TITLE.PM5

894 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th16-2.pm5

Mach number, M 2 :

M 22 =

()

()

γ

γγ

−+

−−

12

21

1

2

1

2

M

M

...[Eqn. (16.49)]

=

()

()

1.4

1.4 1.4

3.6

11.2 0.4

−× +

××− −

=

−

12 2

22 1

2

2 = 0.333

∴ M 2 = 0.577 (Ans.)

Pressure, p 2 :

p

p

2

1

=

21

1

1

γγ^2

γ

M −−

+

()

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

=

2142 141

14 1

11 2 0 4

24

××− −^2

+

.(.)= −

(. )

..

. = 4.5
∴ p 2 = 26.5 × 4.5 = 119.25 kN/m^2 (Ans.)
Density, ρ 2 :
ρ
ρ

2

1

=

()

()

γ

γ

+

−+

1

12

1

2

1

2

M

M ...[Eqn. (16.47)]

= (. )

(. )

.

.

14 1 2

14 1 2 2

96

16 2

2

2

+

−+

=

+

= 2.667

∴ ρ 2 = 0.413 × 2.667 = 1.101 kg/m^3 (Ans.)

Temperature, T 1 :

Since p 1 = ρ 1 RT 1 , ∴ T 1 =

p

R

1

ρ 1

=

26 5 10

0 413 287

.^3
.

×

× = 223.6 K or – 49.4°C (Ans.)

Temperature, T 2 :

T

T

2

1

= [( ) ] [ ( )]

()

[( ) ] [ ( )]

()

γγγ

γ

−+ −−

+

= −+ ××−−

+

122 1

1

12 2 2 2 1

12

12 12

2 12

22

22

MM

M

1.4 1.4 1.4

1.4

= (. )(..

.

16 2 112 0 4)

23 04

+− = 1.6875

∴ T 2 = 223.6 × 1.6875 = 377.3 K or 104.3°C (Ans.)

Velocity, V 1 :

C 1 = γRT 1 = 1 4 287 223 6..×× = 299.7 m/s

Since

V

C

1

1

= M 1 = 2 ∴ V 1 = 299.7 × 2 = 599.4 m/s (Ans.)

Velocity, V 2 :

C 2 = γRT 2 = 1 4 287 377 3..×× = 389.35 m/s

Since

V

C

2

2

= M 2 = 0.577 ∴ V 2 = 389.35 × 0.577 = 224.6 m/s (Ans.)