COMPRESSIBLE FLOW 895

dharm

\M-therm\Th16-2.pm5

16.11.2.Oblique shock wave

As shown in Fig. 16.12, when a supersonic flow
undergoes a sudden turn through a small angle α (posi-
tive), an oblique wave is established at the corner. In
comparison with normal shock waves, the oblique shock
waves, being weaker, are preferred.
The shock waves should be avoided or made as
weak as possible, since during a shock wave conversion
of mechanical energy into heat energy takes place.

16.11.3.Shock Strength

The strength of shock is defined as the ratio of pressure rise across the shock to the upstream

pressure.

i.e. Strength of shock =

pp

p

p

p

21

1

2

1

−

= – 1

=

21

1

1 211

1

1

2

1

γγ^2

γ

γγ γ

γ

MM−−

+

−= −−−+

+

() ()()

=

211

1

22

1

2

1

1

2

1

γγγ^2

γ

γγ

γ

γ

γ

MM−+−−

+

= −

+

=

+ (M^1

(^2) – 1)
Hence, strength of shock =
2
1
γ
γ+ (M^1
(^2) – 1) ...(16.50)
Example 16.19. In a duct in which air is flowing, a normal shock wave occurs at a Mach
number of 1.5. The static pressure and temperature upstream of the shock wave are 170 kN/m^2
and 23°C respectively. Determine :
(i)Pressure, temperature and Mach number downstream of the shock, and
(ii)Strength of shock.
Take γ = 1.4.
Sol. Let subscripts 1 and 2 represent flow conditions upstream and downstream of the
shock wave respectively.
Mach number, M 1 = 1.5
Upstream pressure, p 1 = 170 kN/m^2
Upstream temperature, T 1 = 23 + 273 = 296 K
γ = 1.4
(i) Pressure, temperature and Mach number downstream of the shock :
p
p
2
1

21
1
1
γγ^2
γ
M −−

• 
  

  ()
  ...[Eqn. (16.46)]

  
  

  21415 141
  14 1
  63 04
  24
  ×× − −^2

  
  


• 
  

  ..(.)= −
  .
  ..

  
  

. = 2.458
∴ p 2 = 170 × 2.458 = 417.86 kN/m^2. Ans.
T
T

2

1

=

[( ) ] [ ( )]

()

γγγ

γ

−+ −−

+

122 1

1

12 12

2

1

2

MM

M ...[Eqn. (16.48)]

a

Sharp corner

Shock

Supersonic

flow

Fig. 16.12. Oblique shock wave.