Question

A flow rate of 0.4 m / s of air enters a compressor at 100 kPa. 20ºC and 20m / s and leaves at 500C and 120 m / S. Determine the power of the compressor if the heat losses are 3000 kJ / min.

Answer 1

Solution :

Assumption: This is steady-flow process .Potential energy negligible. Air is an ideal gas.

Properties:

The inlet and exit enthalpies of the air are from (Table A-17)

T1 = 23o C = 293 K    --- > h1 = 292.67 kJ/kg

T2 = 500o C = 773 K --- > h2 = 789.20 kJ/kg

There is only one inlet and one exit , thus mass flow rate m = m1=m2

v1 = RT1/P1 = (0.2870 KJ/kg.K) (293 K) / 100 kpa = 0.841 m3 / kg

so Volume flow rate , V= m . v1 ( m = Mass flow rate , Kg/s) , Given V = 0.4 m3 / s

So, mass flow rate . m = 0.4 / 0.841 = 0.48 kg/s

We take the compressor as the system, which is a control volume because mass crosses the boundary. The enthalpy balance is the rate form as

Ein = Eout

Win +m .( h1 + (U12 / 2) )= Qout +m . ( h2 + (U22 / 2) ) ( Potential energy change negligible) ( U= Velocity )

where Qout = 3000 kJ / min = 3000/60 = 50 KJ/s

Win = Qout + m ( h2 - h1 + ( U22 - U12 ) /2 )

= 50 + 0.48 (kg/s) ( (789.20 - 292.67) ( kJ/kg) + (1202 - 202 ) / 2 x ( 1/1000) KJ/kg /m2/s2

   = 50 KJ/s +0.48 (kg/s) (496.53 ( kJ/kg) + 7000 /1000 ( kJ/kg) ) = 50 + 0.48 (496.53 + 7 )

   = 291.69 KJ/s = 291.69 KW (ans)

So power of the compressor is 291.69 KW.