An airplane flies at \(200 \mathrm{~km} / \mathrm{h}\) through still air of specific weight \(12 \mathrm{~N} / \mathrm{m}^{3}\). The propeller is \(2.4 \mathrm{~m}\) in diameter and its slipstream has a velocity of \(290 \mathrm{~km} / \mathrm{h}\) relative to the fuselage. Calculate

(a) the propeller efficiency,

(b) the velocity through the plane of the propeller,

(c) the power input,

(d) the power output,

(e) the thrust of the propeller,

(f) the pressure difference across the propeller disk.