Calculating Jet Engine Output of an Airplane

In summary, the jet engine of an airplane takes in 100 kg of air per second and burns 4.2 kg of fuel per second. The burned gases are ejected at a speed of 550 m/s relative to the plane. The thrust due to ejected fuel is 4.2*550. The thrust due to accelerated air passing through the engine is determined by calculating the difference in air speeds and the mass of the air. The power delivered can also be calculated using this information.
  • #1
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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.
 
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  • #2
(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.
 
  • #3


(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.
 

What is the formula for calculating jet engine output of an airplane?

The formula for calculating jet engine output of an airplane is Thrust = Mass flow rate x Exit velocity + (Pressure difference x Area).

How do you determine the mass flow rate of a jet engine?

The mass flow rate of a jet engine can be determined by dividing the engine's fuel flow rate by the specific fuel consumption rate.

What is the exit velocity of a jet engine?

The exit velocity of a jet engine is the speed at which the exhaust gases leave the engine. It is dependent on factors such as the size and design of the engine, as well as the amount of thrust produced.

How does pressure difference affect jet engine output?

The pressure difference between the front and back of the engine affects its output by creating a force that propels the engine forward. This force is known as thrust and is responsible for the movement and speed of the airplane.

What role does the area of the jet engine play in calculating its output?

The area of the jet engine's nozzle affects the amount of air that can pass through it, which in turn affects the mass flow rate and exit velocity. Therefore, it is an important factor in calculating the engine's output.

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