TITLE.PM5

896 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th16-2.pm5

=

[(.). ][..(.)]

(. ).

141 15 221415 141

14 1 15

29 59

12 96

22

22

−× + × × − −

+×

= × = 1.32

∴ T 2 = 296 × 1.32 = 390.72 K or 117.72°C. Ans.

M 22 =

()

()

γ

γγ

−+

−−

12

21

1

2

12

M

M

...[Eqn. (16.49)]

= (. ).

..(.)

14 1 15 2

21415 141

29

59

2

2

−× +

×× − −

= = 0.49

∴ M 2 = 0.7. Ans.

(ii) Strength of shock :

Strength of shock = p

p

2

1

• 1 = 2.458 – 1 = 1.458. Ans.

Highlights

1. A compressible flow is that flow in which the density of the fluid changes during flow.


2. The characteristic equation of state is given by :
   p
   ρ = RT
   where p = absolute pressure, N/m^2 ,
   ρ = density of gas, kg/m^3 ,
   R = characteristic gas constant, J/kg K, and
   R = absolute temperature (= t°C + 273).


3. The pressure and density of a gas are related as :
   For isothermal process : p
   ρ
   = constant

For adiabatic process : p

ργ

= constant.

4. The continuity equation for compressible flow is given as :
   ρAV = constant
   dρ
   ρ +

dA

A

dV

V

+ = 0 ... in differential form.

5. For compressible fluids Bernoulli’s equation is given as :

(^) ρpg loge p + V
g
2
2

• z = constant ... for isothermal process
  γ
  γρ−
  F
  HG
  I
  KJ


• 
  

  12
  p^2
  g
  V
  g

  
  


• z = constant ... for adiabatic process.

6. Sonic velocity is given by :

C = dp

d

K

ρρ

= ... in terms of bulk modulus