Question

018 (part 1 of 2) A jet aircraft is traveling at 211 m/s in horizontal flight. The engine takes in air at a rate of 79.2 kg/s and burns fuel at a rate of 4.74 kg/s. The exhaust gases are ejected at 500 m/s relative to the aircraft. Find the thrust of the jet engine. Answer in units of N.

019 (part 2 of 2) Find the delivered power. Answer in units of W.

Answer 1

The speed of the jet v = 211 m/s

The air intake is dM_a/dt = 79.2 kg/s

The fuel burn rate is dM_f/dt = 4.74 kg/s

The speed of the exhaust gas is u = 500 m/s

The rate of mass change in the rocket is

dM/dt = 79.2 kg/s + 4.74 kg/s

          = 83.94 kg/s

The thrust on the rocket is

T = (dM/dt)u - (dM_a/dt)v

    = (83.94 kg/s)(500m/s)-(79.2 kg/s)(211 m/s)

    = 25258.8 N

The power of the rocket is

P = vT

   = (211m/s)(25258.8 N)

   = 5329606.8 W

   = 5.33 MW