Tài liệu PROBLEMS AND SOLUTIONS IN MECHANICAL ENGINEERING doc

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Copyright © 2007, New Age International (P) Ltd., Publishers

Published by New Age International (P) Ltd., Publishers

All rights reserved.

No part of this ebook may be reproduced in any form, by photostat, microfilm,

xerography, or any other means, or incorporated into any information retrieval

system, electronic or mechanical, without the written permission of the publisher.

All inquiries should be emailed to [email protected]

PUBLISHING FOR ONE WORLD

NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS

4835/24, Ansari Road, Daryaganj, New Delhi - 110002

Visit us at www.newagepublishers.com

ISBN (13) : 978-81-224-2551-2

Preface

Mechanical Engineering being core subject of engineering and Technology, is taught to almost all branches

of engineering, throughout the world. The subject covers various topics as evident from the course content,

needs a compact and lucid book covering all the topics in one volume. Keeping this in view the authors

have written this book, basically covering the cent percent syllabi of Mechanical Engineering (TME￾102/TME-202) of U.P. Technical University, Lucknow (U.P.), India.

From 2004–05 Session UPTU introduced the New Syllabus of Mechanical Engineering which covers

Thermodynamics, Engineering Mechanics and Strength of Material. Weightage of thermodynamics is 40%,

Engineering Mechanics 40% and Strength of Material 20%. Many topics of Thermodynamics and Strength

of Material are deleted from the subject which were included in old syllabus but books available in the

market give these useless topics, which may confuse the students. Other books cover 100% syllabus of this

subject but not covers many important topics which are important from examination point of view. Keeping

in mind this view this book covers 100% syllabus as well as 100% topics of respective chapters.

The examination contains both theoretical and numerical problems. So in this book the reader gets

matter in the form of questions and answers with concept of the chapter as well as concept for numerical

solution in stepwise so they don’t refer any book for Concept and Theory.

This book is written in an objective and lucid manner, focusing to the prescribed syllabi. This book

will definitely help the students and practicising engineers to have the thorough understanding of the

subject.

In the present book most of the problems cover the Tutorial Question bank as well as Examination

Questions of U.P. Technical University, AMIE, and other Universities have been included. Therefore, it is

believed that, it will serve nicely, our nervous students with end semester examination. Critical suggestions

and modifications by the students and professors will be appreciated and accorded

Dr. U.K. Singh

Manish Dwivedi

Feature of book

1. Cover 100% syllabus of TME 101/201.

2. Cover all the examination theory problems as well as numerical problems of thermodynamics, mechanics

and strength of materials.

3. Theory in the form of questions – Answers.

4. Included problems from Question bank provided by UPTU.

5. Provided chapter-wise Tutorials sheets.

6. Included Mechanical Engineering Lab manual.

7. No need of any other book for concept point of view.

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IMPORTANT CONVERSION/FORMULA

1. Sine Rule

R

Q

P

O 180– γ

180–α

α

180–β

γ

sin(180 ) sin (180 ) sin(180 )

PQR = = −α −β −γ

2. Important Conversion

1 N = 1 kg X 1 m/sec2

= 1000 gm X 100 cm/sec2

g = 9.81 m/sec2

1 H.P. = 735.5 KW

1 Pascal(Pa) = 1N/m2

1KPa = 103 N/m2

1MPa = 106 N/m2

1GPa = 109 N/m2

1 bar = 105 N/m2

3. Important Trigonometrical Formulas

1. sin (A + B) = sin A.cos B + cos A.sin B

2. sin (A – B) = sin A.cos B - cos A.sin B

3. cos (A + B) = cos A.cos B – sin A.sin B

4. cos (A – B) = cos A.cos B + sin A.sin B

5. tan (A + B) = (tan A + tan B)/(1 – tan A. tan B)

6. tan (A – B) = (tan A – tan B)/(1 + tan A. tan B)

7. sin2 A = 2sin A.cos A

8. sin2A + cos2A = 1

9. 1 + tan2A = sec2A

10.1 + cot2A = cosec2A

11. 1 + cosA = 2cos2A/2

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CONTENTS

Preface v

Syllabus

Important Conversion/Formula

Part– A: Thermodynamics (40 Marks)

1. Fundamental concepts, definitions and zeroth law 1

2. First law of thermodynamics 30

3. Second law 50

4. Introduction of I.C. engines 65

5. Properties of steam and thermodynamics cycle 81

Part – B: Engineering Mechanics (40 Marks)

6. Force : Concurrent Force system 104

7. Force : Non Concurrent force system 141

8. Force : Support Reaction 166

9. Friction 190

10. Application of Friction: Belt Friction 216

11. Law of Motion 242

12. Beam 265

13. Trusses 302

Part – C: Strength of Materials (20 Marks)

14. Simple stress and strain 331

15. Compound stress and strains 393

16. Pure bending of beams 409

17. Torsion 432

Appendix

1. Appendix Tutorials Sheets 448

2. Lab Manual 474

3. Previous year question papers (New syllabus) 503

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Fundamental Concepts, Definitions and Zeroth Law / 1

CHAPTER1

FUNDAMENTAL CONCEPTS, DEFINITIONS

AND ZEROTH LAW

Q. 1: Define thermodynamics. Justify that it is the science to compute energy, exergy and entropy.

(Dec–01, March, 2002, Jan–03)

Sol : Thermodynamics is the science that deals with the conversion of heat into mechanical energy. It is

based upon observations of common experience, which have been formulated into thermodynamic laws.

These laws govern the principles of energy conversion. The applications of the thermodynamic laws and

principles are found in all fields of energy technology, notably in steam and nuclear power plants, internal

combustion engines, gas turbines, air conditioning, refrigeration, gas dynamics, jet propulsion, compressors,

chemical process plants, and direct energy conversion devices.

Generally thermodynamics contains four laws;

1. Zeroth law: deals with thermal equilibrium and establishes a concept of temperature.

2. The First law: throws light on concept of internal energy.

3. The Second law: indicates the limit of converting heat into work and introduces the principle of

increase of entropy.

4. Third law: defines the absolute zero of entropy.

These laws are based on experimental observations and have no mathematical proof. Like all physical

laws, these laws are based on logical reasoning.

Thermodynamics is the study of energy, energy and entropy.

The whole of heat energy cannot be converted into mechanical energy by a machine. Some portion of

heat at low temperature has to be rejected to the environment.

The portion of heat energy, which is not available for conversion into work, is measured by entropy.

The part of heat, which is available for conversion into work, is called energy.

Thus, thermodynamics is the science, which computes energy, energy and entropy.

Q. 2: State the scope of thermodynamics in thermal engineering.

Sol: Thermal engineering is a very important associate branch of mechanical, chemical, metallurgical,

aerospace, marine, automobile, environmental, textile engineering, energy technology, process engineering

of pharmaceutical, refinery, fertilizer, organic and inorganic chemical plants. Wherever there is combustion,

heating or cooling, exchange of heat for carrying out chemical reactions, conversion of heat into work for

producing mechanical or electrical power; propulsion of rockets, railway engines, ships, etc., application

of thermal engineering is required. Thermodynamics is the basic science of thermal engineering.

Q. 3: Discuss the applications of thermodynamics in the field of energy technology.

2 / Problems and Solutions in Mechanical Engineering with Concept

Sol: Thermodynamics has very wide applications as basis of thermal engineering. Almost all process and

engineering industries, agriculture, transport, commercial and domestic activities use thermal engineering.

But energy technology and power sector are fully dependent on the laws of thermodynamics.

For example:

(i) Central thermal power plants, captive power plants based on coal.

(ii) Nuclear power plants.

(iii) Gas turbine power plants.

(iv) Engines for automobiles, ships, airways, spacecrafts.

(v) Direct energy conversion devices: Fuel cells, thermoionic, thermoelectric engines.

(vi) Air conditioning, heating, cooling, ventilation plants.

(vii) Domestic, commercial and industrial lighting.

(viii) Agricultural, transport and industrial machines.

All the above engines and power consuming plants are designed using laws of thermodynamics.

Q. 4: Explain thermodynamic system, surrounding and universe. Differentiate among open system,

closed system and an isolated system. Give two suitable examples of each system. (Dec. 03)

Or

Define and explain a thermodynamic system. Differentiate between various types of

thermodynamic systems and give examples of each of them. (Feb. 2001)

Or

Define Thermodynamics system, surrounding and universe. (May–03)

Or

Define closed, open and isolated system, give one example of each. (Dec–04)

Sol: In thermodynamics the system is defined as the quantity of matter or region in space upon which the

attention is concentrated for the sake of analysis. These systems are also referred to as thermodynamics

system.

It is bounded by an arbitrary surface called boundary. The boundary may be real or imaginary, may

be at rest or in motion and may change its size or shape.

Everything out side the arbitrary selected boundaries of the system is called surrounding or

environment.

Surroundings

Surroundings

Boundary

Cylinder System

Convenient

imaginary

boundary

System

Real

boundary

Piston

Piston

Fig. 1.1 The system Fig. 1.2 The real and imaginary boundaries

The union of the system and surrounding is termed as universe.

Universe = System + Surrounding