An air-conditioning system requires airflow at the main supply duct at a rate of 130 mVmin...

An air-conditioning system requires airflow at the main supply duct at a rate of 130 mVmin. The average velocity of air in the circular duct is not to exceed 8 m/s to avoid excessive vibration and pressure drops. Assuming the fan converts 80 percent of the electrical energy it consumes into kinetic energy of air, determine the size of the electric motor needed to drive the fan and the diameter of the main duct. Take the density of air to be 1.20 kg/m3.