Shivaji University, Kolhapur - :: Welcome :: Sanjay … · · 2018-02-157 5. Fourier Series...
Transcript of Shivaji University, Kolhapur - :: Welcome :: Sanjay … · · 2018-02-157 5. Fourier Series...
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
2
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
3
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
4
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
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
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 ∞
14
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
15
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
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
17
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+⋯
18
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
19
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 √ √
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:
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
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,
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
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
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
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
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
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
29
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
30
(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
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
32
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
33
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]
34
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
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
36
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
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
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
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
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
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
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
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
44
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
45
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
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
47
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
48
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
49
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
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.
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.
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
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.
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
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
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
57
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
58
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
59
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
60
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.