Lecture Notes - Introduction to mechanical engineering

# Lecture Notes - Introduction to mechanical engineering - Notes

``` Page 1

Introduction to mechanical engineering
lecture notes
Csaba H? os Botond Erd? os
December 1, 2011
1
Page 2

Introduction to mechanical engineering
lecture notes
Csaba H? os Botond Erd? os
December 1, 2011
1
Contents
1 A short summary of the basics 4
1.1 Physical quantities, units and working with units . . . . . . . 4
1.3 Linear motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Circular motion . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Newton’s ?rst law . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Newton’s second law . . . . . . . . . . . . . . . . . . . . . . . 8
1.7 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.8 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.9 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Steady-state operation of machines 14
2.1 The sliding friction force due to dry friction . . . . . . . . . . 14
2.2 Rolling resistance . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Statics of objects on inclined planes (restoring forces) . . . . 17
2.4 Pulley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.1 Pulley without friction . . . . . . . . . . . . . . . . . . 19
2.4.2 Pulley with friction . . . . . . . . . . . . . . . . . . . . 20
2.5 Friction drive and belt drive . . . . . . . . . . . . . . . . . . . 20
2.6 Load factor, e?ciency and losses of machines . . . . . . . . . 23
2.7 Average load and e?ciency . . . . . . . . . . . . . . . . . . . 24
2.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Fluid mechanics 28
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Mass conservation - law of continuity . . . . . . . . . . . . . . 29
3.3 Energy conservation - Bernoulli’s equation . . . . . . . . . . . 29
3.4 Application 1 - ?ow in a confuser . . . . . . . . . . . . . . . . 30
3.5 Application 2 - pressure measurement with U-tube . . . . . . 30
3.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Some basic types of machines 34
4.1 Internal combustion engines . . . . . . . . . . . . . . . . . . . 34
4.2 Rankine cycle (steam engines) . . . . . . . . . . . . . . . . . . 36
4.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2
Page 3

Introduction to mechanical engineering
lecture notes
Csaba H? os Botond Erd? os
December 1, 2011
1
Contents
1 A short summary of the basics 4
1.1 Physical quantities, units and working with units . . . . . . . 4
1.3 Linear motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Circular motion . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Newton’s ?rst law . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Newton’s second law . . . . . . . . . . . . . . . . . . . . . . . 8
1.7 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.8 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.9 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Steady-state operation of machines 14
2.1 The sliding friction force due to dry friction . . . . . . . . . . 14
2.2 Rolling resistance . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Statics of objects on inclined planes (restoring forces) . . . . 17
2.4 Pulley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.1 Pulley without friction . . . . . . . . . . . . . . . . . . 19
2.4.2 Pulley with friction . . . . . . . . . . . . . . . . . . . . 20
2.5 Friction drive and belt drive . . . . . . . . . . . . . . . . . . . 20
2.6 Load factor, e?ciency and losses of machines . . . . . . . . . 23
2.7 Average load and e?ciency . . . . . . . . . . . . . . . . . . . 24
2.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Fluid mechanics 28
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Mass conservation - law of continuity . . . . . . . . . . . . . . 29
3.3 Energy conservation - Bernoulli’s equation . . . . . . . . . . . 29
3.4 Application 1 - ?ow in a confuser . . . . . . . . . . . . . . . . 30
3.5 Application 2 - pressure measurement with U-tube . . . . . . 30
3.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Some basic types of machines 34
4.1 Internal combustion engines . . . . . . . . . . . . . . . . . . . 34
4.2 Rankine cycle (steam engines) . . . . . . . . . . . . . . . . . . 36
4.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2
5 Unsteady operation of machines with constant acceleration 40
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.2 Examples of motion with constant acceleration . . . . . . . . 40
5.3 Crank mechanism . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3
Page 4

Introduction to mechanical engineering
lecture notes
Csaba H? os Botond Erd? os
December 1, 2011
1
Contents
1 A short summary of the basics 4
1.1 Physical quantities, units and working with units . . . . . . . 4
1.3 Linear motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Circular motion . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Newton’s ?rst law . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Newton’s second law . . . . . . . . . . . . . . . . . . . . . . . 8
1.7 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.8 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.9 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Steady-state operation of machines 14
2.1 The sliding friction force due to dry friction . . . . . . . . . . 14
2.2 Rolling resistance . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Statics of objects on inclined planes (restoring forces) . . . . 17
2.4 Pulley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.1 Pulley without friction . . . . . . . . . . . . . . . . . . 19
2.4.2 Pulley with friction . . . . . . . . . . . . . . . . . . . . 20
2.5 Friction drive and belt drive . . . . . . . . . . . . . . . . . . . 20
2.6 Load factor, e?ciency and losses of machines . . . . . . . . . 23
2.7 Average load and e?ciency . . . . . . . . . . . . . . . . . . . 24
2.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Fluid mechanics 28
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Mass conservation - law of continuity . . . . . . . . . . . . . . 29
3.3 Energy conservation - Bernoulli’s equation . . . . . . . . . . . 29
3.4 Application 1 - ?ow in a confuser . . . . . . . . . . . . . . . . 30
3.5 Application 2 - pressure measurement with U-tube . . . . . . 30
3.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Some basic types of machines 34
4.1 Internal combustion engines . . . . . . . . . . . . . . . . . . . 34
4.2 Rankine cycle (steam engines) . . . . . . . . . . . . . . . . . . 36
4.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2
5 Unsteady operation of machines with constant acceleration 40
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.2 Examples of motion with constant acceleration . . . . . . . . 40
5.3 Crank mechanism . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3
1 A short summary of the basics
1.1 Physical quantities, units and working with units
The value of a physical quantity Q is expressed as the product of a
numerical value Q and a unit of measurement [Q]:
Q =Q×[Q] (1)
For example, if the temperature T of a body is quanti?ed (measured) as 25
degrees Celsius this is written as:
T = 25×
o
C = 25
o
C, (2)
where T is the symbol of the physical quantity ”temperature”, 25 is the
numerical factor and
o
C is the unit.
built upon base quantities, each of which is regarded as having its own di-
mension.ThesevenbasequantitiesoftheInternationalSystemofQuantities
(ISQ) and their corresponding SI units are listed in Table 1. Other conven-
tions may have a di?erent number of fundamental units (e.g. the CGS and
MKS systems of units).
Name Symbol for
quantity
Symbol for
dimension
SI base
unit
Symbol for
unit
Length l, x, r, etc. L meter m
Time t T second s
Mass m M kilogram kg
Electric current I, i I ampere A
Thermodynamic
temperature
T ? kelvin K
Amount of sub-
stance
n N mole mol
Luminous inten-
sity
I
v
J candela cd
Table 1: International System of Units base quantities
All other quantities are derived quantities since their dimensions are
derived from those of base quantities by multiplication and division. For
example,thephysicalquantityvelocityisderivedfrombasequantitieslength
and time and has dimension L/T. Some derived physical quantities have
dimension 1 and are said to be dimensionless quantities.
The International System of Units (SI) speci?es a set of unit pre?xes
known as SI pre?xes or metric pre?xes.An SI pre?x is a namethat precedes
4
Page 5

Introduction to mechanical engineering
lecture notes
Csaba H? os Botond Erd? os
December 1, 2011
1
Contents
1 A short summary of the basics 4
1.1 Physical quantities, units and working with units . . . . . . . 4
1.3 Linear motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Circular motion . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Newton’s ?rst law . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Newton’s second law . . . . . . . . . . . . . . . . . . . . . . . 8
1.7 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.8 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.9 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Steady-state operation of machines 14
2.1 The sliding friction force due to dry friction . . . . . . . . . . 14
2.2 Rolling resistance . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Statics of objects on inclined planes (restoring forces) . . . . 17
2.4 Pulley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.1 Pulley without friction . . . . . . . . . . . . . . . . . . 19
2.4.2 Pulley with friction . . . . . . . . . . . . . . . . . . . . 20
2.5 Friction drive and belt drive . . . . . . . . . . . . . . . . . . . 20
2.6 Load factor, e?ciency and losses of machines . . . . . . . . . 23
2.7 Average load and e?ciency . . . . . . . . . . . . . . . . . . . 24
2.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Fluid mechanics 28
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Mass conservation - law of continuity . . . . . . . . . . . . . . 29
3.3 Energy conservation - Bernoulli’s equation . . . . . . . . . . . 29
3.4 Application 1 - ?ow in a confuser . . . . . . . . . . . . . . . . 30
3.5 Application 2 - pressure measurement with U-tube . . . . . . 30
3.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Some basic types of machines 34
4.1 Internal combustion engines . . . . . . . . . . . . . . . . . . . 34
4.2 Rankine cycle (steam engines) . . . . . . . . . . . . . . . . . . 36
4.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2
5 Unsteady operation of machines with constant acceleration 40
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.2 Examples of motion with constant acceleration . . . . . . . . 40
5.3 Crank mechanism . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3
1 A short summary of the basics
1.1 Physical quantities, units and working with units
The value of a physical quantity Q is expressed as the product of a
numerical value Q and a unit of measurement [Q]:
Q =Q×[Q] (1)
For example, if the temperature T of a body is quanti?ed (measured) as 25
degrees Celsius this is written as:
T = 25×
o
C = 25
o
C, (2)
where T is the symbol of the physical quantity ”temperature”, 25 is the
numerical factor and
o
C is the unit.
built upon base quantities, each of which is regarded as having its own di-
mension.ThesevenbasequantitiesoftheInternationalSystemofQuantities
(ISQ) and their corresponding SI units are listed in Table 1. Other conven-
tions may have a di?erent number of fundamental units (e.g. the CGS and
MKS systems of units).
Name Symbol for
quantity
Symbol for
dimension
SI base
unit
Symbol for
unit
Length l, x, r, etc. L meter m
Time t T second s
Mass m M kilogram kg
Electric current I, i I ampere A
Thermodynamic
temperature
T ? kelvin K
Amount of sub-
stance
n N mole mol
Luminous inten-
sity
I
v
J candela cd
Table 1: International System of Units base quantities
All other quantities are derived quantities since their dimensions are
derived from those of base quantities by multiplication and division. For
example,thephysicalquantityvelocityisderivedfrombasequantitieslength
and time and has dimension L/T. Some derived physical quantities have
dimension 1 and are said to be dimensionless quantities.
The International System of Units (SI) speci?es a set of unit pre?xes
known as SI pre?xes or metric pre?xes.An SI pre?x is a namethat precedes
4
abasicunitofmeasureto indicatea decimalmultiple orfraction of theunit.
Each pre?x has a unique symbol that is prepended to the unit symbol, see
Table 2.
Pre?x Symbol 10
n
giga G 10
9
mega M 10
6
kilo k 10
3
hecto h 10
2
deca da 10
1
deci d 10
-1
centi c 10
-2
milli m 10
-3
micro µ 10
-6
nano n 10
-9
Table 2: International System of Units pre?xes.
A quantity is called:
extensive when its magnitude is additive for subsystems (volume, mass,
etc.)
intensive when the magnitude is independent of the extent of the system
(temperature, pressure, etc.)
Units can be used as numbers in the sense that you can add, subtract,
multiply and divide them - with care. Much confusion can be avoided if you
work with units as though they were symbols in algebra. For example:
• Multiply units along with numbers:
(5 m)× (2 sec) = (5× 2)× (m× sec) = 10 m sec.
The units in this example are meters times seconds, pronounced as
‘meter seconds’ and written as ‘m sec’.
• Divide units along with numbers:
(10 m) / (5 sec) = (10 / 5)× (m / sec) = 2 m/sec.
The units in this example are meters divided by seconds, pronounced
as ‘meters per second’ and written as ‘m/sec’. This is a unit of speed.
• Cancel when you have the same units on top and bottom:
(15 m) / (5 m) = (15 / 5)× (m / m) = 3.
5
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