An air compressor delivers a volume $0.90\ \mathrm{m^3}$ per minute of air at 6.5 bar pressure (absolute) and $20^\circ\mathrm{C}$. Calculate the mass flow rate of air through the compressor, in kg/s.

The compressor operates steadily, with air entering the compressor at 1.0 bar and temperature $18^\circ\mathrm{C}$, and exiting at 6.5 bar and $140^\circ\mathrm{C}$. The velocity of the air at inlet to the compressor is 90 m/s, and the velocity at the outlet is 35 m/s. If no heat is lost, estimate the power required to drive the compressor.

To reduce the driving power required and to lower the temperature of the delivered air, the compressor is cooled by a water jacket through which water is pumped at a rate 0.04 kg/s. The water enters at $25^\circ\mathrm{C}$ and it leaves at $48^\circ\mathrm{C}$. The compressor continues to pass air at the same mass flow rate and the entry temperature is unchanged, but the temperature of the air at exit is now $66^\circ\mathrm{C}$. Estimate the power now consumed by the compressor, taking the specific heat of water as $4.19\ \mathrm{kJ\,kg^{-1}\,K^{-1}}$, and assuming the same air velocities as before.