Fundamental Dimensions and UnitsFundamental Dimensions and Units

Chapter Chapter 66Chapter Chapter 66

Engineering Problems and Fundamental Dimensions

when someone asks you how old you are, you reply by

saying I am 19 years old.

You dont say that you are approximately 170,000 hours old You dont say that you are approximately 170,000 hours old

or 612,000,000 seconds old, even though these statements

may very well be true at that instant!

Engineering Problems and Fundamental Dimensions

fundamental or base dimensions to correctly express what

we know of the natural world. They are length, mass, time,

temperature, electric current, amount of substance, and

luminous intensity.

Systems of Units

The most common systems of units are :

International System (SI) .

British Gravitational (BG) .

U.S. Customary units.

International System (SI) of Units

International System (SI) of Units

International System (SI) of Units

The units for other physical quantities used in engineering

can be derived from the base units.

For example, the unit for force is the newton. It is derivedfrom Newtons second law of motion.from Newtons second law of motion.

One newton is defined as a magnitude of a force that when

applied to 1 kilogram of mass, will accelerate the mass at a

rate of 1 meter per second squared (m/s2). That is: 1N

(1kg)(1m/s2).

International System (SI) of Units

International System (SI) of Units

British Gravitational (BG) System

In the British Gravitational (BG) system of units, the unit of

length is a foot (ft), which is equal to 0.3048 meter

The unit of temperature is expressed in degree Fahrenheit (F)

or in terms of absolute temperature degree Rankine (R).or in terms of absolute temperature degree Rankine (R).

The relationship between the degree Fahrenheit and degree

Rankine is given by:

British Gravitational (BG) System

The relationship between degree Fahrenheit and degree

Celsius is given by:

The relationship between the degree Rankine and the Kelvin

by:

U.S. Customary Units

The unit of length is a foot (ft), which is equal to 0.3048

meter.

The unit of mass is a pound mass (lbm), which is equal to

0.453592 kg; and the unit of time is a second (s).0.453592 kg; and the unit of time is a second (s).

The units of temperature in the U.S. Customary system are

identical to the BG system

U.S. Customary Units

Unit Conversion

Read about accident caused by NASA loosing a spacecraft

in Pg. :138-139.

Unit Conversion

Example 6.1 :

A person who is 6 feet and 1 inch tall and weighs 185

pound force (lbf) is driving a car at a speed of 65 miles

per hour over a distance of 25 miles. The outside air

temperature is 80F and has a density of 0.0735 poundtemperature is 80F and has a density of 0.0735 pound

mass per cubic foot (lbm/ft3). Convert all of the values

given in this example from U.S. Customary Units to SI

units.

Unit Conversion (Example 6.1 )

Unit Conversion (cont. Example 6.1 )

Unit Conversion (Example 6.2 )

Work out Example 6.2 at home .If you have any question ask

me .

Dimensional Homogeneity

What do we mean by dimensionally homogeneous?

Can you, say, add someones height who is 6 feet tall to hisCan you, say, add someones height who is 6 feet tall to his

weight of 185 lbf and his body temperature of 98F?! Of

course not!

Dimensional Homogeneity (Example 6.3 )

For Equation 6.1 to be dimensionally homogeneous, the units on the left-hand side of the equation must equal the units on the right-hand side. This equality requires the modulus of elasticity to have the units of N/m2, as follows:N/m2, as follows:

Dimensional Homogeneity (cont. Example 6.3 )

Numerical versus Symbolic Solutions

When you take your engineering classes, you need to be awareof two important things:

(1) understanding the basic concepts and principles associatedwith that class

(2)how to apply them to solve real physical problems (situations)

Homework problems in engineering typically require either anumerical or a symbolic solution.

For problems that require numerical solution, data is given. Incontrast, in the symbolic solution, the steps and the final answerare presented with variables that could be substituted with data.

Numerical versus Symbolic Solutions (Example 6.4)

Determine the load that can be lifted by the hydraulic system

shown. All of the necessary information is shown in the Figure.

Numerical versus Symbolic Solutions (Example 6.4)

Numerical Solution:

We start by making use of the given data and substituting

them into appropriate equations as follows.

Numerical versus Symbolic Solutions (Example 6.4)

Symbolic Solution:

For this problem, we could start with the equation that relates

F2 to F1, and then simplify the similar quantities such as p and

g in the following manner:

Significant Digits (Figures)

One half of the smallest scale division commonly is called theleast count of the measuring instrument.

For example, referring to Figure 6.4, it should be clear that theleast count for the thermometer is 1F (the smallest division is2F), for the ruler is 0.05 in., and for the pressure gage is 0.5inches of water.inches of water.

Therefore, using the given thermometer, it would be incorrectto record the air temperature as 71.25F and later use this valueto carry out other calculations. Instead, it should be recorded as71 F.

This way, you are telling the reader or the user of yourmeasurement that the temperature reading falls between 70Fand 72F.

Examples of recorded measurements

Significant Digits (Figures)

Significant digits are numbers zero through nine. However,

when zeros are used to show the position of a decimal point,

they are not considered significant digits.

For example, each of the following numbers 175, 25.5,

1.85, and 0.00125 has three significant digits. Note the

zeros in number 0.00125 are not considered as significant

digits, since they are used to show the position of the

decimal point

Significant Digits (Figures)

The number of significant digits for the number 1500 is not

clear. It could be interpreted as having two, three, or four

significant digits based on what the role of the zeros is.

In this case, if the number 1500 was expressed by 1.5 *10^3, In this case, if the number 1500 was expressed by 1.5 *10^3,

15*10^2, or 0.015 *10^5, it would be clear that it has two

significant digits. By expressing the number using the power

of ten, we can make its accuracy more clear.

However, if the number was initially expressed as 1500.0,

then it has four significant digits and would imply that the

accuracy of the number is known to 1/10000.

Significant Digits (Figures)

Addition and Subtraction Rules

Multiplication and Division Rules

Engineering Components and Systems

The primary function of a car is to move us from one place toanother in a reasonable amount of time. The car must provide acomfortable area for us to sit within. Furthermore, it mustshelter us and provide some protection from the outsideelements, such as harsh weather and harmful objects outside.

The automobile consists of thousands of parts. When viewed inits entirety, it is a complicated system. Thousands of engineershave contributed to the design, development, testing, andsupervision of the manufacture of an automobile.

These include electrical engineers, electronic engineers,combustion engineers, materials engineers, aerodynamicsexperts, vibration and control experts, airconditioningspecialists, manufacturing engineers, and industrial engineers.

Engineering Components and Systems

When viewed as a system, the car may be divided into major

subsystems or units, such as electrical, body, chassis, power

train, and air conditioning (see the following figure)

the electrical system of a car consists of a battery, a starter, an the electrical system of a car consists of a battery, a starter, an

alternator, wiring, lights, switches, radio, microprocessors,

and so on

each of these components can be further divided into yet

smaller components. In order to understand a system, we mustfirst fully understand the role and function of its components.

An engineering System and its components

Engineering Components and Systems

During the next four or five years you will take a number of

engineering classes that will focus on specific topics.

You may take a statics class, which deals with the

equilibrium of objects at rest.

You will learn about the role of external forces, internal

forces, and reaction forces and their interactions

Engineering Components and Systems

Later, you will learn the underlying concepts and equilibriumconditions for designing parts.

You will also learn about other physical laws, principles,mathematics, and correlations that will allow you to analyze,design, develop, and test various components that make up amathematics, and correlations that will allow you to analyze,design, develop, and test various components that make up asystem.

It is imperative that during the next four or five years you fullyunderstand these laws and principles so that you can designcomponents that fit well together and work in harmony to fulfillthe ultimate goal of a given system

Physical Laws and Observations in Engineering

The key concepts that you need to keep in the back of your

mind are the physical and chemical laws and principles and

mathematics.

we use mathematics and basic physical quantities to express we use mathematics and basic physical quantities to express

our observations in the form of a law. Even so, to this day we

may not fully understand why nature works the way it does.

We just know it works.

Physical Laws and Observations in Engineering

There are physicists who spend their lives trying to understand

on a more fundamental basis why nature behaves the way it

does.

Some engineers may focus on investigating the fundamentals,

but most engineers use fundamental laws to design things.

Engineers are also good bookkeepers.

Physical Laws and Observations in Engineering

To better understand this concept, consider the air inside a car tire.

If there are no leaks, the mass of air inside the tire remains

constant. This is a statement expressing conservation of mass,

which is based on our observations.

If the tire develops a leak, then you know from your experience If the tire develops a leak, then you know from your experiencethat the amount of air within the tire will decrease until you have a

flat tire. Furthermore, you know the air that escaped from the tire

was not destroyed; it simply became part of the surrounding

atmosphere.

The conservation of mass statement is similar to a bookkeeping

method that allows us to account for what happens to the mass in

an engineering problem.

Physical Laws and Observations in Engineering

Conservation of energy is another good example. It is againsimilar to a bookkeeping method that allows us to keep trackof various forms of energy and how they may change from

one form to another.

Another important law that all of you have heard about is

Newtons second law of motion.

Newton expressed his observations using mathematics, but

simply expressed, this law states that unbalanced force is

equal to mass times acceleration.

Physical Laws and Observations in Engineering