Question

A jet engine gets its thrust by taking in air, heating and compressing it, and

then ejecting it at a high speed. If a particular engine takes in 20 kg of air per
second at 100 m/s, and ejects it at 500 m/s, calculate the thrust of the engine.​

Answer 1

The thrust of the jet engine is calculated based on the change in momentum per unit time. With an air mass flow rate of 20 kg/s and a change in velocity of 400 m/s, the thrust is found to be 8000 N.

Step-by-step explanation:

To calculate the thrust of a jet engine, we can use the principle of conservation of momentum. The thrust (F) can be found by the change in momentum of the air per unit time. The formula for thrust is:

F = Δ(mv) / Δt

Where:

• m is the mass of air
• v is the velocity of the air
• Δ represents the change in a quantity
• Δt is the change in time

In the given problem, the air mass flow rate (m/t) is 20 kg/s. The change in velocity (Δv) is the difference between the ejection velocity and the intake velocity, which is 500 m/s - 100 m/s = 400 m/s. Thus, the thrust is:

F = (20 kg/s × 400 m/s)

F = 8000 N (newtons)

Therefore, the thrust of the jet engine is 8000 N.

Answer 2

`F=ma=20\ Kg\ 400\ m/s^2=8,000\ Nw`

Step-by-step explanation:

Thrust is known as a reaction force which appears when a system expels or accelerates mass in one specific direction. If we know the acceleration and the mass of the air expelled by the jet engine, we can compute the thrust .

The acceleration is calculated by using the dynamics formula

`\displaystyle a=(v_f-v_o)/(t)`

The values are

`v_f=500\ m/s,\ v_o=100\ m/s,\ t=1\ sec`

`\displaystyle a=(500-100)/(1)=400\ m/s^2`

The thrust is

`F=ma=20\ Kg\ 400\ m/s^2=8,000\ Nw`