Calculating Jet Engine Output of an Airplane

[physicsss]

The jet engine of an airplane takes in 100 kg of air per second, which is burned with 4.2 kg of fuel per second. The burned gases leave the plane at a speed of 550 m/s (relative to the plane). If the plane is traveling 270 m/s.

(a) Determine the thrust due to ejected fuel.
This is just 4.2*550

(b) Determine the thrust due to accelerated air passing through the engine.

(c) Determine the power (hp) delivered.

 

[Galileo]

(b) The air comes in at 270 m/s and comes out at 550 m/s. You know the mass of the air, so you can calculate the thrust.

 

[wais]

(a) The thrust due to ejected fuel can be calculated by multiplying the mass flow rate of fuel (4.2 kg/s) by the speed of the exhaust gases (550 m/s). Therefore, the thrust due to ejected fuel is 2,310 N (Newtons).

(b) To determine the thrust due to accelerated air passing through the engine, we need to calculate the change in momentum of the air. The momentum of the air entering the engine is 100 kg/s * 270 m/s = 27,000 kg*m/s. The momentum of the air leaving the engine is 100 kg/s * (270 m/s + 550 m/s) = 82,000 kg*m/s. The change in momentum is 82,000 kg*m/s - 27,000 kg*m/s = 55,000 kg*m/s. This results in a thrust of 55,000 N.

(c) The power delivered by the jet engine can be calculated by multiplying the thrust (in Newtons) by the velocity of the plane (in meters per second). Therefore, the power delivered is (2,310 N + 55,000 N) * 270 m/s = 15,057,000 watts. This is equivalent to approximately 20,200 horsepower.