### Problem StatementA jet is flying at a velocity of 750 km/h. Still air enters its engine nacelle at point A, which has a cross-sectional area of 0.8 m². Fuel is mixed with the incoming air at a rate of \( \dot{m}_e = 2.5 \, \text{kg/s} \) and is exhausted with a velocity of 900 m/s, measured relative to the plane. The task is to determine the force exerted by the engine on the plane. The density of the air is given as \( \rho_a = 0.850 \, \text{kg/m}^3 \).### Diagram ExplanationThe diagram shows a side view of a jet aircraft, highlighting the engine nacelle. An arrow indicates the entry of still air into the nacelle at point A, and a stream of exhaust is shown exiting the rear of the nacelle. The engine’s operation involves the intake of air, mixing with fuel, and expelling exhaust at high velocity to generate thrust.### Given Data- Speed of the jet: 750 km/h- Cross-sectional area (A) at intake: 0.8 m²- Exhaust velocity: 900 m/s- Rate of fuel-air mixture entering: \( \dot{m}_e = 2.5 \, \text{kg/s} \)- Air density: \( \rho_a = 0.850 \, \text{kg/m}^3 \)### ObjectiveCalculate the thrust force exerted by the engine on the plane. This involves considering the momentum change of the air-fuel mixture as it accelerates from rest (relative to the still air) to the exhaust speed.The problem involves using principles of fluid dynamics and conservation of momentum to determine the thrust produced by the engine.

Answered: Image /qna-images/answer/7be63327-ff07-4d5a-9eb3-8d652c44d45b.jpg

6-79. The jet is flying at 750 km/h. Still air en- ters its engine nacelle at A having a cross- sectional area of 0.8 m2. Fuel is mixed with the air at me = 2.5 kg/s and is exhausted with a velocity of 900 m/s, measured relative to the plane. Determine the force the engine exerts on the plane. Take Pa = 0.850 kg/m3.

6-79. The jet is flying at 750 km/h. Still air en- ters its engine nacelle at A having a cross- sectional area of 0.8 m2. Fuel is mixed with the air at me = 2.5 kg/s and is exhausted with a velocity of 900 m/s, measured relative to the plane. Determine the force the engine exerts on the plane. Take Pa = 0.850 kg/m3.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

### Problem Statement

A jet is flying at a velocity of 750 km/h. Still air enters its engine nacelle at point A, which has a cross-sectional area of 0.8 m². Fuel is mixed with the incoming air at a rate of \( \dot{m}_e = 2.5 \, \text{kg/s} \) and is exhausted with a velocity of 900 m/s, measured relative to the plane. The task is to determine the force exerted by the engine on the plane. The density of the air is given as \( \rho_a = 0.850 \, \text{kg/m}^3 \).

### Diagram Explanation

The diagram shows a side view of a jet aircraft, highlighting the engine nacelle. An arrow indicates the entry of still air into the nacelle at point A, and a stream of exhaust is shown exiting the rear of the nacelle. The engine’s operation involves the intake of air, mixing with fuel, and expelling exhaust at high velocity to generate thrust.

### Given Data

- Speed of the jet: 750 km/h
- Cross-sectional area (A) at intake: 0.8 m²
- Exhaust velocity: 900 m/s
- Rate of fuel-air mixture entering: \( \dot{m}_e = 2.5 \, \text{kg/s} \)
- Air density: \( \rho_a = 0.850 \, \text{kg/m}^3 \)

### Objective

Calculate the thrust force exerted by the engine on the plane. This involves considering the momentum change of the air-fuel mixture as it accelerates from rest (relative to the still air) to the exhaust speed.

The problem involves using principles of fluid dynamics and conservation of momentum to determine the thrust produced by the engine.

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