kit MFL 2 V4

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Kit MFL 2 
V4 
Termodinâmica 
• Para o ar 
– Rg = 287 m
2s-2 K-1 
– k = 1,400 
– cv = 718 m
2s-2 K-1 
– cp = 1.005 m
2s-2 K-1 
 ou g gp R T p R T
ˆ ,v pdu c dT dh c dT
, ,
1 1
g g
v p
R kR
c c
k k
/( 1)
2 2 2
1 1 1
Em processos isentrópicos,
k k k
p T
p T
ga kR T
Escoamento Isentrópico 
/( 1)
20 ( 1)1
2
k k
p k
M
p

 
  
 
1/( 1)
20 ( 1)1
2
k
k
M



 
  
 
20 ( 1)1
2
T k
M
T
 
  
 
1/ 2
20 ( 1)1
2
a k
M
a
 
  
 
/(1 )
2
0
( 1)
1
2
k k
p k
M
p

 
  
 
1/(1 )
2
0
( 1)
1
2
k
k
M



 
  
 
1
2
0
( 1)
1
2
T k
M
T

 
  
 
1/ 2
2
0
( 1)
1
2
a k
M
a

 
  
 
2
0
2 p
V
T T
c
 
max 02 pV c T
20
0.5
20
3.5
20
2.5
20
Para o ar:
1 0.2
1 0.2
1 0.2
1 0.2
T
M
T
a
M
a
p
M
p
M


 
   
   
   
2/ 72/5
2 0 0 0Ar: 5 1 5 1 5 1
T p
M
T p


      
           
           
Valores Críticos 
1
0
1/ 2
0
/(1 )
0
1/(1 )
0
* 1
2
* 1
2
* 1
2
* 1
2
k k
k
T k
T
a k
a
p k
p
k





 
  
 
 
  
 
 
  
 
 
  
 
0
0
0
0
Para o ar:
*
0.8333
*
0.9129
*
0.5283
*
0.6339
T
T
a
a
p
p






* *ga V kR T 
0
2
*
1
g
k
a V R T
k
 

Escoamento em Dutos 
1/ 2 1/( 1)
2
2 3
1 1 ( 1) / 2
* ( 1) / 2
(1 0,2 )
* 1,728
k
A k M
A M k
A M
A M
 
  
  
 


max 0 0
0
max
0
Para o ar
0,6847 *
0,6847 *
g
g
m A R T
p A
m
R T


2
0,45
1/ 2
1/5
2 /3
1 0,27 ( / *)
, 1,34
1,728 ( / *) *
1 0,88 ln , 1,0 1,34
* *
1 1,2 1 , 1,0 2,9
* *
216 254 , 2,9
* * *
A A A
A A A
A A
A A
M
A A
A A
A A A
A A A
 
  

  
    
 
 
        

   
      
    
Subsônico 
Supersônico 
Função Vazão Mássica Local 
2/ ( 1) /
0
0 0 0
2
1
1
k k k
gR Tm k p p
F
A p k p p
    
      
      
0
Se 0,5283:
escoamento bloqueado
p
p

Ar a 15 ºC e Patm 
 
Rg = 287 m
2s-2 K-1, k = 1,400,  = 1,79.10-5 N.s.m-2, 
 = 1,46.10-5 m2s-1, cv = 718 m
2s-2 K-1, cp = 1.005 m
2s-2 K-1