TITLE.PM5

168 ENGINEERING THERMODYNAMICS

dharm

/M-therm/Th4-4.pm5

Pressure of air at outlet to the compressor, p 2 = 7 bar

Specific volume of air at inlet to the compressor, v 1 = 0.85 m^3 /kg

Specific volume of air at outlet to the compressor, v 2 = 0.16 m^3 /kg

Difference of internal energy at the outlet and inlet of the compressor,

(u 2 – u 1 ) = 90 kJ/kg

Heat rejected by air (to cooling water),

Q = –

60

0.5 = – 120 kJ/kg.

(i)Power required to drive the compressor :

Using the steady flow energy equation,

u 1 + C^1

2

2 + p^1 v^1 + Q = u^2 +

C 22

2 + p^2 v^2 + W

∴ W = (u 1 – u 2 ) +

CC 12 22

22 −

F

HG

I

KJ + (p^1 v^1 – p^2 v^2 ) + Q

= – 90 +

1

1000

6

2

5

2

22

−

F

HG

I

KJ +

10

1000

5

(1 × 0.85 – 7 × 0.16) + (– 120)

= – 90 + 0.0055 – 27 – 120 = – 237 kJ/kg (app.).
(Note that the change in kinetic energy is negligibly small in comparison with the other
terms).
i.e., Work input required = 237 kJ/kg = 237 × 0.5 kJ/s = 118.5 kW
Hence, power required to drive the compressor = 118.5 kW. (Ans.)
(ii)Inlet and outlet pipe cross-sectional areas, A 1 and A 2 :
Using the relation,

m& CA

v

=

∴ A 1 = mv&

C

1

1

00

6

= .5× .85m^2 = 0.0708 m^2

i.e., Inlet pipe cross-sectional area, A 1 = 0.0708 m^2. (Ans.)

Again, A 2 = mv&

C

2

2

00

5

= .5× .16m^2 = 0.016 m^2.

i.e., Outlet pipe cross-sectional area, A 2 = 0.016 m^2. (Ans.)
Note. In this example, the steady flow energy equation has been used, despite the fact the compression
consists of : suction of air ; compression in a closed cylinder ; and discharge of air. The steady flow equation can be
used because the cycle of processes takes place many times in a minute, and therefore, average effect is steady flow
of air through the machine.

Example 4.38. In a steam plant, 1 kg of water per second is supplied to the boiler. The
enthalpy and velocity of water entering the boiler are 800 kJ/kg and 5 m/s. The water receives
2200 kJ/kg of heat in the boiler at constant pressure. The steam after passing through the turbine
comes out with a velocity of 50 m/s, and its enthalpy is 2520 kJ/kg. The inlet is 4 m above the
turbine exit. Assuming the heat losses from the boiler and the turbine to the surroundings are