Meriam, Kraige & Bolton — Kinetics of Systems of Particles: Problem 4_53

4/53 The helicopter shown has a mass \( m \) and hovers in position by imparting downward momentum to a column of air defined by the slipstream boundary shown. Find the downward velocity \( v \) given to the air by the rotor at a section in the stream below the rotor, where the pressure is atmospheric and the stream radius is \( r \). Also find the power \( P \) required of the engine. Neglect the rotational energy of the air, any temperature rise due to air friction, and any change in air density \( \rho \).