Mechanical Engineering Science. Volume 1

305 Pages·1970·14.744 MB·English

by  J. L. Gwyther, W. D. Brown and G. Williams (Auth.)

0.1 Mechanical
Engineering Science
In SI Units
J. L. Gwyther, B.Sc.(Eng.), B.Sc.(Econ.), C.Eng.,
F.I.Mech.E.
Vice-Principal, College of Technology, Letch worth
W. D. Brown, M.Sc, C.Eng., M.I.Mech.E., M.T.I.
Sometime Principal Scientific Officer, Ministry of Aircraft Production
G. Williams, B.Sc.(Eng.), C.Eng., M.I.C.E.,
M.I.Struct.E.
Deputy Engineer, Severn River Authority
Heinemann Educational Books Ltd
London
Heinemann Educational Books Ltd
LONDON EDINBURGH MELBOURNE TORONTO
JOHANNESBURG AUCKLAND SINGAPORE
HONG KONG IBADAN NAIROBI NEW DELHI
ISBN 0435 71473 2
© J. L. Gwyther, W. D. Brown and G. Williams 1970
First Published 1970
Published by Heinemann Educational Books Ltd
48 Charles Street, London W1X 8AH
Printed in Great Britain at the Pitman Press, Bath
Preface
The primary objective of the authors in writing this book was to
meet the demand for a new lead-in to the engineering science subjects
of the Ordinary and Higher National Certificates in engineering in
their new forms: but the book will also be found useful for a variety
of other courses in engineering science. The ever-increasing need for
scientific and technical workers is having its effect on the curricula of
secondary schools, and the book will be useful in all courses of post- '0'
level or post-C.S.E. standard in the schools. Also, its use in the colleges
will not be confined to national certificate courses, for its comprehen­
sive approach and breadth of coverage will make it a valuable reference
work in courses in mechanical engineering science for Higher Tech­
nicians.
The book is being produced at a time of changeover of units to the
metric system. Although this changeover will not be complete until
the year 1975 at earliest, it has been deemed essential to plan the
presentation to meet interim needs. This has meant the presentation
of all dynamical theory in both sets of units, as well as the giving of
due regard to the likely change of emphasis in the future from gravita­
tional to absolute units in the SI system. Statical calculations are
also presented in both systems, although it is appreciated that the
change in practice here will be quicker. The units of the thermodynamics
sections have also been presented with the changeover in mind. SI
units are indicated throughout.
The syllabus coverage is adequate to meet the needs of all the ex­
amining boards. Thermodynamics and Heat Engines occupy a larger
place than has been usual in books dealing with mechanical engineering
science at this level, to meet the needs of the new schemes of work.
Students are advised to look at past papers of the examination they are
taking so as to judge the emphasis of the work.
Acknowledgements are gratefully made to the several examining
vi Preface
boards which have allowed the use of their questions here. They include
the Union of Lancashire and Cheshire Institutes (U.L.C.I.), The Union
of Educational Institutions (U.E.I.), The East Midlands Examining
Union (E.M.E.U.), and The Northern Counties Technical Examinations
Council (N.C.T.E.C). The book has gained much from these examples.
Messrs Dobbie Mclnnes have provided the copy for our artist to
draw the diagram of the engine indicator, and their help is much
appreciated.
1
Introduction
Mechanical Engineering Science covers a wide range of topics which will
be developed later into Applied Mechanics and Heat Engines at 02 level.
These subjects may be developed still further at advanced levels.
If you have reached your present grade by taking the Gl and G2
courses, you will already have been introduced to some of the work of
this book, and certainly most of the symbols and abbreviations which
are used, and which have been recommended for use in all the engineering
courses.
Inevitably there will be some overlapping of material, because further
developments of particular aspects may require a greater knowledge
of mathematics, which is only acquired in your next year. The amount
of revision of your previous work lias, however, been reduced to a
minimum, firstly because there will be too little time for you to go
back far, and secondly because a widening of the subject matter must
enlarge its content, and so increase its cost to you.
Aims and scope of this book
The aims in writing this book have been to:
1. Revise, where necessary, and as briefly as possible, work which
has been introduced at previous levels.
2. Expand this material, so that you are able to tackle more difficult
problems.
3. Emphasise certain parts of the syllabus which are considered
important by the various examining bodies.
4. Present new work in a simple manner so that you can understand
it fully.
5. Introduce work which will be explained in greater detail in the
next year of the course, when you will have acquired a greater knowledge
of other subjects, particularly mathematics.
2 0.1 Engineering Science
6. Encourage you to carry out every experiment intelligently, and
to write up your work in a proper manner.
Worked examples, which have been selected with great care to cover
almost every type of question you are likely to meet in an examination,
have been introduced into the text. They are solved simply and in
great detail. Further questions, with answers, can be found at the end
of each chapter. Many of these questions are from back papers of
examining boards. All diagrams bear a prefix number which is the
same as the number of the chapter with which they are associated.
This simplifies reference from one to another.
2
The equations of motion
The fundamental dimensions of mechanics are mass, length, and
time. In this chapter we shall be concerned only with the last two.
In mechanics length is usually specified in feet in the f.p.s. system of
units; or in metres in the SI (Systeme International) system. Time
is specified in seconds in both systems. There are, of course, other units
of length and time, but they must be converted for the purpose of
dynamical calculations. Certain other terms, most of which we have
already met in earlier courses, are defined below.
Vector
A vector is a straight line representing to scale both the magnitude and
direction of some physical quantity. If the direction of the quantity is re­
lated to some fixed or known direction, then the vector provides sufficient
information to enable everyone to define the quantity exactly.
Displacement (symbol s)
Displacement represents the distance moved by a body from its
starting position in a definite direction. It is therefore a vector
quantity, and represents motion in a straight line. For the purposes of
mechanics, displacement should be specified in feet or in metres.
Velocity (symbol v)
Velocity is the rate of change of displacement; in other words, the
change (increase or decrease) of displacement in unit time. This also
is a vector quantity, and represents motion in a straight line.
If the amounts of displacement in successive units of time are
constant, and take place in the same direction, then the velocity is
constant, and we can say
s
4 0.1 Engineering Science
The units of velocity will be feet per second (ft/s), or, in the SI
system, metres per second (m/s).
When the amount of displacement in unit time varies, or the direc­
tion changes, then the velocity is not constant. But if we consider a
unit of time small enough, we can determine an instantaneous velocity,
which is the velocity at a particular instant. An instantaneous velocity
is the amount of displacement which would have occurred in, say, the
next second had the body continued to travel in the same direction
without any change in its motion.
Distance (symbol s)
Whenever we are not concerned with straight line motion, we do not
use the word 'displacement'. Instead we use 'distance'. This is the
actual length of the path taken by the moving body from one point
to the next. Distance is not usually the subject of dynamical calcula­
tions, so we can expect to find it recorded in any length units such as
inches, feet, yards, miles, metres, kilometres, etc.
If the motion happens to be in a straight line, then distance will be
numerically equal to displacement in that direction if the same units
are used, but usually it is not necessary to specify the direction in which
distance is measured.
Speed (symbol v)
Frequently we wish to refer to motion which is taking place along a
route which is not a straight line. The rate at which a distance along
such a route is travelled (meaning distance travelled in a unit of time)
is known as the speed. If the speed is measured by a meter in a motor-car
it will probably be given in miles, or kilometres, per hour. This rate is
an instantaneous speed because it shows the distance which would
have been travelled in one hour if the car continued at constant speed.
If, however, a total of t hours were taken by the car to travel a distance
s, then the average speed throughout the whole journey would be
given by the expression
Average v = sjt
Obviously, if a constant speed were maintained throughout the
journey, the uniform or constant speed would be given by
Constant v = sjt
If the motion is in a straight line, and the speed is constant, then
speed and velocity are the same.
Acceleration (symbol a)
Acceleration is the rate of change of speed or velocity. In this book we
shall be concerned only with constant acceleration, meaning constant
increase or decrease of velocity in successive units of time.
The Equations of Motion 5
When there is an increase in velocity in successive units of time, the
body is said to be accelerating: if there is a decrease in velocity the
body is said to be retarding. Retardation is the same as negative
acceleration.
Acceleration and retardation are usually specified in feet per second
per second, or, on the SI system, metres per second per second, and
abbreviated ft/s2 and m/s2 respectively.
Speed conversions
For a variety of reasons we are not often given speeds in 'feet per
second'. It is much more usual to find the speed of a train or a car
given in 'miles per hour', and that of a ship or aircraft given in
'knots'. Note that we do not refer to time when quoting a speed in
'knots'. This is because 'one knot' is another way of saying 'one
nautical mile per hour'.
If we ore going to use the equations of motion, we must be able to
convert miles per hour, and knots, to feet per second. We can, of course,
convert miles into feet and hours into seconds, thus
1 mile _ 5,280 feet
1 hour 3,600 seconds '
But it is much more convenient to factorize, as follows:
1 mile 5,280 ft 88 ft
1 hour = 3,600 s = 60~s
and to say therefore, that
60 mile/h - 88 ft/s
Similarly,
2,027-3
1 nautical mile — 2,027-3 yd/h — mile/h
- 1-15 mile/h
or,
1 knot = 1-15 mile/h = 1-69 ft/s
The equations of motion
We have seen that motion involves the use of four physical quantities,
namely, distance, time, speed and acceleration. These four quantities
can be related to one another by certain expressions which are known
as the 'equations of motion'. The same equations may be used to
relate the vector quantities displacement, velocity and acceleration,
6 0.1 Engineering Science
but then we must confine their use to linear motion, which means
motion in a straight line. Let
s = distance travelled from the start to some new position
t = time taken to travel distance s
v± = instantaneous speed at starting point
V2 — instantaneous speed at new position
a = constant acceleration during this motion
We will not, in this book, consider any problem involving an accelera­
tion which is varying, but sometimes we might wish to consider a
retardation, which, as we have seen, is a negative acceleration.
When the acceleration is constant we can determine the speed
(or velocity) at any time after the start, because by our definition of
acceleration the speed increases by a every second. Thus, after
1 second the speed is (v± + a)
2 seconds the speed is (v± + 2a)
3 seconds the speed is (v± + 3a)
Therefore after I seconds the instantaneous speed is given by
^2 = vi + at 2.1
This is our first equation of motion. Note that it contains four quantities
and only four.
We have already said that
Average speed = sjt
but, Average speed — —-—
Vi + V S
2
so that —r— = -
Jj t
or, transposing, s = \(vx + v%)t 2.2
This is our second equation of motion. Note again that it contains
four quantities and only four.
Now the first equation can be re-written in the form
v% — v\ = at
and the second in the form
2s
V2 + V± = —
if we multiply these together, we get
s
(V2 + vi)(^2 — *>i) = 2 - X at
or, v 2 — vi2 = 2as 2.3
2