Question

A compressor operates at steady state with Refrigerant 134a as the working fluid. The refrigerant enters at 0.24 MPa, 0°C, with a volumetric flow rate of 0.64 m/min. The diameters of the inlet and exit pipes are 3 and 1.5 cm, respectively. At the exit, the pressure is 1.0 MPa and the temperature is 50°C. If the magnitude of the heat transfer rate from the compressor to its surroundings is 5% of the compressor power input, determine the power input, in kW.

Answer 1

POWER INPUT = 82.989 KW

Step-by-step explanation:

For pressure P =0.24 MPa and T_1 = 0 DEGREE, Enthalapy _1 = 248.89 kJ/kg

For pressure P =1 MPa and T_1 = 50 DEGREE, Enthalapy _1 = 280.19 kJ/kg

Heat loss Q = 0.05w

Inlet diameter = 3 cm

exit diamter = 1.5 cm

volume of tank will be v = area * velocity

velocity at inlet
`= (0.64\60 m/s)/( (\pi)/(4) (3* 10^(-2))^2) = 15.09  m/s`

velocity at outlet
`= (0.64\60 m/s)/( (\pi)/(4) (1.5* 10^(-2))^2) = 60.36  m/s`

steady flow energy equation

`E_(IN) = E_(OUT)`

`h_1 + (v_1^2)/(2g) +wc = h_2 + (v_2^2)/(2g) + 0.05wc`

`248.89 + (15.09^2)/(2) + wc = 280.18 + (60.36^2)/(2) + 0.05 wc`

solving wc = 1830.64 kJ/kg

wc in KWH

we know that
`wc = \dot m wc`

`\dot m = 4.25 kg/m3 * (0.64/60) m^3/s`

`\dot m = 0.04533  kg/s`

`wc = 0.04533 * 1830.64 = 82.989 kW`