TITLE.PM5

COMPRESSIBLE FLOW 881

dharm

\M-therm\Th16-2.pm5

Relevant relations for critical density and temperature are :

ρ

ρ

2

1

=^2

1

1

1

γ

γ

+

F

HG

I

KJ

−

...[16.30 (a)]

T

T

2

1

=

2

γ+ 1 ...[16.30 (b)]

Value of V 2 for maximum rate of flow of fluid :

Substituting the value of

p

p

2

1

from eqn. (16.29) in eqn. (16.27), we get

V 2 =

2

1

1 2

1

2

1

1 2

1

1

1

1

1

1

1

γ

γρ γ

γ

γρ γ

γ

γ

γ

γ

−

−

+

F

HG

I

KJ

L

N

M

M

M

O

Q

P

P

P

=

−

−

+

F

HG

I

KJ

− ×

−

pp

=^2

1

12

1

2

1

1

1

1

1

1

1

γ

γρ

γ

γ

γ

γρ

γ

− γ

+−

+

F

HG

I

KJ

=

−

−

+

F

HG

I

KJ

pp

or V 2 =

2

1

1

1

γ

γρ+

p

(= C 2 ) ...(16.31)

Maximum rate of flow of fluid through nozzle, mmax :

Substituting the value of

p

p

2

1

from eqn. (16.30) in eqn. (16.28), we get

mmax = A 2

2

1

2

1

2

(^111)
1
2
1
1
γ
γ
ρ
γγ
γ
γγ
γ
γ
γ
γ
−
F
HG
I
KJ +
F
HG
I
KJ
−

• F
  HG
  I
  KJ
  L
  N
  M
  M
  M
  O
  Q
  P
  P
  P


• × − ×


• 
  

  p
  = A 2
  2
  1
  2
  1
  2
  (^111)
  2
  1
  1
  γ^1
  γ
  ρ
  γγ
  γ
  γ
  γ
  −
  F
  HG
  I
  KJ +
  F
  HG
  I
  KJ
  −

  
  


• 
  

  F
  HG
  I
  KJ
  L
  N
  M
  M
  M
  O
  Q
  P
  P
  P
  −

  
  


• 
  

  −
  p
  For air, γ = 1.4,
  ∴ mmax = A 2
  2
  1
  2
  1
  2
  (^111)
  2
  1
  1
  ×^1
  −+
  F
  HG
  I
  KJ
  −

  
  


• 
  

  F
  HG
  I
  KJ
  L
  N
  M
  M
  M
  O
  Q
  P
  P
  P
  −

  
  


• 
  

  1.4 −
  1.4 1.4 1.4
  1.4
  1.4
  1.4
  ()
  pρ
  = A 2 7 p 11 ρ (.0 4018 0 3348−. )
  or mmax = 0.685 A 2 p 11 ρ ...(16.32)
  Variation of mass flow rate of compressible fluid with pressure ratio p
  p
  2
  1
  F
  HG
  I
  KJ
  :
  A passage in which the sonic velocity has been reached and thus in which the mass flow
  rate is maximum, is often said to be choked or in choking conditions. It is evident from eqn.
  (16.28) that for a fixed value of inlet pressure the mass flow depends on nozzle exit pressure.