TITLE.PM5

FIRST LAW OF THERMODYNAMICS 175

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/M-therm/Th4-5.pm5

(ii)Ratio of inlet to outlet pipe diameter,

d

d

1

2

:

The mass of air passing through the compressor is given by

m

AC

v

AC

v

==^11

1

22

2

∴

A

A

C

C

v

v

1

2

2

1

1

2

90

12

05

014

=×=×.

. = 26.78

∴

d

d

1

2

F^2

HG

I

KJ

= 26.78 or d

d

1

2

= 5.175

Hence ratio of inlet to outlet pipe diameter = 5.175. (Ans.)
Example 4.44. In a test of water cooled air compressor, it is found that the shaft work
required to drive the compressor is 175 kJ/kg of air delivered and the enthalpy of air leaving is
70 kJ/kg greater than that entering and that the increase in enthalpy of circulating water is
92 kJ/kg.
Compute the amount of heat transfer to the atmosphere from the compressor per kg of air.
Solution. Refer Fig. 4.51.
Shaft work required to drive the compressor, W = – 175 kJ/kg
Increase in enthalpy of air passing through the compressor, (h 2 – h 1 ) = 70 kJ/kg

Air in

1

2

Q

Cooling water out

Cooling water in

Boundary

Win

Air out

Fig. 4.51