Question

A centrifugal air compressor used in a gas turbine receives air at 100 kPa and 300 K and discharges it at 400 kPa and 500 K. The velocity of the compressor's outgoing air is 100 m / s. Ignoring the speed at the compressor inlet. 
Determine the power required to drive the compressor, in kW, if the mass flow is 15 kg / s.
Take the Cp of air equal to 1 kJ / (kg K) and assume that there is no heat transfer from the compressor to the surroundings.

Answer 1

by steady flow energy equation

m(h1+V12/2000+gz1/1000)+Q= W +m(h2+V22/2000+gz2/1000)

m=mass flow rate

h=specific enthalpy in KJ/kg

V =velocity in m/s

z1 = height in m

Q = heat transfer in KW

W =Work transfer in KW

h=cp*T

now V1=0 gz1=gz2 Q=0(insulated)

so W = m(h1-h2-V22/2000)

=15*(1*(500-300)-1002/2000)

W=-2925 KW Ans

negative sign indicates work input to compressor