ACADEMIC PLAN Subject : Thermodynamics Code : 5ME01 Course : B. Tech. Year : 2016- 2017 Class : II Year Semester : I Sem Branch : Mechanical Engineering Section : Name of the Staff : Jayashri Narayana Nair Designation : Assistant Professor SYLLABUS THERMODYNAMICS II Year B. ME I Sem L 3 T/P/D C 1 3 Course Objectives: T o apply the basic concepts of thermodynamics and Thermodynamic Laws for various thermodynamic systems To Evaluate the properties of pure substance and to analyse the concept of irreversibility and availability. To apply the basic concept of power cycles for External combustion engines and internal combustion engines. To Evaluate the behaviour of ideal gas mixtures and Thermodynamic properties. Course Outcomes: Students will be able to T o apply the basic concepts of thermodynamics and Thermodynamic Laws for various thermodynamic systems To Evaluate the properties of pure substance and to analyse the concept of irreversibility and availability. To apply the basic concept of power cycles for External combustion engines and internal combustion engines. Evaluate the behaviour of ideal gas mixtures and Thermodynamic properties of the given mixture of gases. UNIT I Concepts and definitions A thermodynamic system and the control volume; Macroscopic versus microscopic point of view; Properties and state of a substance; Processes and cycles, units for mass, length, time, and force; Energy; Specific volume and density; Pressure; Equality of temperature; The Zeroth law of thermodynamics; Temperature scales; Engineering applications. Work and heat Definition of work; Units for work; Work done at the moving boundary of a simple compressible system; Other systems that involve work; Remarks regarding work; Definition of heat; Heat transfer modes; Comparison of heat and work; Engineering applications. Energy equation for a control mass (The first law of thermodynamics) The first law of thermodynamics for a control mass undergoing a cycle; The first law of thermodynamics for a change in state of a control mass; Internal energy-a thermodynamic
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ACADEMIC PLAN
Subject : Thermodynamics Code : 5ME01
Course : B. Tech. Year : 2016- 2017
Class : II Year Semester : I Sem
Branch : Mechanical Engineering Section :
Name of the Staff : Jayashri Narayana Nair Designation : Assistant Professor
SYLLABUS
THERMODYNAMICS
II Year B. ME I Sem
L
3
T/P/D C
1 3
Course Objectives:
T o apply the basic concepts of thermodynamics and Thermodynamic Laws for various
thermodynamic systems
To Evaluate the properties of pure substance and to analyse the concept of irreversibility and
availability.
To apply the basic concept of power cycles for External combustion engines and internal
combustion engines.
To Evaluate the behaviour of ideal gas mixtures and Thermodynamic properties.
Course Outcomes: Students will be able to
T o apply the basic concepts of thermodynamics and Thermodynamic Laws for various
thermodynamic systems
To Evaluate the properties of pure substance and to analyse the concept of irreversibility and
availability.
To apply the basic concept of power cycles for External combustion engines and internal
combustion engines.
Evaluate the behaviour of ideal gas mixtures and Thermodynamic properties of the given mixture
of gases.
UNIT I
Concepts and definitions
A thermodynamic system and the control volume; Macroscopic versus microscopic point of view;
Properties and state of a substance; Processes and cycles, units for mass, length, time, and force;
Energy; Specific volume and density; Pressure; Equality of temperature; The Zeroth law of
thermodynamics; Temperature scales; Engineering applications.
Work and heat
Definition of work; Units for work; Work done at the moving boundary of a simple compressible
system; Other systems that involve work; Remarks regarding work; Definition of heat; Heat
transfer modes; Comparison of heat and work; Engineering applications.
Energy equation for a control mass (The first law of thermodynamics)
The first law of thermodynamics for a control mass undergoing a cycle; The first law of
thermodynamics for a change in state of a control mass; Internal energy-a thermodynamic
property; Problem analysis and solution technique; The thermodynamic property enthalpy; The
constant-volume and constant-pressure specific heats; The internal energy, enthalpy, and specific
heat of ideal gases; The first law as a rate equation;
Energy equation for a control volume (First law analysis for a control volume)
Conversion of mass and the control volume; The first law of thermodynamics for a control
volume; The steady-state process; Examples of steady-state processes;
Learning Outcomes: Student will be able to
Define and select C.V around some matter and identify storage localities for mass.
Know the P,T,V and density and their units
Recognize force and displacement of system
Will know work and heat is function of path followed in a process.
Distinguish between equilibrium and non equilibrium state
Recognize flow and non flow terms in the energy equation
Analyze steady state single flow devices such as nozzles throttles, turbines, or pumps.
Lecture plan-UNIT-I
S.No. Description of Topic Method of Teaching Cumul
ative
hours
1 (concepts and definitions)
A thermodynamic system and the
control volume; Macroscopic versus
microscopic point of view , Processes
and cycle,
WIT n WIL
Chalk and Talk 1
2 Energy; Specific volume and density;
Pressure
Chalk and Talk 2
3 Equality of temperature; The Zeroth
law of thermodynamics; Temperature
scales; Engineering applications
Chalk and Talk
3
4 Temperature scales; Engineering
applications
Chalk and Talk 4
5 Work and heat
Definition of work; Units for work;
Work done at the moving boundary of
a simple compressible system;
POGIL Activity
5
6 Other systems that involve work;
Remarks regarding work;
Chalk and Talk 6
7 Definition of heat; Heat transfer
modes;
Comparison of heat and work;
Engineering applications
Chalk n Talk
7
8 Tutorial-1 Chalk n Talk 8
9 Energy equation for a control mass
(The first law of thermodynamics)
The first law of thermodynamics for a
control mass undergoing a cycle; The
first law of thermodynamics for a
WIT n WIL
9
change in state of a control mass;
Tutorial-2 10
10 Internal energy-a thermodynamic
property; Problem analysis and
solution technique,
Chalk n Talk
11
11 Enthalpy, sp heats Chalk n Talk 12
12 Tutorial-3 Chalk n Talk 13
13 Energy equation for a control
volume (First law analysis for a
control volume)
Conversion of mass and the control
volume;;
Chalk n Talk
13
14 The first law of thermodynamics for a
control volume
Chalk n Talk 14
15 The steady-state processes;
Engineering applications
Chalk n Talk 15
16 Tutorial-4 Chalk n Talk 16
Assignment-I
Q1.If a gas of volume 6000 cm3 and at pressure of 100 kPa is compressed quasistatically
according to pV2 = constant until the volume becomes 2000 cm
3, determine the final
pressure and the work transfer.
Q2. A milk chilling unit can remove heat from the milk at the rate of 41.87 MJ/h. Heat
leaks into the milk from the surroundings at an average rate of 4.187 MJ/h. Find the
time required for cooling a batch of 500 kg of milk from 45°C to 5°C. Take the cp of
milk to be 4.187 kJ/kg K.
UNIT II
The (classical) second law of thermodynamics
Heat engines and refrigerators; The second law of thermodynamics; The reversible process;
Factors that render processes irreversible; The Carnot cycle; Two propositions regarding the
efficiency of a Carnot cycle; The thermodynamic temperature scale; The ideal-gas temperature
scale; Ideal versus real machines; Engineering applications.
Entropy for a control mass
The inequality of Clausius; Entropy – a property of a system; The entropy of a pure substance;
Entropy of a pure substance, Entropy change in reversible processes; The thermodynamic property
relation; Entropy change of an ideal gas; The reversible polytropic process for an ideal gas;
Entropy change of a control mass during an irreversible process; Entropy generation; Principle of
the increase of entropy; Entropy as rate equation;
Learning outcomes of UNIT-II-Students will be able to
Understand the concept of heat engines, heat pump and refrigerators
Recognize irreversible processes
Understand carnot cycle
Calculate thermal efficiency and COP of heat engines and refrigerators/Heat pump
Know that clausius inequality is an alternative statement of second law
Evaluate changes of entropy for liquids, solids and ideal gases.
Lecture plan UNIT-II
S.No. Description of Topic Method of Teaching Cumul
ative
hours
1 The (classical) second law of
thermodynamics
Heat engines and refrigerators; The
second law of thermodynamics,
PPT
WIT and WIL 17
2 The Carnot cycle Chalk n Talk 18
3 The reversible process; Factors that
render processes irreversible, Two
propositions regarding the efficiency of
a Carnot cycle, The thermodynamic
temperature scale
Chalk n Talk
19
4 Tutorial-4 Chalk n Talk 20
5 Tutorial-5 Chalk n Talk 21
6 Tutorial-6 Chalk n Talk 22
7 Entropy for a control mass
The inequality of Clausius; Entropy – a
property of a system;
Chalk n Talk
WIT n WIL 23
8 The entropy of a pure substance,
Entropy change in reversible process
Chalk n Talk 24
9 Entropy change of an ideal gas; The
reversible polytrophic process for an
ideal gas;
Chalk n Talk
25
10 Entropy change of a control mass
during an irreversible process;
Chalk n Talk 26
11 Entropy generation; Principle of the
increase of entropy; Entropy as rate
equation;
Chalk n Talk
27
12 Problems Chalk n Talk 28
13 Tutorial-7 Chalk n Talk 29
Assignment-II
1. Two reversible heat engines are hooked up in a series so that the heat rejected by the first
engine is absorbed by the second heat engine the upstream engines receives 400 KW of heat
from the source at 875K , while the downstream engine rejects heat to the sink at 275K.If the work
output rate of the upstream engine is twice as much as that of the downstream one,
determine,
1. The thermal efficiency of both engines.
2. The heat rejected by the downstream engine.
3. The temperature of the intermediate reservoir.
2. Write the expression for COP of a heat pump and a refrigerator?
3. Show that violation of Kelvin Planck statement implies violation of Clausius statement
UNIT III
Irreversibility and Availability
Available energy; Reversible work, and irreversibility; Availability and second-law efficiency;
Energy balance equation; Engineering applications.
Properties of a pure substance
The pure substance; Vapor- liquid- solid- phase equilibrium in a pure substance; Independent
properties of a pure substance; Tables of thermodynamic properties; Thermodynamic surfaces;
The P-V-T behavior of low- and moderate- density gases; The compressibility factor; Equations of
state; Introduction to computerized tables; Engineering applications.
Learning Objectives-UNIT-III-Students will be able to
Identify the phase given a state.
Identify the quality of a steam given a state
Use steam tables and Mollier charts
Understand that energy and availability are different concepts
Relate the second law efficiency to the transfer and destruction of availability
Know that destruction of exergy is due to entropy generation
S.No. Description of Topic Method of Teaching Cumul
ative
hours
1 Irreversibility and Availability
Available energy;
Chalk n Talk
WIT n WIL 30
2 Reversible work, Irreversibility Chalk n Talk 31
3 Availability and second-law efficiency; PPT 32
4 Exergy balance equation; Third Law
and concept of absolute entropy
Chalk n Talk 33
5 Tutorial-8 PPT 34
6 Properties of a pure substance
The pure substance; Vapor- liquid-
solid- phase equilibrium in a pure
substance;
Chalk n Talk
35
7 Independent properties of a pure
substance;
Chalk n Talk 36
8 Thermodynamic surfaces; The P-V-T
behavior of low- and moderate- density
gases;
Chalk n Talk
37
9 The compressibility factor; Equations
of state;
Chalk n Talk 38
10 Tutorial-9 Chalk n Talk 39
Assignment-III
Q1. In a steam generator, water is evaporated at 260°C, while the combustion gas (cp =
1.08 kJ/kg K) is cooled from 1300°C to 320°C. The surroundings are at 30°C.
Determine the loss in available energy due to the above heat transfer per kg of water
evaporated (Latent heat of vaporization of water at 260°C = 1662.5 kJ/kg).
Q2. 0.2 kg of air at 300°C is heated reversibly at constant pressure to 2066 K. Find the
available and unavailable energies of the heat added. Take T0 =30°C and cp = 1.0047
kJ/kg K.
UNIT IV
Power and refrigeration systems-with phase change (Cycles)
Introduction to power systems; The Rankine cycle; Effect of pressure and temperature on the
Rankine cycle; Air-standard power cycles; The Brayton cycle; The air-standard cycle for jet
propulsion; Reciprocating engine power cycles; The Otto cycle; The diesel cycle; Dual cycle The
Stirling cycle; The Atkinson and Miller cycles;
Learning Objectives-UNIT-IV-Students will be able to
Apply general laws to control volumes with several devices forming a complete system
Understand on what basic cycles the Heat engines and refrigerators work
Know that most real cycles have modifications to the basic cycle set up.
Lecture Plan
S.No. Description of Topic Method of Teaching Cumul
ative
hours
1 Power Cycles
Introduction to power systems; The
Rankine cycle;
2.PPT & Videos
WIT n WIL 40
2 Effect of pressure and temperature on
the Rankine cycle;
Chalk and Talk 41
3 Air-standard power cycles; The
Brayton cycle
Chalk and Talk 42
4 The air-standard cycle for jet
propulsion
Chalk and Talk 43
5 Reciprocating engine power cycles;
The Otto cycle;
Chalk and Talk 44
6 The Diesel cycle; Chalk and Talk 45
7 The Dual cycle, Chalk and Talk 46
8 The Stirling cycle; Chalk and Talk 47
9 The Atkinson Chalk and Talk 48
10 Miller cycles; Chalk and Talk 49
Tutorial-10 Chalk and Talk 50
Assignment-IV
1.Calculate the state of a steam using steam table.
(a) Steam has a pressure of 15bar and specific volume of 0.12m3/kg
(b) Steam has a pressure of 10bar and temperature of 2000C.
(c) Steam has a pressure of 30bar and Enthalpy 2700kJ/kg.
2.Draw the p-V diagram of pure substance and explain its various regions of the diagram in
details?
3. What is the effect of Rankine’s cycle efficiency when the steam is supplied at the inlet of the
turbine is (a) Dry saturated (a) wet with dryness fraction ‘x’ and (c) Superheated?
UNIT V
(Ideal) Gas mixtures
General consideration and mixtures of ideal gases; ideal gas equation,Daltons law of partial
pressure
Thermodynamic (property) relations
Mathematical relations for a homogeneous phase; The Maxwell relations; Thermodynamic
relations involving enthalpy, internal energy, and entropy; The Clapeyron equation, ,Joule
Thompson coefficient,Volume expansivity, and isothermal and adiabatic compressibility; Real gas
behavior and equations of state; The generalized chart for changes of enthalpy at constant
temperature; The generalized chart for changes of entropy at constant temperature; The property
relation for mixtures; Tables of thermodynamic properties.
Learning Objectives-UNIT-V-Students will be able to
Convert concentrations from a mass to a mole basis and vice versa
Compute average properties for the mixture on a mass or mole basis
Know partial pressures and how to evaluate them
Use cleyperon equation for all three two –phase region
Know that the relations are used to develop expression for changes in h,u,s which cannot
be directly measured.
Lecture Plan
S.No. Description of Topic Method of Teaching Cumul
ative
hours
1 (Ideal) Gas mixtures
General consideration and mixtures of
ideal gases;
WIT n WIL
PPT 51
2 Daltons law of partial pressure PPT 52
3 Properties of mixtures Chalk and Talk 53
4 Tutorial-11 Chalk and Talk 54
5 Thermodynamic (property) relations
The Clapeyron equation; Mathematical
relations for a homogeneous phase;
WIT WIL
Chalk and Talk 55
6 The Maxwell relations; Chalk and Talk 56
7 Thermodynamic relations involving
enthalpy, internal energy, and entropy;
Chalk and Talk 57
8 Volume expansivity, and isothermal
and adiabatic compressibility;
Chalk and Talk 58
9 The property relation for mixtures; Chalk and Talk 59
10 Tutorial-12 Chalk and Talk 60
Assignment-V
1. From the basic principles prove that Cp-Cv=-T
T
v 2p=
v
pT
2. A closed adiabatic cylinder of volume 1 m3 is divided by a partition into two
compartments 1 and 2. Compartment 1 has a volume of 0.6 m3 and contains methane at
0.4 MPa, 40°C, while compartment 2 has a volume of 0.4 m3 and contains propane at 0.4
MPa, 40°C. The partition is removed and the gases are allowed to mix. (a) When the
equilibrium state is reached, find the entropy change of the universe. (b) What are the
molecular weight and the specific heat ratio of the mixture? The mixture is now
compressed reversibly and adiabatically to 1.2 MPa. Compute (c) the final
temperature of the mixture,(d) The work required per unit mass, and (e) The specific
entropy change for each gas. Take p c of methane and propane as 35.72 and 74.56 kJ/kg
mol K respectively.
TEXT BOOK:
1. Fundamentals of Thermodynamics by C. Borgnakke and R.E. Sonntag; Publisher Wiley
India Pvt. Ltd.
2. Engineering Thermodynamics by P.K. Nag, Publisher: McGraw-Hill.
3.
REFERENCES:
1. Fundamentals of Thermodynamics by C. Borgnakke, R.E. Sonntag, and G.J. Van
Wylen; Publisher John Wiley.
2. Engineering Thermodynamics by Burgadt, Harper & Row Publication.
3. Thermodynamics — An engineering approach by Yunus Cengel and Boles; Publisher: TMH.
4.
Power Cycles
Introduction to power systems; The Rankine
cycle;
2.PPT &
Videos
WIT n WIL
40
11
Effect of pressure and temperature on the
Rankine cycle;
Chalk and Talk 41
Air-standard power cycles; The Brayton cycle Chalk and Talk 42
The air-standard cycle for jet propulsion Chalk and Talk 43
Reciprocating engine power cycles; The Otto
cycle;
Chalk and Talk 44
The Diesel cycle; Chalk and Talk 45
The Dual cycle, Chalk and Talk 46
The Stirling cycle; Chalk and Talk 47
The Atkinson Chalk and Talk 48
Miller cycles; Chalk and Talk 49
Tutorial-10 Chalk and Talk 50
5.
(Ideal) Gas mixtures
General consideration and mixtures of ideal
gases;
WIT n WIL
PPT 51
10
Daltons law of partial pressure PPT 52
Properties of mixtures Chalk and Talk 53
Tutorial-11 Chalk and Talk 54
Thermodynamic (property) relations
The Clapeyron equation; Mathematical
relations for a homogeneous phase;
WIT WIL
Chalk and Talk 55
The Maxwell relations; Chalk and Talk 56
Thermodynamic relations involving enthalpy,
internal energy, and entropy;
Chalk and Talk 57
Volume expansivity, and isothermal and
adiabatic compressibility;
Chalk and Talk 58
The property relation for mixtures; Chalk and Talk 59
Tutorial-12 Chalk and Talk 60
VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING & TECHNOLOGY
(Autonomous)
DEPARTMENT OF MECHANICAL ENGINEERING
II B. Tech, Ist Semester (Mechanical Engineering)
Subject : Fluid Mechanics and Hydraulic Machines
Subject Code : 5ME04
Academic Year : 2016 – 17
Number of working days : 90
Number of Hours / week : 3 + 1
Total number of periods planned: 75
Name of the Faculty Member: Mr. K. KRISHNA MURTHY
Course Objectives:
Understanding the properties of fluids, principles of buoyancy, flow, force and head calculations.
Evaluation of types of fluid flow, laminar and dynamic.
Knowledge on boundary layer principles applied to aerofoiles.
Principles of operation of different types of hydraulic machinery.
Course Outcomes (COs): Upon completion of this course, students should be able to:
CO-1: Analyzing the fluid properties to solve flow, force and velocity problems.
CO-2: Evaluating the flow characterizing in static and dynamic nature of flow.
CO-3: Applying fluid flow and dynamics in solving problems in hydraulic machines.
CO-4: understanding the model analysis of hydraulic machinery and select appropriate machines
for hydro plant.
UNIT : I
Syllabus:
Fluid Statics: Properties of fluid – specific gravity, viscosity, surface tension, vapor pressure and
their influence on fluid motion, Pressure at a point, measurement of pressure, Forces on immersed
surfaces, Center of pressure, Buoyancy, Elements of stability of floating bodies.
Fluid Kinematics: Classification of flows, acceleration equations, Stream line, path line and
tool steels; Mold Steels (Group P); Special purpose tool steels; Heat treatment of tool steels;
Overview of tool failures;
Special cutting materials – satellites, cemented carbides, and ceramic tools
Learning Objectives: After completion of the unit, the student must able to:
Understand the purpose of alloying and effecting of alloying on different phases
Identify the type steels and their phases
Know the composition of the different steels alloys and their properties and application
Lecture Plan
S. No. Description of Topic No. of Hrs. Method of Teaching
1. Introduction; Purpose of alloying; Effect
of alloying elements upon Ferrite; Effect
of alloying elements upon carbide
48th
hour Black board + PPT
2. Influence of alloying elements on the
iron-iron carbide diagram; Effect of
alloying elements in tampering
49th
hours Black board + PPT
3. Classification of steels - nickel steel,
chromium steel, nickel-chromium steels,
manganese steels, molybdenum steels,
tungsten steels, vanadium steels
50th
hours Black board + PPT
4. silicon steels, stainless steels, martensitic
stainless steels, ferritic stainless steels,
austenitic stainless steels, precipitation-
hardening stainless steels, maraging
steels, and ausforming.
51nd
& 52rd
hours Black board + PPT
5. Classification of tool steels; Selection of 53th
hour Black board + PPT
tool steels; Comparative properties; Non-
deforming properties; Depth of
hardening
6. Toughness; Wear resistance; Red-
hardness; Machinability; Resistance to
decarburization; Brand names
54th
& 55th
hours Black board + PPT
7 Introduction; Purpose of alloying; Effect
of alloying elements upon Ferrite; Effect
of alloying elements upon carbide
54th
hours Black board + PPT
8 Water-hardening tool steels (Group W);
Shock resisting tool steels (Group S);
Cold-work tool steels; Hot-work tool
steels (Group H); High speed tool steels;
Mold Steels (Group P
55th
hours Black board + PPT
9 Special purpose tool steels; Heat
treatment of tool steels; Overview of tool
failures;
56th
hurs Black board + PPT
10 Special cutting materials – satellites,
cemented carbides, and ceramic tools
57th
hours Black board + PPT
Assignment - 4
1. What is high speed steel? state and explain the important properties of the two types of
high speed steel.
2. List the properties most important for tool steels and give one industrial application where
each property would be required.
3. What would be the influence of each of the following alloying elements on the properties
of a tool steel: chromium, tungsten, molybdenum, vanadium, silicon, manganese, and
cobalt?
UNIT : V
Syllabus:
CAST IRON
Introduction; Types of cast iron; White cast iron; Malleable cast iron; Pearlitic malleable iron;
Gray cast iron; Silicon in cast iron; Sulfur in cast iron; Manganese in cast iron; Phosphorus in cast
iron; Heat treatment of grey iron, Size and distribution of graphite flakes; Mechanical properties
and applications of grey cast iron; Chilled cast iron; Nodular cast iron; Alloy cast irons.
NON-FERROUS METALS AND ALLOYS
Introduction; Copper and its alloys - Copper, temper designation of copper and copper alloys, and
copper alloys; Aluminum and its alloys - Aluminum, Alloy designation system, and temper
designation; Titanium and Titanium alloys.
Learning Objectives: After completion of the unit, the student must able to:
know the type of cast irons ,composition, properties and applications
describe the type of non ferrous metals and alloys
Know the composition ,properties and applications of non ferrous metals and alloys
Lecture Plan
S. No. Description of Topic No. of Hrs. Method of Teaching
1. Introduction; Types of cast iron; White
cast iron; Malleable cast iron; Pearlitic
malleable iron; Gray cast iron; Silicon in
cast iron; Sulfur in cast iron; Manganese
in cast iron
58th
hours Black board + Video
2. Phosphorus in cast iron; Heat treatment
of grey iron, Size and distribution of
graphite flakes
59th
& 60th
hours Black board
3. Mechanical properties and applications
of grey cast iron; Chilled cast iron;
Nodular cast iron; Alloy cast irons.
61st & 62
nd hours Video
4. Introduction; Copper and its alloys -
Copper, temper designation of copper
and copper alloys, and copper alloys;
63rd
hours Video
5. Aluminum and its alloys - Aluminum,
Alloy designation system, and temper
designation; Titanium and Titanium
alloys..
64th
hours Black board
Assignment - 5
1. Discuss the effect of the amount of free carbon on the properties of gray cast iron.
2. Differentiate, in microstructure, gray cast iron, malleable iron, and nodular iron.
3. Why are graphite flakes in gray iron very often surrounded by ferrite areas?
4. Why is malleable iron made only from hypoeutectic white iron?
5. Explain why copper is a suitable material for automobile radiator.
6. What is season cracking? How may it be minimized?
7. Why are most copper – zinc alloys not age- hardenable?
8. What are the outstanding properties of cupronickel alloys?
9. Compare aluminium and magnesium with regard to corrosion resistance.
10. Why is “white metal” suitable for bearing application?
TEXT BOOKS:
1. Introduction to Physical Metallurgy by Sidney H. Avner; Publisher: McGraw-Hill.
2. Materials Science and Metallurgy by Kodigiri, publisher: Everest.
REFERENCES:
1. Essentials of Materials Science and Engineering by Donald R. Askeland and Thomson.
2. Materials Science and Engineering by William and Collister.
3. Elements of Materials Science by V.Raghavan.
VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING & TECHNOLOGY
(Autonomous)
DEPARTMENT OF MECHANICAL ENGINEERING
II B. Tech, Ist Semester (Mechanical Engineering)
Subject : Mechanics of Solids
Subject Code : 5ME01
Academic Year : 2016 – 17
Number of working days : 90
Number of Hours / week : 4 + 1
Total number of periods planned: 80
Name of the Faculty Member: Dr. G. S. Gupta.
Course Objectives:
List and define the Material properties and show the relationships between them.
Describe principles of Mechanics, Stress and Strain.
Demonstrate throughly the concepts of principal stresses applied to solid structural members
and mohr’s circle diagram.
Analyse various types of mechanical engineering problems concern to bending of beams,
torsion of shafts etc.
Course Outcomes (COs): Upon completion of this course, students should be able to:
CO-1 : Show basic stress strain equations with appropriate assumptions
CO-2 : Interpret model and analyze solid mechanics problems on bars,beams and shafts.
CO-3 : Apply the concepts of principal stresses in real life design issues
CO-4 : Analyse and develop beams, shats for various applications UNIT I
Tension, compression, and shear
Introduction; Normal Stress and Strain; Stress-strain diagrams; Elasticity and plasticity; Linear
elasticity and Hooke’s law; Allowable stress and allowable loads. Axially loaded members
Introduction; Deflections of axially loaded members; Strain energy; Dynamic loading;
Learning objectives : after successful completion of unit - I the student must be able to
1. Understant Fundamental stresses and derived stresses.
2. Discuss different types of Properties of Engieering Materials.
3. Understand the terms allowable stress and allowable loads and its importance in design.
4. Discuss the factor of safety values adopted for various materials in design.
5. Develop Expressions for deflection of axially loaded members and draw displacement diagrams.
6. Explain the concept of strain energy.
7. Explain the role of the dynamic loads for inducing stresses in Machine members.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
1 Introduction 1 Black Board + PPT
2 Normal stress and strain, stress-strain diagrams, Elasticity and Plasticity
3 Black Board +
Video
3 Linear elasticity and hooke’s law, Allowable
stress and Allowable loads 1 Black Board + Video
AXIALLY LOADED MEMBERS
4 Introduction, deflections of axially loaded
members 3 Black Board + Video
+ Models
5 Strain energy; Dynamic loading 4 Black Board +
Models
Assignment 1:
1. A steel tube 100mm internal dia., 125mm external dia. is surrounded by a brass tube of inner dia. 126mm and outer dia . 150mm. Both are rigidly connected. The compound tube is subjected to an axial compressive load of 5KN.Find the stresses developed in each tube and the load carried by each tube. Take Es =200GPa and Eb=100GPa. 2. A specimen of dia. 13mm and gauge length 50mm was tested under tension. At20KN load, the extension was observed to be 0.0315mm. Yielding occurred at a load of 35 KN and the ultimate load was 60KN. The final gauge length at fracture was 70mm. calculate E, Yield stress, ultimate strength and % elongation. 3. Two rods, one made of steel and the other of brass, hang vertically, 1.0m apart, from a rigid support. Both are 1.0m long. The rods support a rigid bar horizontally. When a load of 25KN is placed at 400mm from the steel rod on the horizontal bar, the extension of the two rods are found to be equal. If the area of the steel rod is 300mm2, find the stresses and strains in the rods and the area of the brass rod. Take Es = 200Ga and Eb = 85Gpa 4. A steel wire 2.0m long and 3mm in dia. elongates by o.75mm, when a weight W is suspended from the wire. If the same load is suspended from the brass wire 2.5m long and 2mm dia, it is elongated by 4.64mm. Find the modulus of elasticity of brass, if the modulus of elasticity of steel, Es = 200GPa 5. Find the Poisson’s Ratio and Bulk modulus of a material whose modulus of elasticity is 200 GPa and modulus of rigidity is 80GPa. A 2.0m long rod of 40mm dia. made with the same material is stretched by 2.5mm under some axial load. Find the lateral contraction. 6. Rails of 15m length were laid on the track when the temperature was 200 C. A gap of 1.8mm was kept between two consecutive rails. At what maximum temperature the rails will remain stress free? If the temperature is raised further by 150 C, what will be the magnitude and nature of stresses induced in the rails? Take αs = 12×10-6/0C. 7. A flat steel bar 30mm wide and 5mm thick is placed between two bars of aluminum, each 30mm wide and 8mm thick to form a compound bar at 100C. Calculate the temperature stresses induced at55oC, taking. ES =200 GPa, Eal =67 GPa αs = 12× 10-6/0Cand αal = 24×10-6 /0C. 8. A thin tyre is shrunk on a wheel of 1.0m diameter. Find the internal diameter of the tyre, if circumferential stress is limited to 90N /mm2. Find also the least temperature to which the tyre must be heated above that of the wheel, before it could be slipped on. For the tyre material take E= 200 GPa and α =12×10-6 /0C. 9. During a direct tension test on a 20mm dia. Rod 1.0m. long, the longitudinal strain was observed to be 4 times the lateral strain. If its elastic modulus is 200GPa find the bulk modus and modulus of rigidity. If the rod is subjected to hydrostatic pressure of 100 N/mm2 , find the decrease in volume. 10. A bar of length 200mm tapers uniformly from 40mm dia to 35mm. calculate the change in its length due to a an axial pull of 100KN, assuming E as 200 GPa .Derive the formula used in the calculation. 11. A steel bar of length 200mm and 50×50mm in section is connected at its end to an aluminum bar of 250mm length and 80×80mm in section, such that they have a common longitudinal axis. Find the load which will reduce the total length by o.25mm. Find also the total work done. Take Es =200GPa And Eal =70GPa. 12. A uniform metal bar of 1.8m length and area of cross section 100mm2 has an elastic limit of 160N/mm2. Find its proof resilience, if E=200GPa. Find also the maximum load which can be suddenly applied without
exceeding the elastic limit. Calculate the magnitude of the gradually applied load which will produce the same extension. 13. A wagon of weight 25KN attached to wire rope is moving at a speed of 4Km ph. The cross sectional area of the rope is 500mm2. Suddenly the rope jams and the wagon is brought to rest. If the length of the rope is 10m at the time of sudden stoppage, find instantaneous stress and elongation of rope, if E=200GPa and g =9.8m/sec2. 14. Two rods of same length same material are subjected to the same axial load. The first rod is of uniform diameter D. The second bar has a diameter D for 1/3 of its length and 2D for the remaining length, compare the strain energies of the two bars. 15. A steel wire of 2.5mm diameter is firmly held in a clamp from which it hangs vertically. An anvil is secured to the wire 1.5m below the clamp. A weight bored to slide over the wire to drop freely, is dropped freely onto the anvil from a height of 1m. Find the weight required to stress the wire to 900N/mm2, if E=200GPa. Neglect the weight of the anvil and assume the wire to be elastic
Unit 2:
Syllabus: Torsion
Introduction; Torsion of circular bars; Nonuniform torsion; Pure shear; Relationship between
moduli of elasticity E and G; Transmission of power by circular shafts; Shear force and bending moment diagrams
Types of beams; Types of loading; Shear force and bending moment; Relationship between load,
shear force and bending moment; Shear force and bending moment diagrams.
Learning objectives : after successful completion of unit - II the student must be able to
1. Understand the concept of shear stresses induced in a shaft due to the action of twisting.
2. Derive the Torsion formula.
3. Explain the concept of non-uniform torsion.
4. Discuss the concept of pure shear and develop the relation between moduli of elasticity E & G.
5. Explain the procedure to determining the power transmission by circular shafts.
6. Estimate the strain energy in case of pure shear and torsion.
7. Differentiate beam and bar. Understand types of loads and supports in case of beams.
8. Develop the relationship between shear force and bending moment.
9. Understand and draw the shear force and bending moment diagrams.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching SHEAR FORCE AND BENDING MOMENT DIAGRAMS
1 Types of beams; Types of loading; Shear
force and bending moment; 4 PPT
2 Relationship between load, shear force and
bending moment; 2 Black Board + PPT
3 Shear force and bending moment diagrams; 6 Black Board TORSION
4 Introduction; Torsion of circular bars; Non
uniform torsion; 6 Black Board
5 Pure shear; Relationship between modulus of elasticity E and G; Transmission of power
by circular shafts
4 Black Board + PPT
Assignment 2:
1.Sketch the S.F. &B.M. diagrams for an Overhanging beam ABCDE shown. Mark all the salient points with respective values.
2. Draw SF and BM diagrams for the simply supported beam shown. Mark all the salient values and points.
3. Draw SF& BM diagrams for the simply supported beam marking all the salient values.
4. An overhanging beam ABCD supported at Band D has an overhang AB of 3m on the left side. It carries a load of 8KN at the point C, distance of C from D being 3m.Also there is a udl of 2KN/m over AC of length 12m. Draw SF& BM diagrams marking all salient points. 5. A simply supported beam with overhanging ends is loaded as shown. If wx l=P, what is the ratio of a/l for which the B.M. at the middle of the beam will be zero.
6. sketch SFD and BMD for the cantilever beam shown
7. Draw SFD& BMD for a simply supported beam subjected to a clock-wise couple M at L/4 from the left support, where L is the span Also draw the Elastic curve.
Unit III
Syllabus: Area moment of inertia of composite sections.
Stresses in beams
Introduction; Normal strains in beams; Normal stresses in beams; Cross-sectional shapes of beams; Shear stresses in rectangular beams; Shear stress in webs of beams with flanges; Shear
stress in circular beams (solid and hollow sections);
Learning objectives : after successful completion of unit - III the student must be able to
1. Calculate Moment of Inertia of different types of composite sections.
2. Derive a relation for flexure formula for a beam is under pure bending.
3. Determine normal stresses developed in a beam under the action of various types of loads.
4. Develop formulation from fundamentals for shear stresses induced in the beam on application of
loads.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
1 Area moment of inertia of composite sections 2 PPT + Black Board STRESSES IN BEAMS
2 Introduction, Normal strains in beams,
Normal stresses in beams, Cross-sectional
shapes of beams-C, angular and semicircle
structures
6 PPT + Video + Black
Board
3 Shear stresses in rectangular beams, Shear
stress in webs of beams with flanges, Shear stress in circular beams (solid and hollow
sections); Concept of shear center and shear
flow
6 PPT + Video + Black
Board
Assignment 3:
Assignment 1. An I – beam of 200mm depth is simply supported over an effective span of 8m. Find what max. intensity of udl it can carry over entire length if the allowable bending stresses in tension and compression are 30 and 45 N/mm2 respectively. Take INA = 5935.5×104 mm4. Distance of bottom fibre from NA is 87.38mm. 2. Obtain the dimensions of the strongest rectangular section that can be cut from a circular log of wood of 250mm diameter. 3. A T section with a flange of 200×20mm and web of 400mm×50mm is used as a cantilever with an effective span of 2.75m. It is subjected to a couple of 50KNm clockwise at the free end. Sketchthe variation in bending stress at midspan section and at the section carrying max. B.M. 4. If a hole of 20mm is made in the web, of the above section at a distance of 50mm from the junction with flange, sketch the variation in bending stress across the depth. 5. Design a hollow circular section for a beam to carry a B.M .of 100kNm with internal external diameter ratio of 0.75. Also sketch the variation in bending stress. Compare the economy with a solid section of same material and same weight. Take allowable stress as 150N/mm2.
Unit 4
Syllabus: Analysis of stress and strain
Introduction; Plane stress; Principal stresses and maximum shear stresses; Mohr’s circle for
plane stress; Hooke’s law for plane stress; Spherical and cylindrical pressure vessels (biaxial stress; Hoop and longitudinal stresses); Combined loadings (plane stress); Principal stresses in
beams;
Learning objectives : after successful completion of unit - IV the student must be able to
1. Understant General stress element and plane stress condition.
2. Discuss the concept of principal stress and its significance in design of Materials.
3. Develop relations for normal stress and shear stress on any inclined plane of a given stress
element.
4. Explain the types of stresses induced in spherical and cylindrical pressure vessels when stored
with high pressure fluids.
5. Estimate the resultant stresses when a component is subjected with various types of loads
simultaneously.
Lecture Plan
S.No. Description of Topic No. of
Hrs.
Method of
Teaching 1 Introduction, Plane stress, Principal stresses and
3 Combined loadings (plane stress), Principal stresses in beams
2 PPT + Black Board
Assignment 4:
1.(a) A thin spherical shell of 1m internal diameter and 5mm thick is filled with a fluid under pressure until its volume increases by 200cc.Taking E= 200 GPa and µ =0.3, calculate the internal pressure. (b) What happens if the above spherical shell is subjected to a vacuum of same magnitude.? (c) Are these volume changes the changes in the volume of the material of the shell or the volume of the space inside the spherical shell. 2. (a) Show the probable crack pattern of failure of a thin cylinder when it fails due to (i) maximum hoop stress, (ii) maximum longitudinal stress and (iii) maximum shear stress. (b) A boiler of 2m diameter is made of 20mm thick plates. If the maximum tensile stress is not to exceed 100 N/mm2, find the permissible steam pressure in the boiler, taking the efficiency of longitudinal riveted joint as 75%. Calculate the longitudinal stress, if the efficiency of circumferential joint is 65%. 3. A thin cylinder is laid in a vacuum of 3N/mm2
. If the maximum tensile stress is limited to 50N/mm2 with what maximum pressure, above atmosphere, a fluid can be introduced into the cylinder? 4. (a) A long boiler tube has to withstand an internal pressure of 6N/mm2 above atmosphere. The internal diameter of the tube is 60mm. Determine the thickness and mass/m of the tube if the maximum tensile stress is not to exceed 130N/mm2. Mass density of steel is 7850kg/m3. (b) A thick cylinder is designed using thin cylinder theory. Is it safe? (c) A thin cylinder is designed using thick cylinder theory. Will it be safe?
Unit 5
Syllabus:
Deflections of beams
Introduction; Differential equations of the deflection curve; Deflections by integration of the
bending moment equation; Deflections by integration of the shear-force and load equations; Macaulay’s method; Moment area method; Method of superposition;
Learning objectives : after successful completion of unit - V the student must be able to
1. Derive differential equation of the deflection curve for beam under different types of loading.
2. Understand the deflection determined by integration of bending moment diagram.
3. Develop Expressions for deflection by integration of the shear-force and load equations.
4. Estimate the deflections in the beam on loading by Macaulay’s method.
5. Explain the concept of Moment area method for finding slope and deflection for a given loaded
beam.
6. Understand thoroughly concept of method of superposition.
7. Explain the concept of strain energy in bending.
Lecture Plan
S.No. Description of Topic No. of Hrs. Method of Teaching
DEFLECTIONS OF BEAMS:
1 Introduction, Differential equations of the
deflection curve, Deflections by integration of the bending moment equation
4 Black Board +
Models + PPT
2 Deflections by integration of the shear-force and load equations, Macaulay’s method,
Moment area method
6 Black Board +
Models + PPT +
Video
3 Method of superposition; 2 Black Board +
Models + PPT
Assignment 5:
1. A simply supported beam of span L carries a uniformly varying triangular load of intensity per unit length at the right end and zero at the left end. Obtain the slope and Deflection at the left end and at the position of max. B.M. 2.A simply supported beam of span 6m carries two point loads of 60KN and 50KN at 1m and 3m respectively from the left end. Find the position and magnitude of max. deflection. Take E= as 200 GPa and I =8500cm4. Also determine the value of deflection at the same point if one more load of 60KN is placed over the left support. 3.A simply supported beam of 8m carries a partial u d l of intensity 5KN/m and length 2m, sarting from 2m from the left end. Find slope at left support and central deflection. Take E= 200Gpa and I=8×108mm4 4.(a) A cantilever of 4m. Span carries a load of 40KN at its free end. If the defection at the free end is not to exceed 8mm, what must be the moment of inertia of the cantilever section? (b)If the above beam with that moment of inertia and the same span is subjected to a pure couple acting at the free end and the maximum deflection is not to exceed 8mm, what maximum pure couple can be applied? 5. A horizontal beam of uniform section is simply supported at its ends which are at the same level and is loaded at the left support with an anti –clockwise moment ‘M’ and at the right support with a clock –wise moment ‘2M’ both in the same vertical plane. The span of the beam is ‘l’ Find the angles of the slope at each end, deflection of the mid point of the span in terms of M, L, and flexural rigidity.