Question

Air enters a turbojet engine at \(320 \mathrm{m} / \mathrm{s}\) at a rate of \(30 \mathrm{kg} / \mathrm{s},\) and exits at \(650 \mathrm{m} / \mathrm{s}\) relative to the aircraft. The thrust developed by the engine is \((a) 5 \mathrm{kN}\) \((b) 10 \mathrm{kN}\) \((c) 15 \mathrm{kN}\) \((d) 20 \mathrm{kN}\) \((e) 26 \mathrm{kN}\)

Short answer

(a) 5 kN (b) 10 kN (c) 15 kN (d) 20 kN Answer: (b) 10 kN

Step-by-step solution

Identify the given parameters and the thrust formula

We are given: - Air entering velocity (Vi) = 320 m/s - Air exiting velocity (Ve) = 650 m/s (relative to the aircraft) - Mass flow rate (m) = 30 kg/s We'll use the thrust formula: Thrust (T) = m * (Ve - Vi)

Calculate the change in velocity

We need to find the difference between the exiting and entering velocities. So, subtract the entering velocity from the exiting velocity: ΔV = Ve - Vi = 650 m/s - 320 m/s = 330 m/s

Calculate the thrust

Now, use the thrust formula and the values we found for mass flow rate (m) and change in velocity (ΔV): T = m * ΔV = 30 kg/s * 330 m/s = 9900 N

Convert thrust to kN and find the answer

Now, we need to convert the thrust from Newtons (N) to kilonewtons (kN) by dividing by 1000: Thrust (T) = 9900 N / 1000 = 9.9 kN ≈ 10 kN The thrust developed by the turbojet engine is approximately 10 kN. Therefore, the correct answer is (b) 10 kN.

Key concepts

Thrust Formula

Understanding how to calculate the thrust generated by a turbojet engine is critical for students diving into the world of aerospace engineering. Thrust is the forward force that propels the aircraft through the air and is a result of Newton's third law of motion — for every action, there is an equal and opposite reaction.

In the simplest terms, the thrust formula can be expressed as: