The HVAC system of a home typically has a fan that circulates air through the home. Assume that the fan is being run by a small DC electric motor. The HVAC system is in ‘circulate’ mode, i. e. the fan is simply blowing air into the home, without either cooling or heating it. The motor runs on a 50A, 20V DC input. The shaft between the motor and fan rotates at 500rpm and provides a torque of 18.35 N-m to the fan. The fan takes in still, ambient air. The outgoing air is measured to have a speed of 5m/s and a flow rate of 72 kg/s. Calculate the motor and fan efficiencies, and the overall efficiency of the motor-fan pair.