TITLE.PM5

334 ENGINEERING THERMODYNAMICS

DHARM
M-therm\Th6-2.PM5

If N 2 is the final r.p.m. of the flywheel, then

ω 2 2 π^2

60

= N or N 2

17 59 60

2

=

. ×
π = 168 r.p.m.
i.e., Final r.p.m. of the flywheel = 168 r.p.m. (Ans.)

+Example 6.21. The air, in a steady flow, enters the system at a pressure of 8 bar and
180 °C with a velocity of 80 m/s and leaves at 1.4 bar and 20°C with a velocity of 40 m/s. The
temperature of the surroundings is 20°C and pressure is 1 bar. Determine :
(i)Reversible work and actual work assuming the process to be adiabatic ;
(ii)Irreversibility and effectiveness of the system on the basis of 1 kg of air flow.
Take for air : cp = 1.005 kJ/kg K ; R = 0.287 kJ/kg K.
Solution. Initial pressure of air, p 1 = 8 bar
Initial temperature of air, T 1 = 180 + 273 = 453 K
Final pressure of air, p 2 = 1.4 bar
Final temperature, T 2 = T 0 = 20 + 273 = 293 K
Surroundings’ pressure, p 0 = 1 bar
Mass of air = 1 kg
Initial velocity of air, C 1 = 80 m/s
Final velocity of air, C 2 = 40 m/s.
(i)Reversible work and actual work :
Availability of air at the inlet

= (h 1 – h 0 ) – T 0 (s 1 – s 0 ) +

C 12

2

= cp (T 1 – T 0 ) – T 0 (s 1 – s 0 ) + C^1

2

2

(s 1 – s 0 ) = cp loge

T

T

1

0

F

HG

I

KJ – R loge^

p

p

1

0

F

HG

I

KJ

= 1.005 loge

453

293

F

HG

I

KJ – 0.287 loge^

8

1

F

HG

I

KJ

= 0.437 – 0.596 = – 0.159 kJ/kg K

∴ Availability of air at the inlet

= 1.005 (453 – 293) – 293 (– 0.159) +

80

210

2

×^3

= 160.8 + 46.58 + 3.2 = 210.58 kJ

Availability at the exit

= (h 2 – h 0 ) – T 0 (s 2 – s 0 ) +

C 22

2

= – T 0 (s 2 – s 0 ) + C^2

2

2

as h 2 = h 0 because T 2 = T 0 = 293 K

Now s 2 – s 0 = – R loge

p

p

2

0

F

HG

I

KJ = – 0.287 loge^

14

1

F.

HG

I

KJ = – 0.09656 kJ/kg K

∴ Availability at the exit

= – 293 (– 0.09656) +

40

210

2

×^3 = 29.09 kJ/kg