1. The problem statement, all variables and given/known data Fan blades of radius r are mounted directly on the axle of a d.c. electric motor. assuming that the fan imparts a velocity v to a cylinder of air of radius equal to that of the blades, and that the density of the air is ρ, obtain expressions for: i. the rate at which momentum is transferred to the air ii. the thrust on the motor iii. the rate of working of the motor iv. the rate at which kinetic energy is supplied to the air Comment on any apparent conflict between your answers. 3. The attempt at a solution i. ∏r2 . v . ρ . v explanation: rate of supply of mass x velocity of air imparted ii. ∏r2ρv explanation: since thrust = force (newton's third law) iii. ∏r2ρv . v explanation: rate at which momentum is transferred to air x distance travelled by the momentum per second iv. The answer is half that of iii. Could anyone please explain to me why? Does it have anything to do with the centre of "mass" of the air cylinder pushed? Something like "half the amount of energy the cylinder of air gains becomes the potential energy"? It doesn't really make sense to me. Please help. Thank you!