QUESTION $01-$ Centrifugal Compressor

A centrifugal compressor has a pressure ratio of $4$:$1$ with an isentropic efficiency of $80\%$ when running at $15000$ rpm and inducing air at $20C.$ The impeller tip diameter is $590$ mm $.$ Calculate the slip factor of the compressor if the airflow at the entry to the impeller is in the axial direction.

Take $C_P=1\mathrm{.}005k\frac{J}{k}gK$ and $=1\mathrm{.}4$

A centrifugal compressor running at $16000$ rpm takes in air at $17C$ and compresses $\frac{P_1}{P_2}=4$ it through a pressure ratio of $4,$ with an isentropic efficiency of $82\%.$ The airflow at the entry to the impeller is in an axial direction. If the slip factor is $0\mathrm{.}85,$ calculate the impeller tip diameter. Take $C_P=1\mathrm{.}005k\frac{J}{k}gK$ and $=1\mathrm{.}4$