Shivaji University, Kolhapur - :: Welcome :: Sanjay … ·  · 2018-02-157 5. Fourier Series...

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1 Shivaji University, Kolhapur S.E. Mechanical Engineering (Semester III) Sr. No. Name Of Subject Teaching Scheme Examination Scheme L T P TOTAL PAPER TW OE POE TOTAL 1 Engineering Mathematics-III 3 1 - 4 100 25 - - 125 2 Electrical Technology 3 - 2 5 100 25 - - 125 3 Applied Thermodynamics 3 - 2 5 100 25 - 25 150 4 Metallurgy 3 - 2 5 100 25 25 - 150 5 Fluid Mechanics 3 - 2 5 100 25 - 25 150 6 Machine Drawing - - 2 2 - 25 - - 25 7 Computer Graphics - - 2 2 - 25 - - 25 8 Computer Programming using C++ - - 2 1 - 25 - - 25 9 Workshop Practice III - - 2 2 25 - - 25 TOTAL 15 1 14 30 500 225 25 50 800

Transcript of Shivaji University, Kolhapur - :: Welcome :: Sanjay … ·  · 2018-02-157 5. Fourier Series...

Page 1: Shivaji University, Kolhapur - :: Welcome :: Sanjay … ·  · 2018-02-157 5. Fourier Series Definition, ... 2 To find Fourier Series Expansion of f(x) in (0, 𝜋) 3 To find Fourier

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Shivaji University, Kolhapur S.E. Mechanical Engineering (Semester – III)

Sr.

No. Name Of Subject Teaching Scheme Examination Scheme

L T P TOTAL PAPER TW OE POE TOTAL

1 Engineering Mathematics-III 3 1 - 4 100 25 - - 125

2 Electrical Technology 3 - 2 5 100 25 - - 125

3 Applied Thermodynamics 3 - 2 5 100 25 - 25 150

4 Metallurgy 3 - 2 5 100 25 25 - 150

5 Fluid Mechanics 3 - 2 5 100 25 - 25 150

6 Machine Drawing - - 2 2 - 25 - - 25

7 Computer Graphics - - 2 2 - 25 - - 25

8 Computer Programming using

C++ - - 2 1 - 25 - - 25

9 Workshop Practice III - - 2 2 25 - - 25

TOTAL 15 1 14 30 500 225 25 50 800

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Course Plan

Course Engineering Mathematics III Course Code

Examination

Scheme

Theory Term Work POE Total

Max. Marks 100 25 -- 125

Contact

Hours/ week

3 1 -- 4

Prepared by Mr.Powar S M Date 15/6/2015

Prerequisites Basic knowledge of derivative & integration

Basic concepts: periodic function ,even & odd function

Basic Knowledge of trigonometric & hyperbolic function

Basic knowledge of vectors

Course Outcomes

At the end of the course the students should be able to:

CO1 Solves linear differential equation with constant coefficient

CO2 Solve Linear Differential Equations with constant coefficients for solving

problems in Mechanical engineering fields

CO3 Find differentiation of Vectors, Divergence, Gradient, Curl

CO4 Find Laplace and inverse Laplace transform.

CO5 Represent periodic function as a Fourier series

CO6 To solve partial differential equation by using variable separable form

Mapping of COs with POs

POs

COs

A b c d E f G h i j K l

CO1 √ √ √ √ √ √

CO2 √ √ √ √ √

CO3 √ √ √ √ √ √

CO4 √ √ √ √ √

CO5 √ √ √ √

CO6 √ √ √ √ √

Course Contents

Unit

No.

Title No. of

Hours

Section I

1. Linear Differential Equations (LDE)

Linear Differential Equations with constant coefficients Definition,

Complementary function and Particular integral (without method of variation

7

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of Parameters), Homogeneous Linear differential equations

2. Applications of Linear Differential Equations with Constant Coefficients

The Whirling of Shafts. Mass – spring Mechanical system. Free oscillations

Damped Oscillations. Forced oscillations without damping

7

3. Vector Differential Calculus

Differentiation of vectors, Gradient of scalar point function and Directional

derivative, Divergence of vector point function and Solenoid vector fields.

Curl of a vector point function and Irrotational

6

Section II

4. Laplace Transform

Definition, Transforms of elementary functions, Properties of Laplace

transform. Transforms of derivatives and Integral. Inverse Laplace transforms

formulae. Inverse Laplace transforms by using partial fractions and

Convolution theorem. Solution of Linear differential equation with constants

coefficients by Laplace transforms method.

7

5. Fourier Series

Definition, Euler’s Formulae, Dirchilt’s Condition. Functions having

points of discontinuity, Change of interval, Expansion of odd and even

periodic functions, Half range series

6

6. Application of Partial Differential Equations

The Wave Equation.

The method of separation of variables. Fourier Series solution of wave

equation. One dimensional heat flow equation. The method of separation of

variables.Fourier Series solution of heat equation. The Laplace equation in

two dimensional heat flow (Steady State). Solutions of Laplace equations by

the Gauss – Siedel iterative method

7

Reference Books:

Sr.

No.

Title of Book Author Publisher/Edition

1 Higher Engineering Mathematics Dr. B. S. Grewal Khanna Publishers,

Delhi.

2 A text book of Applied

Mathematics, Vol.-I,II,III

P. N. Wartikar& J. N.

Wartikar

Pune

VidyarthiGrihaPrakashan,

Pune.

3 Advanced Engineering

Mathematics

Erwin Kreyszig Wiley India Pvt. Ltd.

4 Advanced Engineering

Mathematics

H. K. Das S. Chand Publication

5 Mathematical methods of Science

and Engineering

Kanti B. Datta Cengage Learning

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6 Engineering Mathematics V. Sundaram Vikas Publication

7 Advance Engineering Mathematics Merle C. Potter Oxford University Press

Scheme of Marks

Section Unit No. Title Marks

I 1 Linear Differential Equations (LDE) 22

2 Applications of Linear Differential Equations with

Constant Coefficients

22

3 Vector Differential Calculus 22

II 4 Laplace Transform 22

5 Fourier Series 22

6 Application of Partial Differential Equations 22

Course Unitization

Section

Unit Course

Outcomes

No. of Questions in

No. Title CAT-I CAT-II

I 1 Linear Differential Equations CO1 Q.1

(15 Marks)

2 Applications of Linear Differential

Equations with Constant Coefficients

CO2 Q.2

(15 Marks)

3 Vector Differential Calculus CO3 Q.1

(15 Marks)

II 1 Laplace Transform CO4 Q.2

(15 Marks)

2 Fourier Series CO5

3 Application of Partial Differential

Equations

CO6

Unit wise Lesson Plan

Section I

Unit

No

1 Unit Title Linear Differential Equations (LDE)

Planned

Hrs.

7

Unit Outcomes

At the end of this unit the students should be able to:

UO1 To solve Linear differential equation CO1

UO2 To solve homogeneous linear differential equation

Lesson schedule

Class Details to be covered

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No.

1 Introduction and Definition

2 To find C.F. for Real & Complex Roots

3 To find P.I. when X= ,sin ,cosaxe ax ax

4 To find P.I. when X=mx

5 To find P.I. when X= ,axe V xV

6 Transformation of Homogeneous LDE to LDE with constant coefficient & to solve

7 Examples

Review Questions

Q1 Solve 4 3 24 8 8 4 0D D D D y

UO1

Q2 Solve 2 2 1 1xD D y e

Q 3 Solve

22

5( 4 4)

xeD D y

x

Q4 Solve

23 2

23 sin(log )

d y d yx x xy x

dx dx

UO2

Q5 Solve 4 23 4 48sin cosD D y x x

Q6 Solve

22 2

23 5 sin(log )

d y dyx x y x x

dx dx

Q7 Solve

3 22 2

3 23 log

d y d y dyx x x x

dx dx dx

Q8 Solve 2 3 3 2 22 1x D x D x D x y

Unit

No

2 Unit Title Applications of Linear Differential Equations

with Constant Coefficients

Planned

Hrs.

07

Unit Outcomes

At the end of this unit the students should be able to:

UO1 To Solve Linear Differential Equations with Constant Coefficients in

Mechanical Engineering fields

CO2

Lesson schedule

Class

No.

Details to be covered

1 The Whirling of Shafts

2 Examples on the Whirling of Shafts

3 Mass – spring Mechanical system

Free oscillations

4 Examples on free oscillations

5 Damped Oscillations

6 Examples on Damped Oscillations

7 Forced oscillations without damping & examples

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Review Questions

Q1 The Whirling speed of shaft of length l is given by

44

40

d ya y

dx where

24 W

agEI

and y is displacement at a distance x from one end. If the ends of

the shaft are constrained in long bearings so that the slope at each end is zero.

Show that shaft will whirl when cos cosh 1al al

UO1

Q2 The differential equation of simple pendulum is

22

0 02sin

d xW x F nt

dt .If

initially x=0 , 0dx

dt .Determine the motion .What happens if 0W n

Q3 A body executes damped forced vibrations given by 2

2 2 2

22 cos

d x dxW x k a pt if k W

dt dt Prove that as t tends to ∞

2

2 2 2 2

cos

4

a pt bx

w p k p

where 2 2

2tan

kpb

W p

Q4 A spring fixed at the upper end supports a weight of 981 gm. at its lower end

.the sprig stretches 0.5cm. under a load 10gm. And the resistance (in gm. Wt.)

to the motion of the weight is numerically equal to1/10 of the speed of the

weight in cm./sec. The weight is pulled down 0.25cm. bellow its equilibrium

position and then released .Find the expression for the distance of weight from

its equilibrium position at time t during its first upward motion. Also find the

time it takes the damping factor to drop to 1/10 of its initial value

Unit

No

3 Unit Title Vector Differential Calculus Planned

Hrs.

6

Unit Outcomes

At the end of this unit the students should be able to:

UO1 To Solve Gradient of scalar point function, Divergence & Curl of vector point

function

CO3

UO2 To verify vector field is irrotationl or solenoidal

Lesson schedule

Class

No.

Details to be covered

1 Introduction and Definition

2 Vector Differential Operator Del

3 To find Gradient of scalar point function & Directional Derivative

4 Divergence of Vector point function

5 Curl of Vector point function

6 Irrotaional&Solenoidal

Review Questions

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Q1 Find the directional derivative of 2 2 2x y y z z x at (2,2,2) in the normal

to the surface 2 24 2 2x y z at (2,-1,3)

UO1

.

Q2 Prove that

3

1 r

r r

where r = xi+yj+zk

Q3 Find the directional derivative of 2 24x yz xz xyz at (1, 2, 3) in the

direction of 2i+j+k

Q4 Calculate divergence and curl of the vector

2 2 2F x yz i y zx j z xy k

Q5 Show that ( ) ( ) ( )f y z i z x j x y k is solenoidal

Q6 Show that 2 2 2F x yz i y zx j z xy k is irrotational and find its

scalar potational.

Q7 If 2sin sin sin 2 cosF y z x i x z yz j xy z y k then prove that it

is irrotational& hence find its scalar potential

UO2

Section II

Unit

No

4 Unit Title Laplace Transform Planned

Hrs.

7

Unit Outcomes

At the end of this unit the students should be able to:

UO1 To solve Laplace Transform & Inverse Laplace Transform CO4

UO2 Apply Laplace Transform to solve Linear Differential Equation

Lesson schedule

Class

No.

Details to be covered

1 Introduction and Definition

2 Laplace Transform of some elementary functions

3 Properties of Laplace Transform

4 Inverse Laplace Transform

5 Inverse Laplace Transform by using Partial Fraction & Convolution Theorem

6 Solution of LDE with constant coefficient by Laplace Transform

7 Examples

Review Questions

Q1 Find the Laplace transform of

2 sin3te t

t

UO1

Q2 Find the Laplace transform of periodic function

( ) , 0 , ( ) ( )kt

f t t T f t T f tT

Q3

Evaluate 3

0

coste t t dt

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Q4 Find

1

2

3 7

2 3

sL

s s

Q5 Using Laplace transform find the solution of initial value problem

21

29 18 ; (0) 0, (0) 0

d yy t y y

dt

UO2

Unit

No

5 Unit Title Fourier Series Planned

Hrs.

6

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Fourier Expansion of f(x) in (0,2𝜋) & (-π,π) CO5

UO2 Fourier Expansion of f(x) in (0,2l) & (-l,l)

UO3 Half range sine & cosine series of f(x)

Lesson schedule

Class

No.

Details to be covered

1 Introduction and Definition Fourier Series

2 To find Fourier Series Expansion of f(x) in (0,2𝜋)

3 To find Fourier Series Expansion of f(x) in (-π,π)

4 To obtain Fourier Series Expansion of f(x) in (0,2l) & (-l,l)

5 To obtain Fourier Expansion of Even & Odd function

6 Half range Sine & Cosine series

Review Questions

Q1

Obtain Fourier series for ;0

( ); 2

a xf x

a x

UO1 Q2 Find the Fourier series for the function𝑓 𝑥 = 𝑥 − 𝑥2 in (-π,π) and hence

deduce that 𝜋2

12=1

12−

1

22+

1

32−

1

42+⋯

Q3 Find the Fourier series for the function 𝑓 𝑥 = 1− 𝐶𝑂𝑆𝑥 in (0,2π) and

hence deduce that ,1

2=

1

(4𝑛2−1)∞𝑛=1

Q4 Find the Fourier series for the function𝑓 𝑥 = 𝑥 +1

4𝑥2 in (-π,π) and hence

deduce that 𝜋2

12=1

12−

1

22+

1

32−

1

42+⋯

Q5 If

2

;0 1( )

;1 2

x

x

xf x

x

with period 2. Show that

2

1

4 1( ) cos 2 1

2 2 1n

f x n xn

UO2

Q6 Find the Fourier series for the function𝑓 𝑥 = 𝑎2 − 𝑥2 in (-a,a)

Q7 Obtain half range sine series for f(x) in (0,2) where,

f(x)= x 0 ≤ x ≤ 1

=2-x 1 ≤ x ≤ 2

UO3

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Unit

No

6 Unit Title Application of Partial Differential Equations Planned

Hrs.

07

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Solve Partial Differential Equations related to Mechanical Engineering CO6

Lesson schedule

Class

No.

Details to be covered

1 The Wave Equation, The method of separation of variables

2 Fourier Series solution of wave equation

3 One dimensional heat flow equation, The method of separation of variables

4 Fourier Series solution of heat equation

5 The Laplace equation in two dimensional heat flow (Steady State)

6 Solutions of Laplace equations by the Gauss – Siedel iterative method

7 Examples

Review Questions

Q1 A string is stretched and fastened to two points l apart. Motion is started by

displacing the string in the form sinx

y al

,from which it is released

at time t=0.Show that the displacement of any point at distance x from one end

at time t is given by , sin cos

x cty x t a

l l

UO1

Q2 Solve

2

2

u uk

t x

for the conduction of heat along a rod without radiation

sub. To following conditions

1. u is not ∞ as t →∞

2. 0 0,

ufor x x l

t

3. u=lx-x2 for t=0 between x=0, x=l

Q3 Solve the wave equation

2 22

2 2

u uc

t x

under the condition u(0,t)=0,u(l,t)=0

for all t ,u(x,0)=f(x) and 0

( ),t

ug x o x l

t

Q4 Solve

2

2

u u

t x

for the conduction u(x,0)=3sinnπx, u(0,t)=0 and u(1,t)=0

Where 0 < x < 1, t>0

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Model Question Paper

Course Title : Engg. Mathematics-III Max.

Marks

Duration 3 hours 100

Instructions:

All questions are compulsory

Figures to the right indicates full marks

Use of non-programmable calculator is allowed

Section-I

1 Attempt any FOUR 20m

a Solve

22

5( 4 4)

xeD D y

x

5m

b Solve

23 2

23 sin(log )

d y dyx x xy x

dx dx

5m

c Solve 2 3 21 3 1D D y x x

5m

d Solve

23 2 22 5 6 3xD D D y e

5m

e Solve

2 2 3( 4 3) cos

2D D y x

5m

2 Attempt any TWO 15m

a The Whirling speed of shaft of length l is given by

44

40

d ya y

dx where

24 W

agEI

and y is displacement at a distance x from one end.If the

ends of the shaft are constrained in long bearings so that the slope at

each end is zero.Show that shaft will whirl when cos cosh 1al al

8m

b The differential equation of simple pendulum is

22

0 02sin

d xW x F nt

dt

.If initially x=0 , 0dx

dt .Determine the motion .What happens if

0W n

7m

c A body executes damped forced vibrations given by 2

2 2 2

22 cos

d x dxW x k a pt if k W

dt dt Prove that as t tends to ∞

2

2 2 2 2

cos

4

a pt bx

w p k p

where 2 2

2tan

kpb

W p

7m

3 Attempt any THREE 15m

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a Find the directional derivative of xy yz xz at (1, 2, 3) in the

direction of 2i+j+k

5m

b Calculate divergence and curl of the vector

2 22F x yz i xyj y xy k

5m

c Show that 2 2 23 3 3 3 3 3F x yz i y zx j z xy k is irrotational

and find its scalar potational

5m

d Prove that

3

1 r

r r

where r = xi+yj+zk

5m

Section-II

4 Attempt any FOUR 20m

a Find the Laplace transform of

cos cosat bt

t

5m

b Find

21 2 4

1 2 3

sL

s s s

5m

c

Find

1

22

1

3L

s s

by Convolution Theorem

5m

d Using Laplace transform find the solution of initial value problem

3 21

3 22 2 0; (0) 0, (0) 0, (0) 6lld y d y dy

y y y ydt dt dt

5m

e Find 4 2L t H t 5m

5 Attempt any THREE 15m

a Obtain Fourier series for

sin ;0( )

0 ; 2

x xf x

x

5m

b

Obtain Fourier series for

2

21

1 ; 0

( )

;0

x

x

x

f x

x

5m

c Find the Fourier series for the function𝑓 𝑥 = 𝑎2 − 𝑥2 in (-a,a) 5m

d Obtain Half range cosine series for 2( )f x x x in 0 1x 5m

6 Attempt any ONE 15m

a A string is stretched and fastened to two points l apart. Motion is started

by displacing the string in the form sinx

y al

,from which it is

released at time t=0.Show that the displacement of any point at distance

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x from one end at time t is given by , sin cos

x cty x t a

l l

b Solve

2

2

u uk

t x

for the conduction of heat along a rod without

radiation sub. To following conditions

1. u is not ∞ as t →∞

2.

0 0,u

for x x lt

3. u=lx-x

2 for t=0 between x=0, x=l

Assignments

Assignment No. 1

Assignment

Title

Linear Differential Equations (LDE)

CO1

Batch I 1.

4

4cos cosh

d yy x x

dx

2. 2( 2 1) logxD D y e x

3. 4

44 sinh

d yy x x

dx

4. 3 2

2 2

3 23 log

d y d y dyx x x x

dx dx dx

5. 2 2 2( 2) 8( sin 2 )xD y e x x

6. 5( ) 5 xD D y e

7. 2 2 3

( 4 3) cos2

D D y x

Batch II 1. 5( ) 5 xD D y e

2. 2 2 3

( 4 3) cos2

D D y x

3. 2

2

22 log

d y dyx x y x x

dx dx

4. 3

2

34 2cosh 2

d y dyx

dx dx

5. 2

2 3 2( 1) 1 0D D D y

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6. 2

3 2

24 4 cos 2xd y dy

y x e xdx dx

Batch III 1.

2 1 1( 3 2) cos

e x xD D y

e e

2. 2 2( ) tanD a y ax

3. 3 2

2 2

3 23 log

d y d y dyx x x x

dx dx dx

4. 2 2 3

( 4 3) cos2

D D y x

5. 2

3 2

24 4 cos 2xd y dy

y x e xdx dx

6. 2

2

2 2

13

(1 )

d y dyx x y

dx dx x

7 .3 2

2

3 22

d y d yx x

dx dx

Assignment No. 2

Assignment

Title

Applications of Linear Differential Equations with Constant

Coefficients

CO2

Batch I 1. The differential equation of simple pendulum is

22

0 02sin

d xW x F nt

dt .If

initially x=0 , 0dx

dt .Determine the motion .What happens if 0W n

2. The Whirling speed of shaft of length l is given by 4

4

40

d ya y

dx where

24 W

agEI

and y is displacement at a distance x from one end.If the ends

of the shaft are constrained in long bearings so that the slope at each end is

zero. Show that shaft will whirl when cos cosh 1al al

Batch II 1. A body executes damped forced vibrations given by 2

2 2 2

22 cos

d x dxW x k a pt if k W

dt dt Prove that as t tends to ∞

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2

2 2 2 2

cos

4

a pt bx

w p k p

where 2 2

2tan

kpb

W p

2. A spring fixed at the upper end supports a weight of 981 gm. at its lower end

.the sprig stretches 0.5cm. under a load 10gm. And the resistance (in gm. Wt.)

to the motion of the weight is numerically equal to1/10 of the speed of the

weight in cm./sec. The weight is pulled down 0.25cm. bellow its equilibrium

position and then released .Find the expression for the distance of weight

from its equilibrium position at time t during its first upward motion. Also

find the time it takes the damping factor to drop to 1/10 of its initial value

Batch III 1. The differential equation of the displacement y of whirling shaft when

the weight of the shaft is taken in to account is 4 2

4

d y WEI y W

dx g

taking the shaft of length 2l with the origin at the center and the short

bearing at both end.Show that the maximum deflection of the shaft is

2sec sec 2

2

ghal al

2. A sprig which scratches by an amount e under a force 2m e is

suspended from support O and has mass m at the lower end. Initially

the mass is at rest in its equilibrium position at a point A bellow O .A

vertical oscillation is now given to the support O such that at any time

(t>0) its displacement bellow its initial position is sina nt .Show that

the displacement x of the mass bellow a is given by 2

2 2

2sin

d xx a nt

dt

Assignment No. 3

Assignment

Title

Vector Differential Calculus CO3

Batch I 1) A vector field is given by 2 2 2 2( ) ( )A x xy i y x y j . Show that the field

is irrotational and find the scalar potential.

2) Show that the gradient field describing a motion is irrotational.

3) Find the unit vector normal to the surface 3 2 4xy z at (-1, -1, 2)

4) Find ( )div at (1, 1, 1) where 2 3xy z and 2 2 2xy zy z x

5) If r xi yj zk and a andb are constant vectors Prove that,

5 3

. . .1. . 3

a r b r a ra b

r r r

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Batch II 1) Prove that, for every field V , div curl V = 0

2) Find the angle between two surfaces 2 3x y z and 2log 4 0x z y at

1,2,1 .

3) Prove that 2

2

1(log )r

r

4) If a is a constant vector and r xi yj zk Prove that curl ( a r ) =2 a .

5) Find the directional derivative of 2

V , where 2 2 2V xy i zy j xz k at the

point (2, 0, 3) in the direction of the outward normal surface to the sphere

2 2 2 14x y z at the point (3, 2, 1).

Batch III 1) If a is a constant vector and r xi yj zk Prove that curl ( a r ) =2 a .

2) Find the directional derivative of 2

V , where 2 2 2V xy i zy j xz k at the

point (2, 0, 3) in the direction of the outward normal surface to the sphere

2 2 2 14x y z at the point (3, 2, 1).

3) A vector r is defined by r xi yj zk . If r r then show that vector

nr r is irrotational.

4) A vector field is given by 2 2 2 2( ) ( )A x xy i y x y j . Show that the field

is irrotational and find the scalar potential.

5) Show that the gradient field describing a motion is irrotational.

6) Find the unit vector normal to the surface 3 2 4xy z at (-1, -1, 2)

Assignment No. 4

Assignment

Title

Laplace Transform CO4

Batch I 1. Find 3 (2sin5 3cos7 )tL e t t

2. Find 3 (2cos5 3sin5 )tL e t t 2 sin 4tL t e t

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16

3. Evaluate 3

0

coste t t dt

4. Find

21 2 4

2 3

sL

s s

5. Find the Laplace transform of cos3 cos 2t t

t

6. Using Laplace transform find the solution of initial value problem

7. 2

1

2

1sin ; (0) 1, (0)

2

d yy t y y

dt

Batch II 1. Find 2 (2sin3 3cosh 4 )tL e t t

2. Find 2 cos3tL t e t

3. Evaluate 2 3

0

t te e

t

4. Find

21

2

10 13

1 5 6

s sL

s s s

5. Find

1

22

1

3L

s s

by Convolution Theorem

6.

Using Laplace transform find the solution of initial value problem

3 21

3 22 2 0; (0) 0, (0) 0, (0) 6lld y d y dy

y y y ydt dt dt

Batch III

1. Find 2 (10cos4 20sin5 )tL e t t

2. Find sin 2d

L t tdt

3. Find the Laplace transform of cos cosat bt

t

4. Find

1

2

4 5

1 2

sL

s s

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5. Find

21

22 2

sL

s a

by Convolution Theorem

6. Using Laplace Transform find the solution of initial value problem 2

2 1

22 12 ; (0) 2, (0) 6td y dy

y e y ydt dt

Assignment No. 5

Assignment

Title

Fourier Series CO5

Batch I 1. Obtain Fourier Series of

2

( )2

xf x

in the interval (0,2π)

2. Obtain Fourier Series of in the interval (0,2π)

, 0( )

2 , 2

x xf x

x x

3. Obtain Fourier Series of ex in –π<x<π

4. Obtain Fourier Series of f(x)=x+x2 when –π<x<π

5. Obtain Fourier Series of f(x)=2-(x2/2) in 0<x<2

6. Find Half range sine series of

, 02

( )

,2

x x

f x

x x

Batch II

1.

1. Obtain Fourier Series of in the interval (0,2π)

sin , 0( )

0, 2

x xf x

x

2. Obtain Fourier Series of e-ax

in –π<x<π

3. Find the Fourier series for the function𝑓 𝑥 = 𝑎2 − 𝑥2 in (-a,a)

4. Find Half range cosine series of

, 02

( )

,2

x x

f x

x x

5. Find the Fourier series for the functionx2 in the interval (-π,π)

6. Find the Fourier series for the function

, 02

( )

, 02

x x

f x

x x

Batch III 1. Find the Fourier series for the function𝑓 𝑥 = 𝑥 +1

4𝑥2 in (-π,π) and

hence deduce that 𝜋2

12=1

12−

1

22+

1

32−

1

42+⋯

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2. Obtain Fourier Series of

2

( )2

xf x

in the interval (0,2π)

3. Find the Fourier series for the function f(x)=4-x2 in the interval (0,2)

4. Find the Fourier series for the function 0, 5 0

( )3, 0 5

xf x

x

5. Find Half range cosine series of 1, 0 1

( ), 1 2

xf x

x x

6. Find Half range sine series of , 0 1

( )2 , 1 2

x xf x

x x

Assignment No. 6

Assignment

Title

Application of Partial Differential Equations CO6

Batch I

1. Solve the wave equation

2 22

2 2

u uc

t x

under the condition

u(0,t)=0,u(l,t)=0 for all t ,u(x,0)=f(x) and 0

( ),t

ug x o x l

t

2. Solve 2

2

u u

t x

for the conduction u(x,0)=3sinnπx, u(0,t)=0 and u(1,t)=0

Where 0 < x < 1, t>0

Batch II 1. A string is stretched and fastened to two points l apart. Motion is started

by displacing the string in the form sinx

y al

,from which it is

released at time t=0.Show that the displacement of any point at distance

x from one end at time t is given by , sin cos

x cty x t a

l l

2. Solve 2

2

u uk

t x

For the conduction of heat along a rod without radiation sub. To following

conditions

u is not ∞ as t →∞

0 0,u

for x x lt

u=lx-x2 for t=0 between x=0, x=l

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Batch III

1. Solve the Laplace equation 2 2

2 20

u u

x y

subject to the conditions

(0, ) ( , ) ( ,0) 0 & ( , ) sinn x

u y u l y u x u x al

2. The ends A & B of a rod 20cm long have the temp at 300C & 80

0C until

steady state. The temp. of the ends are changed to 400C & 60

0C

respectively. Find the temp. distribution in the rod at time t

Course Plan

Course Electrical Technology

Course Code

Examination

Scheme

Theory Term Work POE Total

Max. Marks 100 25 125

Contact

Hours/ week

3 2-Alternate week -- 5/3

Prepared by Prof. I.D.Pharne Date 15/6/2015

Prerequisites The student should know about the basic concepts of electrical engineering.

Course Outcomes

At the end of the course the students should be able to:

CO1 Describe the basics of DC motor.

CO2 Describe the basic concepts related to the three phase induction motor.

CO3 Describe the concept of starter used, speed control methods of three phase

induction motor.

CO4 Describe the working of special purpose motor.

CO5 Describe the basic of drives & types, criterion for selecting the electric drive.

CO6 Describe the processes used for heating.

Mapping of COs with POs

POs COs

a b c d E f G h i j k l

CO1 √

CO2 √ √ √

CO3 √ √

CO4 √

CO5 √ √

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20

CO6 √ √

Course Contents

Unit No. Title No. of

Hours

Section I

1. DC motors:

Construction, Working, Types, Back emf, Speed equation, Torque

equation, Speed torque characteristics, Applications, Power losses in

d.c. Motors. Need of starter, 3 point starter, 4 point starter, face plate

controller. Speed control of D.C. Shunt and series motor (numerical

treatment), Thyristorbased speed control for D.C. Motor. Reversal of

rotation, Electric braking of shunt and series motor.

8

2. Three Phase Induction Motor:

Advantages of induction motor, Construction, Types, Working, Speed

equation, Torque equation, Starting torque, Concept of full load torque,

Torque speed characteristics, Power stages in motor (Numerical

treatment)

6

3. Three Phase Induction Motor Control:

Need of starter, Star delta starter, DOL starter, Autotransformer starter,

Rotor resistance starter. Speed control methods- Pole changing, Voltage

control, VFD (V/f) control, Block schematic of electronic VFD control,

Rotor resistance speed control. Reversal of rotation.

7

4. Special Purpose Motors:

Features, construction, Working, characteristics, Applications of ac

servo motor, dc servo motor, Stepper motor (VR type and PM type).

Introduction to BLDC motor and linear induction motor.

7

5 Electrical Drives:

Advantages of electrical drives, Types – Individual, group, Multi-motor

drive. Types of mechanical loads (active, passive), nature of mechanical

loads (With respect to speed–torque variation, with respect to duty

period), 2 quadrant and 4 quadrant operation of electric machines.

Criteria for selection of motors for applications like lathe, Traction,

pumps, Conveyors, Lift, etc. Determination of power rating of electric

motors for continuous duty – Constant load.

6

6 Electric Heating:

Working and construction of - Indirect resistance furnace, Salt bath

furnace, Direct arc furnace, Indirect arc furnace, Core type induction

furnace, Coreless induction furnace. High frequency eddy current

heating. (Numerical treatment on energy conversion)

6

Reference Books:

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21

Sr. No. Title of Book Author Publisher/Edition Units

1. Text book of Electrical

Technology – Vol-II

B. L. Theraja. S.

Chand publication

All

2. Electrical Power S. L. Uppal,

DBS Publ.

3. Utilization of Electric Power R. K. Rajput,

Laxmi

publication.

4. Electrical Technology U. A. Bakshi

Scheme of Marks

Unit No. Title Marks

1 DC motors 18

2 Three Phase Induction Motor: 18

3 Three Phase Induction Motor Control: 18

4 Special Purpose Motors 18

5 Electrical Drives 18

6 Electric Heating 18

Course Unitization

Section

Unit Course

Outcomes

No. of Questions in

No. Title CAT-I CAT-II

I

1 DC motors CO1 1

2 Three Phase Induction

Motor:

CO2 1

3 Three Phase Induction

Motor Control:

CO3 1

II 4 Special Purpose Motors CO4 1

5 Electrical Drives CO5 1

6 Electric Heating CO6 1

Unit wise Lesson Plan

Section I

Unit No 1. Unit Title DC motors Planned

Hrs.

8

Unit Outcomes

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22

At the end of this unit the students should be able to:

UO1 Describe the basics of DC motor. CO1

Lesson schedule

Class

No.

Details to be covered

1 Construction, Working, Types, Back emf, Speed equation, Torque equation, Speed

torque characteristics, Applications, Power losses in d.c. Motors.

2 Need of starter, 3 point starter, 4 point starter,

3 Face plate controller. Speed control of D.C. Shunt motor

4 Speed control of DC series motor (numerical treatment)

5 Thyristorbased speed control for D.C. Motor.

6 Reversal of rotation,

7 Electric braking of shunt motor.

8 Electric braking of series motor.

Review Questions

Q1 Explain the construction & working principal of DC motor. CO1

Q2 Explain the speed control methods of DC shunt motor CO1

Q3 Explain the speed control methods of DC series motor. CO1

Unit No 2 Unit Title Three Phase Induction Motor: Planned

Hrs.

6

Unit Outcomes

At the end of this unit the students should be able to:

UO2 Describe the basic concepts related to the three phase induction motor. CO2

Lesson schedule

Class

No.

Details to be covered

1 Advantages of induction motor,

2 Construction, Types, Working,

3 Speed equation, Torque equation

4 Starting torque, Concept of full load torque,

5 Torque speed characteristics, Power stages in motor

6 Numerical treatment.

Review Questions

Q1 Explain the speed torque characteristics of three phase induction motor. CO2

Unit No 3 Unit Title Three Phase Induction Motor Control: Planned

Hrs.

7

Unit Outcomes

UO3 Describe the concept of starter used, speed control methods of three phase

induction motor.

CO3

Lesson schedule

Class

No.

Details to be covered

1 Need of starter, Star delta starter,

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23

2 DOL starter, Autotransformer starter,

3 Rotor resistance starter. Speed control methods- Pole changing,

4 Voltage control, VFD (V/f) control,

5 Block schematic of electronic VFD control,

6 Rotor resistance speed control.

7 Reversal of rotation

Review Questions

Q1 Explain the need of starter & types of starters. CO3

Q1 Explain the speed control methods of three phase induction motor. CO3

Unit No 4 Unit Title Special Purpose Motors:

Planned

Hrs.

7

Unit Outcomes

UO4 Describe the working of special purpose motor. CO4

Lesson schedule

Class

No.

Details to be covered

1,2 Features, construction, Working, characteristics, Applications of ac servo motor, dc

servo motor,

3,4 Stepper motor (VR type and PM type).

5,6 Introduction to BLDC motor

7 Linear induction motor.

Review Questions

Q1 Explain the AC servo motor. CO4

Q2 Explain the DC servo motor. CO4

Q3 Explain stepper motor. CO4

Unit No 5 Unit Title Electric Drives Planned

Hrs.

6

Unit Outcomes

UO5 Describe the basic of drives & types, criterion for selecting the electric

drive.

CO5

Lesson schedule

Class

No.

Details to be covered

1 Advantages of electrical drives, Types – Individual, group,

2 Multi-motor drive. Types of mechanical loads (active, passive),

3 nature of mechanical loads (With respect to speed–torque variation, with respect to

duty period),

4 2 quadrant and 4 quadrant operation of electric machines.

5 Criteria for selection of motors for applications like lathe, Traction, pumps,

Conveyors, Lift, etc.

6 Determination of power rating of electric motors for continuous duty – Constant load.

Review Questions

Q1 Differentiate the group drive & individual drive. CO5

Q2 Explain the types of mechanical loads. CO5

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24

Q3 Explain the criterion for selection of drives. CO5

Unit No 6 Unit Title Electric heating Planned

Hrs.

6

Unit Outcomes

UO6 Describe the processes used for heating. CO6

Lesson schedule

Class

No.

Details to be covered

1 Working and construction of - Indirect resistance furnace,

2 Salt bath furnace, Direct arc furnace, Indirect arc furnace,

3 Core type induction furnace, Coreless induction furnace.

4 High frequency eddy current heating.

5,6 (Numerical treatment on energy conversion)

Review Questions

Q1 Explain the working & construction of indirect resistance furnace. CO6

Q2 Explain the working & construction of Salt bath furnace, Direct arc

furnace.

CO6

Q3 Explain the High frequency eddy current heating. CO6

Model Question Paper

Course Title : Electrical Technology

Duration: 3 Hrs Max.

Marks:

100

Instructions:

1] Attempt any three questions from each section.

2] Figure to right indicates full marks.

3] Assume necessary data if required.

Section-I

1 a Explain the construction & working principal of DC motor. 8

b Explain the speed control methods of DC shunt motor 8

2 a Explain the speed control methods of DC series motor. 8

b Explain the speed torque characteristics of three phase induction

motor.

8

3 a Explain the AC servo motor. 8

b Explain the working & construction of indirect resistance furnace. 8

4 a Explain the working & construction of Salt bath furnace, Direct arc

furnace.

9

b Explain the High frequency eddy current heating. 9

Section-II

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25

1 a Explain the need of starter & types of starters. 9

b Explain the speed control methods of three phase induction motor. 9

2 a Differentiate the group drive & individual drive. 8

b Explain the types of mechanical loads. 8

3 a Explain the criterion for selection of drives. 8

b Explain the DC servo motor. 8

4 a Explain stepper motor. 8

b Explain speed reversal of DC motor. 8

Assignments

Assignment No. 1

Assignment Title CO1

Batch I 1. Explain the construction & working principal of DC motor.

2. Explain the speed control methods of DC shunt motor.

3. Explain the speed control methods of DC series motor.

4. Explain the speed torque characteristics of three phase induction

motor.

Batch II 1. Explain the AC servo motor.

2. Explain the working & construction of indirect resistance furnace.

3. Explain the working & construction of Salt bath furnace, Direct arc

furnace.

4. Explain the High frequency eddy current heating.

Batch III 1. Explain the need of starter & types of starters.

2. Explain the speed control methods of three phase induction motor.

3. Differentiate the group drive & individual drive.

4. Explain the types of mechanical loads.

Batch IV 1. Explain the criterion for selection of drives.

2. Explain the DC servo motor.

3. Explain stepper motor.

4. Explain speed reversal of DC motor.

Course Plan

Course Applied Thermodynamics Course Code

Examination

Scheme

Theory Term Work POE Total

Max. Marks 100 25 25 150

Contact

Hours/ week

3 2 -- 5

Prepared by Tanaji B. Shinde / N.S.Desai Date 15/06/2015

Prerequisites Student must have the knowledge of basic physics and chemistry also basic

mathematical skills in terms of derivative and integration to develop equations

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26

for given conditions

Course Outcomes

At the end of the course the students should be able to:

CO1 Understand basic concepts of physics and chemistry behind thermodynamics

CO2 Solve introductory problems on Rankine cycle.

CO3 Understand functioning of steam generators and condensers.

CO4 Design the steam nozzle.

CO5 Understand basic concepts of Impulse turbine.

CO6 Understand basic concepts of Reaction turbine, Governing and trouble shooting

of turbine.

Mapping of COs with POs

POs

COs

a b c d E f G h i j k l

CO1 √ √

CO2 √ √

CO3 √ √

CO4 √ √

CO5 √

CO6 √

Course Contents

Unit No. Title No. of

Hours

Section I

1. Review of Laws of Thermodynamics:

Zeroth law, first law and Second law of thermodynamics, Statement of

third law of thermodynamics. Equivalence and Corrolories of Second

Law, Numerical treatment on first and second law, Clausius theorem,

Entropy, Clausius inequality, Entropy as a property of system, Entropy

of pure substance. T-s and h-s planes, Entropy change in a reversible

and irreversible processes, Increase of entropy principle, Calculation of

entropy changes of gases and vapours,(numerical treatment should be

based on processes) Availability: Available and unavailable energy:

availability of a closed and open system, Availability of work and heat

8

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27

reservoirs, Anergy, energy and exergy,( No numerical on Availability)

2. Properties of Pure Substances and Vapour Power Cycles:

Properties of steam, Use of steam table and Mollier chart, Deviation of

real gases from Ideal gases, Equations of state- Vander Waal, Beattie-

Bridgemen, Virial and Diterici‟sequations, P-V-T surfaces and triple

point of water.(Descriptive treatment) Carnot cycle using steam,

Limitations of Carnot cycle Rankine cycle, Representation on T-s and h-

s planes, Thermal efficiency, Specific steam consumption. Work ratio,

Effect of steam supply pressure and temperature, Condenser pressure on

the performance. (Numerical Treatment), Reheat and regenerative steam

power cycles.

6

3. Steam Generators and Steam Condensers:

Study and classification of Boilers, Thermal efficiency of Boiler,

Functions, Elements of condensing plant, Types of steam condensers,

surface and jet condensers, Comparison, Vacuum efficiency, Condenser

efficiency, Loss of vacuum, Sources of air leakages, Methods of leak

detection, Air extraction methods, Estimation of cooling water required,

Capacity of air extraction pump, Air ejectors.

6

4. Steam Nozzles:

Functions, Shapes, Critical pressure ratio, Maximum discharge

condition, Effect of faction, Design of throat and exit areas, Nozzle

efficiency, Velocity coefficient, Coefficient of discharge, Supersaturated

flow, Degree of under-cooling and degree of super saturation, Effects of

super saturation.

5

5. Impulse Turbines:

Principles of operation, Classification, Impulse and reaction steam

turbine, compounding of steam turbines. Flow through impulse turbine

blades, Velocity diagrams, Work done, Efficiencies, End thrust, Blade

friction, Influence of ratio of blade speed to steam speed on efficiency

of single and multistage turbines and its condition curve and reheat

factors.

8

6. Reaction Turbines:

Flow through impulse reaction blades, Velocity diagram, and degree of

reaction, Parson's reaction turbine, Back pressure and pass out turbine.

Governing of steam turbines.Losses in steam turbines, Performance of

steam turbines. Function of diaphragm, Glands, Turbine troubles like

Erosion, Corrosion, Vibration, Fouling etc.

7

Reference Books:

Sr. No. Title of Book Author Publisher/Edition Units

1 Thermal Engineering R. K. Rajput Laxmi 1-6

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28

Publications

2 Thermal Engineering R.S.

Khurmi&J.K.Gupta S. Chand 1-6

3 Thermodynamics: an engineering

approach Cengel& Boles TMH 1-2

4 Engineering Thermodynamics P.K. Nag TMH 1-2

5 Steam & Gas Turbines R. Yadav CPH Allahabad 4-6

6 Thermal Engineering M.M Rathod TMH 1-6

Scheme of Marks

Section Unit No. Title Marks

I

1 Review of Laws of Thermodynamics

50 2 Properties of Pure Substances and Vapour Power Cycles

3 Steam Generators and Steam Condensers:

II

4 Steam Nozzles

50 5 Impulse Turbines

6 Reaction Turbines

Course Unitization

Section

Unit Course

Outcomes

No. of Questions in

No. Title CAT-I CAT-II

I

1 Review of Laws of

Thermodynamics

CO1 1 -

2 Properties of Pure Substances

and Vapour Power Cycles

CO2 1 -

3 Steam Generators and Steam

Condensers:

CO3 1 -

II

4 Steam Nozzles CO4 - 1

5 Impulse Turbines CO5 - 1

6 Reaction Turbines CO6 - 1

Unit wise Lesson Plan

Section I

Unit No 1 Unit Title Review of Laws of Thermodynamics Planned

Hrs.

8

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Explain zeroth, first and second laws of thermodynamics and how they

can be applied to thermodynamic systems

CO1

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UO2 Identify, formulate and solve problems based on three laws of

thermodynamics

CO1

UO3 Apply the first and second law of thermodynamics to processes CO1

UO4 Define new property called entropy to quantify second law effects CO1

UO5 Establish the increase of entropy principle CO1

UO6 Calculate the entropy changes that takes place during processes for pure

substance

CO1

UO7 Define exergy, which is the maximum useful work that could be obtained

from the system at a given state in a specified environment

CO1

UO8 Define reversible work, which is the maximum useful work that can be

obtained as a system undergoes a process between two specified states

CO1

UO9 Explain the concept of Available and unavailable energy CO1

UO10 Calculate decrease in available energy when heat is transferred through a

finite temperature difference

CO1

Lesson schedule

Class No. Details to be covered

1 Zeroth law, first law & Second law and third law of thermodynamics

2 Equivalence & Corollaries of Second Law

3 Numerical treatment on first and second law

4 Clausius inequality, entropy as a property of system, entropy of pure substance

5 T-sand h-s planes, entropy change in a reversible and irreversible processes, increase

of entropy principle

6 calculation of entropy changes of gases and vapours, Statement of

third law of thermodynamics

7 Available and unavailable energy: availability of a closed and open system

8 availability of work and heat reservoirs, Anergy, energy and exergy

Review Questions

Q1 State the three laws of thermodynamics CO1

Q2

A reversible engine is supplied with heat from two constant temperature

sources at 900 K and 600 K and rejects heat to a constant temperature

sink at 300 K. The engine develops work equivalent to 90kj/s and rejects

heat at rate of 56kj/s Estimate:

1)Heat supplied by each source

2)Thermal efficiency of engine

CO1

Q3 What do you mean by the term ‘Entropy’ ? CO1

Q4 Prove that entropy is a property of a system. CO1

Q5 Derive an expression for the change in entropy of the universe CO1

Q6 Derive expressions for entropy changes for a closed system in the

following cases :

(i) General case for change of entropy of a gas

CO1

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(ii) Heating a gas at constant volume

(iii) Heating a gas at constant pressure

(iv) Polytropic process

Q7 1 kg of air is compressed according to the law pv1.25 = constant from

1.03 bar and 15°C to 16.45 bar.Calculate the change in entropy.

[Ans. 0.255 kJ/kg K]

CO1

Q8 A quantity of gas (mean molecular weight 36.2) is compressed according

to the law pvn = constant, the initial pressure and volume being 1.03 bar

and 0.98 m3 respectively. The temperature at the start of compression is

17°C and at the end it is 115°C. The amount of heat rejected during

compression is 3.78 kJ,cp = 0.92. Calculate :

(i)Value of n, (ii) Final pressure, (iii) Change in entropy.

[Ans. (i) 1.33 ; (ii) 1.107 bar ; (iii) 0.228 kJ/kg K]

CO1

Q9 Explain the concept of available and unavailable energy. When does the

system become dead?

CO1

Q10 Derive an expression for availability in non-flow systems. CO1

Q11 Derive an expression for decrease in available energy when heat is

transferred through a finite temperature difference.

CO1

Unit No 2 Unit Title Properties of Pure Substances and vapour

power cycle

Planned

Hrs.

6

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Introduce the concept of a pure substance CO2

UO2 Illustrate the P-v, T-v, and P-T property diagrams and P-v-Tsurfaces of

pure substances.

CO2

UO3 Demonstrate the procedures for determining thermodynamic properties of

pure substances from table of property data

CO2

UO4 Explain process involved in Carnot and Rankinevapour power cycle CO2

UO5 Differentiate Carnot and Rankinevapour power cycle CO2

UO6 Calculate performance of Carnot and vapour power cycle in terms of

thermal efficiency, specific steam consumption. Work ratio

CO2

Lesson schedule

Class No. Details to be covered

1 Properties of steam, use of steam table and Mollier chart, Deviation of real gases

from ideal gases,

2 Equations of state- Vander Waal, Beattie-Bridgemen, Virial&Diterici’s equations

3 Carnot cycle using steam, limitations of Carnot cycle

4 Representation on T-s and h-s planes, P-V-T surfaces & triple point of water

5 effect of steam supply pressure and temperature, condenser pressure on the

performance, Reheat regenerative steam power cycles

6 Numerical to find out thermal efficiency, specific steam consumption. Work ratio

Review Questions

Q1 Draw and explain a p-v, p-T (pressure-temperature),h-s and T-s diagram

for a pure substance

CO2

Q2 Explain the following terms relating to steam formation : CO2

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31

(i) Sensible heat of water, (ii) Latent heat of steam,

(iii) Dryness fraction of steam, (iv) Enthalpy of wet steam, and

(v) Superheated steam.

Q3 Write a short note on

pure substance

p-V-T surface

Mollier chart

CO2

Q4 Explain the various operation of a Carnot cycle. Also represent it on a T-s

and p-V diagrams

CO2

Q5 Describe the different operations of Rankine cycle. Derive also the

expression for its efficiency

CO2

Q6 State the methods of increasing the thermal efficiency of a Rankine cycle. CO2

Q7 A simple Rankine cycle works between pressure of 30 bar and 0.04 bar,

the initial condition of steambeing dry saturated, calculate the cycle

efficiency, work ratio and specific steam consumption.

[Ans. 35%, 0.997, 3.84 kg/kWh]

CO2

Q8 A steam power plant works between 40 bar and 0.05 bar. If the steam

supplied is dry saturated and the cycle of operation is Rankine, find :

(i) Cycle efficiency (ii) Specific steam consumption.

[Ans. (i) 35.5%, (ii) 3.8 kg/kWh]

CO2

Q9 In a Rankine cycle, the steam at inlet to turbine is saturated at a pressure of

30 bar and the exhaust tpressure is 0.25 bar. Determine :

(i) The pump work (ii) Turbine work

(iii) Rankine efficiency (iv) Condenser heat flow

(v) Dryness at the end of expansion.

Assume flow rate of 10 kg/s. [Ans. (i) 30 kW, (ii) 7410 kW, (iii) 29.2%,

(iv) 17900 kW, (v) 0.763]

CO2

Unit No 3 Unit Title Steam Generators and Steam Condensers Planned

Hrs.

6

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Explains construction, working and functions of steam generators and

condenser

CO3

UO2 Classify steam condensers and steam boilers CO3

UO3 Evaluate the performance of steam condenser and estimation of cooling

water required

CO3

Lesson schedule

Class No. Details to be covered

1 Study and classification of Boilers

2 Thermal efficiency of Boiler ( Theoretical and Actual)

3 Functions, elements of condensing plant, types of steam

condensers

4 surface and jet condensers, comparison

5 vacuum efficiency, condense efficiency, loss of vacuum, sources of air leakages,

methods of leak detection, air extraction methods

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6 Estimation of cooling water required, capacity of air extraction pump, air ejectors.

Review Questions

Q1 Explain construction & working of steam condensing plant CO3

Q2 Explain construction & working of simple vertical steam boiler CO3

Q3 Classify steam boiler CO3

Q4

Classify steam condenser. CO3

Q4 Compare jet and surface condenser CO3

Q6 A surface condenser is designed to handle 10000kg of steam per hour.

The steam enters at 0.08 bar and 0.9 dryness and the condensate leaves at

the corresponding saturation temperature. The pressure is constant

through the condenser. Estimate cooling water temperature rise is limited

to 10 degree C. 514980 kg/hr

CO3

Q7 Explain the following

1. Condenser efficiency

2. Vacuum efficiency

3. sources of air leakages

4. methods of leak detection

5. Edwards air pump

6. Air ejector

CO3

Unit No 4 Unit Title Steam Nozzles Planned

Hrs.

5

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Explain function, working and types of nozzles CO4

UO2 Explain nozzle efficiency, effect of friction on nozzle efficiency and

supersaturated flow in nozzle

CO4

UO3 Design the inlet and throat areas CO4

Lesson schedule

Class No. Details to be covered

1 Functions, shapes, critical pressure ratio, maximum discharge condition

2 design of throat and exit areas, nozzle efficiency, velocity coefficient,

coefficient of discharge

3 supersaturated flow

4 Degree of under-cooling and degree of super saturation, effects of super saturation.

5 effect of friction on nozzle efficiency

Review Questions

Q1 Derive expression for maximum discharge through nozzle CO4

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Unit No 5 Unit Title Impulse Turbine Planned

Hrs.

8

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Explain function, working of impulse Steam turbines CO5

UO2 Evaluate the work done, power and efficiency of impulse with the help of

velocity diagram

CO5

UO3 Explain compounding, Governing of steam turbine and its need CO5

Lesson schedule

Class No. Details to be covered

1 Principles of operation,

2 classification steam turbine

3 compounding of steam turbines

4 Flow through impulse turbine blades

5 velocity diagrams for impulse steam turbine

6 work done, efficiencies, end thrust, blade friction ,

7 influence of ratio of blade speed to steam speed on efficiency of single and

multistage turbines and its condition curve

8 reheat factors

Review Questions

Q1 Compare impulse and reaction turbine with the help of principle of

operation and velocity triangles

CO5

Q2

Write a short note on following

1. Classification of steam turbine

2. compounding of steam turbines

3. Governing of steam turbines

4. Losses in steam turbines

5. Function of diaphragm, glands

CO5

Q3 Derive expression for blade efficiency of impulse turbine CO5

Q4 What do you mean by compounding of steam turbine? Explain with help

of pressure-velocity diagram velocity compounding of steam turbine

CO5

Q2

Write a short note on following

1. Effect of friction on nozzle efficiency

2. Supersaturated flow in nozzle

3. Effects of super saturation

4. Different types of nozzles

CO4

Q3 Dry saturated steam at 10 bar is expanded isentropically in a nozzle to 0.1

bar. Using steam table only, find the dryness fraction of steam at exit.

Also find velocity of steam leaving the nozzle when 1.Initial velocity is

negligible 2.Initial velocity of steam is 135 m/s.

Ans:-[x2=0.791, V2=1176 m/s and if V1=135m/s then V2=1184 m/s]

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Q5 Explain with neat sketch

1. Nozzle governing

2. Bypass governing

3. Throttle governing

CO5

Q6 In a De-level turbine, the steam enters the wheel through a nozzle with a

velocity of 500 m/s and at a angle of 200 to the direction of motion of

blade. The blade speed is 200 m/s and the exit angle of moving blade is

250 .find the inlet angle of the moving blade, exit velocity of steam and

its direction and work done per kg of steam

CO5

Q7 Steam issuing from a nozzle at 600 m/s enters the first set of blades of a

two row wheel impulse turbine. The tips of both the set of moving blades

are inclined at 300 to the plane of motion. Find the speed of the blades, so

that the steam is finally discharged axially, Neglect friction. Also find

power developed by the turbine, if the mass of steam supplied to the

turbine is 3 kg/s.

CO5

Unit No 6 Unit Title Reaction Turbine Planned 7

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Explain function, working of impulse reaction Steam turbines CO6

UO2 Evaluate the work done, power and efficiency of impulse with the help of

velocity diagram

CO6

UO3 Explain Governing of reaction steam turbine and its need CO6

Lesson schedule

Class No. Details to be covered

1 Flow through impulse reaction blades

2 velocity diagram, and degree of reaction

3 parson's reaction turbine, and backpressure and pass out turbine

4 Governing of steam turbines, Losses in steam turbine

5 performance of steam turbines

6 Function of diaphragm, glands

7 turbine troubles like erosion, corrosion, vibration, fouling etc.

Review Questions

Q1 Explain with neat sketch

Nozzle governing

Bypass governing

Throttle governing

CO6

Q2 In a one stage of reaction steam turbine, both the fixed and moving blades

have inlet and outlet blade tip angles of 350 and 20

0 respectively. The

mean blade speed is 80 m/s and steam consumption is 22500 kg/hr.

Determine the power developed in the pair, If the isentropic heat drop for

the pair is 23.5 kJ/kg

CO6

Q3 Write a short note on following

1. Velocity diagram Parson's reaction turbine

2. back pressure and pass out steam turbines

CO6

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35

3. Governing of steam turbines

4. Losses in steam turbines

5. Function of diaphragm, glands

6. Turbine troubles like Erosion, Corrosion, Vibration, Fouling etc.

Model Question Paper

Course Title : Applied Thermodynamics

Duration

3 Hours

Max.

Marks

100

Instructions:

Solve any three from section I and II

Figures to the right indicates full marks

Use of calculators, steam tables and Mollier diagram is allowed

Section-I

1 a State the three laws of thermodynamics 8

b A reversible engine is supplied with heat from two constant

temperature sources at 900 K and 600 K and rejects heat to a constant

temperature sink at 300 K. The engine develops work equivalent to

90kj/s and rejects heat at rate of 56kj/s Estimate:

1)Heat supplied by each source

2)Thermal efficiency of engine

8

2 a Derive expressions for entropy changes for a closed system in the

following cases :

(i) General case for change of entropy of a gas

(ii) Heating a gas at constant volume

(iii) Heating a gas at constant pressure

(iv) Polytrophic process

8

b A system receives 10000 kJ of heat at 500 K from a source at 1000 K.

The temperature of the surroundings is 300 K. Assuming 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.

8

3 a Explain the various operation of a Carnot and Rankine cycle. Also

represent it on a T-s,h-s and p-V diagrams

8

b In a Rankine cycle, the steam at inlet to turbine is saturated at a

pressure of 30 bar and the exhaust pressure is 0.25 bar. Determine :

(i) The pump work (ii) Turbine work

(iii) Rankine efficiency (iv) Condenser heat flow

(v) Dryness at the end of expansion.

Assume flow rate of 10 kg/s.

[Ans. (i) 30 kW, (ii) 7410 kW, (iii) 29.2%, (iv) 17900 kW, (v) 0.763]

10

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4 a Classify steam condenser and Compare jet and surface condenser 8

b A surface condenser is designed to handle 10000kg of steam per hour.

The steam enters at 0.08 bar and 0.9 dryness and the condensate

leaves at the corresponding saturation temperature. The pressure is

constant through the condenser. Estimate cooling water temperature

rise is limited to 10 degree C. [ans:- 514980 kg/hr]

8

Section-II

5 a Derive expression for maximum discharge through nozzle 8

b Dry saturated steam at 10 bar is expanded is entropically in a nozzle

to 0.1 bar. Using steam table only, find the dryness fraction of steam

at exit. Also find velocity of steam leaving the nozzle when 1.Initial

velocity is negligible 2.Initial velocity of steam is 135 m/s.

Ans:-[x2=0.791, V2=1176 m/s and if V1=135m/s then V2=1184 m/s]

8

6 a Compare impulse and reaction turbine with the help of principle of

operation and velocity triangles

8

b In a De-level turbine, the steam enters the wheel through a nozzle with

a velocity of 500 m/s and at a angle of 200 to the direction of motion

of blade. The blade speed is 200 m/s and the exit angle of moving

blade is 250 .find the inlet angle of the moving blade, exit velocity of

steam and its direction and work done per kg of steam

8

7 a What do you mean by compounding of steam turbine? Explain with

help of pressure-velocity diagram velocity compounding of steam

turbine

8

b Steam issuing from a nozzle at 600 m/s enters the first set of blades of

a two row wheel impulse turbine. The tips of both the set of moving

blades are inclined at 300 to the plane of motion. Find the speed of the

blades, so that the steam is finally discharged axially, Neglect friction.

Also find power developed by the turbine, if the mass of steam

supplied to the turbine is 3 kg/s.

8

8 Write a short note on any 3 of the following

Classification of steam turbine

Governing of steam turbines

Losses in steam turbines

Function of diaphragm, glands

Supersaturated flow in nozzle

18

Course Plan

Course Metallurgy Course Code 43594

Examination

Scheme

Theory Term Work POE Total

Max. Marks 100 25 25 150

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37

Contact

Hours/ week

3 2 -- 5

Prepared by Mr.Y B Kumbhar Date 15/06/2015

Prerequisites This course requires the student to know about the basic concepts of metallurgy,

fundamentals of material engineering and crystallography.

Course Outcomes

At the end of the course the students should be able to:

CO1 Explain the basics properties of metals, their alloys, their crystal structures and

imperfections.

CO2 Explain the phase diagrams with respect to typical composition, properties and

applications.

CO3 Describe and perform the destructive &non destructive metallurgical testing

methods.

CO4 Comprehend the principles of different transformations of austenite, significance

and effects of alloying elements on TTT diagrams.

CO5 Explain different heat treatment processes, types of furnaces used for respective

treatment and effect of temperature and time on properties of steel.

CO6 Describes the principles of powder metallurgy, stages of manufacturing and

applications.

Mapping of COs with POs

POs

COs

a b c d E f G h i j k l

CO1 √ √ √ √

CO2 √ √

CO3 √ √ √ √ √ √

CO4 √

CO3 √ √ √ √ √

CO6 √ √ √ √

Course Contents

Unit No. Title No. of

Hours

Section I

1. Metals and alloy systems:

Introduction to Metallic and Non-metallic materials and its

classification (metals/alloys, polymers and composites)

a) Metals, Metallic bonds, Crystal structure (SC, BCC, FCC, HCP),

Imperfections in crystals

07

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38

b) Alloy formation by crystallization, Nucleation and growth, Cooling

curves, Dendritic structure and coring.

c) Solid solutions and intermediate phases

d) Phases and Gibbs phase rule

e) Construction of equilibrium diagrams from cooling curves,

Isomorphous system( Solid Solution), Eutectic, Partial solubility

Peritectic and Intermetallic Compounds Lever arm principles, Long and

short-range freezing.

2. Study of phase diagrams :

(With respect to typical compositions, Properties and Applications for

the following alloys.)

a)Fe- Fe3C equilibrium diagram - Ferrous alloys (Plain carbon steels,

cast iron)

b) Alloy steels- Free cutting steels, HSLA high carbon low alloy steels,

maraging steels. creep resisting steels, Stainless steels- different types.

Tool steels- types,

c) Selection of materials and Specifications based on -IS, BS, SAE,

AISI,

d) Copper based alloys brasses Cu- Zn, Bronzes Cu- Sn, , Cu- Be, Cu-

Ni.

e) Aluminum based alloys Al- Cu(Duralumin) - Al-Si (Modification),

f) Pb- Sn(Solders and fusible alloys)

g)Sn-Sb alloys ( Babbits)

h) Ti (Ti-6Al-4V)

i) Miscellaneous alloys such as super alloys, Heating element alloys.

Study of lowexpansion and controlled expansion alloys.

11

3 Principles of Metallurgical Testing:

a) Destructive Testing methods; Tensile, Compressive, Impact, Fatigue,

Creep, Hardness etc.

b) Non- Destructive Testing: - Dye penetrant, magnetic, ultrasonic,

Radiography, Eddy Current testing.

04

Section II

4. Principles of Heat Treatment :

a) Transformation of Pearlite into austenite upon heating,

b) Transformation of austenite into Pearlite, Bainite and Martensite on

cooling.

c) TTT –Diagram and CCT - Diagrams - significance, Effect of alloying

dements on TTT diagram and its significance.

d) Heat treatment furnaces and equipment‟s, controlled atmosphere.

05

5. Heat Treatment Processes:

a) Heat Treatment of Steels

I. Annealing – Types-Full, Partial and Sub critical annealing (Various

types) and purposes

II. Normalising- Purposes

09

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39

III. Hardening (Hardening types), Purposes, Austempering and

Martempering, Mechanism of quenching and Quenching media,

Hardenability- Concept and methods of determination of hardenability-

Grossmans critical diameter method and Jominy end quench test.

IV. Tempering Types, Structural transformations during tempering,

purposes, sub zero treatment

V. Surface hardening - Flame and Induction

VI. Chemical heat treatments for case hardening - Carburising,

Nitriding, Cyniding, Carbonitriding

b) Heat treatment of Non ferrous Alloys

I. Annealing- Stress relief, Recrystallization and Process annealing

II. Precipitation hardening - Basic requirements, Stages, Common

alloys, Variables,theories

c) Heat treatment defects and remedies.

6. Powder Metallurgy:

a) Advantages, Limitations and Applications of Powder Metallurgy

b) Powder manufacturing types- Mechanical, Physical, Chemical and

Electro- Chemical

c) Mixing/ Blending- (Double cone and Y- Cone mixers)

d) Compaction- types- Conventional, Isostatic, HERF, Powder rolling

and extrussion

e) Sintering- Types liquid stage and solid stage sintering

f) Finishing operations: Sizing, Machining, Infiltration and

Impregnation

g) Flowcharts for – Self-lubricating bearings, Electrical Contacts,

Carbide Tipped Tools, Sintered aluminum products, Filters.

04

Reference Books:

Sr. No. Title of Book Author Publisher/Edition Units

1 Introduction to physical

metallurgy

S.H.Avner Mcgraw Hill 1 to 6

2 Material science and metallurgy V.D. Kodgire Everest

Publishers Pune

1 to 6

3 Material Science And

Engineering

William Callister Wiley India

Edition

1,2

4 Mechanical Metallurgy G.E. Dieter Tata McGraw-

Hill, New Delhi

1 to 6

5 Engineering Metallurgy Clerk Verney 1 to 6

6 Engineering Metallurgy I and II Higgins R. A.,

Hodder

English language

Book Society

1 to 6

7 Physical Metallurgy Vijendra Singh Standard

Publishers, Delhi

1,2,3

8 Heat Treatments Principles and T.V. Rajan / C.P. Prentice Hall of 4,5

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40

Practices Sharma India Pvt Ltd,,

New Delhi

9 Physical Metallurgy V Raghwan - 1 to 6

10 Heat treatment of Steels Prabhudev HMT Handbook 4,5

Scheme of Marks

Section Unit No. Title Marks

I 1,2,3 Metals and alloy systems, Study of phase diagrams,

Principles of Mechanical Testing

50

II 4,5,6 Principles of Heat Treatment, Heat Treatment Processes,

Powder Metallurgy

50

Course Unitization

Section

Unit Course

Outcomes

No. of Questions in

No. Title CAT-I CAT-II

I 1 Metals and alloy systems CO1 Q.1, Q.2, Q.3

Solve any two

questions

-

2 Study of phase diagrams CO2

3 Principles of Mechanical

Testing

CO3

II 4 Principles of Heat

Treatment

CO4 - Q.1, Q.2, Q.3

Solve any two

questions.

5 Heat Treatment Processes CO5

6 Powder Metallurgy CO6

Unit wise Lesson Plan

Section I

Unit No 1 Unit Title Metals and alloy systems Planned

Hrs.

07

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Represent the crystal structures, crystal imperfections of metals and their

alloys.

CO1

UO2 Explain alloy formation by crystallization, nucleation, solidification and

growth.

CO1

UO3 Describe the solid solutions and intermediate phases. CO1

UO4 Explain phases and phase rule. CO1

UO5 Discuss the construction of equilibrium diagrams from cooling curves, CO1

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41

components of different solubility in liquid and solid state.

UO6 Describe Lever arm principle, dendritic structure and coring. CO1

UO7 Differentiate between Eutectic, Eutectoid and peritectic transformation. CO1

Lesson schedule

Class

No.

Details to be covered

1 Metals, metallic bonds, crystal structures, imperfections in crystals,

2 Alloy formation by crystallization, nucleation, solidification and growth.

3 Solid solutions and intermediate phases.

4 Phases and phase rule,

5 Construction of equilibrium diagrams from cooling curves, Lever arm principle

6 Eutectic, Eutectoid and peritectic transformation,

7 dendritic structure and coring

Review Questions

Q1 Sketch and explain BCC, FCC and HCP structures with example. (May

2013)

CO1

Q2 Write a short note on crystal imperfections. (May-2004,Nov-2011) CO1

Q3 Differentiate between crystal, dendrite and grain. CO1

Q4 What is solid solution? What are the types of solid solution? Enumerate the

conditions for their formation [with diagrams]. (May 2004, Nov-2005,

Nov-2009, Nov-2011, May2011, May 2012)

CO1

Q5 Explain with diagram- Gibbs phase rule and Lever arm principle.(May

2004, Nov-2009, Nov-2011, May-2011, Nov-2012)

CO1

Q6 Explain how the equilibrium diagram can be constructed from cooling

curve?

CO1

Q7 Write a short note on Partial Eutectic system.(May-2012) CO1

Q8 Explain the alloy formation by crystallization, nucleation, solidification

and growth.

CO1

Q9 Explain dendritic structure and coring.(Nov-2009, May-2011, Nov-

2012,May-2013)

CO1

Q10 Differentiate between Eutectic, eutectoid and perictic reaction.(Nov-2005,

May-2005, Nov-2012, May-2012, May-2013)

CO1

Unit No 2 Unit Title Study of phase diagrams Planned

Hrs.

11

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Classify Ferrous alloys with respect to composition, properties and CO2

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42

applications.

UO2 Explain the Iron-Iron Carbon diagram with respect to temperature and

composition.

CO2

UO3 Define the structures and Explain carbon solubility in iron along with slow

cooling of steel

CO2

UO4 Explain effect of alloying elements on iron carbon diagram CO2

UO5 Describe selection of materials and specifications based on IS, BS, SAE and

AISI

CO2

UO6 Classify Non-Ferrous alloys with respect to composition, properties and

applications

CO2

UO7 Explain various copper alloys like Cu-Sn, Cu-Zn, Cu-Be with respect to

phase diagram.

CO2

UO8 Explain various Aluminum alloys like Al-Cu, Al-Zn, Al-Si with respect to

phase diagram.

CO2

UO9 Explain various Tin alloys like Pb-Sn, Sn-Sb with respect to phase diagram. CO2

UO10 Explain various Magnesium alloys like Pb-Sn, Sn-Sb with respect to phase

diagram.

CO2

UO11 Explain miscellaneous alloys as super alloys with respect to phase diagram. CO2

Lesson schedule

Class

No.

Details to be covered

1 Cooling curve for pure iron, manufacturing of wrought iron, its properties and

application.

2 Iron-Iron Carbon diagram in accordance with cooling curve.

3 Definition of structures, carbon solubility in iron, slow cooling of steel.

4 Effect of alloying elements on iron carbon diagram

5 Classification of steels, types of alloy steels, Effect of alloying elements, properties

and applications of tool steels.

6 Types of cast iron, its properties and applications.

7 Copper and its alloys- phase diagrams, its properties and applications.

8 Aluminum and its alloys- phase diagrams, its properties and applications.

9 Magnesium and its alloys- phase diagrams, its properties and applications.

10 Nikel and its alloys- phase diagrams, its properties and applications.

11 Tin, zinc and its alloys- phase diagrams, its properties and applications.

Review Questions

Q1 Sketch and explain cooling curve for pure iron. CO2

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43

Q2 Sketch and explain Iron-Iron Carbon diagram.(Nov-2005, May-2005, Nov-

2009, Nov-2011, May-2011, Nov-2012, May-2012, May-2013)

CO2

Q3 Explain Carbon solubility in iron. CO2

Q4 Explain the significance of critical temperature lines. CO2

Q5 Classify Steels in accordance with chemical composition. Properties and

application.(Nov-2005, Nov-2012)

CO2

Q6 What is slow cooling of steel? CO2

Q7 Write a short note on stainless steel. (Nov-2009, Nov-2011, May-2011,

Nov-2012, May-2012)

CO2

Q8 Explain the effect of alloying elements on properties of steel. CO2

Q9 Explain the types of tool steel, their properties and applications. CO2

Q10 Classify cast iron in accordance with chemical composition. Properties and

application.(Nov-2005, Nov-2011, May-2011 )

CO2

Q11 What are the limitations on the use of Iron-Iron carbon diagram? CO2

Q12 Explain types of brasses, their properties and applications.(Nov-2011,

May-2011, May-2012)

CO2

Q13 Define and explain following structures- Austenite, Ferrite, Pearlite,

Cementite, Lediburite.

CO2

Q14 Explain types of bronzes, their properties and applications. (May-2005,

May-2011, Nov-2012, May-2012)

CO2

Q15 Write a short note on babbits. (Nov-2005) CO2

Q16 Explain aluminum alloys with their properties and application. (May-2005,

Nov-2011, May-2011, Nov-2012, May-2012)

CO2

Q17 Explain Tin alloys with their properties and applications. CO2

Q18 What are superalloys? CO2

Unit No 3 Unit Title Principles of Mechanical Testing Planned

Hrs.

04

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Explain the significance of metallurgical testing. CO3

UO2 Describe and perform Tensile and compression test on UTM. CO3

UO3 Describe and perform fatigue, impact and hardness testing. CO3

UO4 Explain the significance of Non Destructive testing. CO3

UO5 Describe and perform dye penetrant and magnetic particle inspection test. CO3

UO6 Describe and perform Ultrasonic crack detection test and radiography. CO3

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Lesson schedule

Class

No.

Details to be covered

1 Introduction to metallurgical testing, tensile testing, compression testing.

2 Hardness, Impact, Fatigue and creep testing.

3 Dye penetrant and magnetic particle inspection testing.

4 Ultrasonic crack detection, eddy current and radiography testing

Review Questions

Q1 Explain the significance of metallurgical testing. CO3

Q2 Differentiate between resilience and toughness. CO3

Q3 Explain the terms- proportional limit, elastic limit, yield point, yield

strength, ultimate strength, modulus of elasticity. (Nov-2005)

CO3

Q4 What is the difference between engineering stress-strain curve and true

stress-strain curve?

CO3

Q5 Sketch and explain Impact test with test specimen. (May- 2005, May-

2005, Nov-2011, May-2013)

CO3

Q6 Sketch and explain magnetic particle inspection. (May 2004, May- 2005,

May- 2009, Nov-2011, Nov-2012, May-2013)

CO3

Q7 What are the limitations of Magnetic particle inspection and ultrasonic

inspection?

CO3

Q8 Explain radiography of metals.(Nov-2005, May- 2005, Nov-2011) CO3

Q9 Sketch and explain ultrasonic inspection test.(May- 2005, May- 2005,

May-2011, Nov-2012)

CO3

Q10 What are the recent developments in non destructive testing? CO3

Q11 Write a short note on tensile testing method.(May 2004, Nov-2005) CO3

Q12 Sketch and explain brinell hardness test.(Nov-2005, May- 2005, May-

2005)

CO3

Q13 Explain fatigue testing method with neat diagram.(May- 2005, May-2013) CO3

Q14 Explain Rockwell hardness testing method with neat diagram. (May 2004,

Nov-2005, May- 2005, May-2012, May-2013)

CO3

Q15 Sketch and explain stress-strain diagram for mild steel. (May-2004, Nov-

2005, May-2012)

CO3

Q16 Write a short note on creep test. (May-2005, Nov-2011, May-2011, Nov-

2012, May-2012)

CO3

Q17 Write a short note on fluorescent penetrant test.(May 2004, May- 2005,

May- 2005, May-2011)

CO3

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Q18 Write a short on Eddy current inspection. CO3

Model Question Paper

Course Title : Metallurgy

Duration Max.

Marks

1 ½ Hrs Instructions:1. Attempt any three questions. 50

2. Figures to right indicates full marks

3.Draw neat sketch wherever necessary

Section-I

1 a What are imperfections in metallic crystals? Explain different point

defects.

08

b Explain why pure metals show under cooling during solidification

using phase rule

08

2 a Sketch and explain Iron-Iron Carbide diagram. List the important

temperatures, reactions, and important compositions on the diagram.

12

b Explain fatigue testing method with neat sketch. 06

Section-II

3 a Draw neat sketch of Cu-Zn equilibrium diagram and explain different

phase changes taking place on the diagram.

08

b Describe impact testing method with neat sketch. 08

4 Write short notes on any four of the following.

a) Types of α brasses

b) Partial eutectic system

c) Solid solutions

d) Tin bronzes

e) Aluminum alloys

f) Stainless steels

16

Section II

Unit No 4 Unit Title Principles of Heat treatment Planned

Hrs.

05

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Explain the effect of temperature and time on transformation. CO4

UO2 Explain Transformation of pearlite into austenite upon heating. CO4

UO3 Explain Transformation of austenite into pearlite, bainite and martensite on CO4

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46

cooling.

UO4 Sketch and explain TTT and CCT diagram and its significance. CO4

UO5 Describe the effect of alloying elements on TTT diagram. CO4

Lesson schedule

Class

No.

Details to be covered

1 Transformation of pearlite into austenite upon heating,

2 Transformation of austenite into pearlite, bainite and martensite on cooling,

3 TTT diagram and its significance, effect of alloying elements on TTT diagram,

4 CCT diagram and its significance,

5 CCT diagram for alloy steels.

Review Questions

Q1 Describe completely the changes that take place during the slow cooling of

a 0.5% carbon steel from austenitic range.

CO4

Q2 What is the effect of increasing cooling rate on – a) temperature of

austenite transformation, b) fineness of pearlite, c) amount of proeutectoid

constituent?

CO4

Q3 Define critical cooling rate. CO4

Q4 What factors influence the critical cooling rate ? Explain. CO4

Q5 Describe how a TTT diagram is determined experimentally. CO4

Q6 What are the limitations on the use of TTT diagram? CO4

Q7 Sketch and explain TTT diagram for 0.8% carbon steel and indicate the

cooling rates you would suggest for annealing, normalizing and

hardening.(Nov-2005, Nov-2009, Nov-2011, Nov-2012, May-2012, May-

2013)

CO4

Q8 Compare between pearlitic and bainitic transformation.(Nov-2009, May-

2011, Nov-2012, May-2013)

CO4

Q9 Write a short note on CCT diagrams.(Nov-2005, 2009, Nov-2011, Nov-

2012, May-2012, May-2013)

CO4

Q10 Explain the mechanism of transformation of austenite into bainite. How

does the transformation of upper and lower bainite differ from each

other?(Nov-2011, May-2011,May-2012, May-2013)

CO4

Q11 What is the effect and significance of alloying elements on TTT diagrams? CO4

Q12 Differentiate between CCT diagram and TTT diagram. (Nov-2005, Nov-

2011, May-2011, Nov-2012)

CO4

Q13 Explain pearlite to austenite transformation. CO4

Q14 What are solid state transformations in metals and alloys? Explain any one CO4

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transformation in detail.

Q15 Sketch and explain TTT diagram for 0.2% carbon steel.(May-2011, Nov-

2012, May-2012)

CO4

Unit No 5 Unit Title Heat treatment Processes Planned

Hrs.

09

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Explain the softening processes- full annealing, spherodising and subcriticle

annealing.

CO5

UO2 Describe the microstructural changes during heating and cooling in

annealing.

CO5

UO3 Explain the toughning treatments- Normalizing, hardening and tempering. CO5

UO4 Differentiate between Austempering and martempering. CO5

UO5 Explain the surface hardening methods- flame and induction hardening. CO5

UO6 Explain the case hardening methods- carburizing, nitriding, cyninding,

carbonitriding.

CO5

UO7 Describe the precipitation hardening- requirements, stages and common

alloys.

CO5

Lesson schedule

Class

No.

Details to be covered

1 Softening processes- Annealing, spherodising.

2 Softening processes- sub criticle annealing, stress relief annealing,

3 Toughning treatments- Normalizing, temperatures applied and its effects on properties

4 Hardening- mechanism of quenching, quenching medium, temperatures and

microstructures

5 Tempering- tempering temperatures, its effect on microstructures and properties.

6 Austempering, martempering- structural transformations and applications.

7 Hardenability, aging and sub-zero treatment.

8 Hardening- Surface hardening- Flame and Induction.

9 Case Hardening- Carburizing, Nitriding, cyniding and carbonitriding

10 Precipitaion Hardening- requirements, stages and common alloys.

Review Questions

Q1 Why do annealed steel show a decrease in tensile strength above 0.8%

carbon?

CO5

Q2 Is it possible to determine the approximate carbon content of a normalized

steel from microscopic study? Explain.

CO5

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Q3 Why do normalized steel show an increase in tensile strength upto 1.2 %

and then a decrease?

CO5

Q4 Explain why the surface hardness of quenched high carbon steel may be

less than the hardness under the surface.

CO5

Q5 What are the advantages of specifying steel on the basis of hardenability? CO5

Q6 Give two different methods of obtaining a spherodised cementite structure. CO5

Q7 What are the principle advantages of austempering compared with

conventional quech and temper?

CO5

Q8 What are the limitations on the use of using high carburising temperatures? CO5

Q9 What are the advantages of gas carburizing over pack carburizing? CO5

Q10 Explain why mild steel requires carburizing before hardening.(May-2012,

May-2013)

CO5

Q11 Explain the mechanism of precipitation hardening. (Nov-2005, May-2005,

Nov-2009, Nov-2011, May-2011, Nov-2012, May-2012, May-2013)

CO5

Q12 Explain the process of liquid carburizing. How is it more advantageous

than solid carburizing?

CO5

Q13 What are the various purposes of annealing ? Enlist the different types of

annealing.

CO5

Q14 Differentiate between Annealing and Normalizing.(Nov-2012, May-2012,

May-2013)

CO5

Q15 Sketch and explain setup for flame hardening. (Nov-2005, Nov-2009,

May-2011, May-2013)

CO5

Q16 Draw self explanatory diagram of- Annealing, normalizing and hardening

bands on Iron Carbon diagram.(Nov-2005, Nov-2012, May-2012, May-

2013)

CO5

Q17 Write a short note on austempering and martempering.(May-2011, Nov-

2012, May-2013)

CO5

Q18 Differentiate between conventional hardening and induction

hardening.(May-2005, Nov-2011, May-2011,May-2012, May-2013)

CO5

Unit No 6 Unit Title Powder Metallurgy Planned

Hrs.

04

Unit Outcomes

At the end of this unit the students should be able to:

UO1 Define and describe the significance of powder metallurgy. CO6

UO2 Explain the powder manufacturing processes and its types. CO6

UO3 Explain the sintering process CO6

UO4 Describe the flow charts for manufacturing for tool materials, bearing, CO6

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bushes, etc.

Lesson schedule

Class

No.

Details to be covered

1 Powder metallurgy processes- preparation of metal powders, characteristics of metal

powders,

2 Mixing, compacting, sintering, hot pressing,

3 Applications of powder metallurgy,

4 flow charts of powder metallurgy products,

Review Questions

Q1 Why is particle size distribution important in the packing of powders? CO6

Q2 Discuss the importance of particle shape on the properties of sintered

compacts.

CO6

Q3 List the three common methods of powder production and discuss their

influences on the properties of the final product.(May-2005, Nov-2009,

Nov-2011, Nov-2012, May-2012, May-2013)

CO6

Q4 Contrast mechanical and hydraulic compacting presses with regard to

advantages, disadvantages and applications. (May-2005, Nov-2011, May-

2011, May-2012, May-2013)

CO6

Q5 Write a short note on sintering and explain why is sintering carried out in

controlled atmosphere furnace ?(Nov-2005, Nov-2009, Nov-2011, May-

2011, Nov-2012, May-2012, May-2013)

CO6

Q6 Why do elevated temperatures tend to favor the sintering process although

sintering forces tend to decrease with increasing temperatures?

CO6

Q7 What are the advantages and disadvantages of hot pressing as compared

with cold pressing and sintering? (Nov-2009, Nov-2011, May-2012, May-

2013)

CO6

Q8 Draw a flow chart for manufacturing of electrical contacts. (May-2005,

Nov-2009, May-2011,May-2012, May-2013)

CO6

Q9 Draw a flow chart for manufacturing of sintered bushes. (May-2011, Nov-

2012, May-2012, May-2013)

CO6

Q10 Give three specific applications of powder metallurgy parts. Describe how

these parts may be manufactured by other methods, and give the

advantages of the powder metallurgy method. (Nov-2005, May-2005, Nov-

2009, Nov-2011, May-2011, Nov-2012, May-2012, May-2013)

CO6

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50

Model Question Paper

Course Title : Metallurgy

Duration Max.

Marks

1 ½ Hrs Instructions: 1. Attempt any three questions. 50

2. Figures to right indicates full marks

3.Draw neat sketch wherever necessary

Section-I

1 a What is a TTT diagram? What is its significance and use? Explain the

experiment and procedure of drawing TTT diagram for an eutectoid

steel.

09

b What is the significance of CCR in TTT diagram? 03

c Explain the mechanism of transformation of austenite into pearlite 06

2 a What are the various purposes of annealing? Enlist the different types

of annealing.

08

b What are the factors influencing selection of bath used for quenching? 04

c Explain the steps and structural transformations that take place during

precipitation hardening.

04

Section-II

1 a What is the importance of controlled atmospheres? Explain chemistry

and applications of endothermic type controlled atmosphere,

05

b Enlist the various advantages of powder metallurgy. 06

c Draw a neat sketch and explain the working of salt bath furnace. 05

2 Write short notes on any four of the following.

a) Normalizing

b) Nitriding

c) Sintering

d) CCT diagrams

e) Spherodizing

f) Martensite transformation

16

Assignments

Assignment No. 1

Assignment Title Metals and Alloy Systems CO1

Batch I 1. Sketch and explain BCC, FCC and HCP structures with example.

2. Explain with diagram- Gibbs phase rule and Lever arm principle.

3. Explain Non equilibrium cooling.

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51

Batch II 1. Write a short note on crystal imperfections.

2. Explain how the equilibrium diagram can be constructed from cooling

curve?

3. Explain why pure metals show under cooling during solidification using

phase rule

Batch III 1. Differentiate between crystal, dendrite and grain.

2. Write a short note on Partial Eutectic system.

3. Differentiate between Eutectic, eutectoid and perictic reaction.

Batch IV 1. What is solid solution? What are the types of solid solution? Enumerate

the conditions for their formation [with diagrams]

2. Explain the alloy formation by crystallization, nucleation, solidification

and growth.

3. Explain dendritic structure and coring.

Assignment No. 2

Assignment Title Study of Phase Diagrams: CO2

Batch I 1. Sketch and explain cooling curve for pure iron.

2. Sketch and explain Iron-Iron Carbon diagram.

3. Explain Carbon solubility in iron.

4. Explain aluminum alloys with their properties and application.

Batch II 1. Explain the significance of critical temperature lines.

2. Classify Steels in accordance with chemical composition. Properties and

application.

3. What is slow cooling of steel?

4. Write a short note on babbits.

Batch III 1. Write a short note on stainless steel.

2. Explain the effect of alloying elements on properties of steel.

3. Explain the types of tool steel, their properties and applications.

4. Explain types of bronzes, their properties and applications.

Batch IV 1. Classify cast iron in accordance with chemical composition. Properties

and application.

2. What are the limitations on the use of Iron-Iron carbon diagram?

3. Explain types of brasses, their properties and applications.

4. Define and explain following structures- Austenite, Ferrite, Pearlite,

Cementite, Lediburite.

Assignment No. 3

Assignment Title Principles of Mechanical Testing CO3

Batch I 1. Explain the significance of metallurgical testing.

2. Explain the terms- proportional limit, elastic limit, yield point, yield

strength, ultimate strength, modulus of elasticity.

3. Sketch and explain Impact test with test specimen.

4. Sketch and explain brinell hardness test.

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52

Batch II 1. Differentiate between resilience and toughness.

2. Sketch and explain magnetic particle inspection.

3. What are the recent developments in non destructive testing?

4. Explain fatigue testing method with neat diagram.

Batch III 1. What is the difference between engineering stress-strain curve and true

stress-strain curve?

2. Sketch and explain ultrasonic inspection test.

3. Explain Rockwell hardness testing method with neat diagram.

4. Write a short note on creep test.

Batch IV 1. What are the limitations of Magnetic particle inspection and ultrasonic

inspection?

2. Explain radiography of metals.

3. Write a short note on tensile testing method.

4. Write a short note on fluorescent penetrant test.

Assignment No. 4

Assignment Title Principles of Heat Treatment CO4

Batch I 1. Describe completely the changes that take place during the slow cooling

of a 0.5% carbon steel from austenitic range.

2. Describe how a TTT diagram is determined experimentally.

3. Write a short note on CCT diagrams.

4. Explain pearlite to austenite transformation.

Batch II 1. What is the effect of increasing cooling rate on – a) temperature of

austenite transformation, b) fineness of pearlite, c) amount of proeutectoid

constituent?

2. What are the limitations on the use of TTT diagram?

3. Explain the mechanism of transformation of austenite into bainite. How

does the transformation of upper and lower bainite differ from each other?

4. What are solid state transformations in metals and alloys? Explain any

one transformation in detail.

Batch III 1. Define critical cooling rate.

2. Sketch and explain TTT diagram for 0.8% carbon steel and indicate the

cooling rates you would suggest for annealing, normalizing and hardening.

3. What is the effect and significance of alloying elements on TTT

diagrams?

4. Sketch and explain TTT diagram for 0.2% carbon steel.

Batch IV 1. What factors influence the critical cooling rate ?

2. Compare between pearlitic and bainitic transformation.

3. Differentiate between CCT diagram and TTT diagram.

4. Write a short on quenching mechanism.

Assignment No. 5

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53

Assignment Title Heat Treatment Processes CO5

Batch I 1. Why do annealed steel show a decrease in tensile strength above 0.8%

carbon?

2. What are the principle advantages of austempering compared with

conventional quech and temper?

3. Explain the mechanism of precipitation hardening.

4. Sketch and explain setup for flame hardening.

Batch II 1. Why do normalized steel show an increase in tensile strength upto 1.2 %

and then a decrease?

2. What are the limitations on the use of using high carburising

temperatures?

3. Explain the process of liquid carburizing. How is it more advantageous

than solid carburizing?

4. Draw self explanatory diagram of- Annealing, normalizing and

hardening bands on Iron Carbon diagram.

Batch III 1. Explain why the surface hardness of quenched high carbon steel may be

less than the hardness under the surface.

2. What are the advantages of gas carburizing over pack carburizing?

3. What are the various purposes of annealing ? Enlist the different types of

annealing.

4. Write a short note on austempering and martempering.

Batch IV 1. Give two different methods of obtaining a spherodised cementite

structure.

2. Explain why mild steel requires carburizing before hardening.

3. Differentiate between Annealing and Normalizing.

4. Differentiate between conventional hardening and induction hardening.

Assignment No. 6

Assignment Title Powder Metallurgy CO6

Batch I 1. Why is particle size distribution important in the packing of powders?

2. Write a short note on sintering and explain why is sintering carried out in

controlled atmosphere furnace ?

3. Draw a flow chart for manufacturing of sintered bushes.

Batch II 1. Discuss the importance of particle shape on the properties of sintered

compacts.

2. Why do elevated temperatures tend to favor the sintering process

although sintering forces tend to decrease with increasing temperatures?

3. Draw a flow chart for manufacturing of carbide tools.

Batch III 1. List the three common methods of powder production and discuss their

influences on the properties of the final product.

2. What are the advantages and disadvantages of hot pressing as compared

with cold pressing and sintering?

3. Draw a flow chart for manufacturing of electrical contacts.

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54

Batch IV 1. Contrast mechanical and hydraulic compacting presses with regard to

advantages, disadvantages and applications.

2. Draw a flow chart for manufacturing of electrical contacts.

3. Enlist the various advantages of powder metallurgy.

Course Plan

Course FLUID MECHANICS Course Code

Examination

Scheme

Theory Term Work POE Total

Max. Marks 100 25 25 150

Contact

Hours/ week

3 2 -- 5

Prepared by Sabnis. N.V. Date 15/6/2015

Prerequisites Applied Mechanics, Physics, Mathematics

Course Outcomes

At the end of the course the students should be able to:

CO1 Describe the basics of Fluid Mechanics and statics

CO2 Explain the concept of Kinematics of the fluid flow

CO3 Describe the basic of Dynamics of Fluid flow and momentum equation

CO4 Elaborate the dimensional analysis and explain the concept of dimension less

nos.

CO5 Describe the concept of Laminar Flow and flow through pipe and explain the

basic of Boundary Layer.

CO6 Describe and evaluate the forces on immersed bodies and Elaborate the concept

of Compressible flow

Mapping of Cos with Pos

COs

POs

a b c d e f g h i j k l m n o

CO1 Y Y Y Y

CO2 Y Y Y Y Y

CO3 Y Y Y

CO4 Y Y Y

CO5 Y Y Y Y Y

C06 Y Y Y

Course Contents

Unit No. Title No. of

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55

Hours

Section I

1. Fluid Properties and Fluid Statics:

A) Fluid Properties: Definition of fluid, Fluid as a continuum, Properties

of fluid, Viscosity, Types of fluid, Compressibility, Surface tension,

Capillarity and vapor pressure.

B) Fluid Statics: Pascal ‟ s law, Hydrostatic law of pressure, Total

Pressure, Centre of Pressure, Buoyancy, Meta centre, Condition of

Equilibrium of floating and submerged bodies (No Numerical

Treatment on fluid Statics)

07

2. Fluid Kinematics:

Eulerian and Langragian approach of fluid flow, Flow visualization,

Total or material derivative for velocity field, Types of flow,

Streamline, Path line, streak line, Stream tube, Continuity equation in

Cartesian coordinates in three dimensional form. Velocity and

Acceleration of fluid particles, Stream function and velocity potential

function.

06

3. Fluid Dynamics:

Equation of motion.Integration of Euler's equation as energy

equation.Energy correction factor, concept of HGL and THL or TEL,

Steady flow through orifice.Orificemeter, Time required to empty the

tank through an orifice at its bottom, Venturimeter, Flow over triangular

and rectangular notches, Pitot tube. Derivation of momentum equation,

momentum correction factor.Applications of momentum equation

08

4. Laminar Flow and Pipe Flow:

A) Laminar Flow: Laminar flow through circular pipes. Laminar flow

through parallel plates, Introduction to NavierStoke‟s equation and its

applications

B) Pipe Flow: Energy losses in transition, expansion and contraction

(Darcy‟s and Chezy‟s equation), Parallel pipe, Siphon pipes, Branching

pipes and equivalent pipes, Moody‟s Diagram. .

07

5. Boundary Layer Theory and Dimensional Analysis, Similitude

A) Boundary Layer Theory: Boundary layer thickness, its

characteristics, laminar and turbulent boundary layers, separation,

boundary layer control

B) Dimensional Analysis, Similitude:Dimensionallyhomogeneous

equations, Buckingham's Pi-theorem, Calculation of dimensionless

parameters. Similitude, complete similarity, Model Scales

06

6. Forces On Immersed Bodies and Compressible Flow

A) Forces on Immersed Bodies: Lift and Drag, Drag on a flat plate and

on aerofoil. Types of drags, Development of lift. (Magnus effect)

stalling condition of aerofoil.

B) Compressible Flow: Propagation of elastic waves, Mach Cone and

Mach number. Energy equation

06

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56

Reference Books:

Sr.

No.

Title of Book Author Publisher/Edition Units

1. Fluid Mechanics, K. L. Kumar S. Chand Publication.

New Delhi.

1,2,3,4,5,6

2. Fluid Mechanics , R. K. Bansal, Laxmi publications.

New Delhi.

1,2,3,4,5,6

3. Fluid Mechanics V. L. Streeter

and E. B. Wylie,

Tata McGraw Hill Pvt

Ltd.

1,2,3,4,5,6

4. Fluid mechanics and

Hydraulic Machines.

Modi and Seth, 1,2,3,4,5,6

5 Introduction to Fluid

Mechanics

Edward J.

Shaughnessy, Jr,

Oxford University press

1,2,3,4,5,6

Scheme of Marks

Section Unit No. Title Marks

I-II

1 Fluid Properties and Fluid Statics 22

2 Fluid Kinematics 22

3 Fluid Dynamics 22

4 Laminar Flow and Pipe Flow 22

5 Boundary Layer Theory and Dimensional Analysis,

Similitude

22

6 Forces On Immersed Bodies and Compressible Flow 22

Course Unitization

Section

Unit Course

Outcomes

No. of Questions in

No. Title CAT-I CAT-II

I

1 Fluid Properties and Fluid

Statics

CO1 Q. No. 1,3

2 Fluid Kinematics CO2 Q. No. 2,3

3 Fluid Dynamics CO3 Q. No. 1,3

5 Laminar Flow & Pipe Flow CO4 Q. No. 2,3

Unit wise Lesson Plan

Section I

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Unit No 1 Unit Title Fluid Properties and Fluid Statics: Planne

d Hrs.

07

Unit Outcomes

At the end of this unit the students should be able to:

UO1 To Explain the concept of fluid , its properties & Viscosity and fluid statics CO1

UO2 To study various types of fluids , and the parameters related to it CO2

Lesson schedule

Class

No.

Details to be covered

1 Definition of fluid, Fluid as a continuum, Properties of fluid,

2 Viscosity, Types of fluid, Compressibility, Surface tension

3 Capillarity and vapor pressure. Pascal‟s law, Hydrostatic law of pressure

4 Total Pressure, Centre of Pressure, Buoyancy

5 Meta centre, Condition of Equilibrium of floating and submerged bodies

6 Problems on the topic

7 Problems on the topic

Review Questions

Q1 Define Fluid and list the various properties of Fluid CO1

Q2 Define Capillarity, surface tension and explain types of fluid, CO1

Q3 Define the Total pressure, centre of pressure and Buoyancy CO1

Unit No 2 Unit Title Fluid Kinematics Planne

d Hrs.

06

Unit Outcomes

At the end of this unit the students should be able to:

UO1 To Explain the concept of Flow Visualization , Types of Flow CO2

UO2 To find Velocity and Acceleration of fluid particles . CO2

UO3 To study the continuity equation CO2

Lesson schedule

Class

No.

Details to be covered

1 Eulerian and Langragian approach of fluid flow, Flow visualization,

2 Total or material derivative for velocity field, Types of flow,

3 Streamline, Path line, streak line, Stream tube,

4 Continuity equation in Cartesian coordinates in three dimensional form..

5 Velocity and Acceleration of fluid particles, Stream function and velocity potential

function

6 Problems

Review Questions

Q1 Explain the concept of types of fluid flow CO2

Q2 Expalin stream line, path line , streak line , stream tube CO2

Unit No 3 Unit Title Fluid Dynamics

Planne

d Hrs.

08

Unit Outcomes

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At the end of this unit the students should be able to:

UO1 To study Euler’s Equation and Bernoulli’s Equation. CO3

UO2 To Explain Venturimeter&Orificemeter. CO3

UO3 To Explain flow over notches CO3

UO4 To get idea about momentum equation CO3

Lesson schedule

Class

No.

Details to be covered

1 Equation of motion. Integration of Euler's equation as energy equation.

2 Energy correction factor, concept of HGL and THL or TEL

3 Steady flow through orifice. Orificemeter

4 Time required to empty the tank through an orifice at its bottom, Venturimeter,

5 Flow over triangular and rectangular notches, Pitot tube.

6 Derivation of momentum equation, momentum correction factor. Applications of

momentum equation.

7 Problems

8 Problems

Review Questions

Q1 Derive Euler’s Equation and from that derive Bernoulli’s Euation CO3

Q2 Derive the equation for flow through Orifice and Venturimeter CO3

Q3 Derive the equation for Time required to empty the tank through an orifice

at its bottom

CO3

Q4 Derivation of momentum equation CO4

Unit No 4 Unit Title Laminar Flow and Pipe Flow

Planne

d Hrs.

07

Unit Outcomes

At the end of this unit the students should be able to:

UO1 To Explain the concept of laminar flow through various pipes

To study NavierStoke’s Equation

CO4

UO2 To study the energy losses in transition CO5

UO3 To determine Darcy’s &Chezy’s Equation CO4

UO4 To Explain the concept of a siphon pipe CO4

Lesson schedule

Class

No.

Details to be covered

1 Laminar flow through circular pipes.

2 Laminar flow through parallel plates, Introduction to NavierStoke‟s equation and its

applications

3 Energy losses in transition, expansion and contraction (Darcy‟s and Chezy‟s

equation),

4 Parallel pipe, Siphon pipes

5 Branching pipes and equivalent pipes

6 Moody‟s Diagram.

7 Problems

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Review Questions

Q1 Derive the equation for stress distribution and velocity distribution in flow

through circular pipes.

CO5

Q2 Derive the equation for stress distribution and velocity distribution iflow

through parallel plates.

CO5

Q3 Explain Energy losses in transition, expansion and contraction ,Darcy‟s

and Chezy‟s equation

CO5

Unit No 5 Unit Title Boundary Layer Theory and Dimensional

Analysis, Similitude

Planne

d Hrs.

06

Unit Outcomes

At the end of this unit the students should be able to:

UO1 To Explain the concept of Boundary Layer CO6

UO2 To Explain its various characteristics CO7

UO3 To Explain Dimensional Homogeneous equations, Buckingham’s π

theorem and the concept of Similitude

CO7

Lesson schedule

Class

No.

Details to be covered

1 Boundary layer thickness, its characteristics

2 Laminar and turbulent boundary layers, separation, boundary layer control

3 Dimensionally homogeneous equations, Buckingham's Pi-theorem

4 Calculation of dimensionless parameters.

5 Similitude, complete similarity, Model Scales.

6 Problems

Review Questions

Q1 Write a short note on Boundary layer thickness, its characteristics CO6

Q2 Explain Dimensionally homogeneous equations, Buckingham's Pi-theorem CO7

Unit No 6 Unit Title Forces On Immersed Bodies and

Compressible Flow

Planne

d Hrs.

06

Unit Outcomes

At the end of this unit the students should be able to:

UO1 To study the types of drags on flat and the drag on an aerofoil CO8

UO2 To Explain concept of development of lift CO8

UO3 To determine energy equation of compressible flows

Lesson schedule

Class

No.

Details to be covered

1 Lift and Drag, Drag on a flat plate and on aerofoil.

2 Types of drags, Development of lift. (Magnus effect) stalling condition of aerofoil.

3 Propagation of elastic waves, Mach Cone and Mach number.

4 Energy equation of compressible flows.

5 Stagnation pressure, Temperature and density.

6 Problems

Review Questions

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Q1 Explain the concept of Lift and Drag, and the drag on a flat plate and on

aerofoil.

CO6

Q2 Explain the energy equation in the compressible flow CO6

Lab Plan

1 Study and demonstration of Pressure Measuring Devices

2 Flow visualization by plotting of streamlines (Heleshaw‟s apparatus).

3 Reynolds experiment.

4 Verification of Bernoulli's equation.

5 Calibration of venturimeter/Orifice-meter

6 Calibration of notches.

7 Orifice under steady and unsteady flow condition

8 Determination of velocity profile through circular pipes for laminar flow.

9 Determination of minor losses in pips-fittings

10 Determination of coefficient of friction in pipes of different materials.

11 Determination of loss of friction in series/parallel pipes.

12 Demonstration or trial on wind tunnel for measurement of lift and drag on

any model.