ACADEMIC PLAN Subject : Thermodynamics Code : · PDF file1 3 Course Objectives: ......

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


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


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


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




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


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


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


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


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


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


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


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


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

streak lines and stream tube, continuity equation, Stream function, velocity potential function.

Learning Objectives: After completion of the unit, the student must able to:

Explain dimensions and units – physical properties of fluids specific gravity, viscosity.

Describe about pressure at a point, Pascals’s law, Hydro-static law.

Solve problems on fundamental dimensions.

Differentiate between atmospheric, gauge and vacuum pressure.

Explain about different Pressure gauges, Manometers: Differential and Micro Manometers.

Solve problems on Pressure measurement.

Explain about hydrostatic forces on submerged plane, Horizontal, Vertical, Inclined and

Curved surfaces.

Derive equation of Centre of pressure.

Solve problems on centre pressure on different surfaces.

Understanding the concept of Buoyancy, Buoyant force and centre of Buoyancy.

Derive equation of Meta centre and Met-centric height.

Understanding the stability of submerged and floating bodies.

Derive the time period of transverse oscillation of a floating body.

Describe about fluid flow, Stream line, Path line and Streak lines and Stream tube.

Differentiate between Steady, Unsteady, Uniform, Non-uniform, Laminar, Turbulent,

Rotational and Irrotational flows.

Explain equation of continuity for one, two and three dimensional flows.

Describe about Stream and Velocity potential functions.

Analyze flownets.

Solve problems on fluid flows and flownets.

Lecture Plan

S.No. Description of Topic No. of Hrs. Method of Teaching

1. Properties of fluid – specific gravity,

viscosity, surface tension, vapor pressure and

their influence on fluid motion

1st ,2

nd , 3

rd &

4th

hour

PPT + Video

2. Capillary effect 5th

hour Black board + Video

3. Pressure at a point, measurement of pressure 6th

hour Black board

4. Type of pressure gauges 7th

& 8th


5. Forces on immersed surfaces, Center of

pressure, Buoyancy

8th

, 9th

, & 10th

hour

Black board

6. Elements of stability of floating bodies 11th

& 12th

hour Black board + PPT

7. Classification of flows, acceleration equations 13th


8. Stream line, path line and streak lines and

stream tube, continuity equation,

14th

& 15th

hour Black board+ Video

9 Stream function, velocity potential function.

16th

& 17th

hours

Black board + Video

10 Tutorial 18th ,

19th

& 20

th

hour

Black board

Assignment – 1

1. (a) What do you mean by the term ‘Viscosity’? State and explain the Newton’s law of

viscosity.

(b) A thin plate is placed between two at surfaces kept h cm apart, such that the viscosities

on top and bottom of the plates are µ1 and µ2 respectively. Determine the position of the

thin plate such that the viscous resistance to uniform motion of the thin plate is minimum.

Assume `h' to be very small.

2. Derive the expression for power developed by the annular bearing.

3. Derive the expression for power developed by the conical bearing.

4. Derive the expression for capillary rise in between the two plates held vertically in the

liquid.

5. Derive the expression for capillary rise in annular tube.

6. A shaft of diameter 120 mm is rotating inside a journal bearing of diameter 122 mm at a

speed of 360 rpm. The space between the shaft and bearing is filled with a lubricating oil

of viscosity 6 poise. Find the power absorbed in oil if the length of bearing is 100 mm.

7. Calculate the capillary rise h in a glass tube of 3 mm diameter when immersed in water at

20ºC. Take surface tension for water at 20ºC as 0.0075 kgf/m. what will be the percentage

increase in the value of h if the diameter of the glass tube is 2 mm?

8. (a) State Pascal's law. What do you understand by the terms atmospheric, gauge and

vacuum pressures.

(b) Prove that the pressure intensity in the liquid is directly proportional to the height of a

point from free surface of liquid.

9. For a compound manometer shown in figure, what is the

gage pressure at C if the manometer fluid is mercury and if

the fluid in the pipe and in the tubing which connects the two

U tubes is water?

10. The profile of a vessel is quadrant of a circle of radius `r'. Obtain from First principles the

horizontal and vertical components of the total pressure force.

11. A trapezoidal plate of parallel sides `l' and `2l' and height `h' is immersed vertically in

water with its side of length `l' horizontal and topmost. The top edge is at a depth `h' below

the water surface. Determine:

(a) Total force on one side of the plate

(b) Location of the centre of pressure.

12. A vertical sluice fate is used to cover an opening in a dam. The opening is 2m wide and 1.2

m high. On the upstream of the gate, the liquid of specific gravity 1.45, lies upto a height

of 1.5 m above the top of the gate, whereas on the downstream side the water is available

upto a height touching the top of the gate. Find the resultant force acting on the gate and

position of the centre of pressure. Find also the force acting horizontally at the top of the

gate which is capable of the opening it. Assume that the gate is hinged at the bottom.

13. A rectangular pontoon 10 m long, 7m broad and 2.5 m deep weight 686.7kN. It carries on

its upper deck an empty boiler of 5m diameter weight 588.6kN. The centre of gravity of

the boiler and the pontoon are at their respective centers

along a vertical line. Find the Meat centre height.

Weight density of sea water is 10.104kN/m3.

14. A cylinder gate of 4 m diameter 2 m long has water

on its both sides as shown in figure. Determine the

magnitude, location and direction of the resultant

force exerted by the water on the gate. Find also the

least weight of the cylinder so that it may not be lifted away from the floor.

15. The following cases represent the two velocity comports, determine the third component of

velocity such that they satisfy the continuity

equation:(i)

16. The velocity components in a two dimensional flow field for an incompressible fluid are

expressed as (a) show that these functions represent

a possible case of an irrotational flow, (b) obtain an expression for stream function (c)

obtain an expression for velocity potential

17. Derive the equation of stream function and velocity potential for a uniform stream of

velocity V in a two dimensional field, the velocity V being inclined to the x-axis at a

positive angle α.

18. Obtain an expression for continuity equation for a three dimensional flow in Polar

Cylindrical Coordinate System.

19. Obtain an expression for continuity equation for a three dimensional flow in Polar

Spherical Coordinate System.

UNIT : II

Syllabus:

Fluid Dynamics: Surface and body forces – Euler’s and Bernoulli’s equation, Venturimeter,

Orifice meter, Pitot tube, Reynolds experiment –Darcy Weisbach equation – Minor losses in pipes

– pipes in series and pipes in parallel. Momentum equation, forces on pipe bend.


Explain surface and body forces.

Define Euler’s and Bernoulli’s equations for flow along a stream line for 3D flow.

State the types of flow measuring devices.

Explain working of Pitot tube, Venturimeter, Office meter.

Describe the Reynold’s experiment.

Explain energy loses in pipes, Darcy – weisbach equation

Explain Pipes in series and parallel

Describe Total Energy Line and Hydraulic Gradient Line.

Solve problems on pipe flow.

Describe the Momentum equation and its application.

Solve problems on forces on pipe bends.

Lecture Plan


1. Surface and body forces. 21th

hour PPT + Video

2. Euler’s equation & Bernoulli’s equation 22th

hours Black board

3. Venturimeter, Orifice meter, Pitot tube 23

rd , 24

th & 25

th


4. Reynolds experiment –Darcy Weisbach

equation 26

th hours Black board

5. Minor losses in pipes – pipes in series and

pipes in parallel

27th

, 28th

& 29th

hours Black board

6. Total Energy Line and Hydraulic Gradient

Line 30

th hour Black board + PPT

7. Momentum equation and its application. 31

th , & 32th

hour Black board

8. Tutorial 33

rd ,34

th & 35

th


Assignment - 2

1. State and prove Bernoullis theorem. Mention its limitations.

2. What is a venturimeter? Derive an expression for the discharge through a venturimeter.

3. Water is flowing through a pipe having diameters 30 cm and 15 cm at the bottom and upper

end respectively. The intensity of pressure at the bottom end is 29.43 N/cm2 and the pressure

at the upper end is 14.715 N/cm2. Determine the difference in datum head if the rate of floe

through pipe is 50 liters/s.

4. A horizontal venturimeter with inlet and throat diameters 30 cm and 15 cm respectively is

used to measure the flow of water. The reading of differential manometer connected to inlet

and throat is 10 cm of mercury. Determine the rate of flow. Take Cd = 0.98.

5. The inlet and throat diameters of a horizontal venturi-meter are 300 mm and 10 cm

respectively. The liquid flowing through the meter is water. The pressure intensity at inlet is

10.734 N/cm2 while the vacuum pressure head at the throat is 37 cm of mercury. Find the rate

of flow. Assume that 4% of the differential head lost between the inlet and throat. Find also the

value of Cd for the venture- meter.

6. An orifice meter with orifice diameter 15 cm is inserted in a pipe 30 cm diameter. The pressure

difference measured by a mercury oil differential manometer on the two sides of the orifice

meter gives a reading if 50 cm of mercury. Find the rate of flow oil of specific gravity 0.9

when the co efficient of discharge of the meter 0.64.

7. A pitot tube is inserted in a pipe of 300 mm diameter. The static pressure in pipe is 100 mm of

mercury (vacuum). The stagnation pressure at the centre of the pipe, recorded by the pitot tube

is 0.981 N/cm2. Calculate the rate of flow of water through a pipe, if the mean velocity of flow

is 0.85 times the central velocity. Take Cv = 0.98.

8. State and derive impulse momentum equation. What are the applications of impulse

momentum equation?

9. 200 liters per second of water is flowing in a pipe having a diameter of 40cm. The pipe is bent

by 1350 and the pressure of water owing in the pipe is 350KPa. Sketch the configuration. Find

the magnitude and direction of resultant force on the bend.

10. A 45º reducing bend is connected in a pipe line, the diameter at the inlet and outlet of the bend

being 600 mm and 300 mm respectively. Find the force exerted by water on the bend if the

intensity of pressure at inlet is 8.829 N/cm2 and rate of flow of water is 600 liters/s.

11. Three pipes of lengths 800 m, 600 m and 300 m and of diameters 400 mm, 300 m and 200 mm

respectively are connected in series. The ends of the compound pipe id connoted to two tanks,

whose water surface levels are maintained at a difference of 15 m. Determine the rate of flow

of water through a pipes if f = 0.005. What will be diameter of a single pipe of length 1700 m

and f = 0.005, which replaces the three pipes?

12. A main pipe divides into two parallel pipes which again forms one pipe. The length and

diameter for the first parallel pipe are 2000 m and 1 m respectively. While the length and

diameter of second pipe are 2000 m and 0.8 m. Find the rate of flow in each parallel pipe, if

total flow in the main pipe is 3 m3/s. the co efficient of friction for each parallel pipe is same

and equal to 0.005.

13. Derive the expression for head loss due to: (i) sudden enlargement, (ii) sudden contraction (iii)

sudden bend (iv) exit loss (v) entry loss (vi) obstruction in pipe and (vii) pipe fittings.

14. Define and explain the terms: (i) Hydraulic gradient line and (ii) Total Energy line.

15. Explain the terms: (i) pipes in parallel (ii) equivalent and (iii) equivalent size of the pipe and

(iv) pipes in series.

16. Prove that the head lost due to friction is equal to one third of the total head at inlet for

maximum power transmission through pipes or nozzles.

UNIT : III

Syllabus:

Boundary Layer Theory: Development of boundary layer along a thin flat plate, laminar

boundary layer and turbulent boundary layer, Laminar sub layer, boundary layer separation, Drag

and lift forces - Aerofoils, pressure and form drags.

Impact of Jets: Hydrodynamic force of jets on flat, inclined and curved vanes - jet striking

centrally and at tip, flow over radial vanes.


Describe the Boundary layer and its growth.

Explain about Characteristics of boundary layer along a thin flat plate.

Differentiate Laminar and Turbulent Boundary layers.

Explain Boundary layer separation and control.

Describe Flow around submerged objects – Drag and Lift – Magnus effect.

Solve problems on boundary theory, drag and lift.

Expressions for force exerted by the water on the plate or blade (vertical, inclined and

curved)

Lecture Plan


1. Development of boundary layer along a thin

flat plate 36

st & 37

th hour Black board + Video

2.

laminar boundary layer and turbulent

boundary layer, Laminar sub layer, boundary

layer separation

38th

, 39th

& 40th


3. Drag and lift forces - Aerofoils, pressure and

form drags

41th

, 42nd

, &

43rd


4.

Hydrodynamic force of jets on flat, inclined

and curved vanes - jet striking centrally and at

tip, flow over radial vanes.

44th

,45th

,46th

&

47th


5. Tutorial 48

th ,49

th & 50

th


Assignment – 3

1. A jet of water having a velocity of 40 m/s strikes a curved vane, which is moving with a

velocity of 20 m/s. the jet makes an angle of 30º with the direction of motion of vane at inlet

and leaves an angle of 90º to the direction of motion of vane at outlet. Draw the velocity

triangles at inlet and outlet and determine the vane angles at inlet and outlet so that the water

enters and leaves the vane without shock.

2. A jet of water of diameter 50 mm, having a velocity of 20 m/s strikes a curved vane which is

moving with a velocity of 10 m/s in the direction of the jet. The jet leaves the vane at an angle

of 60º to the direction of motion of vane at outlet, determine: (i) the force exerted by the jet on

the vane in the direction of motion, (ii) work done per second by the jet.

3. A jet of water having a velocity of 15 m/s strikes a curved vane which is moving with a

velocity of 5 m/s. the vane is symmetrical and it so shaped that the jet is deflected through

120º. Find the angle of the jet at inlet of the vane so that there is no shock. What is the absolute

velocity of the jet at outlet in magnitude and direction and the work done per unit weight of

water? Assume the vane to be smooth.

4. A jet of water moving at 12 m/s impinges on vane shaped to deflect the jet through 120º when

stationary. If the vane is moving at 5 m/s, find the angle of the jet so that there is no shock at

inlet. What is the absolute velocity of the jet at exit in magnitude and direction and the work

done per second per unit weight of water striking per second? Assume that the vane is smooth.

5. A jet of water heading a velocity of 35 m/s impinges on a series of vanes moving with a

velocity of 20 m/s. the jet makes an angle of 30º to the direction of motion of vanes when

entering and leaves at an angle of 120º. Draw the triangles of velocities at inlet and outlet and

find: (a) the angle of vanes tips so that water enters and leaves without shock, (b) the work

done per unit weight of water entering the vanes, and (c) the efficiency.

6. A jet of water having a velocity of 30 m/s strikes a series of radial curved vanes mounted on a

wheel which is rotating at 200 rpm. The jet makes an angle of 20º with the tangent to the

wheel at inlet and leaves the wheel with a velocity of 5 m/s at an angle of 130º to the tangent

of the wheel at outlet. Water is flowing from outward in a radial direction. The outer and inner

radii of the wheel are 0.5m and 0.25 m respectively. Determine: (i) vane angles at inlet and

outlet, (ii) work done per unit weight of water, and (iii) efficiency of the wheel.

7. A jet of water of diameter 25 mm strikes a 20 cm× 20 cm square plate of uniform thickness

with a velocity of 10 m/s at the centre of the plate which is suspended vertically by a hinge on

its top horizontal edge. The weight of the plate is 98.1 N. the jet strikes normal to the plate.

What force must be applied at the lower edge of the plate so that the plate is kept vertical? If

the plate is allowed to deflect freely, what will be the inclination of the plate with vertical due

to the force exerted by the jet of water?

8. Water is flowing through a pipe at the end of which a nozzle is fitted. The diameter of the

nozzle is 100 mm and the head of water at the centre of nozzle is 100 m. find the force exerted

by the jet of water on a fixed vertical plate. The co efficient of velocity is given as 0.95.

9. For the velocity profile for laminar boundary layer u/U = 3/2 (y/δ) – 1/2 (y/δ)2. Find the

boundary layer thickness, shear stress, force and coefficient of drag in terms of Reynolds

number.

10. Differentiate between

i. Stream line and bluff body.

ii. Friction drag and pressure drag.

11. A kite 60cm x 60cm weighing 2. 943 N assumes an angle of 100 to the horizontal. If the pull

on the string is 29. 43 N and it is inclined to the horizontal at 450. When the wind is flowing at

a speed of 40 km/hr, find the corresponding coefficient of drag and lift. Density of air is given

as 1. 25 kg/m3.

12. Explain about the boundary layer separation theory.

13. Explain about the lift and drag.

UNIT : IV

Syllabus:

Hydraulic Turbines: Classification of turbines, design of Pelton wheel, Francis turbine and

Kaplan turbine – working proportion, work done, efficiency, draft tube- theory, functions and

efficiency. Geometric similarity, Unit and specific quantities, characteristic curves, governing of

turbines, selection of type of turbine, cavitation, surge tank and water hammer, elements of

hydropower plant


Classify the types of turbines

describe the difference between impulse and reaction turbine

carry out a simple layout of Hydro Electronic plant

carry out design of Pelton Wheel, Francis and Kaplan Turbine

Explain about Geometric similarity, unit and specific speed of turbine

Explain about the characteristics of the turbine and Draft tube theory.

Describe the caivtation, surge tank and water hammer and elements of hydropower plant.

Lecture Plan

S. No. Description of Topic No. of Hrs. Method of Teaching

1. Classification of turbines, 51th

hour Video

2.

design of Pelton wheel, Francis turbine and

Kaplan turbine – working proportion, work

done, efficiency,

52nd

,53rd

& 54th

hours Black board + Video

3. Draft tube- theory, functions and efficiency. 55th

& 56st hours Black board+ Video

4. Geometric similarity, Unit and specific

quantities, characteristic curves

57th

& 58th

hours Black board+ Video

5. governing of turbines, selection of type of

turbine 54

th & 55

th hour Black board+ Video

6. cavitation, surge tank and water hammer 56th

& 57th

hours Black board+ Video

Elements of hydropower plant 58th

hour Black board+ Video

Tutorial 59

th , 60

th & 61

th

hours Black board

Assignment - 4

1. A pelton wheel is working under a gross head of 400 m. the water is supplied through

penstock of diameter 1m and length 4km from reservoir to the pelton wheel. The co efficient

of friction for the penstock is given as 0.008. The jet of water of diameter 150 mm strikes the

buckets of the wheel and gets deflected through an angle of 165º. The relative velocity of

water at outlet is reduced by 15% due to friction between inside surface of the bucket and

water. If the velocity of the buckets is 0.45 times the jet velocity inlet and mechanical

efficiency as 85% determine: (i) power given to the runner, (ii) shaft power, (iii) hydraulic

efficiency and overall efficiency.

2. An inward flow reaction turbine has external and internal diameters as 0.9 m and 0.45m

respectively. The turbine is running at 200 rpm and width of turbine at inlet is 200 mm. the

velocity of flow through the runner is constant and is equal to 1.8 m/s. the guide blades makes

an angle of 10˚ to the tangent of the wheel and the discharge at the outlet of the turbine is

radial. Draw the inlet and outlet velocity triangles and determine: (i) the available velocity of

water at inlet of runner, (ii) the velocity of whirl at inlet, (iii) the relative velocity at inlet, (iv)

the runner blade angles, (v) width of the runner at outlet (vi) mss of water flowing through the

runner per second, (vii) head at the inlet of the turbine, (viii) power developed and hydraulic

efficiency of the turbine.

3. A reaction turbine works at 450 rpm under a head of 120 meters. Its diameter at inlet is 120 cm

and the flow rate is 0.4 m2. The angles made by absolute and relative velocities at inlet are 20˚

and 60˚ respectively with the tangential velocity. Determine: (i) the volume flow rate (ii) the

power developed, and (iii) hydraulic efficiency. Assume whirl at outlet to be zero.

4. The external and internal diameters of inward flow reaction turbines are 1.2m and 0.6m

respectively. The head on the turbine is 22m and velocity of flow through the runner is

constant and equal to 2.5 m/s, the guide blade angle is given as 10˚ and the runner vanes are

radial at inlet. If the discharge at outlet is radial, determine: (i) the speed of the turbine, (ii) the

vane angle at outlet of the runner, (ii) hydraulic efficiency.

5. Show that the hydraulic efficiency foe a francis turbine having velocity of flow through runner

as constant, is given by the relation where α= guide blade angle and θ = runner

vane angle at inlet. The turbine is having radial discharge at outlet. (b) If vanes are radial at

inlet, then show .

6. A Kaplan turbine develops 24647.6 kW power at an average head 30 m. assuming a speed

ration of 2, flow ratio of 0.6, diameter of the hub equal to 0.35 times the diameter of the runner

and overall efficiency of 90%, calculate the diameter, speed and specific speed of the turbine.

7. A conical draft tube having inlet and outlet diameters 1m and 1.5 m discharges water at outlet

with a velocity of 2.5 m/s. the total length of the draft tube is 6 m and 1.2m of the length of the

draft tube id immersed in water. If the atmospheric pressure head is 10.3 m of water and loss

of head due to friction in the draft tube is equal to 0.2× velocity head at outlet of the tube, find:

(i) pressure head at inlet, and (ii) efficiency of the draft tube.

8. A tribune is to operate under head of 25 m at 200 rpm. The discharge is 9 m3/s. if the

efficiency is 90%, determine: (i) specific speed of the machine, (ii) power generated, and (iii)

type of turbine.

9. Explain about the characteristics curves with neat sketches.

10. Classify the turbines?

11. Explain about the effect of the cavitation in the turbines.

12. Explain about purpose of the surge tank in the power plant.

13. Explain about the elements of the power plants.

14. Write done the design procedure of the Pelton wheel turbine.

15. Write done the design procedure of the Frances turbine.

16. Write done the design procedure of the Kaplan turbine.

17. Explain about the governing mechanisms in the turbines.

UNIT: V

Syllabus:

Hydraulic Pumps: Classification, centrifugal pumps – types, working, work done, Mano-Metric

head, losses and efficiency, specific speed – pumps in series and parallel – performance

characteristic curves, NPSH, Reciprocating Pump – types, Working, Discharge, slip, indicator

diagrams.


Classify the types of pumps

Describe about the difference between Reciprocating and Centrifugal Pump

Explain about Geometric similarity, unit and specific speed of Pump

Explain about the characteristics of the Pump.

Explain about the working principle, slip and percentage slip

Describe about the indicator diagrams of the reciprocating pump,

Lecture Plan


1.

Classification, centrifugal pumps – types,

working, work done, manometric head,

losses and efficiency,

62nd

,63rd

, & 64th


2. specific speed – pumps in series and parallel

– performance characteristic curves, NPSH, 65

th & 66

th hours Black board + Video

3. Reciprocating Pump – types, Working,

Discharge, slip, indicator diagrams.

67st , 68

th & 69

nd


4. Tutorial 70

th , 71

th ,&

72nd


Assignment - 5

1. Classify the centrifugal pumps

2. Explain about the working principle of centrifugal pump

3. Explain about the working principle of reciprocating pump.

4. What is difference between the centrifugal pump and Reciprocating pump.

5. A centrifugal pump having outer diameter equal to two times the inner diameter and

running ar 1000 rpm works against a total head of 40 m. the velocity of flow through the

impeller is constant and equal to 2.5 m/s. the vanes are set back at an angle of 40º at outlet.

If the outlet diameter of the impeller is 500 mm and width at outlet is 50 mm, determine:

(i) vane angle at inlet, (ii) work done by impeller on water per second, and (iii)

Manometric efficiency.

6. A four stage centrifugal pump has four identical impellers keyed to the same shaft. The

shaft is running at 400 rpm and the manometric head developed by the multistage pump is

40 m. the discharge through the pump is 0.2 m3/s. the vanes of each impeller are having

outlet angle as 45º. If the width and diameter of each impeller at outlet is 5 cm and 60 cm

respectively, find the Manometric efficiency.

7. The diameter of a centrifugal pump, which is discharging 0.03 m3/s of water against a total

head of 20 m, is 0.4m. The pump is running at 1500 rpm. Find the head, discharge and

ratio of power of a geometrically similar pump of diameter 0.25 m when it is running at

3000 rpm.

8. A single acting reciprocating pump, running at 50 rpm, delivers 0.01 m3/s of water. The

diameter of the piston is 200 mm and stroke length 400 mm. determine: (i) the theoretical

discharge of the pump, (ii) Co – efficient of discharge, and (iii) slip and the percentage slip

of the pump.

9. A Double acting reciprocating pump, running at 40 rpm is discharging 1 m3 of water per

minute. The pump has a stroke of 400 mm. the diameter of the piston is 200 mm. the

delivery and suction heads are 20 m and 50 m respectively. Find the slip of the pump and

power required to drive the pump.

10. The length and diameter of a suction pipe of a single acting reciprocating pump are 5 m

and 10 cm respectively. The pump has a plunger of diameter 15 cm and a stroke length of

35 cm. the center of the pump is 3 m above the water surface in the pump. The atmospheric

pressure head is 10.3 m of water and pump is running at 35 rpm. Determine: (i) pressure

head due to acceleration at the beginning of the suction stroke, (ii) maximum pressure head

due to acceleration, and (iii) pressure head in the cylinder at the beginning and at the end of

the stroke.

EXTRA TOPICS

73rd

hour : Vortex Flow (Free vortex flow and Forced Vortex flow)

74th

&75th

hour: Laminar Flow and Turbulent Flow

TEXT BOOKS

1. Fluid Mechanics and hydraulics Mechanics by Modi and Seth, Standard Book House,

2011.

2. Introduction to Fluid Mechanics, R. W. Fox, A. T. McDonald and P. J. Pritchard.

REFERENCES

1. Fluid Mechanics by V.L. Streeter, E. Benjamin Wiley and W. Bedford, McGraw-Hill

Companies, 1997.

2. Fluid Mechanics, fundamentals and applications – Yunus A Cengel, Jhon M Cimbala.

3. Fluid Mechanics by Frank.M.White, Tata McGraw-Hill Pvt. Ltd., 2011.

4. Fundamental of Fluid Mechanics by Bruce Roy Munson, Donald F Young, Theodore H.

Okiishi, Wade W. Huebsch Wiley Publication.


(Autonomous)



Subject : Metallurgy and Material Science




Number of Hours / week : 04


Name of the Faculty Member: Mr.D.SARATH CHANDRA

Course Prerequisites: Physics ,Chemistry and Maths,

Course Objectives:

Understand the microstructures of different types of metal and alloys –cast iron, steels, non

ferrous metal and alloys.

Understand the heat treatment principles-annealing, normalizing and hardening.

Understand the different types of tools.

Able to understand the importance of Titanium & its alloys.

Course Outcomes:

After completion of the course the student is able to:

Distinguish different types of metals and alloys.

Design a heat treatment process to change the properties-hardness, ductility, etc.

Analyze the failure of metals and alloys.

Explain & justify the usage of Titanium & its alloys.

UNIT : I

Syllabus:

METAL STRUCTURE AND CRYSTALLIZATION

Introduction - atom binding, ionic bond, covalent bond, metallic bond, and Vander Waals forces;

Crystal imperfections.

OVERVIEW OF METAL STRUCTURE AND CRYSTALLIZATION. CONSTITUTION

OF ALLOYS

Introduction; Classification of alloys or compounds; Pure metal; Intermediate alloy phase or

compound - intermetallic compounds or valence compounds, interstitial compounds, and electron

compounds; Solid solutions; Substitution solid solution - factors that control the range of solubility

in alloy system; Interstitial solid solutions.


Know the bonds in the materials

Know the types of alloys and their phases

Know the type of imperfections in crystals and their identification

Know the types of solutions in the compounds

Lecture Plan


1. Introduction - Atom Binding, Ionic Bond,

Covalent Bond

1st & 2

nd hour Black board + PPT +

Video

2. Metallic Bond, and Vander Waals Forces

3rd


3. Crystal Imperfections. 4th


4. Introduction; Classification of Alloys or

Compounds

5th


5. Pure Metal; Intermediate Alloy Phase or

Compound

6th

&7th


6. Intermetallic Compounds or Valency

Compounds

8th


7. Interstitial Compounds, and Electron

Compounds

9th

& 10th


8. Solid Solutions; Substitution Solid Solution 11th


9. Factors That Control The Range Of

Solubility In Alloy System;

12th

hours Black board + PPT

10. Interstitial Solid Solutions. 13th

& 14th


Assignment – 1

1. What are the different types of atomic binding explain it. How does the metallic bond

differ from the ionic and covalent bonds?

2. What is a solid solution? What are the conditions for obtaining substitutional and

intersticial solid solutions?

3. what is an alloy? Explain the different type of intermediate alloy phases or compounds

what is the difference between interstitial solid solutions and interstitial

compounds?

4. Define the following terms :

(i). phase ( ii) liquidus line( iii) solidus line (iv) solvus line

(v) proeutectic (vi) hypoeutectic (vii) hypereutectic

.

UNIT : II

Syllabus:

PHASE DIAGRAMS Introduction; Coordinates of phase diagrams; Experimental methods - construction of equilibrium

diagrams by thermal analysis, metallographic methods, and X-ray diffraction;

Type-I-Two metals completely soluble in the liquid and solid states; Chemical composition of

phases; relative amounts of each phase; Equilibrium cooling of a solid solution alloy; Diffusion;

Nonequilibrium cooling; Homogenization; Properties of solid-solution alloys; Variation of Type I;

Type II-Two metals completely soluble in the liquid state and completely insoluble in the solid

state; Type III-Two metals completely soluble in the liquid state but only partly soluble in the

solid state; Properties of eutectic alloy systems; Age hardening – solution treatment, and aging

process; Type IV-The congruent-melting intermediate phase; Type V-The peritectic reaction;

Type VI-Two liquids partly soluble in the liquid state: the monotectic reaction; Type VII-two

metals insoluble in the liquid and solid states; Interrelation of basic types;

Transformations in the solid state - allotropy, order-disorder transformation, the eutectoid reaction,

the peritectoid reaction, and complex diagrams;

Study of important binary phase diagrams of Cu-Ni, Al-Si, Sb-Pb, Pt-Ag, Bi-Cd, Cu-Pb, Cu-Sn

and Fe- Fe3C.


Describe phase and gibbes phase rule to find the number of phases existing in the

metal or alloy

Explain the types of phases present in the phase diagram

Construct the phase diagrams based on the thermal analysis method and x-ray

diffractions methods

Construct a phase diagrams and able to identify the behavior of the metals or alloys

with respect to temperature and percentage of carbon.

Identify the type of reaction for the formation of alloy phases

Lecture Plan


1. Introduction; Coordinates of Phase

Diagrams

17th


2. Construction of Equilibrium Diagrams By

Thermal Analysis, Metallographic

Methods, And X-Ray Diffraction

18th

&19 th


3. Type-I-Two Metals Completely Soluble In

The Liquid And Solid States; Chemical

Composition of Phases; Relative Amounts

of Each Phase; Equilibrium Cooling of A

Solid Solution Alloy; Diffusion;

Nonequilibrium Cooling; Homogenization;

Properties of Solid-Solution Alloys;

Variation of Type I

20th

& 21th


4. Type II-Two Metals Completely Soluble In

The Liquid State And Completely

Insoluble In The Solid State

22th

& 23th


5. Type III-Two Metals Completely Soluble

In The Liquid State But Only Partly

Soluble In The Solid State; Properties Of

Eutectic Alloy Systems; Age Hardening –

Solution Treatment, And Aging Process

24th

& 25th


6. TypeIV-TheCongruent-Melting

Intermediate Phase; Type V-The Peritectic

Reaction

24rd


7. Type VI-Two Liquids Partly Soluble In

The Liquid State: The Monotectic

Reaction

25th


8. Type VII-Two Metals Insoluble In The

Liquid And Solid States; Interrelation Of

Basic Types;

26th

& 27th


9. Transformations In The Solid State -

Allotropy, Order-Disorder

Transformation, The Eutectoid Reaction,

The Peritectoid Reaction, And Complex

Diagrams

28th

& 29th


10. Study Of Important Binary Phase

Diagrams Of Cu-Ni, Al-Si, Sb-Pb, Pt-Ag,

Bi-Cd, Cu-Pb, Cu-Sn And Fe- Fe3C.

30th

& 31th


Assignment - 2

1. What is coring ?which alloys show cored structure and under what conditions?

2. Is coring desirable? If not, explain methods of eliminating coring.

3. What is non-equilibrium cooling ? Explain its effect on the properties and microstructure

of alloys.

4. Differentiate between the following:

a. Eutectic transformation and eutectoid transformation.

b. Peritectic transformation and peritectoid transformation.

c. substitutional solid solution and interstitial solid solutions.

5. “Eutectic composition usually does not show any coring whereas a solid solution may

show coring.” Why?

UNIT : III

Syllabus:

THE HEAT TREATMENT OF STEEL

Introduction; Full Annealing; Spheroidizing; Stress-relief annealing; Process annealing;

Normalizing; Hardening; The isothermal transformation diagram; Transformation to Pearlite and

Bainite; Cooling curves and I-T Diagram; Transformation on continuous cooling; Position of the

I-T curves; Hardening or austenitizing temperature; Homogeneity of austenite; Mechanism of heat

removal during quenching - vapor-blanket cooling state (stage A), vapor transport cooling stage

(stage B), Liquid cooling stage (stage C); Quenching medium; Temperature of quenching

medium; Surface condition - methods to minimize the formation of scale - copper plating,

protective atmosphere, liquid-salt pots, and cast-iron chips; Size and Mass; Hardenability; Use of

Hardenability data; Tempering; Austempering; Surface heat treatment or case hardening;

Carburizing; Heat treatment after carburizing; Cyaniding and Carbonitriding; Nitriding; Flame

hardening; Induction Hardening; Residual Stresses; Hardenable carbon steels; Effect of cryogenic

heat treatment – A brief study.


Understand what is heat treatment and its importance to change the properties of the

material

Conduct the heat treatment for different metals and alloys by adapting different heat

treatment methods

Study the different cooling curves with respect to time, temperature and transformations

Practice the heat removal mechanism at different stages

Understand different hardening process and area of importance

Lecture Plan


1. Introduction; Full Annealing;

Spheroidizing; Stress-relief annealing;

Process annealing;

32st & 33

nd hour Black board + PPT

2. Normalizing; Hardening; The isothermal

transformation diagram; Transformation

to Pearlite and Bainite

34rd

& 35th


3. Cooling curves and I-T Diagram;

Transformation on continuous cooling;

Position of the I-T curves

36th

& 37th


4. Hardening or austenitizing temperature;

Homogeneity of austenite;

38th

& 39th


5. Mechanism of heat removal during

quenching - vapor-blanket cooling state

(stage A), vapor transport cooling stage

(stage B), Liquid cooling stage (stage C

40th

& 41th


6. Quenching medium; Temperature of

quenching medium; Surface condition -

methods to minimize the formation of scale

- copper plating, protective atmosphere,

liquid-salt pots, and cast-iron chips.

42st & 43

nd hour Black board + PPT

7. Size and Mass; Hardenability; Use of

Hardenability data; Tempering;

Austempering; Surface heat treatment or

case hardening; Carburizing; Heat

treatment after carburizing.

44rd

& 45th


8. Cyaniding and Carbonitriding; Nitriding;

Flame hardening; Induction Hardening;

Residual Stresses; Hardenable carbon

steels; Effect of cryogenic heat treatment –

A brief study.

46th

& 47th


Assignment – 3

1. Distinguish between the following pair of terms:

a. Annealing and Normalising

b. Induction hardening and flame hardening

c. Hardness and hardenability

d. Cyaniding and nitriding

2. What factors influence the critical cooling rate? Explain.

3. What are the limitations on the use of iron-iron carbide diagram?

4. Explain why the surface hardness of quenched high-carbon steel may be less than the

hardness under the surface.

5. Describe how an I-T diagram is determined experimentally.

6. Explain how alloying elements that dissolve in ferrite increase its strength.

7. Describe the three ways in which precipitation- hardenable steel may be hardened.

UNIT : IV

Syllabus:

ALLOY STEELS

Introduction; Purpose of alloying; Effect of alloying elements upon Ferrite; Effect of alloying

elements upon carbide; Influence of alloying elements on the iron-iron carbide diagram; Effect of

alloying elements in tampering; Classification of steels - nickel steel, chromium steel, nickel-

chromium steels, manganese steels, molybdenum steels, tungsten steels, vanadium steels, silicon

steels, stainless steels, martensitic stainless steels, ferritic stainless steels, austenitic stainless

steels, precipitation-hardening stainless steels, maraging steels, and ausforming.

TOOL STEELS

Classification of tool steels; Selection of tool steels; Comparative properties; Non-deforming

properties; Depth of hardening; Toughness; Wear resistance; Red-hardness; Machinability;

Resistance to decarburization; Brand names; 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); Special purpose tool steels; Heat treatment of tool steels;

Overview of tool failures;

Special cutting materials – satellites, cemented carbides, and ceramic tools


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


1. Introduction; Purpose of alloying; Effect

of alloying elements upon Ferrite; Effect

of alloying elements upon carbide

48th


2. Influence of alloying elements on the

iron-iron carbide diagram; Effect of

alloying elements in tampering

49th


3. Classification of steels - nickel steel,

chromium steel, nickel-chromium steels,

manganese steels, molybdenum steels,

tungsten steels, vanadium steels

50th


4. silicon steels, stainless steels, martensitic

stainless steels, ferritic stainless steels,

austenitic stainless steels, precipitation-

hardening stainless steels, maraging

steels, and ausforming.

51nd

& 52rd


5. Classification of tool steels; Selection of 53th


tool steels; Comparative properties; Non-

deforming properties; Depth of

hardening

6. Toughness; Wear resistance; Red-

hardness; Machinability; Resistance to

decarburization; Brand names

54th

& 55th


7 Introduction; Purpose of alloying; Effect

of alloying elements upon Ferrite; Effect

of alloying elements upon carbide

54th


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


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


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.


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


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


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.


(Autonomous)



Subject : Mechanics of Solids




Number of Hours / week : 4 + 1


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


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


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

maximum shear stresses, Mohr’s circle for plane

stress

06 PPT + Black

Board

2 Hooke’s law for plane stress, Spherical and

cylindrical pressure vessels (biaxial stress, Hoop

and longitudinal stresses);

04 PPT + Black

Board

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


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.

ACADEMIC PLAN Subject : Thermodynamics Code : · PDF file1 3 Course Objectives: ......

Documents

Transcript of ACADEMIC PLAN Subject : Thermodynamics Code : · PDF file1 3 Course Objectives: ......