FENÔMENOS DE TRANSPORTES.- EXERCÍCIOS RESOLVIDOS EM 26 NOV 2013.- 01 COLUNA

Rua 96 nº 45 – Setor Sul – Goiânia – Fone: (62) 3092-2268 afonsoarioa!afonso afonsoarioa!afonsoarioa"o#"$r arioa"o#"$r % afonsoarioa!&ot#ail" afonsoarioa!&ot#ail"o# o#

Dado Dadoss :

µ=? 477 ft 2 / sec sec ν = 477 ,00 ×10 3 kg kg / m 3 = 453,6 lb / ft 3 ρágua = 1,00 d óleo = 0, 738 ρóleo = d óleo × ρágua ⇔ ρ óleo = 0, 738 × 453, 6 lb / ft 3 ∴ ρóleo = 334,76 334,76 lb / ft 3 Assm Assm :

µ ν = ∴µ = νρ ρ !ubsttu"do !ubsttu"do : 477 × 334 334, 76 µ = νρ ⇔ µ = 477

µ = 15#,68

ft sec

×

lb ×ft ft 3

ft 2 sec

×

lb ft 3

15#, 68 ×103 lbs −1ft −1 ∴ µ = 15#

$es%:15# $es%:15#,68 ×10 10 3 lbs −1ft −1

AFONSO CELSO – CEL: (62) 8109-4036

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Dado Dadoss : &=? D = 45 mm = 45 ×10

−3

m

,7# ×10 3 ' / m γ água = #,7# 75 ×10 −3 ' / m 2 σágua = 72, 75 πD2 A= 4 Assm Assm :

σágua =

& A

⇔ σ água =

&

πD2

∴& =

πσágua D2

4 !ubsttu"do !ubsttu"do : &= &=

π × 72,75 ×10 −3 ( 45 ×10 −3 ) 4 0, 228 228 × 2,02 ×10 −3 4

2

'

'

& = 115,14 ×10 −6 ' ∴& = 115,14 µ' $es%:115 $es%:115,14 ,14 µ'

4














Dado Dadoss : D=?

= 0, # ×10 −3 m ,7# ×10 3 ' / m γ água = #,7# 75 ×10 −3 ' / m 2 σágua = 72, 75 θ = 0° ( = 0, # mm

Assm Assm : (=

4σ cos θ

γD

∴D =

4σ cos θ

γ (

!ubsttu"do !ubsttu"do : D= D=

4 × 72, 75 75 ×10 −3 × cos ( 0 ° ) #,7# ×103 2#1×10 −3 8,811

× 0,# ×10 −3

1

m

m ⇔ D = 33, 03 ×10 −3 m

,03 mm ∴ D = 33,03 $es%: 33,03 mm













Rua 96 nº 45 – Setor Sul – Goiânia – Fone: (62) 3092-2268 afonsoarioa!afonso afonsoarioa!afonsoarioa"o#"$r arioa"o#"$r % afonsoarioa!&ot#ail" afonsoarioa!&ot#ail"o# o# Dado Dadoss : % = ? d) )

25* = 0,0125 ,0125 = 1, 25*

+ = 2,1# -a

= 2,1# ×10 # -a

Assm Assm : +=

d% d)

) !ubsttu"do !ubsttu"do : 2,1# ×10 #

=

d% 0,0125

d% = 2,1# ×10 # × 0,012 ,0125 -a d% = 27,375 ,375 ×10 6 -a d% = 27,375 27,375 .-a .-a $es%: 27,37 27,375 5 .-a .-a













Rua 96 nº 45 – Setor Sul – Goiânia – Fone: (62) 3092-2268 afonsoarioa!afonso afonsoarioa!afonsoarioa"o#"$r arioa"o#"$r % afonsoarioa!&ot#ail" afonsoarioa!&ot#ail"o# o# Dado Dadoss :  = 0, 03 03 m 3 / s 30 m = 300 mm = 0, 30 D 2 = 150 mm = 0,15 m )1 = ? )2 = ? D1

+uao +uao da o"t"udade o"t"udade :  = )1A1

= )2A 2

"de: A1

=

πD12

4 !ubsttu"do !ubsttu"do : A1

=

π × ( 0,30 ) 2

m 2 ∴ A1

4

= 70, 7 ×10 −3 m 2

Assm Assm :  = )1A1 ∴ )1

=

 A1

!ubsttu"do !ubsttu"do : )1 A2

= =

0,03 70,7 ×10 −3

m / s ∴ )1

= 0, 424 m / s

πD22

4 !ubsttu"do !ubsttu"do : A2

=

π × ( 0,15 ) 2 4

m2 ∴ A 2

= 17, 7 ×10 −3 m 2

Assm Assm :  = )2 A 2 ∴ )2

=

 A2

!ubsttu"do !ubsttu"do : )2

=

0,03 17,7 ×10

−3

m / s ∴ )2

= 1, 6#5 m / s














emos emos ue : e"ta

= sa ⇔ 1 + 3 =  2

Assm Assm :

= 2 − 1 3 = 7 − 3 = 4 m3 / s ∴ 3 = 4 m3 / s

3

Assm Assm :

= 3 m3 / s d1 = 0, 3 cm cm = 3×10−3 m 1

Assm Assm : A1

=

)1

=

πd

2 1

=

4 Assm Assm : 1 A1

π × ( 3 ×10−3 )

m 2 ∴ A1 = 7, 07 ×10−6 m2

4 3

=

2

−6

7, 07 07 ×10

m / s ∴ )1 = 4, 24 ×105 m / s

Assm Assm :

= 7 m3 / s d 2 = 0, 7 cm = 7 ×10−3 m 2


=

)2

=

πd 22

4 Assm Assm : 2 A

=

=

π × ( 7 ×10−3 ) 4 7 −5

3, 85 85 ×10

2

m2 ∴ A 2

m / s ∴ )2

= 3, 85 ×10−5 m2

= 1, 82 ×105 m / s















Rua 96 nº 45 – Setor Sul – Goiânia – Fone: (62) 3092-2268 afonsoarioa!afonso afonsoarioa!afonsoarioa"o#"$r arioa"o#"$r % afonsoarioa!&ot#ail" afonsoarioa!&ot#ail"o# o# Assm Assm :

= 4 m3 / s d 3 = 0, 2 cm cm = 2 ×10 −3 m 3


=

)3

=

πd

4 Assm Assm : 3 A3

2 3

=

=

π × ( 2 ×10 −3 ) 4 4

3,14 ×10

−6

2

m2 ∴ A3

m / s ∴ )3

= 1, 27 ×106 m / s

Dado Dadoss : d óleo

= 0, 75

D = 150 mm = 0,15 m % = 103 k-a

= 103 ×10 3 -a

 = 2, 4 m

d óleo

= 0, 75 γ água = #7#0 ' / m 3

Assm Assm :

γ óleo = d óleo × γ ág ua

= 3,14 ×10 −6 m 2














%

)

2

∆ =  + + γ 2g "de:

∆ = 17,# m 7343 ' / m 3 γ óleo = 7343 g = #, 7# 7# m / s 2 Assm Assm : )2

%

∆ =  + + ⇔ γ 2g

)2 2g

= ∆ −  −

%

γ

Assm Assm : )2

 %  = 2g  ∆ −  − ÷∴ ) = γ 

 

2g  ∆ −  −

!ubsttu"do !ubsttu"do :

 

) = 2 ×#, 7# 17, # − 2, 4 −

103000  ÷m / s 7343 

) = 1#, 58 58 ( 17, # − 2, 4 −14, 03 03 ) m / s ) = 28, 78 m / s ∴ )

36 m / s = 5, 36

) = 5, 36 36 m / s A=

πD2 4

=

π × ( 0,15 ) 2 4

m 2 ∴ A = 17, 7 ×10 −3 m 2

%

γ ÷














Dado Dadoss :

γ = #7#0 '/m 3 -ot -ot = 450 k9  = 0, 60 60# m 3 / s ,87 η = 87* = 0,87 Η = ? Assm Assm : -ot

= ηγ  

!ubsttu"do !ubsttu"do : 450000 = 0,87 × #7#0 × 0,60# ,60# ×   450000 = 5187 ×   Assm Assm : 

76 m = 86, 76

$e s% s% :  

76 m = 86, 76

⇔  =

450000 5187

m














−7 2 υ = 6, 48 48 ×10 m / s

−6 2 υ = 1, 02 02 ×10 m / s

emos emos ue : $e  =

)D 

υ

∴) =

$e  ×υ D

Assm Assm : )=

$e  ×υ D

"de "de : $e  = 2000 48 ×10 −7 m 2 / s υ = 6, 48 D  = 20 mm = 20 ×10 −3 m !ubsttu"do !ubsttu"do : )=

$e  ×υ D

=

2000 × 6, 6, 48 48 ×10 −7

Assm Assm : ) = 0,06 ,0648 m /s

20 ×10 −3

m/s













Rua 96 nº 45 – Setor Sul – Goiânia – Fone: (62) 3092-2268 afonsoarioa!afonso afonsoarioa!afonsoarioa"o#"$r arioa"o#"$r % afonsoarioa!&ot#ail" afonsoarioa!&ot#ail"o# o# "de: $e  = 2000 02 ×10 −6 m 2 / s υ = 1, 02 D  = 20 mm = 20 ×10 −3 m !ubsttu"do !ubsttu"do : )=

$e  ×υ D

=

2000 ×1, 02 02 ×10 20 ×10 −3

−6

m/s

Assm Assm : ) = 0,102 m/ s $es% es% : ) = 0,102 m /s

−5 2 υ = 11,03 ,03 ×10 m / s

53 ×10 −5 m 2 / s υ = 20, 53

emos emos ue : $e  =

)D 

υ

"de: −5 2 ,03 ×10 m /s υ = 11,03 D = 305 mm = 0, 30 305 m















Rua 96 nº 45 – Setor Sul – Goiânia – Fone: (62) 3092-2268 afonsoarioa!afonso afonsoarioa!afonsoarioa"o#"$r arioa"o#"$r % afonsoarioa!&ot#ail" afonsoarioa!&ot#ail"o# o# !ubsttu"do !ubsttu"do : $e  =

)D 

υ

=

1,07 × 0,305 0,305 11,03 ×10

−5

Assm Assm : $e

= 2#58,75

.as: $e  ≤ 2000 2000 ∴ +sco +scoam ame" e"to to ;a m"a 2000 2000 < $e  < 4000 4000 ∴+sco +scoam ame" e"to to de a" a"s s o o $e  ≥ 4000 4000 ∴ +sco +scoam ame" e"to to ub ubul ule" e"to to $es% : $e  = 2#58 2#58,, 75∴ +sco +scoam ame" e"to to de a" a"s s o o

emos emos ue : $e  =

)D 

υ

"de: 53 ×10 −5 m 2 / s υ = 20, 53














−6 2 υ = 6, 0# 0# ×10 m / s

emos emos ue : $e  = D=

)D

υ $e  ×υ )

( 1)

.as:

 πD2   = )A )A ⇔  = )  ÷  4  D2

=

4

( 2)

π) .as ( 2 ) ÷ ( 1) : 4 D

2

D

4 ) = π) ⇔ D = × $e  ×υ π ) $e ×υ














ε = 0,0004 m Dado Dadoss :

µ = 0,101's/m 2 d óleo = 0, 85 ; = 3000 m  = 0,444 ,444 m 3s D = 300 mm = 0,30 ,30 m ∆ = ? < =? Assm, Assm,tem temos os :

ρóleo = d óleoρágua = 0, 85 ×1000 kg / m 3 8500 kg / m 3 ∴ ρóleo = 8500 µ 0,101 2 m / s ∴ υ = 1,1# ×10 −5 m 2 / s υ= = ρ 8500 '= de $e "olds "olds :














f =

1,325

  ε 5,74   l" +   3, 7D 0,# ÷   7D $e   

2

!ubsttu"do !ubsttu"do : f =

f =

f

=

1,325

    5, 74 l"  0, 0004 + ÷ 0,#   3,7 × 0,30 ( 158,3 ×10 3 ) ÷     1,325

l" ( 3, 3, 6 ×10 −4 + 1, 2 ×10 −4 )   1,325 58,4

∴ f = 0, 023

-eda -eda de ag a Dstbu Dstbu>da >da :

∆ =

f;)2 2gD

!ubsttu"do !ubsttu"do :

2

2














υ = 41,24 ×10 −5 m 2 /s d = 0,#1 ,#18

Dado Dadoss : ,24 ×10 −5 m 2 /s υ = 41,24 d = 0,#1 ,#18 ; = #14,#0 m D = 150 mm = 0,15 m % A = 1068,68 k-a = 1068,68 ×10 3 -a 3 % @ = 34, 47 k-a = 34, 47 ×10 -a $e  = 2000 =? Assm Assm :















Rua 96 nº 45 – Setor Sul – Goiânia – Fone: (62) 3092-2268 afonsoarioa!afonso afonsoarioa!afonsoarioa"o#"$r arioa"o#"$r % afonsoarioa!&ot#ail" afonsoarioa!&ot#ail"o# o# Assm: Assm:

∆ =

f;)2 2gD

=

%A

− %@ γ

Assm: Assm: f;) 2

 % − %  = 2gD  A @ ÷  γ 

Assm: Assm: )2

=

2gD  % A − % @  f;

 

÷ γ 

!ubsttu"do: )

2

3 3  106 1068,68 ×10 − 34,47 ×10  2 = ( m / s)  ÷ 0, 03 032 ×#14, #0 #0  8#87, 2 

2 ×#,7# #,7# ×0,1 0,15 5














Dados Dados : 24 ×10 −5 m 2 / s υ = 41, 24 d = 0, #1 #18 ; = #14,#0 14,#0 m D = 150 mm = 0,15 m % A = 1068,68 1068, 68 k-a = 1068,68 1068, 68 ×10 3 -a % @ = 34, 47 k-a = 34, 47 ×103 -a $e  = 2000 =? Assm Assm













Rua 96 nº 45 – Setor Sul – Goiânia – Fone: (62) 3092-2268 afonsoarioa!afonso afonsoarioa!afonsoarioa"o#"$r arioa"o#"$r % afonsoarioa!&ot#ail" afonsoarioa!&ot#ail"o# o# Assm: 2

=

 % A − % @   γ ÷ 0,0828f;  D5

!ubsttu"do: !ubsttu"do: 

2

=

5

 1068 1068,68 ,68 ×103 − 34,47 34,47 ×103  2 ( m / s)  ÷ 0, 08 0828 ×0, 03 032 ×#14, #0 #0  8#87, 2  ( 0,15)

Assm: 7,5#4 7,5#4 ×10−5  1034 1034,21 ,21 ×103 

 ÷( m 2, 42 424  8#87, 2  2 2 = 3,133 ×10 −5 ×115, 08 08 ( m 3 / s )

/ s)

2

2

=

2

= 3, 60 605 ×10−3 ( m 3 / s ) ∴  = 0, 06 060 m 3 / s

2

3

3














A

+

% A

γ

+

)A2 2g

=

@

+

% @

γ

Assm Assm : )@2 2g

−

)A2 2g

)@2 − )A2 ;ogo ;ogo :

=

%A

γ

−

%@

γ

 % %  = 2g  A − @ ÷  γ γ 

+

)@2 2g














 = )A ×A A

πDA2  = )A ×

4 !ubsttu"do !ubsttu"do : = =

6, 07 07 × π × ( 0,15 )

2

4 0,42# 0, 42#1 1 4

m 3 / s ∴

m3 / s 0,107 m 3 / s = 0,















Rua 96 nº 45 – Setor Sul – Goiânia – Fone: (62) 3092-2268 afonsoarioa!afonso afonsoarioa!afonsoarioa"o#"$r arioa"o#"$r % afonsoarioa!&ot#ail" afonsoarioa!&ot#ail"o# o# Assm Assm :

πDA2  = )A × 4

"de:














 = )A A A ou

= )@A @














Ɛ













Rua 96 nº 45 – Setor Sul – Goiânia – Fone: (62) 3092-2268 afonsoarioa!afonso afonsoarioa!afonsoarioa"o#"$r arioa"o#"$r % afonsoarioa!&ot#ail" afonsoarioa!&ot#ail"o# o# 1ssi# 1ssi# : f =

*)325

  ε 5)<4   + ln  3) <' 0)9 ÷   <' Re   

2














1ssi#: f =

*)325 2   ε 5)<4   + ln  3)<' ÷ )< ' Re 0)9    







































FENÔMENOS DE TRANSPORTES.- EXERCÍCIOS RESOLVIDOS EM 26 NOV 2013.- 01 COLUNA

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