Problem $4$:

A centrifugal compressor features an impeller tip speed of $360\frac{m}{s}.$ Determine the following:

The absolute Mach number of the flow as it exits the radial vanes of the impeller.

The mass flow rate.

Given data:

Impeller Tip Speed: $360\frac{m}{s}$

Radial Component of Flow Velocity at Impeller Exit: $30\frac{m}{s}$

Slip Factor: $0\mathrm{.}9$

Flow Area at Impeller Exit: $0\mathrm{.}1m^2$

Power Input Factor: $1\mathrm{.}0$

Isentropic Efficiency: $0\mathrm{.}9$

Inlet Stagnation Temperature: $300$ K

Inlet Stagnation Pressure: $100k\frac{N}{m^2}$

Gas Constant $($R$)$ for air: $287\frac{J}{k}g*K$

Ratio of Specific Heats $()$ for air: $1\mathrm{.}4$