Answer:
(a) the mass flow rate of air is 5.351 kg/s
(b) the input power required is 2090.786 kW
Explanation:
Given;
initial pressure, P₁ = 100 kPa
initial temperature, T₁ = 20 °C
Final pressure, P₂ = 1.8 MPa
Final temperature, T₂ = 400 °C
Inlet area of the compressor = 0.15 m²
outlet area of compressor = 0.078 m²
velocity of air = 30 m/s
Part (a) mass flow rate of air through the inlet
Mass flow rate = Area x velocity = density x volumetric rate
m = Av = ρV
from ideal gas law, PV = nRT and ρ = m/V
substitute these values in the above equations, we will have;


Part (b) the required power input

where;
W is the input power
m is the mass flow rate
h₁ is the initial enthalpy
h₂ is the final enthalpy
initial and final enthalpy are obtained from steam table using interpolation;
h₁ = 293.166 kJ
h₂ = 684.344 kJ
