A turbocharger is used to increase the power output of a reciprocating engine by compressing the air/fuel mixture prior to induction into the engine. The power to run the compressor is provided by a...

A turbocharger is used to increase the power output of a reciprocating engine by compressing the air/fuel mixture prior to induction into the engine. The power to run the compressor is provided by a turbine in the exhaust gas stream. The compressor and the turbine share a common shaft and hence rotate at the same speed. Consider a turbocharger with the following specifications: Compressor inlet air—14.0 psia, 70◦F, cp = 0.24 Btu/lbm ◦R, γ = 1.4, m˙ = 0.5 lbm/s; Compressor discharge pressure = 28 psia; Turbine exhaust gas properties are 1100◦F, c_p
= 0.27 Btu/lbm ◦R, and γ = 1.3; the turbine exhausts to atmospheric pressure. Neglect the fuel mass added between the compressor discharge and the turbine inlet. a. Assuming an optimum choice for the compressor, estimate its speed and size.  b. What power must the turbine supply to run the compressor?   c. Since turbines are naturally more efficient than compressors, assume that (η_t,s
= η_c,s
+ 0.05) and estimate the pressure at the turbine inlet.                             d. What type of turbine would be expected to yield this efficiency? What would be its size?