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Mechanical Engineering SystemsMechanical Engineering Systems Richard Gentle Peter Edwards Bill Bolton OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHIButterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801-2041 A division of Reed Educational and Professional Publishing Ltd A member of the Reed Elsevier plc group First published 2001 Richard Gentle, Peter Edwards and Bill Bolton 2001 All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1P 0LP. Applications for the copyright holders written permission to reproduce any part of this publication should be addressed to the publishers While every effort has been made to trace the copyright holders and obtain permission for the use of all illustrations and tables reproduced from other sources in this book we would be grateful for further information on any omissions in our acknowledgements so that these can be amended in future printings. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0 7506 5213 6 Composition by Genesis Typesetting, Laser Quay, Rochester, Kent Printed and bound in Great BritainContents Series Preface vii 1 Introduction: the basis of engineering 1 1.1 Real engineering 1 1.2 Units 3 1.3 Units used in this book 5 2 Thermodynamics 7 2.1 Heat energy 7 2.2 Perfect gases, gas laws, gas processes 13 2.3 Work done and heat energy supplied 24 2.4 Internal combustion engines 33 2.5 The steady flow energy equation 54 2.6 Steam 66 2.7 Refrigeration 89 2.8 Heat transfer 101 3 Fluid mechanics 112 3.1 Hydrostatics fluids at rest 113 3.2 Hydrodynamics fluids in motion 135 4 Dynamics 169 4.1 Introduction to kinematics 170 4.2 Dynamics analysis of motion due to forces 183 5 Statics 204 5.1 Equilibrium 205 5.2 Structures 222 5.3 Stress and strain 235 5.4 Beams 249 5.5 Cables 275 5.6 Friction 282 5.7 Virtual work 287 5.8 Case study: bridging gaps 292 Solutions to problems 295 Index 307Series Preface There is a time for all things: for shouting, for gentle speaking, for silence; for the washing of pots and the writing of books. Let now the pots go black, and set to work. It is hard to make a beginning, but it must be done Oliver Heaviside, Electromagnetic Theory, Vol 3 (1912), Ch 9, Waves from moving sources Adagio. Andante. Allegro Moderato. Oliver Heaviside was one of the greatest engineers of all time, ranking alongside Faraday and Maxwell in his field. As can be seen from the above excerpt from a seminal work, he appreciated the need to communicate to a wider audience. He also offered the advice So be rigorous; that will cover a multitude of sins. And do not frown. The series of books that this prefaces takes up Heavisides challenge but in a world which is quite different to that being experienced just a century ago. With the vast range of books already available covering many of the topics developed in this series, what is this series offering which is unique? I hope that the next few paragraphs help to answer that; certainly no one involved in this project would give up their time to bring these books to fruition if they had not thought that the series is both unique and valuable. This motivation for this series of books was born out of the desire of the UKs Engineering Council to increase the number of incorporated engineers graduating from Higher Education establishments, and the Institution of Incorporated Engineers (IIE) aim to provide enhanced services to those delivering Incorporated Engineering Courses. How- ever, what has emerged from the project should prove of great value to a very wide range of courses within the UK and internationally from Foundation Degrees or Higher Nationals through to first year modules for traditional Chartered degree courses. The reason why these books will appeal to such a wide audience is that they present the core subject areas for engineering studies in a lively, student-centred way, with key theory delivered in real world contexts, and a pedagogical structure that supports independent learning and classroom use. Despite the apparent waxing of new technologies and the waning of old technologies, engineering is still fundamental to wealth creation. Sitting alongside these are the new business focused, information and communications dominated, technology organisations. Both facets have an equal importance in the health of a nation and the prospects of individuals. In preparing this series of books, we have tried to strike a balance between traditional engineering and developing technology.The philosophy is to provide a series of complementary texts which can be tailored to the actual courses being run allowing the flexibility for course designers to take into account local issues, such as areas of particular staff expertise and interest, while being able to demonstrate the depth and breadth of course material referenced to a common framework. The series is designed to cover material in the core texts which approximately corresponds to the first year of study with module texts focussing on individual topics to second and final year level. While the general structure of each of the texts is common, the styles are quite different, reflecting best practice in their areas. For example Mechanical Engineering Systems adopts a tell show do approach, allowing students to work independently as well as in class, whereas Business Skills for Engineers and Technologists adopts a framework approach, setting the context and boundaries and providing opportunities for discussion. Another set of factors which we have taken into account in designing this series is the reduction in contact hours between staff and students, the evolving responsibilities of both parties and the way in which advances in technology are changing the way study can be, and is, undertaken. As a result, the lecturers support material which accom- panies these texts, is paramount to delivering maximum benefit to the student. It is with these thoughts of Voltaire that I leave the reader to embark on the rigours of study: Work banishes those three great evils: boredom, vice and poverty. Alistair Duffy Series Editor De Montfort University, Leicester, UK Further information on the IIE Textbook Series is available from bhmarketingrepp.co.uk Please send book proposals to: rachel.hudsonrepp.co.uk Other titles currently available in the IIE Textbook Series Business Skills for Engineers and Technologists Design Engineering1 Introduction: the basis of engineering Summary The aim of this chapter is to set the scene for the rest of the book by showing how the content of the remaining chapters will form the basis of the technical knowledge that a professional mechanical engineer needs during a career. By considering a typical engineering problem it is shown that the four main subjects that make up this text are really all parts of a continuous body of knowledge that will need to be used in an integrated manner. The chapter concludes by looking at the units that are used in engineering and showing the importance of keeping to a strict system of units. Objectives By the end of this chapter the reader should be able to: understand the seamless nature of basic engineering subjects; appreciate the way in which real engineering problems are tackled; recognize the correct use of SI units. 1.1 Real engineering Cast your mind forward a few years; you have graduated successfully from your course, worked for a spell as a design engineer and now you are responsibile for a team which is being given a new project. Your job is to lead that team in designing a new ride-on lawnmower to fill a gap in the market that has been identified by the sales team. The sales people think that there is scope to sell a good number of low-slung ride-on lawnmowers to places which use a lot of barriers or fences for crowd control, such as amusement parks. Their idea is that the new mower could be driven under the fences, cutting the grass as it goes, without the time wasting activity of having to drive to a gateway in order to move from one area to another. They have produced something they call a2 Introduction: the basis of engineering concept specification which is really a wish list of features that they would like the new lawnmower to have. (1) It must be very low, like a go-kart, to go under the barriers. (2) It must be fast when not mowing so that it can be driven quickly around the park. (3) It should dry and collect the grass cuttings as it goes so that the park customers do not get their shoes covered in wet grass. Now comes the worst part of any engineering design problem Where do you start? Perhaps you should start with the framework of the mower because this is the part that would support all the other components. You have a good understanding of statics, which is the field of engineering concerned with supporting loads, and you could design a tubular steel frame without too much of a problem if you know the loads and their distribution. The trouble, however, is that you do not know the load that needs to be carried and you cannot base your design on the companys existing products as all their current ride-on mowers are shaped more like small versions of farm tractors. You could calculate the load on the basis of an average driver weight but you do not yet know how much the engine will weigh because its power, and hence its size, has not been established. Furthermore, if the mower is to be driven fast around the park over bumpy ground then the effective dynamic loads will be much greater than the static load. It is therefore probably not a good idea to start with the frame design unless you are willing to involve a great deal of guesswork. This would run the risk of producing at one extreme a frame that would break easily because it is too flimsy and at the other extreme a frame that is unnecessarily strong and hence too expensive or heavy. Time to think again! Perhaps you should start the design by selecting a suitable engine so that the total static weight of the mower could be calculated. You have a good basic knowledge of thermodynamics and you understand how an internal combustion engine works. The trouble here, however, is that you cannot easily specify the power required from the engine. So far you have not determined the maximum speed required of the mower, the maximum angle of slope it must be able to climb or the speed at which it can cut grass, let alone considered the question of whether the exhaust heat can dry the grass. In fact this last feature might be a good place to start because the whole point of a mower is that it cuts grass. First of all you could decide on the diameter of the rotating blades by specifying that they must not protrude to the side of the mower beyond the wheels. This would give you the width of the cut. A few measurements in a field would then allow you to work out the volume and mass of grass that is cut for every metre that the mower moves forward. Lastly you could find the forward speed of your companys other ride-on mowers when cutting in order to calculate the mass of grass which is cut per second. From this you can eventually work out two more pieces of key information. Using your knowledge of fluid mechanics you could calculate the flow rate of air which is needed to sweep the grass cuttings into the collection bag or hopper as fast as they are being produced.Introduction: the basis of engineering 3 Using your knowledge of thermodynamics you could calculate the rate at which heat must be supplied to the wet grass to evaporate most of the surface water from the cuttings by the time they reach the hopper. At last you are starting to get somewhere because the first point will allow you to calculate the size of fan that is required and the power that is needed to drive it. The second point will allow you to calculate the rate at which waste heat from the engine must be supplied to the wet grass. Knowing the waste power and the typical efficiency of this type of engine you can then calculate the overall power that is needed if the engine is to meet this specification to dry the grass cuttings as they are produced. Once you have the overall power of the engine and the portion of that power that it will take to drive the fan you can calculate the power that is available for the mowing process and for driving the mowers wheels. These two facts will allow you to use your knowledge of dynamics to estimate the performance of the mower as a vehicle: the acceleration with and without the blades cutting, the maximum speed up an incline and the maximum driving speed. Of course this relies on being able to estimate the overall mass of the mower and driver, which brings us back to the starting point where we did not know either of these two things. It is time to put the thinking cap back on, and perhaps leave it on, because this apparently straightforward design problem is turning out to be a sort of closed loop that is difficult to break into. What can we learn from this brief look into the future? There are certainly two important conclusions to be drawn. The engineering design process, which is what most engineering is all about, can be very convoluted. While it relies heavily on calcula- tion, there is often a need to make educated guesses to start the calculations. To crack problems like the one above of the new mower you will need to combine technical knowledge with practical experi- ence, a flair for creativity and the confidence to make those educated guesses. The engineering courses that this textbook supports must therefore be seen as only the start of a much longer-term learning process that will continue throughout your professional career. A good engineer needs to think of all the subjects that are studied on an undergraduate course in modular chunks as being part of a single body of technical knowledge that will form the foundation on which a career can be built. At the introductory level of this book it is best to keep the distinction between the various topics otherwise it can become confusing to the student; it is difficult enough coming to terms with some of the concepts and equations in each topic without trying to master them all at the same time. The lawn mower example, however, shows that you must be able to understand and integrate all the topics, even though you may not have to become an expert in all of them, if you want to be a proficient engineer. 1.2 Units The introduction is now over and it is almost time to plunge into the detailed treatment of the individual topics. Before we do that, however, we must look at the subject of the units that are used, not only in this book but also throughout the vast majority of the worlds engineering industry.4 Introduction: the basis of engineering Every engineering student is familiar with the fact that it is not good enough to calculate something like the diameter of a steel support rod and just give the answer as a number. The full answer must include the units that have been used in the calculation, such as millimetres or metres, otherwise there could be enormous confusion when somebody else used the answer in the next step of a large calculation or actually went ahead and built the support rod. However, there is much more to the question of units than simply remembering to quote them along with the numerical part of the answer. The really important thing to remember is to base all calculations on units which fit together in a single system. The system that is used in this book and throughout engineering is the International System of Units, more correctly known by its French name of Syst eme Internationale which is abbreviated to SI. SI units developed from an earlier system based on the metre, the kilogram and the second and hence is known as the MKS system from the initial letters of those three units. These three still form the basis of the SI because length, mass and time are the most important fundamental measurements that need to be specified in order to define most of the system. Most of the other units in the system for quantities such as force, energy and power can be derived from just these three building blocks. The exceptions are the units for temperature, electrical current and light intensity, which were developed much later and represent the major difference between the SI and the MKS system. One of these exceptions that is of concern to us for this book is the unit for measuring temperature, the kelvin (K). This is named after Lord Kelvin, a Scottish scientist and engineer, who spent most of his career studying temperature and heat in some form or another. The Kelvin is actually equal to the more familiar degree Celsius (C), but the scale starts at what is called absolute zero rather than with the zero at the freezing point of water. The connection is that 0C = 273K. The SI is therefore based on the second, a unit which goes back to early Middle East civilization and has been universally adopted for centuries, plus two French units, the metre and the kilogram, which are much more recent and have their origin in the French Revolution. That was a time of great upheaval and terror for many people. It was also, however, a time when there were great advances in science and engineering because the revolutionaries idealistic principles were based on the rule of reason rather than on inheritance and privilege. One of the good things to come out of the period, especially under the guidance of Napoleon, was that the old system of measurements was scrapped. Up to that time all countries had systems of measurement for length, volume and mass that were based on some famous ruler. In England it was the length between a kings nose and the fingertip of his outstretched arm that served as the standard measure of the yard, which could then be subdivided into three feet. This was all very arbitrary and would soon have caused a great deal of trouble as the nations of Western Europe were poised to start supplying the world with their manufactured goods. Napoleons great contribution was to do away with any unit that was based on royalty and get his scientists to look for a logical alternative. What they chose was to base their unit of length on the distance from one of the earths poles to the equator. This was a distance which could be calculated by astronomers in any country around the world and so it could serve as a universal standard. They then split this distance into ten million subdivisions called measures. In French this isIntroduction: the basis of engineering 5 the metre (m). From here it was straightforward to come up with a reproducible measure for volume, using the cubic metre (m 3 ), and this allowed the unit of mass to be defined as the gram, with one million grams being the mass of one cubic metre of pure water. In practice the gram is very small and so in drawing up a system of units for calculation purposes, later scientists used the kilogram (kg) which is equal to one thousand grams. It is worth noting that the French Revolutionaries did not always get things right scientifically; for example, they took it into their heads to do away with the system of having twelve months in a year, twenty-four hours in a day and so on, replacing it with a system of recording time based on multiples of ten. It did not catch on, largely because most people at the time did not have watches and relied on the moon for the months and church clocks for t