Question

Assume both the compressor and the nozzle in Air at 100 kPa, 17°C is compressed to 400 kPa after which it is expanded through a nozzle back to the atmosphere. The compressor and the nozzle are both reversible and adiabatic and kinetic energy in and out of the compressor can be neglected. have an isentropic efficiency of 90% the rest being unchanged. Find the actual compressor work and its exit temperature and find the actual nozzle exit velocity.

Answer 1

C.V. Ideal compressor, inlet: 1 exit: 2

Adiabatic : q = 0.

Reversible: sgen= 0

The ideal nozzle then expands back down to state 1 (constant *). The actual compressor discharges at state 3 however, so we have:

wC= wCs/ηC = -157.18 ⇒ T3 = T1 - wC/Cp = 446.6 K

Nozzle receives air at 3 and exhausts at 5. We must do the ideal (exit at 4) first.