06 mat31 – engineering mathematics iii - mvjce mat31 – engineering mathematics iii . ... solve...

DEPT.OF MECHANICAL ENGINEERING MVJCE

III SEMESTER COURSE DIARY

29

06 MAT31 – ENGINEERING MATHEMATICS III



30

SYLLABUS

SUB CODE : 06MAT31 EXAM MARKS : 100 IA MARKS : 25 TOTAL HOURS : 52

HOURS / WEEK : 04 EXAM HOURS : 03

PART A

UNIT – I

FOURIER SERIES

Periodic functions,conditions for Fourier series expansions , Fourier series expansion of continuous

functions and functions having infinite number of discontinuities, even and odd functions.Half

range series ,Practical harmonic analysis. 07 hrs.

UNIT – II

FOURIER TRANSFORMS

Finite and Infinite fourier transforms, fourier sine and cosine transforms, properties, Inverse

transforms. 06 hrs.

UNIT – III

PARTIAL DIFFERENTIAL EQUATIONS Formation of PDE- by elimination of arbitrary constants and arbitrary functions, solution of non

homogeneous P.D.E by direct integration, Solution of homogeneous PDE involving derivative with respective to one independent variable only.(Both types with given set of conditions) Method

of separation of variables. (First and second order equations) Solution of Lagrange’s linear P.D.E of the type Pp +Qq = R. 06 hrs.

UNIT – IV

APPLICATIONS OF P.D.E

Derivation of one dimensional wave and heat equations. Various possible solutions of these by the

method of separation of variables. D’ Alembert’s solution of wave equation. Two dimensional

Laplace’s equation – various possible solutions. Solution of all these equations with specified

boundary conditions. (Boundary value problems). 07 hrs.

PART – B

UNIT – V

NUMERICAL METHODS

Roots of transcendental equation using Newton-Rapson and Regula Falsi method.Solutions of

linear simultaneous equations - Gauss elimination , Gauss jordon methods, Gauss-Seidel iterative

methods. Definition of Eigen values and Eigen vectors of a square matrix. Computation of largest

Eigen value and the corresponding Eigen vector by Rayleigh’s power method. 06 hrs.

Unit – VI Finite differences (Forward and Backward differences) Interpolation, Newton’s forward and backward

interpolation formulae. Divided differences – Newton’s divided difference formula. Lagrange’s interpolation and inverse interpolation formulae. Numerical Integration – Simpson’s one third and

three eighth’s rule, Weddle’s rule. (All formulae/ rules without proof). 07 hrs



31

Unit – VII

CALCULUS OF VARIATIONS:

Variation of a function and a functional , Extremal of a functional , Variational problems , Euler’s equations, standard variational problems including Geodesics,minimal surface of

revolution , Hanging chain and Brachitochrone problems. 06 hrs

Unit – VIII

DIFFERENCE EQUATIONS AND Z-TRANSFORMS

Difference equations – Basic definitions, Z-transforms – Definition, Standard Z-transforms,

Linearity property, Damping rule, Shifting rule. Initial value theorem, Final value theorem,

Inverse Z-transforms. Application of Z-transforms to solve difference equations. 06 hrs.

TEXT BOOKS:

Higher Engg. Mathematics (36th

edition-2002) by Dr. B.S.Grewel, Kanna publishers, New Delhi.

REFERENCE BOOKS:

1. Higher Engineering Mathematics by B.V. Ramana (Tata-Macgraw Hill).

2. Advanced Modern Engineering Mathematics by Glyn James – Pearson Education.



32

LESSON PLAN

SUB CODE : 06MAT31 HOURS / WEEK : 04

SUB : ENGINEERING MATHEMATICS III TOTAL HOURS : 52

No. of

Hrs. TOPIC TO BE COVERED

1. FOURIER SERIES

2. Even and odd functions, properties, sectional continuity, periodic functions

3. Dirichlets conditions, fourier series –examples.

4. Half range series –examples

5. Complex form of Fourier series

6. Problems

7. Practical Harmonic Analysis – Examples

8. Problems

9. FOURIER TRANSFORMS

10. Finite Fourier transforms –Examples

11. Infinite Fourier transforms – properties and Examples

12. Fourier Sine and Cosine transforms –Examples

13. Invers Fourier Sine and Cosine transforms –Examples

14. Convolution Theorem (without proof) – Examples

15. Parseval’s Identities (without proof)-Examples

16. Problems

17. PARTIAL DIFFERENTIAL EQUATIONS:

18. Formation of PDE -Examples

19. Solutions of non homogeneous PDE by direct integration-examples

20. Solutions of homogeneous PDE involving the derivatives

21. Method of separation of variables-examples

22. Examples

23. Solution of Lagrange’s linear PDE of the type Pp+Qq=R -Examples

24. APPICATIONS OF PDE

25. Derivations of One-dimensional heat and wave equation -Examples

26. Various possible solutions by method of separation of variables

27. D’Alemberts solution of wave equation

28. Two dimensional Lap lace’s equation-examples

29. Various possible solutions

30. Solutions boundary value problems

31. NUMERICAL METHODS

32. Numerical solutions of algebraic and transcendental equations: Newton-

Raphson method - examples

33. Regula-Falsi method -examples

34. Solutions of linear simultaneous equations: Gauss elimination method

35. Gauss Jordon method - examples

36. Gauss- Seidal iterative method

37. Definition of Eigen values and eigen vectors of square matrix –problems

38. . Largest eigen value and eiggen vector Rayleigh’ power method

39. Finite differences interpolation : Forward and



33

40. Backward Interpolation- examples

41. Divided Differences- Newton’s divided difference formula

42. Lagrange’s Interpolation and Inverse Interpolation

43. Numerical Differentiation using Forward and Backward formulae Examples

44. Numerical Integration-Simpson’s one third and three eighth rule-examples

45. Numerical Integration-Weddle’s rule

46. Problems

47. CALCULUS OF VARIATION

48. Variation of function and functional ,Extremal of functioal

49. Variational problems

50. Euler’s eqation - Problems

51. Standard variational problems including Geodesics

52. Minimal surface of revolution problems

53. Hanging chain and Brachitochrone problem

54. Problems

55. DIFFERENCE EQUATIONS AND Z TRANSFORMS

56. Difference equations-Basic definitions

57. Z-transforms-Definition, standard Z-transforms

58. Linearity property, Damping rule

59. Shifting rule, Initial value and Final value theorem

60. Inverse Z-transforms

61. Application of Z- Transforms to solve differential equations.

62. Problems



34

QUESTION BANK

PART-A

UNIT – I

FOURIER SERIES

Obtain the Fourier expansion of the following functions over the indicated interval.

a) f(x) = 0, -π<x<0

x2, 0<x<π

b) f(x) = xCosx over (-π π)

c) f(x) = sinax, a is not an integer over (-π π)

d) f(x) = 0, -π<x<0

x, 0<x<π and hence deduce π2/8 = Σ1/(2n-1)

2

e) f(x) = 0, -π<x<0

Sinx, 0<x<π and hence

deduce (π-2)/4 =1/(1.3)-1/(3.5)+1/(5.7)--------------

f) f(x) = 1+Sinx over (-1 1)

g) f(x) = 1+2x, -3<x<0 1-2x, 0<x<3 over (-3 3)

h) f(x) = x-x2 over (-l l )

i) f(x) = x Cosx over ( 0 2π )

j) f(x) = √(1-Cosx) over ( 0 2π ) and hence prove that Σ 1/(4n2-1) =

1/2

k) f(x) = 2x-x2 over (0 3)

l) f(x) = Sin(x/2), 0<x<π

--Sin(x/2), π<x<2π

1. Obtain the half-range cosine series for the following functions over the given intervals

i) f(x) = x Sinx over (0 π)

ii) f(x) = Cosx , 0<x<π/2

0, π/2<x<π

iii) f(x) = x2 over (0 π)

iv) f(x) = Sin(mπ/l ) x, where m is positive integer, over (0 l )

v) f(x) = ex over ( 0 1 )

vi) f(x) = x-x2 in (0 π)



35

2. Obtain the half-range sine series for the following functions over the given intervals

i) f(x) = x, 0<x<π/2

π -x , π/2<x<π

ii) f(x) = x (π2 – x2) over (0 π )

iii) f(x) = ex over ( 0 1 )

iv) f(x) = Sin(mπ/l ) x, where m is positive integer, over (0 l )

v) f(x) = ( lx – x2) over (0 l )

3. Find the first and second harmonics for the function f(θ) defined by the following table

θ 0 π/3 2π/3 π 4π/3 5π/3 2π

f(θ) 1.0 1.4 1.9 1.7 1.5 1.2 1.0

4. Find the Fourier series to represent y up to the second harmonic from the following data.

X 30 60 90 120 150 180 210 240 270 300 330 360

Y 2.34 3.01 3.68 4.15 3.69 2.20 0.83 0.51 0.88 1.09 1.19 1.64

5. Find the constant term and first three coefficients in the Fourier cosine series for the function

f(x) described by the following Table.

x 0 1 2 3 4 5

f(x) 4 8 15 7 6 2

6. Obtain the Complex(exponential) Fourier series for the following functions over the given

intervals

i) f(x) = Cosax over ( -π π)

ii) f(x) = eax over ( -l l )

iii) f(x) = k for 0<x<l

-k for l<x<2l

iv) f(x) = ax + bx2 over ( -π π)

UNIT-II

FOURIER TRANSFORMS

>

<=

ax

axx

,0

, f(x) of TransformFourier theFind 8.

>

<=

ax

ax

,0

,1 f(x) of TransformFourier theFind 9.



36

>

<=

ax

ax

,0

,1 f(x) of TransformFourier theFind 10.

and hence evaluate

∫

∫∞

∞

∞−

0

sin)

cossin)

s

sii

dss

sxsai

11. Find the Fourier sine and cosine Transform of x e

-ax

12. State and prove the Modulation Theorem for the Fourier transforms.

13. Find the Fourier cosine transform of e-x2

14. Find the Fourier sine transform of x / (1+x2)

15. Find the Fourier cosine transform of 1/(1+x2)

16. Find f(x) if its Fourier cosine transform is 1 / (1+s2)

17. Find the Fourier transform of e-|x|

13. Find the Sine transform of e-ax

/x

>

<−=

10

11 f(x) of ansformFourier tr theFind 14.

2

x

xx

dxx

and

∫∞

2cos

x

sinx-xcosx evaluate hence

0

2

15. s

-ase

is transformsineFourier its if f(x) Find

UNIT-III

PARTIAL DIFFERENTIAL EQUATIONS

1. form the P.D.E. by eliminating the arbitrary constants for the following:

a)z=ax+by+ab

b) z=(x-a)2+(y-b)2

2. Form the P.D.E. by eliminating the arbitrary functuions for the following:

a)xyz=f(x+y+z)

b)z=f(x)+eyg(x)

3. Solve:

a) ptanx+qtany = tanz

b) yzp+zxq=xy

c) x2(y-z)p+y

2(z-x)q=z

2(x-y)



37

4. Solve the following non-linear equations:

a) p3-q

3=0

b) p=logq

c) xp+yq=1 by using x=eu , y=ev

d) p2=qz

e) z(p2-q

2)=1

f) p2-q

2=x-y

g) p/x+q/y=x+y

5. Obtain the complete solution and singular solution of the equation z=px+qy+p2+q

2.

6. Solve z=pxlogx+qylogy-pqxy by using x=eu,y=e

v find also the singular solution.

7. Solve the following P.D.E. by the method of separation of variables:

04)

0)

2

2

=∂

∂+

∂

∂−

∂

∂

=∂

∂+

∂

∂

y

u

x

u

x

ub

y

uy

x

uxa

8. Solve the following non-homogeneous P.D.E. by the method of direct integration:

yxx

ua +=

∂

∂2

2

)

0)32sin()2

3

=−++∂∂

∂yxxy

yx

zb

CHAPTER-I

NUMERICAL ALGORITHAMS

1. Using the bisection method find the approximate root of the following equations. i) x3-5x+1=0

ii) x3-4x-9=0 in (2.5 3)

iii) xlog10 X=1.2 in (2 3)

iv) ex-x-2=0

v) x+logx=5

vi) cosx-1.3x=0 in (0 1)

2. Using the Regula-Falsi method find the approximate root of the following equations (correct to three decimal places)

i) xex=3 in (1 1.5)

ii) x2-logx=7

iii) x3-sinx+1=0 in (-2 -1)

iv) x3-2x-5=0

v) Cosx=3x-1 in (0.5 1.0)



38

3. By using Regula – Falsi method find the approximate value of √3.

4. Using the Newton Raphson method find the approximate root of the following equations

(correct to three decimal places)

i) x3-8x-4 = 0

ii) cosx = xex near 0.5

iii) logx-x+3 = 0 near 0.1

iv) x3-x-1 = 0

v) xtanx = 0.5 near 0.6

vi) x2+x = cosx near 0.5

5. Evaluate the following by using Newton- Raphson method

i) √5 ii) √41 iii) (12)1/3 iv) 1/√15

6. Solve the following using Gauss Elimination method

i) x+2y-z = 3, 3x-y+2z = 1, 2x-2y+3z = 2

ii) 5x+3y+7z = 5, 3x+10y+2z = 9, 7x+2y+10z = 5

iii) 10x+2y+z = 9, 2x+20y-2z = -44, -2x+3y+10z = 22

iv) 4x-2y+6z = 8, x+y-3z = -1, 15x-3y+9z = 21

7. Solve the following systems of equations by using the Gauss-Jordan method

i) 10x+y+z = 12, x+10y+z = 12, x+y+10z = 12 ii) x+y+z = 9, 2x-3y+4z = 13, 3x+4y+5z = 40

iii) x-2y+3z = 2, 3x-y+4z = 4, 2x+y-2z = 5 iv) 2x1+x2+5x3+x4 = 5, x1+x2-3x3-4x4 = -1, 3x1+6x2-2x3+x4 = 8, 2x1+2x2+2x3-

3x4 = 2 8. Employ the Crout’s method (LU- decomposition method) to solve the following equations

i) x+y+z = 3, x+2y+3z = 6, x+y+4z = 6

ii) 10x+y+2z = 13, 3x+10y+z = 14, 2x+3y+10z = 15

iii) x+y+z = 3, 2x-y+3z = 16, 3x+y-z = -3

iv) 2x+3y+z = 9, x+2y+3z = 6, 3x+y+2z = 8

9. Using the Gauss- Seidal method solve the following equations.

i) 10x+y+z = 12, x+10y+z = 12, x+y+10z = 12

ii) 20x+y-2z = 17, 3x+20y-z = -18, 2x-3y+20z = 25

iii) 5x+2y+z = 12, x+4y+2z = 15, x+2y+5z = 20

iv) 83x+11y-4z = 95,7x+52y+13z = 104, 3x+8y+29z = 71

10. Given that y/ = 1-2xy, y(0)= 0, find an approximate value y at x = 0.6 by Euler’s method

with step length h = 0.2.

11. Given that y/ = -2xy

2, y(0)= 1, find an approximate value y(0.4) by Euler’s method with step

length h = 0.05.

12. Given that y/ = 1+(y/x), y(1)= 2, find an approximate value y at x = 1.4 by Euler’s method

with step length h = 0.2.



39

13. Using modified Euler’s method, solve the initial-value problem y/ = x-y

2, y(0) = 1 at x =

0.2. Take step length h = 0.1

14. Using modified Euler’s method, solve the initial-value problem y/ = x + y

2, y(0) = 1 at x =

0.2. Take step length h = 0.1

15. Using the fourth order Runge-Kutta method, find the solution of the problem y/ =2x-y, y(1)

= 3 at the point 1.1

16. Using the fourth order Runge-Kutta method, find the solution of the problem y/ =3e

x+2y,

y(0) = 0 at the point x=0.1

17. By employing Runge-Kutta method of order four, solve the differential equation y/ = 1+y2,

y(0) = 0 to find y(0.2) and y(0.4).

18. Solve the initial value problem y/ = xy1/3, y(1) = 1 at x = 1.1 by using the Runge-Kutta method.

19. Define the Z-transform and Prove the following

i) ZT(kn)=z/(z-k)

ii) ZT(nk)= -z d/dz ZT (n

k-1)

iii) ZT(un+1)=z(u(z)-u0)

20. Obtain the z-transform of coshnθ and cosnθ

21. Solve the system

yxzz

uzx

y

uzxy

x

u−=

∂

∂−=

∂

∂+=

∂

∂ 223 3,3,6

22. Solve the wave equation

)()0,(,00),(,0),0(0

2

22

2

2

xfxut

utlutu

nditionundertheco

x

uc

t

u

t

==

∂

∂==

∂

∂=

∂

∂

= where f(x) are given below:

a) λx(l-x)

b) 2sin(3πx/2l)cos(3πx/2l)

23 Solve the wave equation utt=4uxx given that the string of length π is initially at rest and the initial deflection f(x) are below:

a) 2sin(x/2)cos(x/2)cos(x/2) + 2sin(3x/2)cos(3x/2) b) 4sin3x

c) x(π-x) in 0≤x≤π

24. A tightly stretched string of length πfastened at both endsis set into vibration by pulling the

mid point to distance h and releasing it from rest. Find the expression for the displacement at any

subsequent time t.



40

25. A string of length 2l is initially at rest the motion of the string is started by displacing the string

into form x(2l-x) then released from rest. Find the displacement at any time.

26.A string of length 1 is fixed tightly between two points x=0 and x=1. The points x=1/3and

x=2/3 are pulled to one side through a small distance k and let go. Find the motion.

LINEAR ALGEBRA

1. Find the ranks of the following matrices by elementary row transformations.

4115

3103

1012

6128

)a

2. Find the ranks of the following matrices by reducing it to the normal form.

10587

6464

2341

4123

)a

3. Test for consistency and solve the following system of equations. a) x + y + z = 9

2x + 5y + 7z = 52 2x + y – z = 0

b) 4x – 2y + 6z = 8

x + y – 3z = - 1 15x - 3y + 9z = 21

c) 2x + 6y + 11 = 0

6x + 20y –6z + 3 = 0

6y – 18z + 1 = 0

4. Find the values of λ and µ such that the following system of equations,

2x + 3y + 5z = 9, 7x + 3y – 2z = 8, 2x + 3y + λz = µ

d) Unique solution b) Many solution c) No solution.

5. Find all eigen values and the corresponding eigen vectors for the following

matrices.

−−

−

425

313

132

)a

11-3

010

001

)b



41

6. For the following matrices verify Cayley Hamilton theorem and also compute the inverse.

22-5

5-615-

11-3

)a

121

1-43

432

)b

7. Use Rayleigh’s power method to determine the largest eigen value and the corresponding

eigen vector of the following matrices.

200

021

161

)a

1012

1102

1210

)b

8. Solve the following using Gauss Elimination method

e) x+2y-z = 3, 3x-y+2z = 1, 2x-2y+3z = 2 f) 5x+3y+7z = 5, 3x+10y+2z = 9, 7x+2y+10z = 5

g) 10x+2y+z = 9, 2x+20y-2z = -44, -2x+3y+10z = 22

h) 4x-2y+6z = 8, x+y-3z = -1, 15x-3y+9z = 21

9. Solve the following systems of equations by using the Gauss-Jordan method i) 10x+y+z = 12, x+10y+z = 12, x+y+10z = 12

j) x+y+z = 9, 2x-3y+4z = 13, 3x+4y+5z = 40 k) x-2y+3z = 2, 3x-y+4z = 4, 2x+y-2z = 5

l) 2x1+x2+5x3+x4 = 5, x1+x2-3x3-4x4 = -1, 3x1+6x2-2x3+x4 = 8, 2x1+2x2+2x3-3x4 = 2

10. Employ the Crout’s method (LU- decomposition method) to solve the following equations m) x+y+z = 3, x+2y+3z = 6, x+y+4z = 6

n) 10x+y+2z = 13, 3x+10y+z = 14, 2x+3y+10z = 15 o) x+y+z = 3, 2x-y+3z = 16, 3x+y-z = -3

p) 2x+3y+z = 9, x+2y+3z = 6, 3x+y+2z = 8

11. Using the Gauss- Seidal method solve the following equations.

q) 10x+y+z = 12, x+10y+z = 12, x+y+10z = 12

r) 20x+y-2z = 17, 3x+20y-z = -18, 2x-3y+20z = 25

s) 5x+2y+z = 12, x+4y+2z = 15, x+2y+5z = 20

t) 83x+11y-4z = 95,7x+52y+13z = 104, 3x+8y+29z = 71

Calculus of variation;

1. Define the following:

a) Variation of a function

b) Extremal of a function.



42

c) Variational problem

2. Derive the Euler’s equation.

3. Find the extremal of functional

2)1(,0)0(

,0,])'(}1)'{(3[ 3

1

0

22

==

≠+−= ∫

yy

nsheconditiosubjecttot

ydxyyyxyI

4. Find the extremals of the following functions:

dxy

yc

dxyyyyb

dxyyxa

x

x

x

x

x

x

∫

∫

∫

+

−+

++

2

1

2

1

2

1

2

2

22

2

)'(

1)

}16'2)'{()

)'()

5. Show that the general solution of the Euler’s equation for the functional

.222' )(11 2

1

0

ByAAxdxisyy

x

x

=+−+∫

6. Show that an extremal of

dxyyf

x

x

∫ +1

2

2)'(1)(

Where y has fixed values at x=x1 , x2is equal

BxyfA

dy−=

−∫

1)({ 2

where A and B are constants.

7. Show that an extremal of

dxy

yx

x∫2

12

2)'(

can be expressed in the form y=AeBx

8. Find the extremal of the functional

dxyxI )( 2

1

0

2

∫ +=

under the conditions y(0)=0, y(1)=0 and subject to the constraint

.2

1

0

2 =∫ dxy



43

9. Find the extremal value of

dxy

x

x

∫2

1

2)'(

under the conditions y(x1)=y1,y(x2)=y2 and subject to the constraints

,2

1

2 adxy

x

x

=∫ a constant.

10. Find the plane curve of length l joining the points(x1,y1)and (x2,y2) which,when rotated

about the x axis,will give minimum area.

11. Of all closed plane curves enclosing a given area A,show that the circle is the one which has

minimum length.

12. Find the extremal of

{

.1)2/(',0)0(',0)2/(,1)0(

.})''() 22

2/

0

2

−====

+−= ∫

ππ

π

yyyy

dxxyyIa



44



45



46

06 ME 32 A -MATERIAL SCIENCE & METALLURGY



47

SYLLABUS

SUB CODE : 06 ME 32 A HRS/WEEK : 04

EXAM HOURS : 03 IA MARKS : 25

TOTAL HRS : 52 EXAM MARKS : 100

PART – A

UNIT 1: Structure of crystalline solids: Fundamental concepts of unit cell space lattice, Bravaias space

lattices, unit cells for cubic structure & HCP, study of stacking of layers of atoms in cubic structure

& HCP, calculations of radius, Coordination Number and Atomic Packing Factor for different cubic

structures. Crystal imperfections-point, line, surface & volume defects. Diffusion, Diffusion

Mechanism, Fick’s laws of diffusion. 07 hrs

UNIT 2:

Concepts of stress & strain, tensile properties, true stress & strain, Hardness, Rockwell, Vickess &

Brinell Hardness testing. Plastic deformation, slip & twinning. 06 hrs

UNIT 3:

Fracture: types, stages in cup & cone fracture, Griffith’s criterion. Fatigue: fatigue tests, S-N curves,

Factors affecting fatigue life and protection methods. Creep: The creep curves, Mechanisms of

creep. Creep-resistant materials. 07 hrs

UNIT 4:

Solid solutions, Types, Rules of governing the formation of solids solutions. Phase diagrams: Basic

terms, phase rule, cooling curves, construction of phase diagrams, interpretation of equilibriums

diagrams, Types of phase diagrams. Lever rule. 06 hrs

PART – B

UNIT 5:

Iron carbon equilibrium Diagram, phases in the Fe–C system, Invariant reactions, critical

temperatures, Microstructure of slowly cooled steels, effect of alloying elements on the Fe-C

diagram, ferrite & Austenite stabilizers. The TTT diagram, drawing of TTT diagram, TTT diagram

for hypo-& hypereutectoid steels, effect of alloying elements, CCT diagram. 07 hrs

UNIT 6:

Annealing, and its types, normalizing, hardening, tempering, martemering, austempering, surface

hardening like case hardening, carburizing, cyaniding, nitriding Induction hardening, hardenabilty,

Jominy end-quench test, Age hardening of Al & Cu alloys. 06 hrs

UNIT 7: Engineering Alloys: Properties, composition and uses of low carbon, mild medium & high carbon

steels. Steel designation & AISI –SAE designation. Cast irons, gray CI, white CI, malleable CI, SC

iron. Microstructures of cast iron. The light alloys, Al & Mg & Titaniu m alloys. Copper & its

alloys: brasses & bronzes. 07 hrs



48

UNIT 8: Corrosion & Its Prevention: Galvanic Cell, The Electrode Potentials, Polarization, Passivation,

General methods of Corrosion Prevention, Cathodic Protection, Coatings, Corrosion Prevention by

Alloying, Stress Corrosion Cracking. 06 hrs

TEXT BOOKS:

1. “Materials Science & Engineering- An Introduction”, William D.Callister Jr. Wiley India

Pvt. Ltd. 6th Edition, 2006, New Delhi.

2. “Essentials of Materials For Science And Engineering”, Donald R. Askeland, Pradeep

P.Phule Thomson-Engineering, 2006.

REFERENCE BOOKS:

1. “Introduction to Material Science for Engineering”, 6th edition James F. Shackel ford.

Pearson, Prentice Hall, New Jersy, 2006.

2. “Physical Metallurgy, Principles & Practices”, V Raghavan.PHI 2nd

Edition 2006, New

Delhi.

3. “Foundation of Material Science and Engineering”, Smith, 3rd Edition McGraw Hill,

1997.

SCHEME OF EXAMINATION:

One Question to be set from each chapter. Students have to answer any FIVE full questions out of

EIGHT questions, choosing at least 2 questions from part A and 2 questions from part B.



49

LESSON PLAN

SUB CODE : 06 ME 32 A HRS/WEEK : 04

SUB : MATERIAL SCIENCE & METALLURGY TOTAL HRS : 52

NO.

OF HRS TOPICS TO BE COVERED

1. Structure of crystalline solids: Fundamental concepts of unit cell space lattice,

2. Bravaias space lattices, unit cells for cubic structure & HCP

3. study of stacking of layers of atoms in cubic structure & HCP

4. calculations of radius,Coordination Number for different cubicstructures

5. calculations Atomic Packing Factor for different cubicstructures

6. Crystal imperfections-point, line, surface & volume defects

7. Diffusion, Diffusion Mechanism

8. Fick’s laws of diffusion

9. Concepts of stress & strain,

10. Tensile properties,

11. True stress & strain

12. Rockwell Hardness, Testing

13. Vickess & Brinell Hardness testing

14. Plastic deformation

15. slip &twinning.

16. Fracture: types, stages in cup,

17. Fracture: cone fracture

18. Griffith’s criterion

19. Fatigue: fatigue tests,

20. Fatigue: S-N curves

21. Factors affecting fatigue life and protection methods

22. Creep: The creep curves, Mechanisms of creep

23. Creep-resistant materials.

24. Solid solutions, Types

25. Rules of governing the formation of solids solutions

26. Phase diagrams: Basic terms, phase rule,

27. cooling curves

28. construction of phase diagrams,

29. interpretation of equilibriums diagrams

30. Types of phase diagrams. Lever rule.

31. Iron carbon equilibrium Diagram,.

32. phases in the Fe–C system,

33. Invariant reactions, critical temperatures

34. Microstructure of slowly cooled steels,

35. effectof alloying elements on the Fe-C diagram

36. ferrite & Austenite stabilizers.



50

37. TheTTT diagram, drawing of TTT diagram

38. TTT diagram for hypo-& hypereutectoid steels

39. effect of alloying elements, CCT diagram

40. Annealing, and its types,

41. normalizing, hardening, tempering, martemering, austempering

42. surface hardening like case hardening, carburizing,

43. cyaniding, nitriding

44. Induction hardening,

45. hardenabilty, Jominy end-quench test

46. Age hardening of Al & Cu alloys

47. Engineering Alloys: Properties,

48. composition and uses of low carbon, mild steels.

49. Composition and uses of medium & high carbon steels

50. Steel designation & AISI –SAE designation

51. Cast irons, gray CI, white CI,

52. malleable CI, SC iron

53. Microstructures of cast-iron.

54. The light alloys, Al & Mg & Titaniu m alloys

55. Copper & its alloys: brasses & bronzes.

56. Corrosion & Its Prevention: Galvanic Cell, ,

57. The Electrode Potentials

58. Polarization, Passivation,

59. General methods of Corrosion Prevention,

60. Cathodic Protection, Coatings

61. Corrosion Prevention by Alloying,

62. Stress Corrosion Cracking



51

QUESTION BANK UNIT-1

1. Define the term Unit cell, Lattice Parameter, Co ordination, Atomic packing factor with

respect to crystal structure

2. With neat sketch explain Edge dislocation & screw Dislocation & compare them

3. From fundamentals, calculate the atomic packing factor for a BCC crystal

4. Explain Plastic deformation of metals & the mechanisms that contributes to it

5. Calculate basic atoms (Average atoms per unit cell relationship between lattice constant

(a), Atomic radius(r), & atomic packing Factor for BCC & FCC crystal structure

6. Draw a Unit Cell HCP & Find the effective No. Of atoms in the unit cell & its atomic

packing factor

7. Define Diffusion. Name the factors, which control the coefficient of diffusion.

UNIT-2

8. With neat sketches, Explain the difference between slip & Twinning

9. Sketch the Stress-Strain diagram for perfect Ductile & Brittle Materials

10. Explain the mechanism of ductile – brittle transition.

11. Write briefly about Dislocation & their role in Plastic deformation

12. Distinguish between Brinell & Rockwell hardness test

13. Distinguish between Charpy & Izod’s Impact testing

UNIT-3

14. Define Fatigue. Name the factors, which control the fatigue.

15. Explain fatigue testing.

16. Define fracture and explain all types of fracture.

17. Define creep and explain three stags in creep with fatigue testing

18. Explain Factors affecting fatigue life and protection methods

UNIT-4

19. Compare between Homogenous & heterogeneous Nucleation

20. Write briefly about constitutional cooling

21. Write briefly about eutectic solidification

22. Explain briefly the process of Nucleation & growth of Pure Metals

23. Define & Explain the Linear elastic properties of metals

24. From the concept of free energy and with the help of cooling curve explain how

solidification process begins in pure metals.

25. Explain briefly the solidification of Alloys

26. Describe the Structures of cast metals with neat sketches

27. Define Solid solution. Compare between Interstitial & substitutional solid solution

28. With example

29. Draw the following type of Phase Diagrams- Eutectic, Eutectoid and Peritectic.



52

30. At Eutectic temperature three phase, liquid of 61%B solid α of 10% B and solid βof

95% are in equilibrium for a binary alloy of A & B. Find the ratio of α & β phases in the

eutectic phase.

31. Two Metals A & B of melting point 650 °C & 450 °C respectively. When alloyed

together they do not form any compound or intermediate phase but form a eutectic at

300 °C of composition of 40% A. The maximum solid solubilities of B in A & A in B

occurring at 300 °C, are 10% B & 8% A respectively and they reduce to 5% B & 4% A

respectively at 0 °C. Assume that the solidus, liquidus & solvus lines to be straight.

i. Draw the phase diagram of the series and mark all salient regions

ii. Find the temperature at which an alloy with 30% B starts & ends

Solidification

iii. Find the relative amounts, percentage, composition, number, type &

distribution of the phases in the above alloy at 0° C

32. Write briefly about Gibb’s Phase rule & how it can be applied for unary phase diagram?

33. What criteria favoring the formation of substitution solid solutions. Explain clearly.

34. Explain Hume-Ruthary rules giving examples

35. Explain the method of construction of a phase diagram for general A-B system with the

following data

i. A & B are mutually soluble in liquid state

ii. A & B are partially soluble in liquid state

iii. A & B form an Eutectic

36. Two metals A & B have 100% mutual solubilities in the liquid and solid states .The

melting point of pure metal A & B are 800 °C& 600 °C respectively. Details of start and

end of solidification of various alloys in the series are as follows:

Alloy of Composition Temp. at start of

solidification

Temp at end of

solidification

90 % A + 10% B 798 °C 750 °C

70% A + 30%B 785 °C 705°C

50% A+ 50% B 757°C 675°C

30% A + 70% B 715°C 645°C

10% A + 90%B 650°C 615°C

i. Draw the phase diagram of the series if there are no solid state reactions &

label all regions

ii. Predict the number, type, relative amounts & concentration of phases present

in an alloy of 40% A & 60% B at 700°C & 20 °C.

37. Two metals A and B are used to form an alloy containing 75% A and 25 % B. A melts

at 750°C and B at 550°C. When alloyed together A and B do not form any compound or

intermediate phase. The solid solubility of metal A in B do not form any compound or

intermediate phase. The solid solubility of metal A in B and B in A are negligible. The

metal pair forms a eutectic at 40%A and 60%B which solidifies at 300°C. Assume the

liquidus and solidus lines to be straight. Draw the phase diagram for the alloy series and

find

i. The temperature at which the alloy starts and completes solidification.

ii. The percentage of eutectic in the alloy at room temperature.



53

UNIT-5

38. Draw Iron-Iron Carbide phase diagram & indicate the temperature compression and

phases on it. Elaborate the invariant reactions involved in it

39. Explain the equilibrium coding of a Hypo eutectoid steel from liquid-state with phase

transformation that takes place

40. Compare the microstructure of steels & cast irons

41. What is TTT diagram? How is it different from phase diagram?

42. Describe the various transformed products of Austenite on cooling

43. Draw a neat Fe-Fe3C equilibrium diagram, label all the salient fields, temperatures &

compositions on it & explain the mode of solidification, solid state reaction & room

temperature microstructure of the following alloy: cast iron with 3.5% carbon.

44. Explain clearly the three invariants reactions in the above question

45. Define the following with respect to steel: Pearlite, Ferrite, Ledubrite, Cemenite,

Austenite

46. Draw the Fe-Fe3Cphase diagram & label all temperatures (in 0°C), compositions &

phases.

47. Sketch the microstructure of eutectoid steel & S G iron & identify the phases in it

48. Differentiate between plain carbon steel & alloy steels

49. Explain general classification of steel

50. Explain briefly CCT Curve with neat diagram

51. Discuss the chemical composition, properties & engineering applications of Grey Cast

Iron & S G Iron

52. Describe how TTT diagrams are constructed How is different from phase diagram

UNIT-6

53. Explain the difference between annealing & Normalizing and the need for each.

54. Write briefly about Critical cooling rate & precipitation Hardening

55. Using the relevant portion of the Fe-Fe3 equilibrium diagram & the TTT diagram with

cooling curve super imposed on it discuss the normalizing heat treatment of a 1.5%,

plain carbon Steel with respect to the process, Micro structural changes & its properties.

Changes due to the process.

56. Explain briefly the metmorphing process & its advantages over traditional Quench

Hardening

57. Describe the various transformed products of Austenite on cooling

58. Define heat treatment of steel. What are the steps involved in it & its purpose

59. Describe the following heat treatment process of steels with regard to thermal cycle

involved, microstructure and properties aimed

60. i) Annealing ii) hardening iii) Spheroidising

61. Distinguish between Aus tempering & Mar tempering with neat diagram. What are the

practical difficulties in these treatments?

62. Write short note on Surface Heat treatment (Case Hardening, Nitriding, Cyaniding)

63. Explain the process of flame hardening and induction hardening with neat sketch.

64. Explain Jominy end –quench test.



54

UNIT-7

65. 1. Mention the properties, Composition & applications of following steels

66. Low-Carbon steel ii) High Carbon steel iii)18/8 Stainless steel iv) 18/4/1 HSS

67. Compare the composition, microstructure, properties & applications of Gray C I & S G

Iron with neat diagram

68. Discuss the importance of aluminum alloys in engineering field & name few Alloys

69. Mention the composition & properties of Bronze, Brass & Al-Si alloy.

70. Write a short note on Age Hardening.

71. Write a note on a)light alloys like Al & Mg & Titanium alloys

b)Copper & its alloys,brasses & Bronzes

UNIT -8

72. What do you mean by corrosion how to prevent it .

73. Explain general methods of preventing corrosion.

74. Explain cathodic protection.

75. Explain concept of Stress corrosion cracking.

76. Explain corrosion prevention by alloying.

SHORT NOTES ON

77. Crystal Imperfections

78. BIS designation of Steels

79. Alloy Steels

80. Ductile & Brittle Fracture

81. Lever Rule applied to Eutectoid steel

82. Microstructures of Eutectoid steel & grey cast iron

83. Difference between Annealing & Normalizing

84. Effects of Chromium & Nickel as alloy7ing elements in steel

85. Laminated Composites

86. Fick’s law of Diffusion

87. Nucleation & Growth

88. Ceramics as insulators

89. Izod impact test

90. Gibb’s phase rule

91. Age Hardening

92. Case Hardening.



55



56



57

06ME33-BASIC THERMODYNAMICS



58

SYLLABUS SUB CODE : 06 ME 33 IA MARKS : 25

HRS/WEEK : 04 EXAM HOURS : 03


PART-A

UNIT 1: Fundamental Concepts & Definitions: Thermodynamics; definition and scope. Microscopic and

Macroscopic approaches. Engineering Thermodynamics Definition, some practical applications of

engineering thermodynamic. System (closed system) and Control Volume (open system);

Characteristics of system boundary and control surface, examples. Thermodynamic properties;

definition and units, intensive and extensive properties. Thermodynamic state, state point, state

diagram, path and process, quasi-static process, cyclic and non-cyclic processes; Thermodynamic

equilibrium; definition, mechanical equilibrium; diathermic wall, thermal equilibrium, chemical

equilibrium- Zeroth law of thermodynamics, Temperature; concepts, scales, measurement. Internal

fixed points. 07 Hrs

UNIT 2:

Work & Heat: Mechanics, definition of work and its limitations.Thermodynamic definition of

work; examples, sign convention. Displacement work; at part of a system boundary, at whole of a

system boundary, expressions for displacement work in various processes through PV diagrams.

Shaft work; Electrical work. Other types of work. Heat; definition, units and sign convention, what

heat is not. 06 Hrs

UNIT 3: First Law of Thermodynamics: Joule’s experiments, equivalence of heat and work. Statement of

the First law of thermodynamics, extension of the First law to non -cyclic processes, energy, energy

as a property, modes of energy, pure substance; definition, two-property rule, Specific heat at

constant volume, enthalpy, specific heat at constant pressure. Extension of the First law to control

volume; steady state-steady flow energy equation, important applications, analysis of unsteady

processes such as filling and evacuation of vessels with and without heat transfer. 06 Hrs

UNIT 4: Second Law of Thermodynamics: Devices converting heat to work; (a) in a thermodynamic cycle,

(b) in a mechanical cycle. Thermal reservoir. Direct heat engine; schematic representation and

efficiency. Devices converting work to heat in a thermodynamic cycle; reversed heat engine,

schematic representation, coefficients of performance. Kelvin -Planck statement of the Second law

of Thermodynamic; PMM I and PMM1I. Clasiu's statement .of Second law of Thermodynamic;

Equivalence of the two statements; Reversible and irreversible processes; factors that make a

process .irreversible, reversible heat engines, Carnot cycle, Carnot principles. Thermodynamic

temperature scale. 07 Hrs



59

PART – B

UNIT 5: Entropy: Clasiu’s inequality; statement, proof, application to a reversible cycle. QR/T as

independent of the path. Entropy; definition, a property, principle of increase of entropy, entropy as

a quantitative test for irreversibility, calculation of entropy using Tds relations, entropy as a

coordinate. Available and unavailable energy. 07 Hrs

UNIT 6: Availability and Irreversibility: - Maximum Work, maximum useful work for a system and a

control volume, availability of a system and a steadily flowing stream, irreversibility. Second law

efficiency. 06 Hrs

UNIT 7:

Pure substances: P-T and P-V diagrams, triple point and critical points. Sub- cooled liquid,

saturated liquid, mixture of saturated liquid and vapor, saturated vapor and superheated vapour

states of a pure substance with water as example. Enthalpy of change of phase (Latent heat).

Dryness factor (quality), T-S and h-s diagrams, representation of various processes on these

diagrams. Steam tables and its use. Throttling calorimeter, separating and throttling calorimeter.

06 Hrs

UNIT 8: Real and ideal gases: Introduction; Vander Waal's Equation Van der Waal's constants in terms of

critical properties, law of corresponding states, compressibility factor; compressibility)" chart. Ideal

gas; equation of state, internal energy and enthalpy as functions of temperature only, universal and

particular gas constants, specific heats, perfect and semi-perfect gases. Evaluation of heat, work,

change in internal energy, enthalpy and entropy in various quasi-static processes. Ideal gas mixture;

Dalton's law of additive pressures, Amagat's law of additive volumes, evaluation of properties.

Analysis of various processes. 07 Hrs

TEXT BOOKS:

1) “Basic and Applied Thermodynamics” by P .K. Nag, Tata McGraw Hill, 3rd Edi. 2002

2) “Thermodynamics an engineering approach”, by Yunus A. Cenegal and Michael A. Boles.

Tata McGraw hill Pub. 2002

REFERENCE BOOKS:

1. Engineering Thermodynamics. By Rajput, Laxmi Publications pvt ltd., 3rd Edi. 2007.

2. Engineering Thermodynamics by J.B. Jones and G.A.Hawkins, John Wiley and Sons.

3. Thermo Dynamics by S.C.Gupta, Pearson Edu. Pvt. Ltd., 1st Ed. 2005.



60

LESSON PLAN SUB CODE : 06ME33 HRS/WEEK : 04

SUB : BASIC THERMO DYNAMICS TOTAL HRS : 52

NO.

OF

HRS TOPICS TO BE COVERED

UNIT 1: Fundamental Concepts & Definitions

1. Thermodynamics; definition and scope. Microscopic and Macroscopic approaches.

2. Thermodynamic properties; definition and units, intensive and extensive properties.

3. Characteristics of system boundary and control surface, examples.

4. Engineering Thermodynamics Definition, some practical applications of engineering

5. Thermodynamic state, state point, state diagram,

6. Thermodynamic equilibrium; definition, mechanical equilibrium; diathermic wall,

thermal equilibrium, chemical equilibrium

7. Zeroth law of thermodynamics, Temperature; concepts, scales

8. Numericals Solving

UNIT 2:Work & Heat

9. Mechanics, definition of work and its limitations.

10. Displacement work; at part of a system boundary.

11. Shaft work; Electrical work. Other types of work

12. Expression for displacement work in various processes through p-v diagrams.

13. Heat; definition, units and sign convention, what heat is not.


UNIT 3:First Law of Thermodynamics

15. Joule’s experiments, equivalence of heat and work. Statement of the First law of

thermodynamics,

16. Extension of the first law to non-cyclic process energy energy as a property modes of

energy pure substance.

17. extension of the First law to non -cyclic processes, energy, energy as a property, modes

of energy, pure substance

18. definition, two-property rule,

19. Extension of the First law to control volume; steady state-steady flow energy equation

20. Important applications, analysis of unsteady processes such as filling and evacuation of

vessels with and without heat transfer.

21. path and process, quasi-static process,

22. cyclic and non-cyclic processes;


UNIT 4:Second Law of Thermodynamics

24. Devices converting heat to work; (a) in a thermodynamic cycle, (b) in a mechanical

cycle.

25. Thermal reservoir. Direct heat engine; schematic representation and efficiency.

26. Devices converting work to heat in a thermodynamic cycle;



61

27. Specific heat at constant volume, enthalpy, specific heat at constant pressure

28. reversed heat engine, schematic representation, coefficients of performance.

29. Kelvin -Planck statement of the Second law of Thermodynamic; PMM I and PMM1I.

30. Clasiu's statement .of Second law of Thermodynamic; Equivalence of the two statements;

Reversible and irreversible processes;

31. Carnot cycle, Carnot principles.


UNIT 5:Entropy

33. Clasiu’s inequality; statement, proof, application to a reversible cycle.

34. QR/T as independent of the path. Entropy; definition, a property,

35. Entropy definition a property, principle of increases of entropy

36. Entropy as a quantitative test for irreversibility,

37. Calculation of entropy using Tds relations, entropy as a coordinate. Available and

unavailable energy


UNIT 6:Availability and Irreversibility

39. Maximum Work, maximum useful work for a system and a control volume

40. availability of a system and a steadily flowing stream

41. Irreversibility. Second law efficiency



UNIT 7:Pure substances

44. P-T and P-V diagrams, triple point and critical points

45. Sub- cooled liquid, saturated liquid, mixture of saturated liquid and vapor,

46. Saturated vapor and superheated vapor states of a pure substance with water as example.

47. Enthalpy of change of phase (Latent heat). Dryness factor (quality), T-S and h-s diagrams

48. Representation of various processes on these diagrams. Steam tables and its use

49. Throttling calorimeter, separating and throttling calorimeter.


UNIT 8:Real and ideal gases

51. Introduction; Vander Waal's Equation Van der Waal's constants in terms of critical

properties, law of corresponding states

52. Compressibility factor; compressibility)" chart

53. Ideal gas; equation of state, internal energy and,

54. enthalpy as functions of temperature only

55. Evaluation of heat, work, change in internal energy

56. Universal and particular gas constants.

57. specific heats, perfect and semi-perfect gases

58. enthalpy and entropy in various quasi-static processes

59. Ideal gas mixture; Dalton's law of additive pressures

60. Amagat's law of additive volumes, evaluation of properties. Analysis of various processes.

61. Problems

62. Problems



62

QUESTION BANK

CHAPTER 1: FUNDAMENTAL CONCEPTS 1. Define the following terms with reference to thermodynamics

a) System b) property c) process d) cycle e) thermodynamic equilibrium

2. Define Zeroth law of thermodynamics and Prove that T(K)=T(C) +273

3. Distinguish between i) open and closed system ii) Intensive and Extensive Properties.

iii) Mechanical and thermal equilibrium.

4. Explain thermodynamic system. Whether the following systems are open (or) closed

i) a scooter engine ii) Centrifugal water pump iii) An electric fan iv) A

motor car battery

5. Fahrenheit and centigrade thermometers are both immersed in a fluid. Fahrenheit reading is

numerically twice that of the centigrade reading. What is temperature of The Fluid expressed

as R and K

6. A temperature T on a thermometric scale is defined in terms of property P by Relation T= a

log e p + b Where A and B are constants. The temperature at ice point and steam points are

00c and 100

0c respectively. An instrument gives values of P as1.86 and 6.81 at ice and

steam point respectively. Evaluate temperature Corresponding to a reading of p =2.5.

7. The normal body temperature is 96.6 0F. What is the temperature in

0c, K and R?

CHAPTER 2: WORK AND HEAT

8. Define Work and Heat from the thermodynamic point of view.

9. Define point function and path function. Prove that heat is a path function.

10. Differentiate between Work and Heat.

11. What is meant by displacement work? Explain the same with reference to different

Quasistatic processes.

12. A home cooler has fan of 170 watts rating .If the cooler operates for 10 hrs. Find the energy

consumed by the cooler.

13. A battery is charged with a battery charger. The charger operates 1 hour at 15v and

14. a current of 30 Amps. Ccalculate the work done on the battery.

15. Aspherical balloon has a diameter of 20cm and contains air at 1.5 bars. The diameter of the

balloon increases to 30cm in a certain process during which pressure is proportional to the

diameter. Calculate the work done by the air inside the balloon during the process.

16. A gas in the cylinder and piston arrangement comprises the system. It expands from 1m3 to

2m3 while receiving 200kJ of work from a paddle wheel. The pressure on the gas remains

constant at 5 bars. Determine the network done by the system

CHAPTER 3: FIRST LAW OF THERMODYNAMICS 17. Derive an expression for displacement work for polytropic process

18. Write a brief note on perpetual motion machines.

19. Define internal energy and prove that it is a property

20. State first law of thermodynamics for a closed system undergoing a cyclic process. Show that

internal energy is property of the system.

21. Explain the word “Enthalpy” of a system and the term pV with reference to an open system.



63

22. A cylinder containing the compressor the system cycle is completed as follows. 1) 8200N-m

of work is done by the piston on the air during compression stroke and 45 kJ of heat are

rejected to the surroundings.2) During expansion stroke 1000N-m of work is done by the air

on the piston. Calculate the quantity of heat added to the system

23. One kg of air having an initial volume of 0.3m3 is heated at constant pressure of 3.2 bar until

the volume is doubled. Calculate (a) initial and final temperature of air, (b) work done (c)

Heat added Take Cp = 1.003kJ/kg K, R = 0.2927 kJ/kg K

24. A tank contains 12 kg of water used for determining mechanical – thermal energy equalities.

The total work input is 40Nm. assuming the system is adiabatic find the change in specific

and total internal energy. If a heat loss of 0.1J/kg is noted, what is the internal energy

change?

25. An engine cylinder of diameter 22.5 cm has a stroke length of 37.5 cm. The swept volume is

4 times the clearance volume. The pressure of gases at the beginning of expansion stroke is

1569 kPa. Find the work done during expansion stroke assuming the process as reversible

adiabatic Take, γ = 1.4

26. A cylinder contains 1 kg of certain fluid at an initial pressure of 20 bar. The fluid is allowed

to expand reversible behind a piston according to law pV2 = constant until the column is

doubled. The fluid is then cooled reversibly at constant pressure until the piston regains its

original position. Heat is then supplied reversibly with the piston firmly licked in position

initial the pressure raises to the original value of 200 bar. Calculate the net work done by the

fluid for an initial volume of 0.5 m3

27. Derive steady flow energy equation stating the assumption made

28. Apply the steady flow energy equation for the following system a) Gas turbine b) Nozzle c)

Condenser d) Throttle valve

29. A steam turbine operating under steady flow conditions receives 4500kg of steam per our.

The steam enters the turbine at a velocity of 42 m/s at the elevation of 4m and a specific

enthalpy of 2800kJ/kg. It leaves the turbine at a velocity of 9.4m/s at an elevation of 1m and

specific enthalpy of 2262kJ/kg. The heat losses from the turbine to the surroundings amounts

to 16780kJ/hr. determine the power output of the machine.

30. A centrifugal pump delivers 60kg of water per second. The inlet and outlet pressure are 10

kPa and 400 kPa respectively. The suction is 2 m below and delivery is 8 m about the

centerline of the pump. The suction and delivery pipe diameter are 20cm and 10cm

respectively. Determine the capacity of the electric motor to run the pump.

CHAPTER 4: SECOND LAW OF THERMODYNAMICS

31. Write the Kelvin- Plancks and Clausius statement of second law of thermodynamics and

prove that they are equivalent.

32. Define irreversibility and mention at least 3 factor which render a process irreversible.

33. state carnot’s theorem

34. Show that C O P of the heat pump minus C O P of a refrigerator is unity.

35. Define the term source, sink, and heat reservoir

36. Define heat engine and differentiate between heat engine and a reversed heat engine.



64

37. There are 3 reservoirs at temperature 8270C, 1270C and 270C parallel. A reversible heat

engine operates between 8270C &1270C and a reversible refrigerator operates between 27

and 1270C respectively. 502kJ of heat are extracted for the reservoir at 8270C by the heat

engine and the refrigerator from the reservoir at 270C abstracts 251 kJ of heat. Find the net

amount of heat delivered to the reservoir at 1270C. Can the heat engine drive the refrigerator

and still delivers some net amount of work? IF so how much

38. A heat engine working on Carnot cycle converts one-fifth of the heat input into work. When

the temperature of the sink is reduced by 800C the efficiency gets doubled. Calculate for the

temperature of source and sink.

39. The working substance in a carnot engine is 0.05kg of air. The maximum cycle temperature

is 940 K, and the maximum pressure is 8.4 x 103 kPa. The heat added per cycle is 4.2 kg.

Determine the maximum cylinder volume if the minimum temperature during the cycle is

300k

40. A reversible engine operates between 3 heat reservoirs 1000K, 800K & 600K and rejects

heat to a reservoir at 300K, the engine develops 10kW and rejects 412kJ/min. If heat

supplied by the reservoir at 1000K is 60% of heat supplied by the reservoir at 600 K, find

quantity of heat supplied by each reservoir

41. An inverter claims to have developed a refrigerator, which maintains the refrigerated space at

–100 c, and it has a cop of 8.5. How would you evaluate his claim as patent officer?

42. A reversible engine works between temperature limits of 2600 C and 600 C., which is

preferable? Raising the source temperature to 3000 C or lowering the sink temperature to

300 C.

CHAPTER 5: ENTROPY AND

43. Define entropy and show that entropy is a property of a system.

44. Explain the principle of increase of entropy.

45. Derive an expression for entropy

46. Explain availability of a system with heat transfer.

47. What do you mean by available and non –available energy.

48. Derive an expression for decrease in available energy and unavailable energy.

49. Write short note on Helmholtz and Gibb function.

50. 0.5kg of air initially at 250C is heated reversibly at constant volume until pressure is

doubled, for the total path determine the work transfer, the heat transfer and the

change in entropy.

51. A 30 kg of steel ball at 4270 C is dropped in 150kg oil at 270 C, the specific heat of steel and

2.5kj/kg k respectively. Estimate the entropy change of steel, oil and that of system

Containing oil and steel.

52. One kg of air at 1bar pressure and 150C is heated in a cylinder under constant pressure

Conditions to 150 0C. Find the volume, the work done and the changes in internal energy,

enthalpy and entropy.

53. 10gms of water at 200 C is converted into ice at –100c at constant pressure, assuming the

specific heat of liquid water to remain constant at 4.2kj /kg k and that of ice to be half of

this value and taking the latent heat of fusion of ice at 00 c to 335j/g, calculate the total

entropy.



65

CHAPTER –6: AVAILABILITY AND IRREVERSIBILITY

54. A System receives 10000KJ of heat at 500 K from a source at 1000K.the temperature of the

surroundings is 300 K .Assume that the temperature of the system and source remains

constant during heat transfer,

Find:

i. The entropy production due to above mentioned heat transfer,

ii. Decrease in available energy

55. Determine the availability per unit mass for combustion products (say air) in an engine

Cylinder at 11870 C and 15Mpa. Assume the environmental at 0.101Mpa and T0 =250 C.

56. Making use of a availability equation, determine the maximum thermal efficiency of a heat

engine operating between a high reservoir at Th and a low –temperature heat reservoir at

TL.40kg of water at 1400 C mix 50kg of water at 550 C at constant pressure. If the

Surroundings were at temperature 270 C, calculate the decrease in available energy.

57. A liquid of specific heat 6.3 KJ/Kg K is heated at approximately constant pressure from150

C. to 700 C. by passing it through tubes which are immersed in furnace. the furnace

temperature is constant at 14000 C. Calculate the effectiveness of the heating process when

the atmospheric temperature is 100 C.

58. Differentiate between availability function and Gibbs energy function

59. Derive a general expression for irreversibility in Non flow process and Steady flow process

CHAPTER –7: PURE SUBSTANCES

60. Define the following terms with reference to pure substances

i. Heat of fusion

ii. Sensible heat

iii. Wet steam

iv. Triple point

v. Enthalpy

vi. Critical point

vii. Dryness fraction

viii. Sensible heat

61. Explain with neat sketch the method of estimating quality of steam by throttling calorimeter.

62. Explain with neat sketch the method of determining the quality of steam by combined

separating and throttling calorimeter.

63. Draw a P-T diagram for pure substance and indicate all the necessary points on it.

64. A pressure cooker contains 1.5 kg of saturated steam at 5 bar. Find the quantity of heat which

must be rejected so as to reduce quality to 60 % dry. Determine the pressure and temperature

at the new state.

65. Find the enthalpy, specific volume and internal energy if the pressure of steam is 50 bar and

temperature is 443 0C.

66. 0.5 Kg of steam has a dryness fraction of 0.8 initially. This steam is heated at constant

pressure till it reaches 8 bar till the volume is double. Determine the final temp



66

67. Two boilers one with super heater and without super heater are delivering equal quantities of

steam into a common main. The pressure in the boiler is 20bar. The temperature of steam

from a boiler with a super heater is 3500C and temperature of the steam in the main is 2500C

determine the quality of the steam supplied by other boiler take Cps=2.25KJ/Kg.

68. Steam from a boiler is delivered at 15 bar absolute and dryness fraction of 0.85 into a steam

superheater where an additional heat is added at constant pressure. Steam temperature now

increases to 573 K. Determine amount of heat added and change in internal energy for unit

mass of steam

69. A piston cylinder assembly had steam at 100kPa with quality 20 percent wet. Temperature of

steam rises to 3000C due to energy transfer. Determine the work done and heat supplied.

70. A pressure cooker contains 4 kg of steam at 6 bar and 0.96 dryness. Fine the quantity of heat

which must be rejected so as the quality of steam becomes 0.7 dry



67



68



69



70



71

06 ME34 – MECHANICS OF MATERIALS



72

SYLLABUS SUB CODE : 06ME34 IA MARKS : 25



UNIT – I.

SIMPLE STRESS AND STRAIN:

1. Introduction.

2. Properties of Material

3. Stress, Strain, Hook's law.

4. Poisson's Ratio

5. Stress - Strain Diagram for structural steel and non ferrous materials

6. Principles of superposition,

7. Total elongation of tampering bars of circular and rectangular cross sections. Elongation

due to self –weight 07 hrs

UNIT – II

SIMPLE STRESSES AND STRAINS CONTINUED

8. Composite section

9. Volumetric strain, expression for volumetric strain

10. Elastic constants, relationship among elastic constants

11. Thermal stresses including compound bars 06 hrs

UNIT – III.

COMPOUND STRESSES 12. Introduction

13. Stress components on inclined planes,

14. General two-dimensional stress system,

15. Principal planes and stresses,

16. Mohr's circle of stresses.

17. Thin culinders subjected to pressure, change in length, diameter and volume

18. Thick cylinders – Lame’s equation(excluding compond cylinders) 08 hrs

UNIT– IV.

BENDING MOMENT AND SHEAR FORCE IN BEAMS 19. Introduction ,Types of beams loading and supports, Shearing force in beam,

20. Bending moment, Sign convention, Relationship between loading shear force and

bending moment,

21. Expression for shear and bending moment equations, SFD and BMD with sailent values

for cantilever beams simply supported beams and overhanging beams considering point

loads, UDL, UVL and Couple. 07 hrs



73

UNIT –V.

BENDING STRESS AND SHEAR STRESS IN BEAMS

22. Introduction, Bending stress in beam,

23. Assumption in simple bending theory,

24. Pure bending derivation of Bernoulli's equation,

25. Modulus of rupture, section modulus

26. Flexural rigidity,

27. Expression for horizontal shear stress in beam,

28. Shear stress diagram for rectangular, symmetrical I and T section (Flitched beams not

included) 06 hrs

UNIT– VI.

DEFLECTION OF BEAMS

29. Introduction, Definition of slope, deflection,

30. Elastic curve - derivation of differential equation of flexure,

31. Sign convention

32. Slope and deflection for standard loading classes using Maccualay's method for

prismatic beams and overhanging beams subjected to point loads, UDL and Couple.

06 hrs

UNIT– VII.

TORSION OF CIRCULAR SHAFTS

33. Introduction, Pure torsion - torsion equation of circular shafts

34. Strength and stiffness,

35. Torsional rigidity, torsional flexibility and polar modulus,

36. Power transmitted by shaft solid and hollow circular sections. 06 hrs

UNIT –VIII.

ELASTIC STABILITY OF COLUMNS 37. Introduction, Short and long columns

38. Euler's theory on columns,

39. Effective length slenderness ratio,

40. Radius of gyration, bucking load,

41. Assumptions, derivations of Euler's Bucking load for different end conditions,

42. Limitations for Euler's theory,

43. Rankine's formula and problems

06 hrs



74

TEXT BOOKS:

1. Strength of Materials, B.C.Punima, Ashok Jain, Arun Jain, Lakshmi Publications, New

Delhi.

2. Strength of Materials, Basavarajaiah and Mahadevappa, Khanna Publishers, New Delhi.

3. Strength of Materials, Ramamrutham Dhanapath Rai Publishers, New Delhi.

REFERENCE BOOKS:

1. Strength of Materials L.S. Srinath Desai and Ananth Ramu, McMillan Publishers,

Chennai.

2. Strength of Materials, Singer Harper and Row Publication.

3. Strength of Materials, SS Bhavikatti Vikas Publications House pvt. Ltd.

4. Elements of Strength of Materials, Timoshenko and Young Affiated East-West Press.



75

LESSON PLAN

SUB CODE : 06ME34 HRS/WEEK : 04

SUB : MECHANICS OF MATERIALS TOTAL HRS : 52

NO.


1. Introduction to concept of Stress, Strain, types of Stresses and properties of

metallic materials.

2. Hook's Law, definition of poisson's ratio

3. Typical Stress - Strain diagram for steel and non-ferrous materials subjected to

Static Tension Test

4. Determination of axial deformation of prismatic bars subjected to Static axial

load and solving of some numerical problems.

5. Solving some numerical problems on deformation of prismatic bars.

6. Explaining the principal of Superposition for evaluation of total deformation of

bars with stepped variation in cross section along its length.

7. Solving some numerical problems on evaluation deformations of bars

8. Solving some numerical problems on evaluation deformations of bars with

stepped variation in cross section by principal of super position concept

9. problems.

10. Evaluation of expression for deformation of tapering bars of circular and

rectangular cross sections.

11. Solving some numerical problems on deformation of tapering bars with circular

and rectangular cross section.

12. Determination of deformation due to self- weight of the bar and solving some

numerical problems.

13. Concept of composite bar action and evaluation stresses and deformation of

composite bar subjected to axial force.

14. Solving some numerical problems on composite bar action..

15. Explanation of Elastic constants and deriving the relation ship between various

elastic constants



76

16. Solving some numerical problems on elastic constants.

17. Concept of Thermal Stresses and its evaluation simple bars and compound bar.

18. Solving some numerical problems on evaluation of Thermal Stresses in simple

bars.

19. Introduction to compound Stress and

20. Its importance in the design of Structural components.

21. Determination of Stress components on inclined planes for uni-axial Stress

System.

22. Determination of Stress components on inclined planes for general two-

dimensional Stress System.

23. Determination of principal planes and principal Stresses.

24. Introduction to thin and thick cylinders, stresses iron the walls of thin cylinder,

Assumptions made in the analysis of thin cylinders

25. Relationship between hoop stress and longitudinal stress

26. Strains in thin cylindrical shells, problems on above

27. Derivation of Lame's equation, assumptions made in analysis of theory on thick

cylinders

28. Problems concerned to thick cylinders

29. Problems concerned to thick cylinders

30. Determination of Bending moment and Shear force with salient values for over

hanging beams.

31. Introduction to Bending stresses and Shear stress in Bending members ..

32. Assumption made in deriving pure Bending of Bernoulli's equation

33. Derivation of Bernoulli's equation. And definition of modulus of rupture and

section modulus.

34. Definition of flexural rigidity , derivation of expression form Shear stress in

Beam's

35. Solving some numerical examples for determining bending stress and Shear

stress for rectangular section Beams.

36. Solving some numerical examples for determining bending stress and Shear

stress for I and T section Beams.

37. Introduction to deflection of Beams assumptions made in deriving diffraction

equation for the Deflected curve Beam.

38. Derivation of second order deflection equation. sign convention for various

loading cases



77

39. Use of Maccualay's method for evaluating the deflection of Beams.

40. Solving some numerical examples for evaluating the deflection of Beams by

Maccualay's method.


Maccualay's method.


Maccualay's method.

43. Introduction to torsion,

44. Pure torsion, torsion equation of circular shaft

45. Strength and stiffness

46. Torsional rigidity and polar modulus

47. Power transmitted by a shift for solid and hollow circular sections.

48. Problems on above concepts



51. Introduction to column behavior

52. differences between bulking and bending, and end conditions of column

53. Classification of columns, Assumptions made in Euler's theory, Euler's formula

derivation for both end hinged condition.

54. Euler's formula derivation for both ends fixed

55. Euler's formula derivation for one end fixed other end hinged

56. Euler's formula derivation for one end fixed and other end free

57. Limitations of Euler's theory, Rankine's formula

58. Problems on above

59. Euler's formula derivation for one end fixed and other end free, Limitations of

Euler's theory,

60. Rankine's formula





78

QUESTION BANK

1. Define Stress, Strain and State Hooke's Law.

2. Explain with an example the difference between lateral strain and longitudinal strain and

hence define Poisson's ratio.

3. A bar of diameter 20mm and length 100mm extends by 0.2 mm. If E of the materials of

the rod is 2x 105 N/mm2, what load and type of load applied to the rod? If an extension of

20% greater is required for the same load applied above, how the diameter of the bar need

to be reduced.

4. What is proof stress? Explain the concept of proof stress with the help of a stress strain

diagram.

5. Derive an expression for the elongation of a vertically Supported bar due to its self-

weight.

6. Find the total elongation of a bar shown in Fig 1. Take E= 1.05 X 105 N/mm2.

7. Define Principal Plane and Principal Stress." All Principal Stresses are normal Stress, but

all normal Stresses are not Principle Stresses" State Whether this Statement is true or false

Justify your answer.

8. Explain the step by step procedure for drawing Mohr's Circle diagram for an element

under combined stresses as shown in fig 2, to find the principal stresses and principal

planes.

9. An element is subjected to stresses as shown in fig. 3 Determine (i) Principal Stresses and

their directions analytically. (ii) Find the normal and tangential Stress on the plane BC

graphically.



79

10. What is abeam? How are they classified? What are the different types of loads a beam can

carry or which can apply on it.

11. Enumerate the assumptions made in theory of pure bending.

12. Define Section modules of rupture. Derive an expression for the section of a hollow

rectangular Cross section as shown in Fig 5

13. A cast Iron test beam 25mm X 25mm Cross Section and 1 m long, supported at its ends

fails when a central load of 800 N is applied on it. What UDL will break a Cantilever of

the same materials 50 mm Wide and 100mm deep and 2m long?

14. What is flexural rigidity? What are the different methods of finding the slope and

deflection of beams? Find expressions for slope and deflection for a Cantilever beam with

a point load P at its free end as shown in fig. 6, by double integral method.



80

15. A Cantilever beam of length 3m, Carries an UDL of 3000 N/m for a length of 1.5 m from

its fixed end and a point load of 1500 N at its free end. If the Cross Section of the beam is

a rectangle of 150mm Wide and 300mm deep, find the deflection of the beam at its free

end. Take E=1.05 X105 N/mm2.

16. Define torsional rigidity and polar modulus.

17. What are the assumptions made in the theory of pure tension?

18. Explain each term in the relation.

T/Ip = C/r = C@/1 with units.

19. A hollow shaft has an outside diameter 'd' and inside diameter half of it. Calculate the

minimum Value of d, if it is to transmit 400kw at 100rpm with a working stress of 40

N/mm2. Determine the twist in a length of 15 times the external diameter, take C=1 X105

N/mm2.

20. What is meant by thin and thick Cylinders? Derive an expression for longitudinal and loop

stress for a thin Cylinder of diameter 'd' thickness 't' under the influence of an internal

pressure p.

21. A pipe of 500mm internal diameter and 75mm thick is filled with a fluid at a pressure of 6

N/mm2. Find the maximum and minimum hoop stress across the Cross Section of the

Cylinder, Also Sketch the radial pressure and hoop stress distribution across its thickness.

22. Derive an expression to show the relationship between Young's modulus. Bulk modulus.

Rigidity modulus and Poisson's ratio.

23. A steel rod is of 18m long at a temperature of 25% c. Find the free expansion of the length

when the temperature is raised to 85% c. Also find the temperature stress produced.

(i) When the expansion is fully prevented.

(ii) When the rod is permitted to expand by 4.5mm. Take a = 12x 106

per 0C, E = 200 KN/mm2.

24. Define Neutral axis and moment of resistance. Also mention the assumptions made in the

theory of pure bending.

25. A rolled steel joist of I section has the following dimensions: Flange 250mm wide and

25mm thick. Web of 15mm thickness and has an overall depth of 650mm. If this beam

carries a UDL of 50 KN/m on a span of 6m.Calculate the maximum bending stress

produced.

26. Derive an expression for the slope and deflection at the free end of a cantilever loaded by

a UDL throughout its span.

27. A steel shaft transmits 125KW at 175 rpm. The diameter of shaft is 100mm. determine

the torque on the shaft and the maximum shearing stress indeed. Also calculate the twist

of the shaft in a length of 6m. Take C= 8.5 X 104 N/mm2.

28. A load of 270 KN is acting on a short RCC column of size 200mm X 200mm. The column

is reinforced with 10 bars of 12mm diameter. Determine the stresses in steel and concrete

if modulus of elasticity of steel is 16.5 times of that of concrete.

29. Draw the Mohr's circle for two unequal like principal stresses acting on a body. Get the

expressions for normal and tangential stresses.

30. Differential between thin and thick cylinders. Also explain hoop stress and longitudinal

stress in connection with thin cylinders. Draw neat sketches. Write the expression.

31. Derive an expression for Euler's formula for a column when one end is fixed and the

other end is hinged.



81

32. Find the shortest length L for a pin ended steel column having a cross section of 70mm X

110mm for which Euler's formula applies. Take E = 2.1 X 105 N/mm2 and critical

proportional limit is 250 N/mm2.

33. Derive an expression for the theory of pure torsion.

34. A steel bar of 2mm diameter is subjected to a tensile test. Determine stress. Strain, E %

Elongation from the following data.

i. Gauge length 200mm

ii. Extension at a load of 100KN = 0.140mm

iii. Total Extension = 50mm.

35. Also determine the percentage decrease in area if the diameter of rod at failure is 16mm.

Further determine the breaking load if ultimate stress of bar material is 600N/mm2.

36. Two vertical rods one of steel and the other of copper are each rigidly fixed at top and are

500mm apart. Diameter and length of each rod are 20mm and 3.5m respectively. A cross

bar is fixed at the lower ends of the rods.

37. Determine the location of a 5000N load to be placed on the cross bar so than the cross bar

remains horizontal. Calculate the corresponding stresses in both the rods.



82



83



84

06ME35 – MANUFACTURING PROCESS-I



85

SYLLABUS SUB CODE : 06ME35 IA MARKS : 25



PART – A

CASTING PROCESS

UNIT 1:

Introduction: Concept of Manufacturing process, its importance. Classification of Manufacturing

processes. Introduction to Casting process & steps involved. Varieties of components produced by

casting process. Advantages & Limitations of casting process.

Patterns: Definition, functions, Materials used for pattern, various pattern allowances and their

importance. Classification of patterns.

Binder: Definition, Types of binder used in moulding sand.

Additives: Need, Types of additives used. 06 Hrs

UNIT 2: Sand Moulding : Types of base sand, requirement of base sand. Types of sand moulds.

Sand moulds: Moulding sand mixture ingredients (base sand, binder & additives) for different sand

mixtures. Method used for sand moulding.

Cores: Definition, Need, Types. Method of making cores, Binders used. Concept of Gating &

Risering. Principle involved. and types. Fettling and cleaning of castings. Basic steps involved.

Casting defects - causes, features and remedies.

Moulding machines : Jolt type, squeeze type, Jolt & Squeeze type and Sand slinger. 07 Hrs

UNIT 3: Special moulding Process :Study of important moulding processes Green sand, Core sand, Dry

sand, Sweep mould, CO2 mould, Shell mould, Investment mould.

Metal moulds : Gravity die-casting, Pressure die casting, centrifugal casting, Squeeze Casting,

Slush casting, Thixocasting and continuous casting processes. 07 Hrs

UNIT 4:

Melting Furnaces: Classification of furnaces. Constructional features & working principle of Gas

fired pit furnace, Resistance furnace, Coreless Induction furnace, Electric Arc Furnace, Cupola

furnace. 06 Hrs



86

PART – B

WELDING

UNIT 5: Welding process: Definition, Principles, Classification, Application, Advantages & limitations of

welding.

Arc Welding : Principle, Metal Arc welding (MAW), Flux Shielded Metal Arc Welding

(FSMAW), Inert Gas Welding (TIG & MIG) Submerged Arc Welding (SAW) and Atomic

Hydrogen Welding processes. (AHW) Gas Welding : Principle, Oxy – Acetylene welding,

Reaction in Gas welding, Flame characteristics, Gas torch construction & working. Forward and

backward welding. 07 Hrs

UNIT 6:

Special type of welding: Resistance welding - principles, Seam welding, Butt welding, Spot

welding and projection welding. Friction welding, Explosive welding, Thermit welding, Laser

welding and Electron beam welding. 07 Hrs

UNIT 7: Metallurgical aspect in welding : Structure of welds, Formation of different zones during welding.

Heat affected zone (HAZ). Parameters affecting HAZ. Effect of carbon content on structure and

properties of steel. Shrinkage in welds & Residual stresses. Concept of electrodes, Filler rod and

fluxes. Welding defects – Detection causes & remedy. 06 Hrs

UNIT 8: Principles of soldering & brazing: Parameters involved & Mechanism. Different Types of

Soldering & Brazing Methods.

Inspection Methods – Methods used for Inspection of casting and welding. Visual, Magnetic

particle, Fluorescent particle, Ultrasonic, Radiography, Eddy current, Holography methods of

Inspection. 06 Hrs

Text Books:

1. “Manufacturing & Technology: Foundry Forming and Welding”, P.N.Rao 2nd Ed., Tata

McGraw Hill, 2003.

2. “Manufacturing Process-I”, Dr.K.Radhakrishna, Sapna Book House, 2nd Edition 2007.

Reference Books:

1. “Manufacturing Technology”, Serope Kalpakjain, Steuen.R.Sechmid, Pearson Education Asia,

5th Ed. 2006.

2. “Process and Materials of Manufacturing :, Roy A Lindberg, 4th Ed. Pearson Edu. 2006.



87

LESSON PLAN

SUB CODE : 06ME35 HRS/WEEK : 04

SUB : MANUFACTURING PROCESS-I TOTAL HRS : 52

NO.


1. Introduction: Concept of Manufacturing process, its importance.

2. Classification of Manufacturing processes Introduction to Casting process

&steps involved

3. Varieties of components produced by casting process.

4. Advantages & Limitations of casting process.

5. Patterns: Definition, functions, Materials used for pattern

6. Various pattern allowances and their importance. . Classification of patterns

7. Binder: Definition, Types of binder used in moulding sand.

8. Additives: Need, Types of additives used.

9. Sand Moulding : Types of base sand, requirement of base sand. Types of sand

moulds.

10. Types of sand moulds. Method used for sand moulding

11. Moulding sand mixture ingredients

12. Cores: Definition, Need, Types. Method of making cores, Binders used.

13. Concept of Gating & Risering. Principle involved. and types

14. Fettling and cleaning of castings. Basic steps involved Casting defects -causes,

features and remedies.

15. Moulding machines : Jolt type, squeeze type, Jolt & Squeeze type and Sand

slinger.

16. Special moulding Process

17. Study of important moulding processes Green sand, Core sand, Dry sand

18. Sweep mould, CO2 mould

19. Shell mould,Investment mould.

20. Metal moulds : Gravity die-casting, Pressure die casting

21. centrifugal casting,

22. Squeeze Casting

23. Slush casting,.

24. Thixocasting and continuous casting processes

25. Melting Furnaces: Classification of furnaces.

26. Constructional features &working principle of Gas fired pit furnace

27. Resistance furnace,

28. Electric Arc Furnace

29. Coreless Induction furnace

30. Cupola furnace.

31. Welding process: Definition, Principles, Classification, Application,

32. Advantages & limitations of welding.



88

33. Arc Welding : Principle, Metal Arc welding (MAW)

34. Flux Shielded Metal Arc Welding (FSMAW),

35. Inert Gas Welding (TIG & MIG) Submerged Arc Welding (SAW)

36. Atomic Hydrogen Welding processes. (AHW) Gas Welding : Principle, Oxy –

Acetylene welding Reaction in Gas welding

37. Flame characteristics, Gas torch construction & working. Forward and

backward welding

38. Special type of welding: Resistance welding - principles, Seam welding, Butt

welding, Spot welding and projection welding. Friction welding, Explosive

welding, Thermit welding, Laser welding and Electron beam welding

39. Spot welding and projection welding.

40. Friction welding

41. Explosive welding

42. Thermit welding

43. Laser welding and

44. Electron beam welding

45. Metallurgical aspect in welding : Structure of welds,

46. Formation of different zones during welding. Heat affected zone (HAZ).

47. Parameters affecting HAZ. Effect of carbon content on structure and properties

of steel.

48. Shrinkage in welds & Residual stresses

49. Concept of electrodes, Filler rod and fluxes

50. Welding defects – Detection causes & remedy.

51. Principles of soldering & brazing: Parameters involved & Mechanism

52. Principles of soldering & brazing: Mechanism

53. Different Types of Soldering Methods

54. Different Types of Brazing Methods

55. Inspection Methods – Methods used for Inspection of casting and welding

56. Visual

57. Magnetic particle

58. Fluorescent particle

59. Ultrasonic

60. Radiography

61. Eddy current

62. Holography methods of Inspection



89

QUESTION BANK Unit-1

1. Write the basic steps in the casting process.

2. Write the advantages of casting process.

3. Enumerate the applications of casting process.

4. Discuss the types of mould casting. (Expendable, permanent and semi-permanent mould).

5. Discuss the following methods of sand mould casting process: Bench moulding, floor

molding, and pit moulding.

6. Discuss the types of sand moulds.

7. Compare the different types of sand moulds.

8. Write the advantages of machine moulding.

9. With the help of diagrams, explain the following machine moulding methods: Squeeze

moulding, Jolt moulding and sand slingers.

10. Explain the function of a pattern in the casting process.

11. Write the requirements of a good pattern.

12. List the common pattern materials.

13. Write the advantages and limitations of different pattern materials.

14. Write the advantages of plastics as the pattern material.

15. Discuss the various pattern allowances.

16. With the help diagrams discuss the different types of patterns.

17. Why a colour scheme for patterns is needed? Illustrate a common colour scheme.

Unit -2

18. Name the various moulding materials used in foundry.

19. Name the essential constituents of moulding sand.

20. Write the advantages of silica sand as a moulding material.

21. What are the functions of a binder in moulding sand?

22. What is meant by sand “at temper”?

23. What are the functions of additives in moulding sand?

24. How the moulding sand is classified on the basis of clay matter it contains?

25. Discuss: natural sand, synthetic sand and chemically coated sand.

26. Discuss the various binders used in moulding sand.

27. Write on parting materials used in sand moulding.

28. Write about the following types of sands: Facing sands, Backing sand, system sand,

parting sand.

29. Discuss the various properties of moulding sand.

30. Discuss the essential qualities of a core. What is core sand?

31. What is a core dryer?

32. What is core venting?

33. Discuss synthetic resin core binders.

34. With the help of diagrams discuss the various types of cores used in sand mould casting.

35. Explain functions of splash core, skim bob, runner and runner extension.

36. What is the function of riser? Write the requirements of good riser.

37. What is directional solidification? Explain it with the help of a diagram.



90

38. Discuss the various types of risers and shapes of risers?

39. Sketch and compare: parting line gate, top gate and bottom gate.

40. Sketch the various sand mould casting defects. Give their causes and remedies.

Unit-3

41. Differentiate between Pressure die casting and permanent mould casting.

42. What are the limitations and applications of pressure die casting method.

43. Write the steps for making a casting by die casting process.

44. Compare cold-chamber and hot-chamber methods of die casting.

45. Name the various types of die-casting dies.

46. List the materials commonly used to make permanent moulds.

47. Define gating ratio. Distinguish between pressurized & non-pressurized gating.

48. Discuss the mould coatings.

49. List the steps needed for permanent mould casting operation.

50. List the advantages and limitations of permanent mould casting method.

51. Define the method of centrifugal casting.

52. With the help of diagrams discuss the following casting methods with the advantages,

disadvantages and applications:

a. True-centrifugal casting.

b. Semi-centrifugal casting

c. Centrifuge casting.

53. What is meant by “precision investment casting”/

54. With the help of diagrams, discuss the shell moulding method.

55. Discuss the various methods of cleaning the surfaces of castings

Unit-4

56. Explain the construction details of cupola furnace.

57. Explain the different stages of melting in cupola.

58. Explain the advantages and disadvantages of cupola furnace.

59. Give classification of melting furnaces.

60. Explain with a neat sketch oil fired crucible furnace.

61. Explain with a neat sketch i)direct electric arc furnace ii)Indirect electric arc furnace

iii)core type induction furnace iv)coreless type induction furnace v) resistance furnace

Unit-5 62. Define the welding process. Give the applications of the welding process.

63. Write the advantages and drawbacks of the welding process.

64. How the welding process may be classified?

65. Sketch the various types of welds used in making a joint.

66. Sketch and write on the various edge preparations used for welded joints.

67. Sketch and write on the various welding positions.

68. What is meant by fluxing? Why it is done? What are the properties which a good flux

should possess?

69. Define “electric are welding”.

70. List the advantages and disadvantages of D.C. arc welding over A.C. arc welding.

71. Write on the different types of electrodes used in arc welding.



91

72. What is purpose of coating on an arc welding electrode? Write the constituents of a

coating and write the function of each.

73. Write on coding of electric arc electrodes.

74. Explain principle of oxy acetylene welding.

75. Explain on flame characteristics & gas torch construction.

76. Explain the following electric arc welding processes with the help of neat sketches:

a) SMAW b) FCAW c) GTAW d) GMAW e) SAW

Unit-6

77. Explain the following electric arc welding processes

78. Name six types of resistance welding methods. For what kind of production is resistance

welding mainly employed?

79. With the help of a neat sketch explain the all types of resistance welding process.

80. How does seam welding differ from spot welding?

81. What are the special features of resistance projection welding?

82. With the help of neat sketches explain the following welding methods:

a. Ultra-sonic welding. b. Explosive welding

c. Electron-beam welding d. Laser-beam welding

e. Thermit welding. f. Friction welding

Unit -7

83. Discuss on metallurgical aspect of welding.

84. Discuss on residual stresses in welding.

85. Explain heat effected zone & formation of different zones during welding.

86. What is purpose of preheating a part to be welded?

87. Write briefly on “Testing and Inspection of welded joints”.

88. How do you classify the welding defects. List out the weld defects.

89. Explain concept of electrodes , filler rods & fluxes.

Unit -8

90. Write about the various fluxes used in brazing process.

91. Distinguish between brazing and braze welding.

92. Write about the filler materials used in brazing process.

93. Write a note on the various brazing methods.

94. Write the advantages and limitations brazing process.

95. Distinguish between soft solder and hard solder.

96. Write about the various soldering techniques used.

97. Give the reasons for weld defects and suggest the remedies.

98. Discuss the following methods of inspection and testing of castings:

i. Radio-graphic testing

ii. Magnetic particle testing

iii. Ultrasonic testing.

iv. Liquid penetrate testing



92



93

06 ME36A– COMPUTER AIDED MACHINE

DRAWING



94

SYLLABUS SUB CODE : 06 ME36A IA MARKS : 25



Introduction: Review of graphic interface of the software. Review of basic sketching commands

and navigational commands. Starting a new drawing sheet. Sheet sizes. Naming a drawing. Drawing

units, grid and snap. 2 Hrs

PART A

UNIT 1: Section of Solids: Sections of prisms, pyramids, cylinders, cones and tetrahedrons resting

only on their bases (No problems on axis inclinations, spheres and hollow solids)True shape of

sections .

Orthographic Views: Conversion of Pictorial views into orthographic projections of simple

machine parts with or without section. B.I.S conventions to be followed for the drawings. Hidden

line conventions. Precedence of lines. 8 Hrs

UNIT 2: Thread Forms: Thread terminology, sectional view of threads. ISO metric (Internal and

External), BSW (Internal and External), Square, Acme, Sellers thread and American Standard

Thread

Fasteners: Hexagonal headed bolt and nut with washer (Assembly), square headed bolt and nuts

with washer (Assembly), Simple assembly using stud bolts with nut and lock nut. Flanged nut,

Slotted nut and Wing nut, Taper and Split pin for locking. Counter sunk head screw, Grub screw

and Allen screw. 8 Hrs

PART B

UNIT 3: Keys: Parallel key, Taper key, Feather key, Gib-head key, Woodruff key.

Riveted Joints: Single and double riveted lap Joints, butt joints with single/ double cover straps

(Chain and zigzag, using snap head rivets), Cotter joint (socket and spigot joint), Knuckle joint (pin

joint) for two rods. 8 Hrs

UNIT 4: Couplings: Split muff coupling, Protected type flange coupling, pin (bush) type flexible

coupling, Oldham’s coupling, Universal coupling (Hooks’ joint). 8 Hrs



95

PART C

Assembly Drawings

(Part Drawings to be given)

1. Plummer block (Pedestal Bearing)

2. Petrol Engine piston

3. IC Engine connecting rod

4. Screw Jack (Bottle type)

5. Tailstock of lathe

6. Machine Vice

7. Tool head of a Shaper 18 Hrs

Text Books:

1.‘A Primer on Computer Aided Machine Draiwng –2007’, Published by VTU, Belgaum.

2.‘Machine Drawing’, Sri. N.D. Bhat & V.M. Panchal

3.‘Machine Drawing’, N. Siddeshwar, P. Kanniah, v.V.S. Sastri, Tata McGraw Hill, 2006

Reference Book: 1. ‘A Textbook of Computer Aided Machine drawing’, S.Trymbaka Murthy, CBS Publishers,

New Delhi, 2007

2. ‘Machine Drawing’ , Sri. K.R. Gopal Krishna, Subhas Publications, Bangalore

3. ‘Machine drawing with AutoCAD’, Goutam pohit & Goutam Ghosh, 1st Indian print, Pearson

Education, 2005

4. ‘AutoCAD, 2006, for Engineers and Designers’, Sham Tickoo, Dream Tech, 2005

Note:

Internal Assessment: 25 marks

All sheets should be drawn in the class using software. Sheet sizes should be A3 /A4. All sheets

must be submitted at the end of the class by taking printouts.

Scheme of Examination:

Two questions to be set from each part: A, B & C

Student has to answer one question from part A and part B for 20 marks each, and one question

from part C for 60 marks.

i.e. Part A 1 x 20 = 20 marks

Part B 1 x 20 = 20 marks

Part C 1 x 60 = 60 marks

Total = 100 marks



96

LESSON PLAN

SUB CODE : 06ME36A HRS/WEEK : 04

SUB : COMPUTER AIDED MACHINE DRAWING TOTAL HRS : 52

NO.


01 Introduction: Review of graphic interface of the software. Review of basic

sketching commands and navigational commands.

02 Starting a new drawing sheet. Sheet sizes. Naming a drawing. Drawing units, grid

and snap.

03 UNIT 1: Section of Solids: Section of Regular Prisms and their true shapes.

04 Section of Regular Pyramids and their true shapes.

05 Continued

06 Section of tetrahedrons and their true shapes.

07 Section of Regular cone and Cylinder and true shapes

08 Orthographic Views: Conversion of Pictorial views into orthographic projections

of simple machine parts with section

09 Continued

10 Conversion of Pictorial views into orthographic projections of simple machine parts

without section. B.I.S conventions to be followed for the drawings.

11 Continued

12 Hidden line conventions.

13 Precedence of lines

14 UNIT 2: Thread Forms: Thread terminology, sectional view of threads. ISO

metric (Internal and External)

15 BSW (Internal and External)

16 Continued

17 Square, Acme, Sellers thread

18 American Standard Thread

19 Fasteners: Hexagonal headed bolt and nut with washer (Assembly),

20 Square headed bolt and nuts with washer (Assembly),

21 Simple assembly using stud bolts with nut and lock nut.

22 Flanged nut, Slotted nut and Wing nut,

23 Taper and Split pin for locking.

24 Continued

25 Counter sunk head screw, Grub screw and Allen screw.

26 UNIT 3: Keys: Parallel key, Taper key

27 Feather key, Woodruff key

28 Gib-head key

29 Riveted Joints: Single and double riveted lap Joints,

30 Butt joints with single cover straps (Chain and zigzag, using snap head rivets),

31 Continued

32 Butt joints with double cover straps (Chain and zigzag, using snap head rivets)

33 Continued



97

34 Cotter joint (socket and spigot joint),

35 Continued

36 Knuckle joint (pin joint) for two rods.

37 UNIT 4: Couplings: Split muff coupling

38 Continued

39 Protected type flange coupling

40 Continued

41 Pin (bush) type flexible coupling

42 Continued

43 Oldham’s coupling,

44 Continued

45 Universal coupling (Hooks’ joint).

46 Continued

47 Plummer block (Pedestal Bearing)

48 Continued

49 Petrol Engine piston

50 Continued

51 IC Engine connecting rod

52 Continued

53 Screw Jack (Bottle type)

54 Continued

55 Tailstock of lathe

56 Continued

57 Machine Vice

58 Continued

59 Tool head of a Shaper

60 Continued

61 Revision

62 Revision



98

QUESTION BANK

SECTIONS OF SOLIDS

1) A cube of 30 mm edges rests with one of its square faces on HP such that one of its vertical

square faces is inclined at 300 to VP. A section plane perpendicular to VP and inclined at 60

0

to HP passes through a point on the vertical axis 5mm below its top end. Draw its sectional top

view, front view and the true shape of section.

2) A cube of 40 mm edges rests with one of its faces on HP such that one of its vertical square

faces is inclined at 300 to VP. A section plane perpendicular to HP and inclined at 60

0 to VP

passes through the cube such a square face making 300

with VP is cut into two halves. Draw

the sectional front view and the true shape of section.

3) An equilateral triangular prism of side of base 50 mm and axis 70 mm long rests with its base

on HP such that two of its rectangular faces being inclined to VP at 450 and 75

0 . If a section

plane, inclined at 600 to HP cuts the axis of the prism at a height of 50 mm, draw the sectional

top view, front view and true shape of section.

4) A square prism, side of square faces 50 mm and height 80 mm rests with its base on HP such

with two of its vertical faces equally inclined to VP. A section perpendicular to VP & inclined

to HP at 600 cuts the prism so as to pass through a point on the axis 10 mm below its top end.

Draw the sectional top view & the auxiliary view showing the true shape of section. Add the

profile view showing the sectioned surface.

5) A square pyramid of side of base 40 mm and height 80 mm stands on its base with the sides of

the base inclined at 450 to VP. It is cut by a plane equally inclined to both HP and VP passing

through the midpoint of its axis. Draw the sectional views and the true shape of section.

6) A right regular hexagonal pyramid with edge of base 40 mm and height 100 mm stands with

its base on HP with two of its base edges parallel to VP. It is cut by a plane passing through a

point on the axis 50 mm from the base and inclined at 200

to the horizontal plane &

perpendicular to the profile plane. Project the sectional view and the true shape of section.

7) A cylinder base 50 mm diameter and axis 75mm has a square hole of 25 mm cut through it so

that the axis of the hole coincides with that of the cylinder. The faces of the hole are equally

inclined to VP. The cylinder is lying with its base on ground . It is cut by two section planes

which are perpendicular to VP and intersect each other at the top end of the axis. The cutting

planes cut the cylinder on opposite sides of the axis and are inclined at 300 and 45

0 respectively

to it. Draw the sectional top view and auxiliary top views on the planes parallel to the two

section planes.

8) A cylinder 60 mm diameter and 80 mm long stands with its circular base on HP. A section

perpendicular to VP & inclined to HP at 600 cuts the axis at a point 28 mm below its top end.

Draw the sectional top & right views & the true shape of section.

9) A cone diameter of base 60 mm & axis 70 mm stands with its base on HP. A section plane

perpendicular to HP and parallel to VP cuts the cone at a distance of 10 mm from the axis. The

section plane is passed in front of the axis of the cone. Draw the sectional front view and the

top view. Name the true shape of the curve.



99

10.A right circular cone of base 50 mm diameter & height 75 mm stands with its base on HP.

A cutting plane perpendicular to HP and inclined at 450 to VP cuts the cone at a distance of 5

mm from the axis of the cone & in front of it. Draw the apparent and true shape of sections.

CONVERSION OF PICTORIAL VIEWS INTO ORTHOGRAPHIC PROJECTIONS with

SECTIONS

Pictorial view of a dove tail stock is shown in Fig above draw to scale 1:1 the follwing views of the

Dove Tail Stock

i) Sectional views from the front looking in the direction F

ii) View from above looking in the direction T

iii) Right view looking in the directions R

Indicate all the dimensions on the views. Do not show the invisible edges on the sectional view

Print the title and scale of the drawing name the views



100

The Pictorial view of a machine part

is shown in Fig Draw the following

views

i) Sectional front view along the axis

of symmetry

ii) Top view

iii) Right View

State the convenitions employed in

the sectional view

Indicate the section plane on the

appropriate view

Show the invisible edges in the top

and right views

Distribute the dimensions judiciously

on all the three views

All holes are through holoes

The Pictorial view of a machine part is shown in

Fig Draw the following views

i) Front view looking in the direction F

ii) Sectional left view for the sectional plane SS

looking in the direction L

iii) Top View

State the convenitions employed in the sectional

view

The Picture view of a machine part is shown in

Fig Draw the following views

i) Front view taking section AA along the axis

of symmetry

ii) Top view

iii) Right View



101

THREAD FORMS, BOLTS, NUTS AND SCREWS, JOINTS & COUPLINGS, BEARINGS 1. Draw the profile of ISO screw thread of pitch 40 mm. Indicate all the proportions &

dimensions.

2. Sketch neatly any three types of profiles of V-thread of pitch 50 mm. Indicate the angle &

depth of the thread.

3. Draw the dimensional sketches of the following:

a) Square thread

b) Trapezoidal thread

c) Knuckle thread

4. Draw three views of hexagonal nut for a 20 mm diameter bolt. Indicate the empirical

proportions & the calculated dimensions.

5. Draw the three views of the square headed bolt with a hexagonal nut. Show the bolt head and

the nut across corners in the front view. The nut is screwed on the bolt. The bolt is 20 mm

diameter, 120 mm long with a thread length of 50 mm. The end of the bolt is chamfered to 450.

6. Draw neat-dimensioned sketches of any three types of the nuts.

7. Show the method of locking a nut by a) set screw, b) split pin, c) Washer.

8. Sketch a countersunk screw & any two types of grub screws.

9. Sketch the sectional front view, top view and right view of a cotter joint with sleeve. Show all

the dimensions.

10. Sketch the sectional front view, top view and right view of a knuckle joint to connect two

shafts 25 mm diameter. Show all the dimensions.

11. Sketch the sectional front view & side view of a flanged coupling to connect two shafts of 25

mm diameter. Show all the dimensions.

12. Sketch the front view and right view of a Universal coupling. Show all the dimensions.

13. Draw to 1:1 scale the top and front views of a single riveted lap joint. The thickness of the

plates is 9mm show atleast three rivets indicate all the dimensions. Use snap head revets.

14. Draw to 1:1 scale The top and sectional front views of a double riveted lap joint with chain

and Zig Zag riveting the thickness of the plates is 9 mm Show atleast three rivets in each row

indicate the dimensions use snap head rivets



102

ASSEMBLY DRAWINGS

Views of the parts of a PLUMMER BLOCK are shown in the figure below. Draw to 1:1 scale the

following views of the bearing.

a) Front view showing right half in section.

b) Top view with right half in section.

c) Right view.

The figure1 below shows the details of a PETROL ENGINE PISTON. Assemble all the parts and

draw the following views of the assembled piston with its axis horizontal to 2:1 scale.

a) Front view

b) Top view showing one half in section

c) End view in section, the section plane is passed along AA.

Figure below shows the different parts of a CONNECTING ROD. Assemble all the parts and draw

the following views of the assembly.

a) Front view in half section

b) Top view.

c) View looking from the big end.

Figure below shows the different parts of a SCREW JACK. Assemble all the parts and draw the

following views of the assembly when the top face of the load-bearing cup is raised to a height of

350 mm above the bearing surface of the body.

a) Front view in half section

b) Top view



103



104



105



106



107



108



109



110

06MEL37A

METALLOGRAPHY & MATERIAL TESTING

LABORATORY



111

SYLLABUS

Sub Code: 06MEL37A IA Marks:25

Hrs /week : 03 Exam Hours: 03

Total Lecture Hrs: 42

PART A

1. Preparation of Specimen for metallographic examination of different engineering materials.

Identification of microstructures of plain carbon steel, tool steel, gray C.I. SG iron, brass,

bronze & Composites

2. Heat treatment: Annealing, normalizing, hardening and tempering of steel, hardness studies

of heat treated samples.

3. To study the wear characteristics of ferrous, non ferrous and composite materials for

different parameters.

4. Non destructive test experiments like,

a. Ultrasonic flaw detection

b. Magnetic crack detection

c. Dye penetration testing to study the defects pf casted and welded specimens

PART B 1. Tensile shear and compression tests of metallic and non metallic specimens using a

universal testing machine

2. Torsion tests

3. Bending test on metallic and non nonmetallic specimens

4. Izod and Charpy tests on MS specimen

5. Brinell, Rockwell and Vicker’s Hardness test

6. Fatigue test

Scheme of examination:

One question from Part-A 20 Marks

One question from Part-B 20 Marks

Viva Voce: 10 Marks

Total Marks 50 Marks



112

06MEL38A - FOUNDRY & FORGING LAB



113

SYLLABUS

Sub Code: 06MEL38A IA Marks:25

Hrs /week : 03 Exam Hours: 03

Total Lecture Hrs: 42

PART A

1.Testing of moulding sand and core sand: Preparation of sand specimen and conduction of the

following tests:

1. Compression, shear and tensile tests on universal tests on universal sand testing machine

2. Permeability test

3. Core Hardness & Mould hardness test

4. Grain Fineness number test (Sieve Analysis Test)

5. Clay content test

6. Moisture content test

PART B

2. Foundry Practice

1. Use of Foundry tools and other equipments

2. Preparation of moulds using two moulding boxes using patterns or without patterns (Spilt

pattern, match plate pattern and core boxes)

3. Preparation of one casting (Aluminum or cast iron-Demonstration only)

PART C

3. Forging Operations 1. Preparation of three forged models involving upsetting, drawing and bending operations

2. Out of these three models, at least one model is to be prepared by using power hammer

Scheme of examination:

One question is to be set from Part-A 10 Marks

One question is to be set from either Part B of Part-C 30 Marks

Viva Voce: 10 Marks

Total Marks 50 Marks

06 mat31 – engineering mathematics iii - mvjce mat31 – engineering mathematics iii . ... solve...

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