9 10

x/H#2

4 5 6 7 8 9 10

x/H

#3 #4

# posição das aletas para β=18°

#2 #3

Nu

x

(β)

Pico de Nux

rr♥♦ s♥♦

0

50

100

150

200

0.08 0.10 0.12 0.14 0.16 0.18 0.20

18° 36° 54° 72° 90°Parede superior

Nu

x

# posição das aletas para β=18°

(β)

4 5 6 7 8 9 10

x/H#2 #3 #4

Platô de Nux

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ❱rçã♦ ♦ ♥ú♠r♦ sst ♦ Nux ♦♠ ♦ â♥♦ ♥♥çã♦ t β r③ã♦ ♦q♦ rba = 0,4 ♣r ♠♦s ♦s rr♥♦s ♥s ♦♠trs ♦♠s♣ç♠♥t♦ ♥tr ts b = 3H

0

50

100

150

200

250

300

350

0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26

18° 36° 54° 72° 90°

0

50

100

150

200

250

300

350

0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26

Parede superior

Parede inferior

Nu

x

#2 #3 #4

#2 #3

Nu

x

(β)

Pico de Nux

5 6 7 8 9 10 13

x/H

11 12

5 6 7 8 9 10 13

x/H

11 12

rr♥♦ s♥♦

0

50

100

150

200

0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26

18° 36° 54° 72° 90°Parede superior

Nu

x

# posição das aletas para β=18°

(β)

Platô de Nux

5 6 7 8 9 10 13

x/H

11 12

#2 #3 #4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 18 r③ã♦ ♦q♦ rba = 0,4 s♣ç♠♥t♦ ♥trts b = 2H

0

50

100

150

200

250

0.08 0.10 0.12 0.14 0.16 0.18 0.20

9 m/s

3 m/s

1 m/s

0

50

100

150

200

250

0.08 0.10 0.12 0.14 0.16 0.18 0.20

Parede superior

Parede inferior

4 5 6 7 8 9 10

Nu

x

aleta n°2 aleta n°3

aleta n°2 aleta n°3

aleta n°4

rr♥♦ s♥♦

0

100

200

300

0.08 0.10 0.12 0.14 0.16 0.18 0.20

9 m/s 3 m/s 1 m/sParede superior

4 5 6 7 8 9 10

Nu

x

aleta n°2 aleta n°3

x/H

aleta n°4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 54 r③ã♦ ♦q♦ rba = 0,4 s♣ç♠♥t♦ ♥trts b = 2H

0

100

200

300

400

500

600

0.08 0.10 0.12 0.14 0.16 0.18 0.20

9 m/s 3 m/s 1 m/s

0

100

200

300

400

500

600

0.08 0.10 0.12 0.14 0.16 0.18 0.20

Parede superior

Parede inferior

Nu

x

aleta n°2 aleta n°3 aleta n°4

4 5 6 7 8 9 10

x/H

aleta n°2 aleta n°3

aleta

rr♥♦ s♥♦

0

100

200

300

400

0.08 0.10 0.12 0.14 0.16 0.18 0.20

9 m/s 3 m/s 1 m/sParede superior

Nu

x

4 5 6 7 8 9 10

x/H

aleta n°2 aleta n°3 aleta n°4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ♥t♥sçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ ♦ rrê♥ ue ♣r ♥♥çã♦ β = 90 r③ã♦ ♦q♦ rba = 0,4 s♣ç♠♥t♦ ♥trts b = 2H

0

100

200

300

400

500

600

0.08 0.10 0.12 0.14 0.16 0.18 0.20

9 m/s 3 m/s 1 m/s

0

100

200

300

400

500

600

0.08 0.10 0.12 0.14 0.16 0.18 0.20

Parede superior

Parede inferior

4 5 6 7 8 9 10

x/H

aleta n°2aleta n°3 aleta n°4

aleta n°2 aleta n°3 aleta n°4

rr♥♦ s♥♦

0

50

100

150

200

250

300

350

0.08 0.10 0.12 0.14 0.16 0.18 0.20

9 m/s 3 m/s 1 m/sParede superior

Nu

x

4 5 6 7 8 9 10

x/H

aleta n°2aleta n°3 aleta n°4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦rba ♣r ♥♥çã♦ β = 18 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ue = 9 m/s

0

100

200

300

0.08 0.10 0.12 0.14 0.16 0.18 0.20

rba=0,2 rba=0,4 rba=0,6

0

100

200

300

0.08 0.10 0.12 0.14 0.16 0.18 0.20

Parede superior

Parede inferior

Nu

x

4 5 6 7 8 9 10

x/H

4 5 6 7 8 9 10

x/H

Nu

x

aleta n°3aleta n°2

aleta n°2 aleta n°3

rba=0,4rba=0,2 rba=0,6

aleta n°4

rr♥♦ s♥♦

0

100

200

300

400

0.08 0.10 0.12 0.14 0.16 0.18 0.20

rba=0,2 rba=0,4Parede superior

4 5 6 7 8 9 10

x/H

Nu

x

aleta n°2 aleta n°3

rba=0,4rba=0,2

aleta n°4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦rba ♣r ♥♥çã♦ β = 54 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ue = 9 m/s

0

100

200

300

400

500

600

0.08 0.10 0.12 0.14 0.16 0.18 0.20

rba=0,2 rba=0,4 rba=0,6

0

100

200

300

400

500

600

0.08 0.10 0.12 0.14 0.16 0.18 0.20

Parede superior

Parede inferior

Nu

x

4 5 6 7 8 9 10

x/H

4 5 6 7 8 9 10

x/H

Nu

x

aleta n°3aleta n°2

aleta n°2 aleta n°3

rba=0,4rba=0,2 rba=0,6

aleta n°4

aleta

n°4

rr♥♦ s♥♦

0

100

200

300

400

0.08 0.10 0.12 0.14 0.16 0.18 0.20

rba=0,2 rba=0,4Parede superior

4 5 6 7 8 9 10

x/H

Nu

x

aleta n°2 aleta n°3

rba=0,4rba=0,2

aleta n°4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r strçã♦ ♦ ♥ú♠r♦ sst ♦ ♦♠ ♦ ♠♥t♦ r③ã♦ ♦q♦rba ♣r ♥♥çã♦ β = 90 s♣ç♠♥t♦ ♥tr ts b = 2H ♦ rrê♥ue = 9 m/s

0

200

400

600

800

0.08 0.10 0.12 0.14 0.16 0.18 0.20

rba=0,2 rba=0,4 rba=0,6

0

200

400

600

800

0.08 0.10 0.12 0.14 0.16 0.18 0.20

Parede superior

Parede inferior

Nu

x

4 5 6 7 8 9 10

x/H

4 5 6 7 8 9 10

x/H

Nu

x

aleta n°3aleta n°2

aleta n°2 aleta n°3

rba=0,4rba=0,2 rba=0,6

aleta n°4

aleta n°4

rr♥♦ s♥♦

0

100

200

300

400

0.08 0.10 0.12 0.14 0.16 0.18 0.20

rba=0,2 rba=0,4Parede superior

4 5 6 7 8 9 10

x/H

Nu

x aleta n°2aleta n°3

rba=0,4rba=0,2

aleta n°4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ú♠r♦ sst ♦ ♠♦s ♦s rr♥♦s t ♣r s ♦♠trs♦♠ s♣ç♠♥t♦ ♥tr ts b = 2H ♦♥ sqr b = 3H ♦♥ rt

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

18 36 54 72 90

β ( ° )

Nu/N

u0

restrição da área de

escoamento

rba = 0,6

rba = 0,4

rba = 0,2

rr♥♦ s♥♦

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

18 36 54 72 90

β ( ° )

Nu

/Nu

0

restrição da área de

escoamento

rba = 0,6

rba = 0,4

rba = 0,2

rr♥♦ s♥♦

0.0

1.0

2.0

3.0

4.0

18 36 54 72 90

β ( ° )

Nu/N

u0

rba = 0,4

rba = 0,2

rr♥♦ ♥♦

0.0

1.0

2.0

3.0

4.0

18 36 54 72 90

β ( ° )

Nu/N

u0

rba = 0,4

rba = 0,2

rr♥♦ ♥♦

ue=1 m/s ue=3 m/s ue=9 m/s

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r r♥srê♥ ♦r ♥ ♥tr rçã♦ ♦ ①♦ ♦r t♦t ♠♥s♦♥ ♣r ♦ ♦r tr♦ trés s ts ♦♠ ♦ â♥♦ ♥♥çã♦ t β ♣r ♦s r♥ts s♣ç♠♥t♦s t b = 2H ♦♥ sqr b = 3H♦♥ rt

rr♥♦ s♥♦ rr♥♦ s♥♦

rr♥♦ ♥♦ rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r ❱rçã♦ rçã♦ ♦ ♦r tr♦♦ trés ♥tr ♦♠ ♦ â♥♦ ♥♥çã♦ t β ♣r ♦s s♦s ♦ s♣ç♠♥t♦ t b = 2H ♦ rrê♥ ue = 9 m/s

0

25

50

75

100

18 36 54 72 90

paredes

aletas

rba=0,2

rba=0,4

rba=0,6

rba=0,2

rba=0,4

rba=0,6

β (°)

Fra

ção

de

calo

r (%

)

rr♥♦ s♥♦

0

25

50

75

100

18 36 54 72 90

paredes

aletas

β (°)

Fra

ção

de

calo

r (%

)

rba=0,2

rba=0,4

rba=0,2

rba=0,4

rr♥♦ ♥♦

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r

♥

ê♥

♦

rrê♥

u

e♥

str

çã♦

tr♦

tér♠

tré

s

♥tr

♥♦

♦rtr♥

sr♦t♦t

♠

♥s♦♥

♣

r♦s

rr♥♦s

t

s♥

♦

s♣

r♦r

♥

♦♥r♦r

β=18

β=54

β=90

β=18

β=54

β=90

♦♥t

♣r♦

çã♦

♦♣r

ó♣r♦

t♦r

♥ê♥ r③ã♦ ♦q♦ t

r é ♣♦ssí ♦srr ♦ t♦ s r③õs ♦q♦ ♣s ♣r

t♣♦ rr♥♦ s♦r tr♦ tér♠ t♦t s strçã♦ ♥tr s♣rí

♣r s♣rí t srs q st r ♦ ♦♥strí ♦♠ ♦s rst♦s

♣r s ♦♠trs ♦♠ s♣ç♠♥t♦ ♥tr ts b = 2H ♣r ♦ rrê♥

ue = 9 m/s♦ rr♥♦ s♥♦ q ♣♦ss três rçõs rba ♦ ♠♦r ♥r♠♥t♦

♥♦ ♦r tr♥sr♦ ♣s ts ♦♦rr ♣r ♦ ♠♥♦r â♥♦ ♥♥çã♦ r

q♥♦ r③ã♦ ♦q♦ t é ♠♥t ♣r Pr st

rr♥♦ ♥ ♦ ♦r t♦t ♠♥s♦♥ r ♠ ♦ ♦r♦ q♥♦ s r

r③ã♦ ♦q♦ t ♣r β = 90 r

♥tr s s r③õs ♦q♦ t ♦♥rçã♦ ♥ ♦ ♠♥t♦

♣r ♦r tr♥sr trés s ts ♦ ♠♥♦r ♣♦ré♠ t♠é♠ ①♣rss♦ té

♣r β = 18 r ♠♦r ♠♥t♦ ♦ ♦r tr♦♦ ♣s ts ♦

♦sr♦ t♠é♠ ♣r ♦ s♦ ♠♥♦r â♥♦ ♥♥çã♦

P♦rt♥t♦ ♦♥stts q ♠♥r ♥♣♥♥t ♦ rr♥♦ ♦ ♠♥t♦

r③ã♦ ♦q♦ rst ♠ ♠♥t♦ tr♦ tér♠ t♦t ♣r t♦s s ♥♥çõs

t

r

t♦

r③ã

♦

♦q

♦

trb as♦r

♣

r

♦rtr♦

tré

s

sts

s♦r

♦

♦rtr♥

sr♦t♦t

♠

♥s♦♥

♣

r♠

♦s♦s

rr♥♦s

♦♠trs

♦♠b=2H

β=18

β=54

β=90

β=18

β=54

β=90

♦♥t

♣r♦

çã♦

♦♣r

ó♣r♦

t♦r

♦♠♣rt♦s s q♥ts ♦s

♦♠ ♦ ♦t♦ r♦♥r ♣r s♦ ♠♦r tr♥t ♥tr ♦s

s♦s ♣rs♥t♦s ♣r ♠ ♠s♠ r③ã♦ ♦q♦ t rba s r③õs ♥tr s

q♥ts ♦s ♦s r♥ts rr♥♦s sã♦ ♣rs♥ts ♥s s

s r③õs sã♦ ♥s ♦♠ q♥t ♦ ♦ rr♥♦ ♥♦ ♥♦ ♥♠r♦r

s ♦ ♥ú♠r♦ sst Nualinhado ♦ ♦ ♦♥t ♣rssã♦ Cpalinhado s

s ♣rs♥t♠ r③ã♦ ♣r ♦ ♦♥t ♣rssã♦ s s

♣r ♦ sst ♦ ♠s s r③õs ♦q♦ t rba = 0,2 rba = 0,4Prs q ♠♥r r s q♥ts ♦s sã♦ ♠♦rs ♣r ♦ rr♥♦

♥♦ ①t♦ ♣r ♦ ♥ú♠r♦ sst ♦s ♦s ♠♦rs â♥♦s ♥♥çã♦ t

♥♦ s♣ç♠♥t♦ b = 2H ♦♥♦r♠ st ♦r♠ ♣r st rr♥♦ ♥♦♥tr

s ♠♦r s♠♣♥♦ tér♠♦ ♥ ♠♦r ♣rt ♦s s♦s ♣♦ré♠ t♠é♠ ♠♦r ss♣çã♦

♥r ♠â♥ ♦♥sr♥♦ ♦ s♠♣♥♦ tér♠♦ ♣r ♦ s♣ç♠♥t♦ b = 2H t♥ê♥ ♦sr é q ♠♥♦rs â♥♦s ♥♥çã♦ ♦r♠ ♦

rr♥♦ ♥♦ té ♣♦r ♦t β = 54 ♦♠ ♦ ♠♥t♦ ♦ s♣ç♠♥t♦ ♥tr ts

r♥ç ♠é ♦♥sr♥♦ ♦ sst ♦ rr♥♦ ♥♦ é ♠♦r

♣r t♦s s ♥♥çõs t ♥t♦ ♦ s♠♣♥♦ rá♦ s

♦ rr♥♦ ♥♦ ♣rs♥t ♠♦r ♣r r ♣r t♦♦s ♦s s♦s

♥♦s ♠♥r ♣♦♥t ♦ ♠♦r s♠♣♥♦ tér♠♦ ♠é♦ ♣r ♦

rr♥♦ ♥♦ r♥t ♦ s♥♦ ♦rrs♣♦♥ rba = 0,4 β = 18 ♣r ♦ s♣ç

♠♥t♦ ts b = 3H st s♦ ♦ s♠♣♥♦ ♦ rr♥♦ ♥♦ é

r ♠♦r q ♦ s♥♦ P♦ré♠ ♦rrs♣♦♥♥t ♣r r é

♠♦r ♣r ♦ rr♥♦ ♥♦

Pr ♦ rr♥♦ s♥♦ ♦ ♠♦r s♠♣♥♦ tér♠♦ ♦sr♦ ♥♦♥trs

♥ ♣r rba = 0,4 β = 90 ♠s q r③ã♦ ♦ sst ♦ é

♠♦r ♣r ♦ rr♥♦ s♥♦ P♦r ♦tr♦ ♦ ♥♦ts q ♣r st s♦ ♦♠étr♦

ss♣çã♦ ♥r ♠â♥ ♠é é r ♠♥♦r ss♠

sts q t♥t♦ ♦ s♠♣♥♦ tér♠♦ q♥t♦ ♦ rá♦ sã♦ ♦rás ♣r

♠s♠ ♦♥rçã♦ ♦♠étr

③ã♦ ♦ ♦♥t ♣rssã♦ Cpdesalinhado/Cpalinhado r♥ç ♠é♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 2H

β ❭ue ♠s ♠s ♠s r♥ç

rba = 0,2

rba = 0,4

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

③ã♦ ♦ ♦♥t ♣rssã♦ Cpdesalinhado/Cpalinhado r♥ç ♠é♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 3H

β ❭ue ♠s ♠s ♠s r♥ç

rba = 0,2

rba = 0,4

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

③ã♦ ♦ ♥ú♠r♦ sst Nudesalinhado/Nualinhado r♥ç ♠é♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 2H

β ❭ue ♠s ♠s ♠s r♥ç

rba = 0,2

rba = 0,4

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

③ã♦ ♦ ♥ú♠r♦ sst Nudesalinhado/Nualinhado r♥ç ♠é♦♠ rçã♦ ♦ rr♥♦ ♥♦ ♣r s♣ç♠♥t♦ ♥tr ts b = 3H

β ❭ue ♠s ♠s ♠s r♥ç

rba = 0,2

rba = 0,4

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

❯Õ PP❱ ❯❯

s♦♠♥t♦ tr♥t♦ ♣r♠♥♥t ♠é♦ ♠ ♦ ♥t♦♥♥♦ ♠ ♥s

♦r③♦♥ts ♠♥s♦♥s ♦♠ ts ♣♥s tr♥srs♠♥t ♥♥s s♣♦sts

♦r♠ ♥ ♦ s♥ ♦ st♦ trés s♠çã♦ ♥♠ér ♠

♣r ♥ t③♦s ♠ ♦♥♥t♦ ♦♠♣♦st♦ ♣♦r ♥♦ ts ❯♠ ③ q ♠s

s ♣rs ♦ ♥ ♠ ♦♠♦ s ts ♣rs♥t♠ s♣ssrs ♣rétr♠♥s sã♦

♦♥t♦rs tr♥srê♥ ♦r ♦♥ ♦ ♠ ♦♥srçã♦ s t♦s

♣rs♥ç s ts t♥t♦ ♥♦ s♣t♦ r♦♥â♠♦ ♦ s♦♠♥t♦ q♥t♦ ♥♦ tér♠♦

♦r♠ ♥st♦s ♦r♠ ♦ t♠é♠ ♥ ♦r♠ ♦rs ♠é♦s ♦ ♦s

P♦r ♠♦ ♠ çã♦ ♣ré à ♦♥strçã♦ ♦s s♦s ♦ ♣r♦♠ ♦ st

tr♦ ♦♥stt♦s ♣ ♦ ♣r♦r♠ ♦♠r CFX ♠ ♦♠♦ ♦ ♠♦♦

trê♥ ♣r s♦çã♦ ♦ ♣r♦♠ ♦s ♥s t♦s srt③çã♦ ♣♦r

♠♦ ♦ ♠ét♦♦ ♦♠s ♥t♦s s♦ ♠ ♠♥t♦s ❱ ♦ r ♣r

s♦çõs ♦ ♦ ♥ú♠r♦ t♥t♦♥ ♥r ♥ét tr♥t ♣♦r ♠♦

♦ ♦♠♣rt♦ ♦♠ ♦trs ♣rsõs ♥♠érs ①♣r♠♥t♦s s♣♦♥ís ♥ trtr

♠♦♦ trê♥ ♠♦♥str♦ ♦ rá ♣r s♦çõs ♦

tr♥srê♥ ♦r ♠ s♦♠♥t♦s ♦♠ r♥t ♣rssã♦ rs♦ ♠ ♦♠♦ ♣r

♦ ♣r ♥r ♥ét tr♥t ♠ ♠ ♥ ♣♥♦

♠♥r r ♦♥stt♦s q ♥srçã♦ ts tr♥srss ♠ ♥s

♣rs♥t ♠ ♣♦t♥ ♦♥srá ♣r ♠♥tr tr♥srê♥ ♦r st♦ s

♠ ♦ ♣rt ♣ ♥t♥sçã♦ s q♥ts tr♥ts st♦ é s ♣r♦♣rs ♦

s♦♠♥t♦ ♦♠♦ s♦s tr♥t ♦♥sq♥t♠♥t ♦♥t tér♠

tr♥t P♦r ♦tr♦ ♦ ♦r♦ ♦♠ ♠♦♠ tçã♦ ♦s

♣rs♥t ♥♦s s♦♠♥t♦s tr♥t♦s ♣rs♥ç s ts ♦ ♠♥t♦ ♣rssã♦

t ♦ q ♠♣ ♠ ♠♦rs ①s ♣rssã♦ ♦♣rçã♦ ♦ q♣♠♥t♦

♥ê♥ ♠s s♥t ♦s ♣râ♠tr♦s ♦♠étr♦s ♦ r③ã♦ ♦

q♦ t s ♦ â♥♦ ♥♥çã♦ t ♣♦r ♠ ♦ s♣ç♠♥t♦ ♥tr

ts sqê♥ t♠s s ♦♥sõs ♣♦♥ts ♦s ♣r♥♣s rst♦s

❼ s q♥ts ♦s

♦ às rq♥ts ♠♥çs rçã♦ ♦ s♦♠♥t♦ ♣r♥♣ ♦♠ ♦♦rrê♥

♦ r♦♠♥t♦ ♥♦ tr♦ ♥tr s ts s ♠♦rs rçõs ♥s q♥ts

♦s Cfx Nux ♦r♠ ♦srs ♣r ♦ rr♥♦ s♥♦ rã♦ ♦♥

♦♦rr ♦ r♦♠♥t♦ ♦ rtr③ tr♠♠♥t ♣♦r ♠ ♠♥t♦ r♣♥t♥♦

tr♥srê♥ ♦r ♦ ♣♦ Nux r♦♥♠♠♥t ♣♦r ♠ rçã♦

♥ ♦ ♥t♦ à ♣r ♣♦♥t♦ st♥çã♦ ♦♠ Cfx ♥♦

♦♠ ♦ s♦ ♦ ♦♥t trt♦ s♣r ♥t♦s ♦s ♠♥s♠♦s st♥

t♦s q rst♠ ♥s ♣rs ♥r ♠â♥ ♦s ♥♦ tr♦ ♥ t♦

s rõs rrçã♦ Cfx ♥t♦ ♥r ♠â♥ ♦ s♦♠♥t♦ ♣r♥

♣ é ♠♥í ♣ çã♦ ♦ s♠♥t♦ st ♦♠ ♦s órts ♦r♠♦s ♣♦r

♦sã♦ ♦ s s♦♠♥t♦ ♣♦ré♠ ①st♠ tr♦s ♣r ♥ ♦♥

♥r ♠â♥ é ♠♥í ♦ s♦♠♥t♦ ♣ çã♦ s♥t ♦r♠ rt

♦♠ s ♣rs Cfx ♣♦st♦ srs q ♠♦r ♥ã♦ t♥ s♦ ♦♠♥t

q♥t♦ st rrst♦ ♣♦r trt♦ s♣r ♦♦rr t♠é♠ ♥s s ♣♦♥ts

s ts

♦♠ s ♥ t♦♣♦♦ s♦♠♥t♦ ♣rs q ♦♦rr ♦ ♠♦ s♦

♠♥t♦ ♣rtr s ♣♦♥ts s ts sr♥♦ rõs ♦ rr♥t

s♥t s ♠s♠s sqê♥ ♦ s rs♦ ♦ s♦♠♥t♦ ♣r♥♣ té ♦

♣♦♥t♦ r♦♠♥t♦ ♦♥ rt♦♠ ♦ ♦♥tt♦ ♦♠ ♠ s♣rí ♦ ♥ t

♦ ♣r s rõs rrçã♦ r♦♠♥t♦ sã♦ s q ♣rs♥t♠ s

♠♦rs ♥trrê♥s ♥ tr♥srê♥ ♦r ♦ s ③♦♥s rrçã♦

♣♦rçã♦ ♦ rr♥t t♥ s ♦♠♦♥③r tr♠♠♥t ♦♠ ss♦

①♦s r♥ts t♠♣rtr sã♦ ♥♦♥tr♦s ♥sts ♦s P♦r ♦tr♦ ♦

♥ rã♦ ♦ r♦♠♥t♦ ♦ s♦♠♥t♦ ♣r♥♣ ♦s r♥ts tér♠♦s sã♦ s

♥t♦s ♣♦s ♠s s ♠s ♠ts stã♦ ♠ r♦♥strçã♦ srs q

♠♦♥t♥t s ts ♥t♦ às ss ss t♠é♠ ♦♦rr ♦r♠çã♦ rrçã♦

♣♦ré♠ s ♥ê♥ s♦r ♦s rst♦s é ♠♥♦s s♥t

❼ s q♥ts ♦s

❯♠ ♦♥sã♦ ♥trss♥t rt ♣r s q♥ts ♦s Nu Cp é q

♦ rr♥♦ ♥♦ ♥ã♦ ♣rs♥t♦ s♥s ♦♥srá ♥tr ♦s r♥ts â♥

♦s ♥♥çã♦ ♥♣♥♥t r③ã♦ ♦q♦ t t③ P♦ré♠

♥♦ rr♥♦ s♥♦ q♥t♦ ♠♦r ♦ â♥♦ ♥♥çã♦ ♠♦r ♦ ♦♥t

♣rssã♦ t♠é♠ ♦ ♥ú♠r♦ sst ♠é♦ ♥♦♥tr♦ t♦ q é ♣♦t♥

③♦ ♣r ♠♦rs r③õs ♦q♦ ♦♥t♦ ♣r r③ã♦ ♦q♦ rba = 0,6①s ♣r ♦ rr♥♦ s♥♦ ♦ ♥♦♥tr ♠ ♥rsã♦ ♥st t♥ê♥

st♦ é ♦s ♠♥♦rs â♥♦s ♥♥çã♦ ♥ã♦ ♦r♠ ♦s q ♣rs♥tr♠ s ♠♥♦rs

q♥ts ♦s Nu Cp ♦♥stt♦s q st ♦♦rrê♥ s à ♦r♠

çã♦ t③ ♥ rçã♦ s ♦♠tr q ♣r♦③ ♠ rstrçã♦ ár ♠♦r

♦ q ♠♣♦st ♣ r③ã♦ ♦q♦ ts

♠♥r ♦ s ♣rs ♥r ♠â♥ ♦ s♦♠♥t♦ ♦♥srr♠

♦ t♦ ♦ rrst♦ s♦s♦ q ♦♦rr ♥s s♣rís sós ♣rs ts

♥tr♥♠♥t ♦ ♦ ♥s Pr t♥t♦ t③♦s ♦ ♦♥t ♣rssã♦

Cp q ♦ tr♠♥♦ ♣r ♦ tr♦ ♥ ♥tr sçã♦ ♥tr ♠

sçã♦ x = 30H ♦ ♦ ♥♠♥t♦ s ts ♦ ♦♥t ♣rssã♦ Cp

♣r ♦ rr♥♦ ♥♦ ♦ s♣r♦r ♦ ♦s s♦s rr♥♦ s♥♦ té r

③s ♣r rba = 0,4 b = 3H ♦♥t♦ ♦s ♠♦rs ♦rs Cp sã♦

♥♦♥tr♦s ♣r ♠♦r r③ã♦ ♦q♦ ♦♥rçã♦ s♥ Pr ♦

t♦ s ♦♥çõs ♦♥t♦r♥♦ r♦♥â♠s á ♠ rçã♦ qrát ♥tr

rçã♦ ♦ ♥tr ♥♦ ♥ ♦ rs♣t♦ Cp ♦

♦r♠çã♦ ♦ ♥ú♠r♦ sst ♦ ♣r ♦ s♦♠♥t♦ ♦ ♦r ♣r

r ♠ ♦♥srçã♦ ♦ t♦ ár s♣r tr♦ tér♠ s ts ♦♥

sr♥♦ s r③õs ♦q♦ t ♦♠♥s ♦s ♦s rr♥♦s rba = 0,2

rba = 0,4 ♦♥rçã♦ ♥ ♣rs♥t♦ ♠ s♠♣♥♦ r s♣

r♦r P♦ré♠ sts q ♦s ♠♦rs ♦rs ♥♦♥tr♦s ♣r ♦ sst ♠é♦

♦r♠ ♣r ♦♥rçã♦ s♥ ♥ r③ã♦ ♦q♦ rba = 0,6 rçã♦

s ♦♥çõs r♦♥â♠s rst ♠ ♠♥t♦ té ♦ sst ♠é♦

❼ tr♥srê♥ ♦r ♦♥

çã♦ tr♦ tér♠ ♦r♠ ♦♥ ♣r♠t r ♦s r♥ts

t♦s s rçõs ♦♠étrs r♦♥â♠s s♦r strçã♦ t♠

♣rtrs ♥♦ ♦♠í♥♦ só♦ ♥s s rst♦s ♥ ♦r♠ ♦♥t♦r♥♦s

t♠♣rtr ♠♦strr♠ ♦ ♠s♠♦ ♦♠♣♦rt♠♥t♦ ♣r ♠♦s ♦s rr♥♦s ♠♦rs

rçõs tér♠s sã♦ ♦srs ♥s ts ♦♠ ♠♥çã♦ ♦ â♥♦ ♥

♥çã♦ β → 0 ♦♠ ss♦ ♦s r♥ts tér♠♦s q ♣r♠ ♥s ♣rs s

♦♥♥tr♠ ♥s ♣r♦①♠s s ss s ts Pr stçã♦ ♦♥trár ♥s

qs s ts ♣rs♥t♠ ♠♦rs â♥♦s ♥♥çã♦ ♦s r♥ts t♠♣

rtr sã♦ ♠s ♦♠♦ê♥♦s ♦ ♦♥♦ s ♣rs ♦ ♥

♦♠♦ ♠ ♦s ♣r♥♣s rst♦s ♣♦ssís ♥ç♦s s♦♠♥t trés ♥ás

tr♥srê♥ ♦r ♦♥ ♥♦♥tr♦s q tr♦ tér♠ trés s

ts é ♠ ♠é ♠♦r ♥♦s s♦s ♦ rr♥♦ ♥♦

t♥ê♥ srt ♠ ♦ r ♣r ♦s rst♦s q q♥tr♠

♣r ♦ ♦r t♦t tr♦♦ trés s s♣rís s ts trés ♦s qs

s ♦♥stt♦ q q♥t♦ ♠♥♦r ♦ â♥♦ ♥♥çã♦ β → 0 ♠♦r ♥ê♥

s ts ♥ tr♦ tér♠ ♦ st ♦rrçã♦ é t q ♣r ♦ ♠♥♦r â♥♦

♥♥çã♦ t β = 18 ♦ rr♥♦ s♥♦ ♠s ♠t ♦ ♦r

tr♦♦ ≈ 67% ♦♦rr trés s ts ♣r rba = 0,6♦♠ s ♥s q♥ts ♦s ♥ás ♣♦r ♠♦ s r③õs ♦ ♥ú♠r♦

sst ♦ ♦♥t ♣rssã♦ ♥tr ♦s rr♥♦s ♥ ♠ ♣rá rçã♦ ♥tr

s♠♣♥♦ tér♠♦ r♦♥â♠♦ ♣r ♦ rr♥♦ s♥♦ ♦♠ ♠♥♦r s♣ç♠♥t♦

♥tr ts ♠♦rs â♥♦s ♥♥çã♦ t ♥♠♥t ♥t ♦ ♣♦t♥

♦♥stt♦ ♦ s♦ ts ♣r ♦ ♥r♠♥t♦ ♥♦ ♣r♦ss♦ tr♥srê♥ ♦r

♠ ♥s ♦♠♥tár♦s s♦r ♣rs♣ts trs sr stã♦ ♦♠♥t♦s ♥s

s♣t♦s q ♣♦♠ sr ①♣♦r♦s

❼ s♣t♦s ♦♠étr♦s

é♠ s rtrísts ♥sts ♥st tr♦ srs ①♣♦rr ♦ t♦

r♥ts trçõs ♦♠étrs ts ♦♠♦ r♥ts s♣ç♠♥t♦s ♥tr ts

r♥ts trs t ♦r♠ ♥♣♥♥t r③ã♦ ♦q♦ t

♥s r♥ts ♦r♠t♦s t s ♥ã♦ ♣rs sts ♣râ♠tr♦s

♣♦♠ trr t♦♣♦♦ ♦ s♦♠♥t♦ ♦r♠ s♥t t♥♦ ♦r♠

çã♦ s ③♦♥s rrçã♦ ♦③çã♦ ♦s ♣♦♥t♦s r♦♠♥t♦ ♦♥♦r♠

♣rs♥t♦ ♥ sçã♦ ♦s rst♦s st♦ ♠♣ ♠ ♠♦çõs s♥ts ♥

strçã♦ t♠♣rtrs t♥t♦ ♦ só♦ q♥t♦ ♦ ♦ tr♥t♠♥t

sts ♠s ♦♠étrs ♣♦♠ sr rs ♥tr♦ ♠ ♠s♠♦ s♦ ♣♦r ①♠

♣♦ t③♥♦ t♠♥♦s t rás ♦ ♦♥♦ ♦ ♥ sts q ♥tr

♦tr♦s ♣♦ssís s♣t♦s ♦♠étr♦s rçã♦ s♣ssr t ♥ã♦ ♣rs♥t

♣♦t♥ ♥♦tá ♦r♦ ♦♠ ♦s rst♦s Prã♦ t

❼ s♣t♦s ♥s♦tró♣♦s

é♠ s rtrísts ♦♠étrs srs ♥stçã♦ r♥ts ♠trs

♦♥strçã♦ ♦ tr♦♦r ♦r r♥ts ♣çõs ♠ ♠♦s ♦s s♦s á

♣♦ss ♦♥srr ♣♥ê♥ s ♣r♦♣rs tér♠s ♦♠ ♦ ♠♣♦

t♠♣rtrs ♥s♦tr♦♣ t♥t♦ ♣r ♦ só♦ q♥t♦ ♣r ♦ ♦ ♠♣♥♦

r♥ç t♠♣rtrs s ♦♥çõs ♦♥t♦r♥♦ ♦♠ rçã♦ à ♥s♦tr♦♣

♥ t♠s ♣♦ss tr♠♥r ♦s t♦s ♦ tr♥s♣♦rt s q♥ts

tr♥ts ♦r♠ ♥s♦tró♣ ♣♦r ♠♦ ♦ ♦♦ ♥sõs ②♥♦s ♦

♦ ♥ês ②♥♦s trss ♦ ♣♦r ①♠♣♦ srs q ♣r ♦

s♦ ♦ s♦ ♦ ♠♦♦ rqr çã♦ st qçõs tr♥s♣♦rt

♠s♠ ♦r♠ q ♦♥srçã♦ ♦s t♦s ♦ à ♥s♦tr♦♣ ♦♥srçã♦

♣r♦tót♣♦s rts ♠ t♠é♠ ♥rq ♥ás rá ♦s rst♦s

❼ s♣t♦s tr♠♥s♦♥s

♦♠♦ ♦♥sê♥ ♣óts ♠♥s♦♥ ♦ s♦♠♥t♦ ♦ s♠♣♦ ♣r

çã♦ ♦ s♦♠♥t♦ ♣r♥♣ st♦ é s♣r③r♠s ♦s t♦s ♦s s♦♠♥t♦s

s♥ár♦s ♥trçã♦ ♦ ♦ ♦♠ s ♣rs trs ♦ ♥ rs♥tr

rtrísts ♠s r♣rs♥tts trê♥ q é ♥tr♠♥t ♠♦r

tr♠♥ trés ♦r♠çã♦ ♠t♠át tr♠♥s♦♥ ♠♥t♦ s

rás ♦ ♣r♦♠ t♦r♥ ♦ s♦ ♦t♠③çã♦ ♠ ♦♣çã♦ ♥ ♠s ♣r♦♠ss♦r

❼ s♣t♦s ót♠♦s

♦ ♦ r♥ ♥ú♠r♦ rás ♥♦s ♥♦ ♣r♦t♦ tr♦♦rs ♦r

♦ às rtrísts ♦♥ô♠s ♣çã♦ ♦ tr♠♥çã♦ ♦♠tr

♦♥çõs ♦♣rçã♦ ót♠ rqr t③çã♦ té♥s ♦t♠③çã♦ ét♦

♦s ♦t♠③çã♦ ♦♥sst♠ ♥ tr♠♥çã♦ ♣râ♠tr♦s ♦ ♣r♦♠ trés

♠♥♠③çã♦ ♠ ♥çã♦ st♦ ♥ ♣rtr ♠s tr♦

♦r ♣r r rçã♦ ♥tr♦♣ st♦ ♦♥ô♠♦ ♠ss t♦t ♦ tr♦♦r

♦r ♦ ♦tr♦ ♣râ♠tr♦ rtríst♦ ♣çã♦ s á ♠ r♥

r strtés ♦t♠③çã♦ ♥tr s ♠ét♦♦s s♦s ♠ r♥t

r ♥çã♦ st♦ ♠ rçã♦ às rás ♥trss ♠ét♦♦s ♥s♣r♦s

♥ ♥tr③ ts ♦♠♦ ♦s ♦rt♠♦s ♥ét♦s ♠ét♦♦s s rt st

♦r♠ srs ♦♠♦ tr♦ s♥♦♠♥t♦ ♦ st♦ ♣çã♦ strtés

♦t♠③çã♦ st ss ♣r♦♠s

srs q é♠ strté st♦ ♦t ♣r sr tr♦♦rs

♦r ♦♠ ♠♦r s♠♣♥♦ é r♦♠♥á ♦tr ♠ t♦r q ① ♥tr

♠♦r ♦♥rçã♦ ♠♦r ♣r♥♣ ♠♦tçã♦ s ♥♠ ♣r♠r♦ ♠♦♠♥t♦ ♦

♠♥t♦ tr♥srê♥ ♦r ♦r♠çã♦ ♠ t♦r q♦ ♥ çã♦

♥♦♦s tr♦♦rs ♦r ♣♦rá r ♠ ♦♥srçã♦ ♦tr♦s s♣t♦s ♦♠♦ ♦s

rçã♦ ♦♣rçã♦ ♠♥t♥çã♦ t

s♣t♦s ♥â♠ ♦s ♦♠♣t♦♥

Pr ♦tr s♦çã♦ ♣r♦♠s ♣rát♦s ♥♥r ♥♦♥♦ ♦ s♦♠♥t♦

♦s ♠ ♦r♠ ♥♠ér sr ♦t ♥ q s qçõs r♥s ♦

♣r♦♠ sã♦ ssttís ♣♦r ♣r♦①♠çõs érs rs♦s t③♥♦s ♠

♠ét♦♦ ♥♠ér♦ ❯♠ ③ q ♥st tr♦ t③♦s ♠ ♣r♦r♠ ♦♠r ♦s t♥s

s♥ts t♠ ♣r rtr③çã♦ s ♣r♥♣s ♥çõs ♣s à rr♠♥t

t③ ♥ s♦çã♦ ♦ ♣r♦♠ s♠♥t

rçã♦ ♠ ♥♠ér

t③çã♦ ♠ ♠ ♦♠ qs ♦♠étrs qs é ♣rt ♥

♠♥t ♥♦ ♦♥tr♦ ♦s rr♦s srt③çã♦ ♠♥t ♠♣♦rt♥t ♣r tr rr♦s

rr♦♥♠♥t♦ r♥t ♣♦r ①♠♣♦ s♦çã♦ s qçõs ♥rs q sã♦ ♦ts

♣♦ ♣r♦ss♦ srt③çã♦ ❩ P st tr♦ t③♦s ♦

r♦r ♠s ♥s②s s♥ ♣r t♦♦s ♦s s♦s

r stã♦ strs três ♦♥srçõs áss sttíst ♠

♣r ♦ CFX rs ♣♦ ó♦ ♥♠ér♦ ♣r♠♥t à ①çã♦ ♦ ♦rt♠♦

s♦çã♦ ♦ sst♠ ♥r ♦♥♦r♠ str♦ t♠s

❼ q ♦rt♦♦♥ ♥♦ s♦ r q ♦rt♦♦♥ ♣r ♠ ♠♥t♦ é ♦♠

♣t t③♥♦ ♦ t♦r ♥♦r♠ Ai ♦ t♦r q ♥ ♦s ♥trós

♠♥t♦s ♥ts ci ♦ t♦r q ♥ ♦ ♥tró ♦ ♠♥t♦ ♦ ♥tró

♠ ss s fi s q♥ts ♦♠♣ts ♣r sã♦ ♦

♦ss♥♦ ♦ â♥♦ ♥tr ♦ t♦r Ai ♦ t♦r ci ♦ ♦ss♥♦ ♦ â♥♦ ♥tr ♦ t♦r

Ai ♦ ♦ t♦r fi ♦r ♠í♥♠♦ ♦t♦ ♦ á♦ sts q♥ts ♣r t♦s

s s é ♥♦ ♦♠♦ q ♦rt♦♦♥ ♦ ♠♥t♦ s ♣♦rs ♠♥t♦s

♠ sã♦ ♦s q ♣rs♥t♠ st ♠étr ♣ró①♠ ③r♦ ♥q♥t♦ q ♣r ♦s

♠♦rs q ♦rt♦♥♦ é ♣ró①♠ ♠ P♦rt♥t♦ ♦ ♦♥t♦ ♦rt♦♦

♥ ♠ stá r♦♥♦ ♦ q♥t♦ ♦s â♥♦s ♥tr s s ♥ts

♠ ♠♥t♦ ♦ r♦♥trs ♥tr ♠♥t♦s ♥ts s ♣r♦①♠ ♦ â♥♦

ót♠♦ 90 ♣r ♠♥t♦s qrtrs ❨

❼ t♦r ①♣♥sã♦ ♦ ♦♥t♦ ①♣♥sã♦ ♠ stá r♦♥♦ ♦♠ t①

♠♥ç ♥ ♠♥t ♦s ♦♠s ♦ s árs ♠♥t♦s ♥ts

♠ ♠s r♥t ①♣♥sã♦ ♠ ♣r ♦ CFX♥♦ r③ã♦ ♥tr

stâ♥ ♠á①♠ stâ♥ ♠í♥♠ ♥tr ♦ ♥ó ♦ ♦♠ ♦♥tr♦ s ss

r♦♥trs ❯♠ ♦r♠çã♦ tr♥t é t③ ♥♦ s♦ ♦♠s ♦♥tr♦

r s ♦♠étrs r♥ts ♣r ♦ CFX rs ♥ts ①çã♦♦ ó♦ ♥♠ s♠çã♦ ♥♠ér

q ♦rt♦♦♥

A3

A1 A2

c2

c3

c1

f1

f2f3

t♦r ①♣♥sã♦

dmin

dmax

volume mín.

do setor

volume máx.

do setor

r③ã♦ s♣t♦

Amin

Amax

♦♥t ♣t♦ ❨

♦r♠s rtrárs q é r③ã♦ ♥tr ♦ ♠á①♠♦ ♦ ♠í♥♠♦ ♦♠s ♦s ss

st♦rs ❨

❼ r③ã♦ s♣t♦ ♦ str♠♥t♦ ♦ ♦♥t♦ r③ã♦ s♣t♦ ♠ stá

r♦♥♦ ♦♠ ♦ r q ♦s ♠♥t♦s ♠ sã♦ str♦s ♠ ♠s

r♥t q♥t♦ à r③ã♦ s♣t♦ ♠ ♣r ♦ CFX ♥♦ r③ã♦ ♥tr

♠á①♠ ♠í♥♠ árs s♣rs ♦♠ rçã♦ ♦s ♣♦♥t♦s ♥trçã♦ ❨

é♠ ♠♣♦rtâ♥ ♦ q ♠ é ♥ssár♦ ssrr ♥♣♥

ê♥ s♦çã♦ ♥♠ér ♦♠ rçã♦ à ♠ st♦ é r③♦ ♣♦r ①♠♣♦ trés

♦ st♦ r♥♦ ♠ Pr t♥t♦ r③s ♠ sqê♥ s♦s ♦♠ rçã♦

♥♦ ♥ú♠r♦ ♦s ♠♥t♦s ♠♥t♦ ♦ ♥í r♥♦ ♠

tr♦ s♣t♦ ♥♠♥t râ♥ ♣r rçã♦ s ♠s ♥♦s s♦s

♦♥â♠ ♦♠♣t♦♥ é ♦ ♥í ♦ r♥♠♥t♦ ♥s rõs ♥t♦ às s♣rís

st ♣r♦♠♥t♦ s ♦s rr♦s tr♥♠♥t♦ ①ê♥s ♦ ♠♦♦ trê♥

t③♦ ♦ s♦ ♣r ♦ ♠♦♦ trê♥ s♦♦ ♦ r♥♦ ♠

♦r à ♦♥çã♦ y+ < 1,0

ét♦♦ ♥♠ér♦ ♦r♠ ❱

st tr♦ s♦çã♦ ♣r s rás ♣♥♥ts s qçõs r♥s

♦♥srçã♦ ♦ tr♥s♣♦rt q r♣rs♥t♠ ♦ ♣r♦♠ ís♦ é ♦t ♣♦ ♠ét♦♦

♦♠s ♥t♦s s♦ ♠ ♠♥t♦s ♦ ♥ês ♠♥ts ♥t ❱♦♠ t♦

❱

♣♦♥t♦ ♣rt ♦s ♠ét♦♦s ♦♠s ♥t♦s é ♥trçã♦ s qçõs

♦♥srçã♦ s♦r ♠ ♦♠ ♦♥tr♦❱ ♣ós ♣çã♦ ♦ ♦r♠ rê♥

♦ ♦r♠ ss q ♦♥rt ♥trs ♠ ♦♠ ♣r ♥trs ♠ s♣rí

s qçõs ♠ sr srt③s s ♥trs ♠ ♦♠ sã♦ srt③s ♣r

s♦♠ ♠s ♣r ♦ ❱ ♦ q ♦ st♦r ♣rt♥ s ♥trs ♠ s♣rí

sã♦ srt③s ♥♦s ♣♦♥t♦s ♥trçã♦ pi ♦③♦s ♥♦ ♥tr♦ s♠♥t♦

s♣rí ♠ ♠♥t♦ ♠ ♥tã♦ strís ♣r ♦s ❱s ♥ts

♦♠♦ s ♥trs s♣rí sã♦ s ♦♣♦sts ♣r ❱s ♥ts ♦s ♣♦♥t♦s

♥trçã♦ s ♦♥srçã♦ ♦ é ssr ❨

r str ♦♥strçã♦ ♠ ♦♠ ♦♥tr♦ ❱ ♥♦ q s

rás ♣♥♥ts s ♣r♦♣rs ♦ ♦só♦ sã♦ r♠③♥s ♥♦s érts

♦s ♠♥t♦s ♠ ♠ ♥ã♦strtr st rtríst sr ♥♦♠♥çã♦

s ♦r♠çã♦ ♥tr ♥♦s érts ♦ ♥ês rt① st é ♦r♠çã♦

t③ ♣♦ ♠ét♦♦ ❱ ♦ ♣♦í♦♥♦ q ♦r♠ ♦ ♦♠ ♦♥tr♦ t③ s

ssõs ♦s ♠♥t♦s q ♣♦ss♠ ♠ ♠s♠♦ ért ♠ ♦♠♠ P

s s♦♠s ♦♥tr♦ ♦ ♠ ♠♥t♦ ♠ ♦

♣♦♠ sr ♥♦s ♥♦s ♦ ♣♦♥t♦ ♠é♦ ♦s ss ♦s ♦♠ ♦ s r♥tr♦

st ♦r♠ ♠ ♠♥t♦ qrtr ♣♦ssrá s♠♣r qtr♦ s♦♠s ♦♥tr♦

♥ ♣♦ sr st♦ ♥ r ♦s ♠♦s ♣♦♥t♦s ♥trçã♦ ♣ t③♦s

♥♦ á♦ ♦s ①♦s ♥s s ♦ ♣♦í♦♥♦ q r♣rs♥t ♦ ♦♠ ♦♥tr♦ ❱

é♠ ss♦ ♣r srr rçã♦ ♠ rá qqr ♥tr♦ ♠ ♠♥t♦

♦ ♠ét♦♦ t③ s ♥çõs ♦r♠ ♦s ♠♥t♦s ♥t♦s

r ♦♥strçã♦ ♦ ♦♠ ♦♥tr♦ ❱ s♥♦ ♦r♠çã♦ ❱

A

B

C

D

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

♥çõs ♦r♠

♦ ♠ét♦♦ ❱ t♦♦s ♦s á♦s sã♦ t♦s ♠ ♥í ♦ ♥tã♦ ♠♦♥t♦s

♠ ♠ ♠tr③ ♦ ♣r♥í♣♦ tr♥s♦r♠çã♦ ♦♦r♥s ♦s ♣r ♦♦r

♥s ♦s é str ♥ r q ♠♦str ♠ ♠♥t♦ ♠ rtrár♦ ♥♦

sst♠ ♦♦r♥s ♦s x y ♥ r ♦ rs♣t♦ ♠♥t♦ ♣rã♦

♥♦ sst♠ ♦♦r♥s ♦s ξ η ♥ r ♦♠♥t t♦♦s ♦s ♥ós ♣r

q t♣♦ ♠♥t♦ qrtr srã♦ ♥♠r♦s té ♣♦r ♠♦ ♠

t ♦♥t r♦♥♦s ♦♠ ♦s ♥ós ♥♠rçã♦ ♦

r r♥s♦r♠çã♦ ♥tr s ♦♦r♥s ♦s ♦ sst♠ s ♦♦r♥s♦s t③s ♣s ♥çõs ♦r♠

3

2

1

1

4 43

2

2

2

3

3

4

4

1

1

x

y

(a) (b)

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

s♦ s ♥çõs ♦r♠ Ni ♣r♠t ①♣rssr ♠ ♦♦r♥s ♦s q

qr ♣♦♥t♦ ♦③♦ ♥♦ ♥tr♦r ♠ ♦ ♠♥t♦ ♦r♦ ♦♠ s tr♥s♦r♠çõs

♥rs sr

x(ξ, η) = 4∑j=1

Nj(ξ, η)xj,y(ξ, η) = 4∑

j=1

Nj(ξ, η)yj

♥s qs Nj r♣rs♥t s ♥çõs ♦r♠ ξ η sã♦ s ♦♦r♥s ♦s xj yjsã♦ s ♦♦r♥s ♦s ♦s ♥ós ♥♦s érts ♦ ♠♥t♦ ♦r♦ ♦♠ ♥♠rçã♦

♦

Pr ♦ ♠♥t♦ qrtr r ♦ ♦♥♥t♦ qçõs ♥

s ss ♥çõs ♦r♠ st ♦♥♥t♦ qçõs ♦ ♥tr♦ rçã♦ s ♦♦r

♥s ♦s ♥♦ ♥tr♦r ♦ ♠♥t♦ ♣rã♦ r ♥♠r♠♥t ♣rsr♠

rá rr ♦ ♣♦♥t♦ ♠é♦ ss♠ s ♦♦r♥s ♥♦s ♣♦♥t♦s ♥trçã♦

♥st t♣♦ ♠♥t♦ srã♦ (12,0) (0, 1

2) (1

2,0) (0, 1

2)

N1(ξ, η) = 1

4(1 + ξ)(1 + η),

N2(ξ, η) = 1

4(1 − ξ)(1 + η),

N3(ξ, η) = 1

4(1 − ξ)(1 − η),

N4(ξ, η) = 1

4(1 + ξ)(1 − η)

r♠♦s s♦s

s rs s♣s ♣r t♦♦s ♦s tr♠♦s s♦s sã♦ s ♥♦s ♣♦♥t♦s

♥trçã♦ t③♥♦ s ♥çõs ♦r♠ s♥♦ ♦r♠ tr♦♥ ♠♥t♦s

♥t♦s

∂Λ

∂x∣ξ, η

= ∑j

∂Nj

∂x∣ξ, η

Λj

∂Λ

∂y∣ξ, η

= ∑j

∂Nj

∂y∣ξ, η

Λj

♥s qs Λ é ♠ rá ♥ér s♦♠tór♦ é ♦♠♣t♦ s♦r t♦s s ♥çõs

♦r♠ ♣r q ♠♥t♦ s rs rts♥s s ♥çõs ♦r♠ ♣♦♠

sr ①♣rsss ♠ tr♠♦s ss rs ♦s trés ♠tr③ tr♥s♦r♠çã♦

♦♥

⎡⎢⎢⎢⎢⎣∂N1

∂x⋯∂Nj

∂x∂N1

∂y⋯∂Nj

∂y

⎤⎥⎥⎥⎥⎦= ⎡⎢⎢⎢⎢⎣

∂x∂ξ

∂y

∂ξ

∂x∂η

∂y

∂η

⎤⎥⎥⎥⎥⎦

−1 ⎡⎢⎢⎢⎢⎣

∂N1

∂ξ⋯∂Nj

∂ξ∂N1

∂η⋯∂Nj

∂η

⎤⎥⎥⎥⎥⎦

♥ q ♠tr③ ♦♥ é ♣♦r

[J] = ⎡⎢⎢⎢⎢⎣∂x∂ξ

∂y

∂ξ

∂x∂η

∂y

∂η

⎤⎥⎥⎥⎥⎦

①♣rssã♦ ♠tr ♣r ♦ r♥t ♠ rá ♥ér Λ ♣♦rt♥t♦ é

♦t ♣rtr ♦♠♥çã♦ s qçõs

[Λ] = [J]−1[Θ][Λ]

s♥♦ [Θ] ♠tr③ s rs s ♥çõs ♦r♠ ♦♠ rçã♦ às rás ♦s

r♠♦s ♦♥t♦s

s tr♠♦s t♦s rqr♠ q ♦s ♦rs rá ♥♦s ♣♦♥t♦s

♥trçã♦ s♠ ♣r♦①♠♦s ♠ tr♠♦s ♦s ss ♦rs ♥♦s s sq♠s

çã♦ ♣♦ss♠ s♥t ♦r♠ ①♣rss ♣r rá ♥ér Λ

Λpi = Λup + ϑ∇Λ ⋅∆ri

♥ q Λup é ♦ ♦r ♥♦ ♥ó ♠♦♥t♥t ri é ♦ t♦r ♣rtr ♦ ♥ó ♠♦♥t♥t té ♦

♣♦♥t♦ ♥trçã♦ ♣

s♥♦ tr♠♦ ♦ ♦ rt♦ qçã♦ é ♠♦ ♦rrçã♦ ♥♠é

r t st tr♦ ♦rrçã♦ t③ é ♦ sq♠ t rs♦çã♦

rs♦t♦♥ s♠ q ♦♥sst ♠ ór♠ ♥ã♦♥r s♣ ♣r ϑ ♠ ♥ó

♦♠♣t♦ ♣r sr ♦ qã♦ ♣ró①♠♦ ♣♦ssí ①♦ t♦ é ♦ t③♥♦

♦rs ϑ Λ ♣rtr ♦ ♥ó ♠♦♥t♥t ór♠ ♣r ♦ ϑ é s♦ ♠ rtér♦s

♠tçã♦ P ♣ ❨

♦♣♠♥t♦ ♣rssã♦♦

❯♠ ①♦ ♠áss♦ srt♦ trés ♠ s♣rí ♦ ♦♠ ♦♥tr♦ é ♦

♣♦r

mpi = (ρfuj∆nj)pi

s♥♦ uj ♦♠♣♦♥♥t ♦ ∆nj ♦ t♦r srt♦ ♥♦r♠ s♣rí ♣♦♥

t♥♦ ♣r ♦r

♦r♠ srt③ s qçõs rt♦s ♣r s♦çã♦ ♦ ♠♦♠♥t♦

sr ♣♥ê♥ ♥r ♦ ♦♠ ♣rssã♦ rs st ♦r♠

♣rssã♦ sr ①trí s qçõs ♠♦♠♥t♦ ♣r q s ♦s stsç♠

♦♥srçã♦ ♠ss ♦♥t♦ é ♣♦ssí rs♦r sts qçõs

♠♥r ♦♣ trés ♠♦♥t♠ ♠ ♠tr③ s♦çã♦ q ♣r♠♥ ú♥

♦r♠çã♦ ♣rã♦ ♦ CFXé rst♥t ♦ tr♦ ❲ st

srt③çã♦ tr♥t ♦ ①♦ ♠ss t ♦ s♦♣♠♥t♦ ♣rssã♦♦ ♥

♠ ♦♦③ ♥r♥t ♦ ♣r♦r♠ ♦♠♣t♦♥

s♥t ①♣rssã♦ ♣r ♦ ♦♥t é t③ ♠ ♣♦♥t♦

♥trçã♦

ui,pi = ui,pi + fpi ⎛⎝ ∂p∂xi ∣pi −∂p

∂xi∣pi

⎞⎠ − cpifpi(uoi,pi − uoi,pi)

♥ q

fpi = dpi

1 − cpidpi , dpi = VA, cpi = ρf

∆t

s♥♦ A ♣r♦①♠çã♦ ♦ ♦♥t ♥tr qçã♦ q♥t ♠♦♠♥t♦

①♥♦ ♦ tr♠♦ tr♥s♥t srs q ♥st s♦ s rrs s♦r s rás

♥♠ ♠ ♠é s♦r ♦s ♦rs ♥♦s érts ♥ts ♦s ♣♦♥t♦s ♥trçã♦ á

♦ s♦rsrt♦ o ♥♦t ♦rs ♥♦ ♣ss♦ t♠♣♦ ♥tr♦r

sst♠ ♦♣♦ qçõs

♦♥♥t♦ qçõs ♥rs q é ♦r♥♦ ♣ ♣çã♦ ♦ ❱ é ♠

♦♥♥t♦ ♦♥♥t♦ qçõs srts ♦♥srçã♦ srt♦ ♥ ♦r♠

∑nbi

anbi φnbi = Bi

s♥♦ φ s♦çã♦ B ♦ ♠♦ ♦ rt♦ a ♦s ♦♥ts qçã♦ i ♦ ♥ú♠r♦

q ♥t ♦ ♦♠ ♦♥tr♦ ♦ ♥ó ♠ qstã♦ nb r♣rs♥t ♦s ③♥♦s ♠s

t♠é♠ ♥ ♦ ♦♥t ♥tr ♠t♣♥♦ s♦çã♦ ♥ és♠ ♣♦sçã♦ ❨

Pr ♦ sst♠ ♦♣♦ ♦ ♦♥♥t♦ qçõs ♠ss♠♦♠♥t♦ tr♠♥s♦♥

é ①♣rss♦ ♣♦r

anbi =⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

auu auv auw aup

avu avv avw avp

awu awv aww awp

apu apv apw app

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

nb

i

, φnbi =⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

u

v

w

p

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

nb

i

Bi =⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

Bu

Bv

Bw

Bp

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦i

♦♠♦ strté s♦çã♦ ♦ CFXt③ ♠ sq♠ ♦♣♦ q s♦♦♥

s qçõs r♦♥â♠s ♦s ♣rssã♦ ♥♠ ú♥♦ sst♠ st ♦r♠

t③ ♠ srt③çã♦ t♦t♠♥t ♠♣ít s qçõs ♥♦ t♠♣♦ Pr ♣r♦♠s

st♦st♦♥ár♦ ♦ ♣ss♦ t♠♣♦ s ♦♠♣♦rt ♦♠♦ ♠ ♣râ♠tr♦ rçã♦

q ♦♠ s ♠ ♦♥srçõs íss ♦♥③ s s♦çõs ♣r♦①♠s ♣r s s♦çõs

♦ st♦ st♦♥ár♦ st♦ r③ ♦ ♥ú♠r♦ trçõs ♥ssárs ♣r t♥r ♦♥

rê♥ Pr rs♦r ♦ sst♠ srt♦ s qçõs ♥r③s CFXt③ ♠

té♥ t♦rçã♦ ❯ ♥♦♠♣t ♦♠ r♦r ♠tr

rtér♦ ♣r ♦ rtér♦ ♦♥rê♥ ♦t♦ ♣r t♦s s s♠çõs

r③s ♥st tr♦ ♦ ♠é qrát ♦ rsí♦ ǫRMS ≤ 1 × 10−6é♠ ss♦ ♣ós s t♥r st rtér♦ t♦s s s♠çõs ♦r♠ rs q♥t♦ ♦

♠♥ q r♣rs♥t ♦♥srçã♦ q♥t tr♥s♣♦rt trés ♦ ♦♠í♥♦

s q♥ts ♠♦♥t♦rs q♥t♦ ♦ rtér♦ ♣r ♣♥♠ s qçõs q

stã♦ s♥♦ rs♦s ♥ s♠çã♦ ♥♠ér

♦♥çõs ♦♥t♦r♥♦

tr♦ ♠♣♦rt♥t s♣t♦ ♥â♠ ♦s ♦s ♦♠♣t♦♥ sã♦ s ♦♥

çõs ♦♥t♦r♥♦ s s♠çõs ♥♠érs s t♣♦s ♦♥çõs ♦♥t♦r♥♦ ♠s

rq♥t♠♥t t③s sã♦ ♦ rt ♦ ♠♥♥ ♦♥çã♦ ♦♥t♦r♥♦

♦ t♣♦ rt rtr③s ♣ s♣çã♦ ♦ ♦r s rás ♥♦s ♥ós ♦♠♣

t♦♥s s r♦♥trs ♥♦ s ♦♥çõs ♦♥t♦r♥♦ ♥♦♠ rs ♦♥çõs

♠♥♥ s ♠ sr srt③s ♦♥tr♥♦ ♦♠ ♠ qçã♦ ♦ ♦♥♥t♦

qçõs q sr rs♦♦ ♥ s♠çã♦ ❩ P

♦♥çã♦ s♠tr t♠é♠ ♦ t③ ♠ t♦♦s ♦s s♦s st é ♠

♦♥çã♦ ♦♥t♦r♥♦ ♦♥ t♦s s rás ①t♦ ♦ sã♦ ♠t♠t♠♥t

s♠étrs ♥ã♦ ♣♦ r sã♦ ♦ s♦♠♥t♦ trés r♦♥tr s ♦s

♣rs st r♦♥tr t♠é♠ sã♦ s♠étrs s ♦s ♥♦r♠s ♦ ♣♥♦ sã♦

♥s ❨

♦♦ trê♥

♠♦♦ trê♥ t♠ r♥ ♠♣t♦ ♥ ♥ás ♥♠ér ss♠ ♦♠♦

♠ s ♦♥çõs ♦♥t♦r♥♦ ♣r♦♣rs íss ♦ trt♠♥t♦ ♦♣♦ s♦çã♦

tér♠ t

♦♥♦r♠ ♦♥stt♦s ♥ rsã♦ ♦s tr♦s rrê♥ ♥♦ ♣ít♦

♠s ♠ ♠♦♦ trê♥ ♦ t③♦ ♥qs st♦s s♦ ♦ ♠♦♦

trê♥ ♦♥sr s♣t♦s té♥♦s ♦♥ô♠♦s ts ♦♠♦ ís ♣rs♥t ♥♦

♣r♦♠ sr rs♦♦ ♦ st♦ ♦♠♣t♦♥ ♣♦r ①♠♣♦

st tr♦ ss♠s ♣óts ♦ss♥sq ♣r ♠♦♠ s♦

s tr♥t ♦ ♠♦♦ ír♦ ♥tr ♦ s♦♥♦ ♣r rs♦ê

sr ♥ ♣óts ♦ss♥sq s♦s tr♥t é ♠ ♣r♦♣r ♦ s♦

♠♥t♦ ♣♦rt♥t♦ ♥sst ♠♦♠ ♠t♠át s s♣♠♥t ♠ q

♠ ♦♥srçã♦ ♦ stór♦ ♦ s♦♠♥t♦ ♠ s ♦♠♣r♠♥t♦ tr♥t

st♦ r ♦ t♦ q s♦s tr♥t é ♦♥sr ♠♥r ♥á♦ à

s♦s ♠ ás ♣rt♦ s♥♦ t♦r ♥ét ♦s ss P♦rt♥t♦ s♦s

tr♥t ss♠ ♠ ①♣rssã♦ ♥♦ s♥t ♦r♠t♦

µt = ρfvtlt

♥♦ q lt vt sã♦ q♥ts rtrísts s trê♥ ♦ ♣r♦♠

♦♠♣r♠♥t♦ ♦ rs♣t♠♥t

❯♠ ♦♥t♦ stór♦ ♥♠♥t ♥♦ s♥♦♠♥t♦ s qçõs trê♥

♦ ♦ ♦♠♣r♠♥t♦ ♠str ❲❳ t st ♣r♦♣♦sçã♦ Pr♥t

♦r♠ ♦ ♠♦♦ ér♦ trê♥ ♠s tr ♠ ♦ ♠s♠♦ Pr♥t ♦♥

♦ ♠♦♦ trê♥ ♠ qçã♦ ♥tr♦③♥♦ ♦ ♦♥t♦ ♥r ♥ét

s tçõs tr♥ts κ

♠ ♦♠♦♦r♦ s♥♦ ♦ ♣r♠r♦♠♦♦ trê♥ ♦♠♣t♦ ♦♥

sr♥♦ ♦ ♣râ♠tr♦ ♦♥ ω t① ss♣çã♦ ♥r ♣♦r ♥ t♠♣♦

♦♠ é♠ ♦ κ ❲❳ t ❯♠ ♠♦♦ trê♥ ♦♠♣t♦ é t♠é♠

♦♥♦ ♦♠♦ ♠♦♦ trê♥ s qçõs ♣♦s sã♦ ♥tr♦③s q♥ts

r♣rs♥tts s t♠♣♦ tr♥t t♠é♠ s ♦♠♣r♠♥t♦ r

tríst trê♥ ♥ã♦ ♥♦ ♥ss s♣r ♥♥♠ s ♣r♦r

sr ①st♠ ♥ ♦s ♠♦♦s três qçõs ♣r ♠♦♠ trê♥

❲

♠♦♦ ír♦ ♥tr ♦♥♦ ♦♠♦ ♦ ♥ês r trss

r♥s♣♦rt ♠ ♦♥srçã♦ ♦ tr♥s♣♦rt s t♥sõs s♠♥t♦ tr♥ts

rst♥♦ ♠ t rá ♥ ♣rsã♦ ♦ ♥í♦ q♥t s♣rçã♦ ♦ s♦

♠♥t♦ s♦ r♥ts ♣rssã♦ rs♦s ♠♦♦ s s ♥ ♦r♠çã♦ κ−ω♦r♥ ❲❳ ♣r rã♦ ♣ró①♠ às ♣rs ♥ ♦r♠çã♦ κ− ε ♣rã♦❯ P ♣r rõs str ♦ s♦♠♥t♦ r ♦♥t♦

♠ ♠♦çã♦ ♥ ♥çã♦ s♦s tr♥t é t ♣r ♦♥srr ♦ tr♥s

♣♦rt s t♥sõs ②♥♦s rst♥♦ ♥♦ ♠♦♦ r trss r♥s♣♦rt

♠♦♦ ♦r♦ ♦♠ ♥tr ♣rs♥t ♠♦r ♦♠ rçã♦ às ♦r♠çõs

κ − ω κ − ε ♦r♥s

♠♦♦ κ − ω é t♠é♠ t③♦ ♥ ♣rt ♦rít♠ ♠ ♠t ♣♦s

♣rs♥t ♦♠♣♦rt♠♥t♦ s♣r♦r ♦ ♠♦♦ κ − ε ♥st rã♦ ♣r s♦♠♥t♦s ♦♠

r♥t ♣rssã♦ rs♦s s♦♠♥t♦s ♥♦♠♣rssís ❯♠ ssã♦ áss

♣r ♠ ♠t sr♥ ①♣r♠♥t♠♥t ♣♦ sr st ♥ r á

♥ rã♦ str ♦ rõs sts ♣r ♦ ♠♦♦ κ − ω sr ♥♦♥♦

♠ ♦r ♦ s♦ ♦ ♠♦♦ κ − ε r③ã♦ ♣r st tr♥â♥ é q ♦ ♠♦♦ κ − ω♣rs♥t ♠ ♦rt s♥s ♣r ♦s ♦rs ♦rr♥t r s♣♦s ♣r ω

♦r ♠ ♠t Pr s♦♠♥t♦s rs s♠♥t♦ st♥ts s♣rís ♦

♠♦♦ κ−ε ♣rã♦ é t③♦ Pr ♥çr sts rtrísts ss ♠ r♥ts

rõs rsã♦ ♦♥ ♣♦r t♦②♥♦s ♦ ♠♦♦ κ − ε é tr♥s♦r♠ ♣r ♠

♦r♠çã♦ κ − ω ♦r♠çã♦ ③♦♥ é ♣♦rt♥t♦ s ♠ ♥çõs ♠str s qs r♥t♠

sçã♦ q κ − ω ♦ κ − ε ♣r♥♣ ♦♠♣① ♦♥ ♥ ♦r♠çã♦

♦ ♠♦♦ r s♦r ♥ss tr♠♥r stâ♥ ♣rtr ♣r q é

rqr ♣r s ♥çõs ♠str t

rt♠♥t♦ ♥t♦ à ♥tr só♦♦ ♥çõs ♣

r sás ① ♦r♠çã♦ ①♦ ②♥♦s

s♦çã♦ s qçõs ♦♥srçã♦ srts ♥s rõs ♣r é r♥

♠♣♦rtâ♥ ♣r ♠♦r s ♣çõs ♥strs q t③♠ ♥â♠ ♦s

♦♠♣t♦♥ P♦r ss♦ ♠ts ③s ♦s ♠♦♦s s♦s ♠ ω ♦♠♦ é ♦ s♦ ♦

sã♦ ♣rr♦s Pr sts ♠♦♦s ♦♥♦s ♣♦r ①♦②♥♦s ♦♥t♦ á

♥ss ♠ ♠ t♠♥t r♥ ♥t♦ às s♣rs sós ♦ q ♣♦

r Pr ♦ tí♣♦ ♠ ♠t tr♥t

Subcamada

viscosaCamada

logarítmica

Camada

turbulenta

U+

60

40

20

01 10 102

U+

y+

U+

103 104

= y+

1 ln y++ B

=

♦♥t ♣t♦ ❲❳ t

♥ã♦ sr ♥ç♦ ♦♠ sss♦ ♣r t♦t s ♣rs P♦r ♦tr♦ ♦ s♦ ♠

♠♦♦ t♦ ②♥♦s s t③♦ ♦♠ ♠s ♠t♦ r♥s rá s♦çã♦

♦♠♣r♦♠t ♠s♠ ♦r♠ Pr ♦♥t♦r♥r sts ♥♦♥♥♥ts ♦ CFXt③

♣♦r ♣rã♦ ♠ trt♠♥t♦ t♦♠át♦ ♥t♦ à ♣r ♣r ♠♦♦s s♦s ♠ ω

t♦♠t ♥r trt♠♥t ❨ st ♦r♠ ♦ ó♦ tr♥ ♥çã♦

♣r ♦ ♦ t ♣r ♠ ♦r♠çã♦ ①♦ ②♥♦s ♦♠ ♦ r♥♠♥t♦

♠

♦r♠ s ♥çõs ♣r ♥♦ CFXé ♠ ①t♥sã♦ ♦ ♠ét♦♦

❯ P ♠♦♦ q ♥ rã♦ ♦rít♠ ♦ t♥♥

é r♦♥ ♦♠ t♥sã♦ s♥t ♣r ♣♦r ♠♦ ♠ rçã♦ ♦rít♠

❨

s ♦r♥s ♥çõs ♣r rã♦ s♠ s♦s é ♥♦r

♣ ♣çã♦ ór♠s ♠♣írs sts ór♠s ♦♥t♠ s ♦♥çõs ♣r

♦♠ s rás ♣♥♥ts ♦s ♥ós ♣ró①♠♦s à ♣r ♦③çã♦ ss♠s str

♥ rã♦ ♦♠♣t♠♥t tr♥t rçã♦ ♦rít♠ ♣r ♦ ♣ró①♠

♣r é ♣♦r

u+ = Utan

uτ= 1K ln(y+) +C

♦♠

y+ = ρfuτ∆yµf

uτ =√

τint

ρf

♥ q u+ uτ Utan sã♦ s ♦s ♠♥s♦♥s ♣ró①♠ ♣r trt♦

t♥♥ à ♣r ♠ stâ♥ ∆y ♣rtr ♣r rs♣t♠♥t y+ é

stâ♥ ♠♥s♦♥ ♣rtr ♣r τint t♥sã♦ s♥t ♥ ♣r ♦ ♥trK ♦♥st♥t ♦♥ ár♠á♥ C é ♠ ♦♥st♥t ♣♥♥t r♦s ♣r

Pr strr ♦ trt♠♥t♦ ♣r ♦ à trê♥ sã♦ ♣rs♥ts s

♦r♥s ♣r ♦ ①♦ ♠♦♠♥t♦ ①♦ ♦r srs q ①st ♥ ♠

♦r♠çã♦ ss♠ ♣♦ trt♠♥t♦ t♦♠át♦ ♣r ♣r t① ss♣çã♦

s♣í ω

①♦ ♠♦♠♥t♦ ♥ rã♦ ♣r

♦r♦ ♦♠ ♥s②s s ♥çõs ♣r sás s ♥t

♦♥s sã♦ ss ♠ ♣ótss q sã♦ ♣r♦♠áts s♣♠♥t ♣r s♦♠♥t♦s

①♦s ♥ú♠r♦s ②♥♦s Re < 105 ♣♦s ♣♦rçã♦ s♠ s♦s ♥ ♠

♠t é ♥♥ ♥♦ ♥ç♦ ♠ss ♠♦♠♥t♦ Pr s♦♠♥t♦s ①♦ ♥ú♠r♦

②♥♦s st♦ ♣♦ sr ♠ rr♦ té ♥ s♣ssr s♦♠♥t♦

trt♠♥t♦ t♦♠át♦ ♣r ♦ CFX♣♦ss s♥t ♦r♠çã♦ ♣r

♦ ①♦ ♠♦♠♥t♦ FU ❨

FU = ρfuτu∗

♥ q

u∗ = 4

¿ÁÁÁÀ(√µf

ρf∣∆U∆y∣)4 + (√a1κ)4 uτ = 4

√(uvisτ )4 + (ulogτ )4.

ss♠ u∗ r♣rs♥t ♠ s ♦ tr♥t a1 ♠ ♦♥st♥t ♦s s♦rs

rt♦s vis log ♥♥♦ ♠str ♥tr s rõs s♦s ♦rít♠

s tr♠♦s ♦ trt♦ sã♦ ①♣rss♦s ♣♦r

uvisτ = ⎛⎝√

µf

ρ∣∆U∆y∣⎞⎠ ulogτ = U

1/K ln(y+) +C

①♦ ♦r ♥ rã♦ ♣r

♣r t♠♣rtr ♠♥s♦♥ ♣ró①♠ ♥tr só♦♦ s ♠

♣r ♥rs trés s♠ s♦s rã♦ ♦rít♠ t♠♣rtr

♠♥s♦♥ T + é ♥ ♦♠♦ ❨

T + = ρfcfu∗(Tint − Tf)qint

♥ q Tint qint sã♦ t♠♣rtr ♦ ①♦ ♦r ♥ ♥tr

qçã♦ ♣♦ sr rrr♥ ♠♦♦ ♦r♥r ♠ ♦r♠ ♣r

tr♠♥çã♦ ♦ ①♦ ♦r trés ♥tr só♦♦

qint = ρfcfu∗(Tint − Tf)T +

Pr ♦ ♠♦ trt♠♥t♦ t♦♠át♦ ♣r t♦♠t trt♠♥t ♦

CFX ♠ ♠t tér♠ é ♠♦ t③♥♦ ♥çã♦ ♣r tér♠

r strçã♦ t♠♣rtr ♠♥s♦♥ T + é ♠♦ trés

♠str s♠ s♦s ♦♠ ♦rít♠ ♣r

T + = Pry∗e(−Γ) + [2,12ln(y∗) +ψ]e(−1/Γ) ,

s♥♦

ψ = (3,85Pr1/3 − 1,3)2 + 2,12ln(Pr) Γ = 0,01(Pry∗)41 + 5Pr3y∗ .

♥ú♠r♦ Pr♥t é ♥♦ ♦r♠ tr♦♥

Pr = µfcf

kf.

♥♠♥t q♥t y∗ é ♠ ♥çã♦ tr♥t ♦ y+

y∗ = ρfu∗∆yµf

.

rr♥♦ ♥♦

r ❱rçõs ♦♠étrs ♦♥rçã♦ ts ♥s ♣r ♠ s♣ç♠♥t♦ ♥tr ts b ♣r s r♥ts r③õs ♦q♦ t rba ♦♥ ♦♥

90°

18°

36°

54°

72°

(a) (b)

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

rr♥♦ s♥♦

r ❱rçõs ♦♠étrs ♦♥rçã♦ ts s♥s ♣r ♠ s♣ç♠♥t♦ ♥tr ts b ♣r s r♥ts r③õs ♦q♦ t rba ♦♥ ♦♥ ♦♥

90°

18°

36°

54°

72°

(a) (b) (c)

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

r♦r s♦s

r ♦♠♥çã♦ s rçõs ♦♠étrs b rba ♦♠ s rçõs s ♦♥çõs ♦♥t♦r♥♦ r♦♥â♠s ue ♦ Re ♣r ♦ ♠ ♥♥çã♦ t β

ts s♥s

b = 2Hrba = 0,2

Re1

Re2

Re3

rba = 0,4Re1

Re2

Re3

rba = 0,6Re1

Re2

Re3

b = 3Hrba = 0,2

Re1

Re2

Re3

rba = 0,4Re1

Re2

Re3

rba = 0,6Re1

Re2

Re3

ts ♥s

b = 2Hrba = 0,2

Re1

Re2

Re3

rba = 0,4Re1

Re2

Re3

b = 3Hrba = 0,2

Re1

Re2

Re3

rba = 0,4Re1

Re2

Re3

♦♥t ♣r♦çã♦ ♦ ♣ró♣r♦ t♦r

❨ ♥ ♦ ♦tr ♥s②s ❬❪ ❱t♦♥ t♦♦♦② ♥ ♦♠♣tt♦♥ ②♥♠s

P s♥ ♥ ♣♣t♦♥ ♦ ♣♥ s♠s ♦♥♥strtr ♠ss

❩ t ♠r s♠t♦♥ ♦ t ②♥♠ tr♥t ♦ tr♦ ♥♥ ♣r♦ t s ♦♠♣rt st② t♥ t♦ ♠♦s ♦ s r♥srs ♥ tr♣③♦ s ♥rs ♥♦s ♥ ♣

P P ❱ ♥♠♥ts ♦ t ♥ ♠sstr♥sr ❬❪ ♦♥ ❲② ♦♥s

❯ ♦ r♦♥ s ♦r♥ ♦ t tr♥sr♠r♥ ♦t② ♦ ♥ ♥♥rs ♥ ♣

❲❯ ♠r ♣rt♦♥ ♦r ♠♥r ♦r ♦♥t♦♥ ♥ ♣r♣t ♥♥s t tr♥srs ♥ rr②s ♥tr♥t♦♥ ♦r♥ ♦ t♥ ss r♥sr sr ♥ ♣

❱ P r♥ ♥ ♥tr♦t♦♥ ♦r s♥tsts ♥ ♥♥rs ❬❪ ①♦r❯♥rst② Prss ❯

❱❯ ①♣r♠♥t ♥stt♦♥ ♦ ♠① ♦♥t♦♥ ttr♥sr r♦♠ ♦♥t♥ ♥s ♥ ♦r③♦♥t rt♥r ♥♥ ♥tr♥t♦♥ ♦r♥ ♦ t ♥ ss r♥sr sr ♥ ♣

❩ ❨ ❲ ♥ t ♥ ♠ss tr♥sr ❬❪♦ t Prss

❩ P ♦♠♣tt♦♥ ♠t♦s ♦r ②♥♠s ❬❪ ♣r♥r♥ s♥ss

❳ ❲ P P ♥tr♦çã♦ à ♠â♥ ♦s ♦s❬❪ r♣♦ ♥

t ①♣r♠♥t ♥stt♦♥ ♦ t tr♥sr ♥ ♦ ♦r s ♦r♥t ts ♦r♥ ♦ t tr♥sr ♠r♥ ♦t② ♦ ♥ ♥♥rs ♥ ♣

❩ ❯ ♠r t tr♥sr ♥ ♣rssr r♦♣ ♥stt♦♥ ♦ r♥t t s ♠♦♥t s♠t♥♦s② ♥ ♥♥ ♥♦r♥ ♥ ♣

♠r ♦♠♣tt♦♥ ♦ ♥tr♥ ♥ ①tr♥ ♦s ♥♠♥ts ♦♦♠♣tt♦♥ ②♥♠s ❬❪ ttr♦rt♥♠♥♥

t ♦♥t t tr♥sr ♣rt♦♥s ♥ t♦♠♥s♦♥ r♣sss ♥tr♥t♦♥ ♦r♥ ♦ t ♥ ♦ sr ♥ ♣

♠♣rtr ♥ ♦♥♥trt♦♥ ♣r♦s ♥ ② tr♥t ♦♥r② ②rs♥tr♥t♦♥ ♦r♥ ♦ t ♥ ss r♥sr sr ♥ ♣

♥stt♦♥ ♦ rtt♥ tr♥t sr ②r♦ ♦r r♥ st♣ ♦r♥ ♦ s ♥♥r♥ ♠r♥ ♦t② ♦♥ ♥♥rs ♥ ♣

❩❯ ❯ ts ♦ r rr♥♠♥ts ♦♥ t tr♥sr♥ ♦ ♦r ♥ rt♥r rr♦♥ ♣ss ♣♣t♦♥ t♦ ♦♦♥ ♦ str♥ tr♥ ♦r♥ ♦ t tr♥sr ♠r♥ ♦t② ♦ ♥♥♥rs ♥ ♣

P t ♠r s♠t♦♥ ♦ t tr♥sr ② ♠① ♦♥t♦♥ ♥♦r③♦♥t ♥♥ ♥♥s ♥ ♥tr♥t♦♥ ♦♥rss ♦ ♥ ♥♥r♥ st t Pr♦♥s ♦ ♥r♦

❯ P ♥♠r ♦♠♣tt♦♥ ♦ tr♥t ♦s♦♠♣tr ♠t♦s ♥ ♣♣ ♠♥s ♥ ♥♥r♥ sr ♥ ♣

❩ ❨ ♠r st② ♦ tr♥t ♦ ♥ t tr♥sr ♥ r♦ss♦rrttr♥r ts t ts♣ s ♥tr♥t♦♥ ♦r♥ ♦ t ♥ ss r♥sr sr ♣

P❩ t tr♥sr ♥ tr♠♥s♦♥ ♥♥t s ♠r t r♥sr Prt ♣♣t♦♥s ②♦r r♥s ♥ ♣

r♥srê♥ ♦r ♠â♥ ♦s ♦s ♦♠♣t♦♥ çã♦

❯ P ♥stt♦♥ ♦ tr♥t ♦s ♦r r ♥st♣ s ♥ ♠♦r♥♠ ♣

❯ P ②♥♦sstrss ♥ ss♣t♦♥rt ts ♥ tr♥t ♥♥ ♦ ♦r♥ ♦ ♥s ♠r ❯♥ Prss ♣

❨ t ♠r ♥②ss ♦ tr♥t ♦r♦♥t♦♥ ♦ ♥ ♥♥ tstr s♣ s ♦r♥ ♦ ♥♦♦② ♥ trs P ♥ ♣

❯❩ ❨ ♥ ②rs ♦ ♥str ①♣r♥ t tsst tr♥ ♠♦ r♥ t ♥ ♠ss tr♥sr tsr ♥ ♣

♦qt♦♥ ②s♦st② tr♥ ♠♦s ♦r ♥♥r♥ ♣♣t♦♥s ♦r♥ ♥ ♣

❯❱ t ♥ ♦ ♥ ♥tr♥ r♦♥ ♦ ♥♥t str s ♥r② ♦♥rs♦♥ ♥ ♥♠♥t sr ♥ ♣

P ❲ ❯ ❱t♦♥ ♠t♦♦♦② ♥ ♦♠♣tt♦♥ ②♥♠s ♣♣r ♣

P ❱❩ r ❩ P st♦ ♥♠ér♦ tr♥srê♥ ♦r ♦♥ ♠ ♥s ♦♠ ts ♥♥s ♣r ①♦ ♥ú♠r♦ r②♥♦s ♥ ❳♦♥rss♦ ♦♥ ♥♥r â♥ ♦rt③ ♦ ♥r♦

P ❱❩ r ❩ P ♠r ssss♠♥t ♦ ♠♥r ♦♥ ♦♥t t tr♥sr ♥ ♣r♣t ♥♥s t ♥♥ ♥s t ♦ r②♥♦s♥♠r ♥ r③♥ ♦♥rss ♦ r♠ ♥s ♥ ♥♥r♥ t ❱tór ♦ ♥r♦

P ❱❩ r ❩ P ♦♥srt♦♥s ♦♥ ♦♥t t tr♥sr ♥ ♣r♣t ♥♥s t ♥♥ ♥s ♥ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♥♦♠♣tt♦♥ ♥♥r♥ ♥ ①♣r♠♥t♥ t strt ♦♦ ❱♥♥ str ❱♥♥ ❳ ♦♥r♥

P ❲ ♦ t♥ t♦ s t ♥q ♥tst r♥t s♣♥ r♦r♥s ♥ ♣

❲ ❲ ♠r st② ♦ t tr♥t ♦ ♣st ♥ r♦ t tr♥ s♣rt♦♥ ♦r♥ ♥ ♣

♦ ♥ t tr♥sr ♥ ♣r♣t t s♦s♣♦r♦s ♥ s♦ s ♠r t r♥sr ②♦r r♥s ♥ ♣

❯ t t tr♥sr ♠♥tt♦♥ ♥ t ①♥r t s♥ ♥tr♥t♦♥ ♦r♥ ♦ t ♥ ♦ sr ♥ ♣

t tr♥sr ♥ ♦ tr♦ r ♣ss ♥ strrr♥♠♥t r♥♥ ♦r♥ ♦ ♥ ♥♦♦② r♥st♦♥ ♥♥r♥ ♥ ♣

PPP P❱ P ♠r ♥②ss ♦ ♠♥r t tr♥sr♥ ♥♥ t ♠♦♥s♣ s ♥tr♥t♦♥ ♦♠♠♥t♦♥s ♥ t ♥ss r♥sr sr ♥ ♣

❯❨ rst ♦rs ♥ tr♥ ❬❪ ♣rss

❱ ❲ t tr♥sr ♣rt♦♥s s♥ ♥ t♦qt♦♥ tr♥ ♠♦s ❳ ❱t♦♥ ♣♦rt ♣♦rt ♦ ❳❱ ♣

❱ ♦♠♥ t tr♥sr ♥ ②♥♠ ♠sr♠♥ts ♦♥str♠ ♦ r♥ st♣ ♦r♥ ♦ t tr♥sr ♠r♥ ♦t② ♦ ♥♥♥rs ♥ ♣

❲ trqt♦♥ ②s♦st② ♠♦ ♦r r②♥♦sr ♥rst♦s s♠t♦♥s ♦ tr♥st♦♥ ♦ ♦r♥ ♦ s ♥♥r♥♠r♥ ♦t② ♦ ♥ ♥♥rs ♥ ♣

❲❳ ssss♠♥t ♦ t str♠♥♥ qt♦♥ ♦r ♥ tr♥♠♦s ♦r♥ ♥ ♣

❲❳ t r♥ ♠♦♥ ♦r ❬❪ ❲ ♥strs ♥

❨ ❨ ❲ ♦r ♦♥t ♦♦♥ ♦ ♥ ♥ ♥♥♥r② ♦♥rs♦♥ ♥ ♠♥♠♥t sr ♥ ♣

❨ ❨ ❲ ❩ t♦♥ ♦ tr♥t ♦ ♥ t tr♥sr ♥ ♣♦r♦s ♥♥ ♥tr♥t♦♥ ♦r♥ ♦ t ♥ ss r♥sr sr ♥ ♣

❨❯ ❩ ♠r st② ♦ ♣r♦② tr♥t ♦ ♥ t tr♥sr ♥ ♥♥t tr♥srs ♥ rr②s ♥tr♥t♦♥ ♦r♥ ♦ ♠r t♦s ♦r t ♦ ❯P t ♥ ♣

❨❯ ❩ ❩ ❩ ♥ ♥ t ♦♥ tr♥t t tr♥sr ♥ ♣r♣t ♥♥ t ♦♥♥♥ ♥s ♥tr♥t♦♥ ♦r♥ ♦ ♠r t♦s ♦rt ♦ ♠r r♦♣ Ps♥ ♠t ♥ ♣

❩ P t tr♥sr sts ♥ t ♦ ♦r s♦ts ♦r♥ ♦ t tr♥sr ♠r♥ ♦t② ♦ ♥ ♥♥rs ♥ ♣

❩ P ❱❩ ♦♥t♦♥ t tr♥sr ♥♥♠♥t♦♥ rrt♥ ♦s ♥ r ♥ st♣ t ts ♦ s♠ sqr tr♥♣r♦♠♦tr t r♥sr ♥♥r♥ ②♦r r♥s ♥ ♣