Engineering Science

W. Bolton

• Publisher: Routledge
• Year: 2015
• ISBN:
  9781317572299
• Edition: 6
• Topic: Technology & Engineering
• Subtopic: Engineering General
• Index: Technology & Engineering

Comprehensive engineering science coverage that is fully in line with the latest vocational course requirements

• New chapters onheat transfer and fluid mechanics
• Topic-based approach ensures that this text is suitable for all vocational engineering courses
• Coverage of all the mechanical, electrical and electronic principles within one volume provides a comprehensive exploration of scientific principles within engineering

Engineering Science is a comprehensive textbook suitable for all vocational and pre-degree courses. Taking a subject-led approach, the essential scientific principles engineering students need for their studies are topic-by-topic based in presntation. Unlikemost of the textbooksavailable for this subject, Bill Bolton goes beyond the core science to include the mechanical, electrical and electronic principles needed in the majority of courses.A concise and accessible text is supported by numerous worked examples and problems, with a complete answer section at the back of the book. Now in its sixth edition, the text has been fully updated in line with the current BTEC National syllabus and will also prove an essential reference for students embarking on Higher National engineering qualifications and Foundation Degrees.

Chapter 1
Basics

1.1 Introduction

In this chapter there is a review of some basic engineering science terms and, as within this book and your studies you will come across many equations, the manipulation of equations and the units in which quantities are specified. Engineers make measurements to enable theories to be tested, relationships to be determined, values to be determined in order to predict how components might behave when in use and answers obtained to questions of the form ‘What happens if?’ Thus, there might be measurements of the current through a resistor and the voltage across it in order to determine the resistance. Thus, in this introductory chapter, there is a discussion of the measurement and collection of data and the errors that can occur.

1.2 Basic terms

1. Mass
   The mass of a body is the quantity of matter in the body. The greater the mass of a body the more difficult it is to accelerate it. Mass thus represents the inertia or ‘reluctance to accelerate’. It has the SI unit of kg.
2. Density
   If a body has a mass m and volume V, its density ρ is:

• Density has the SI unit of kg/m3.
• 3 Relative density
• Relative density is by what factor the density of a substance is greater than that of water and is thus defined as:

• Since relative density is a ratio of two quantities in the same units, it is purely a number and has no units.

Example

If the density of water at 20°C is 1000 kg/m³ and the density of copper is 8900 kg/m³, what is the relative density of copper?

Relative density of copper = 8900/1000 = 8.9

• 4 Force
  We might describe forces as pushes and pulls. If you pull a spring between your hands we can say that your hands are applying forces to the ends of the spring. If there is an unbalanced force acting on an object it accelerates. Force has the SI unit of the newton (N).
• 5 Weight
  The weight of a body is the gravitational force acting on it and which has to be opposed if the body is not to fall. The weight of a body of mass m where the acceleration due to gravity is g is mg. Weight, as a force, has the SI unit of N.

Example

What is the weight of a block with a mass of 2 kg if the acceleration due to gravity is 9.8 m/s²?

Weight = mg = 2 x 9.8 = 19.6 N

• 6 Pressure
  If a force F acts over an area A, the pressure p is:

• It has the SI unit of N/m², this being given the special name of pascal (Pa).

1.3 Manipulating equations

The following are basic rules for manipulating equations:

1. Adding the same quantity to, or subtracting the same quantity from, both sides of an equation does not change the equality.
2. Multiplying, or dividing, both sides of an equation by the same non-zero quantity does not change the equality.

In general, whatever mathematical operation we do to one side of an equation, provided we do the same to the other side of the equation then the balance is not affected.

The term transposition is used when a quantity is moved from one side of an equation to the other side. The following are basic rules for use with transposition:

1. A quantity which is added on the left-hand side of an equation becomes subtracted on the right-hand side.
2. A quantity which is subtracted on the left-hand side of an equation becomes added on the right-hand side.
3. A quantity which is multiplying on the right-hand side of an equation becomes a dividing quantity on the left-hand side.
4. A quantity which is dividing on the left-hand side of an equation becomes a multiplying quantity on the right-hand side.

Suppose we have the equation F = kx and we want to solve the equation for x in terms of the other quantities. Writing the equation as kx = F and then transposing the k from the left-hand side to the right-hand side (or dividing both sides by k) gives

Example

Determine L in the equation

Squaring both sides of the equation gives us the same as multiplying both sides of the equation by the same quantity since 2 is the same as √(L/10):

Hence, we have L = 40. We can check this result by putting the value in the original equation to give 2 = √(40/10).

Brackets are used to show terms are grouped together, e.g. 2(x + 3) indicates that we must regard the x + 3 as a single term which is multiplied by 2. Thus when removing brackets, each term within the bracket is multiplied by the quantity outside the bracket. When a bracket has a + sign in front of the bracket then effectively we are multiplying all the terms in the bracket by +1. When a bracket has a - sign in front of the bracket then we are multiplying all the terms in the bracket by -1. When we have (a - b) (c + d) then, following the above rule for the removal of brackets, each term within the first bracket must be multiplied by the quantity inside the second bracket to give:

a(c + d) + b(c + d) = ac + ad + bc + bd

As an example, consider the following equation for the variation of resistance R of a conductor w...