ACADEMIC HAND BOOK 2017-2018 II - vnr vjiet

VALLURUPALLI NAGESWARA RAO VIGNANA JYOTHI INSTITUTE OF ENGINEERING & TECHNOLOGY

AN AUTONOMOUS INSTITUTE

(Approved by AICTE - New Delhi, Govt. of A.P.)

Accredited by NBA and NAAC with ‘A’ Grade

Vignana Jyothi Nagar, Bachupally, Nizampet (S.O.), Hyderabad-500 090. A.P., India.

ACADEMIC HAND BOOK

2017-2018

II– B. TECH AE

I SEMESTER

VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING AND TECHNOLOGY

AN AUTONOMOUS INSTITUTE

VISION

A Deemed University of Academic Excellence, for National and International Students Meeting

global Standards with social commitment and Democratic Values

MISSION

To produce global citizens with knowledge and commitment to strive to enhance quality of life

through meeting technological, educational, managerial and social challenges

QUALITY POLICY

• Impart up to date knowledge in the students chosen fields to make them quality Engineers

• Make the students experience the applications on quality equipment and tools.

• Provide quality environment and services to all stock holders.

• Provide Systems, resources and opportunities for continuous improvement.

• Maintain global standards in education, training, and services


BACHUPALLY, NIZAMPET (S.O), HYDERABAD – 500090

LESSON PLAN: 2017-18

A Good Lesson Plan is instrumental for the delivery of course content in a competent way so that students get benefited in view of

learning, developing good skill set, updating with current trends in industry etc., Delivery including latest trends in the technology and

applications brings deep insight of the course in students. As the plan includes the home assignments, quizzes, course projects etc., it

carries out the continuous assessment of student learning (course outcomes).

The course delivery in adherence to the lesson plan is ensured through course level audit forms on regular basis.

II B. Tech : I Sem : MECHANICAL, ELECTRICAL AND AUTOMOBILE L T/P/D C

3 1 4

Course Name: PDE&CA Course Code: 5BS14

Names of the Faculty Member: Dr.G.Sireesha, Dr.G.V.P.N Srikanth

Dr.J.Srinivas

Number of working days: 60

Number of Hours/week: 4

Total number of periods planned: 62

1. PREREQUISITES

Integral and Differential Calculus

2. COURSE OBJECTIVES

(Objectives define the importance of course and how the course is helpful to the students in their career. Objectives

must be defined first and contents must be developed later.)

The student should be able

• Computing Fourier coefficients.

• Understand the properties of Fourier transforms.

• Apply method of separation of variables to solve partial differential equations.

VNR VJIET/ACADEMICS/2017/Formats/ I

• Apply Cauchy’s theorem, Cauchy’s integral formula and residue theorem to evaluate complex intregation.

3. COURSE OUTCOMES (COs)

(Outcomes define what the student will be able to do upon completion of the course. Course outcomes must be

assessable. The blooms taxonomy terms are used as reference in defining course outcomes)

Upon completion of this course the student is able to

• Solve problems using Fourier series.

• Evaluate problems involving Fourier and inverse Fourier transforms.

• Solve the second order linear partial differential equations by method of separation of variables and Fourier series.

• Evaluate line and contour intregals.

4. MAPPING OF COs WITH POs

(This mapping represents the contribution of course in attaining the program outcomes and there by program

educational objectives. This also helps in strengthening the curriculum towards the improvement of program.)

Course

Outcomes

(COs)

Program Outcomes (POs)

a B c d E f g h i j K L

CO 1 3 3 2 1 2

CO 2 3 3 1 3 3

CO 3 2 3 2 2 2 3 2 2 2 3

3: High correlation, 2: Moderate correlation and 1: Low Correlation

5. LEARNING RESOURCES

(i) TEXT BOOKS

T1. Higher Engineering Mathematics – B. S. Grewal, Khanna publisher.

T2. Advance Engineering Mathematics - Peter O’Neil,(2000),5th Edition, Cengage Learning

T3. Schaum’s Outline Of Complex Variables - Murray.R.Spiegel,(2011), 2nd Edition, Tata McGraw Hill.

T4. Complex Variables & Its Applications- Churchill and Brown, (1996), International Edition, McGraw Hill.

(ii) REFERENCES (Publications/ Open Learning Resources)

(Course delivery including latest trends brings good insight of the course in students and also inculcates the habit of self

learning among the students.

Publications referred can be given unit wise or at course level.)

(a) Publications

PI. David Maslen ; Daniel N. Rockmore; Sarah Wolff “The Efficient Computation of Fourier Transforms on Semisimple Algebras” pp 1–24, 11 July 2017.

P2.

(b) Open Learning Resources for self learning

L1. http://nptel.ac.in/courses/117101055/18

L2. https://www.youtube.com/watch?v=gZNm7L96pfY

L3. https://www.mooc-list.com/tags/fourier

L4. www.mathworks.com/help/matlab/math/partial.

L5. www.youtube.com/watch?v=VBn1diQCykQ.

https://link.springer.com/article/10.1007/s00041-017-9555-5#article-dates-history

http://nptel.ac.in/courses/117101055/18

https://www.youtube.com/watch?v=gZNm7L96pfY

https://www.mooc-list.com/tags/fourier

http://www.mathworks.com/help/matlab/math/partial

http://www.youtube.com/watch?v=VBn1diQCykQ

(iii) JOURNALS

J1. Journal Of Fourier Analysis and Applications

J2. Complex Analysis and Operator Theory

J3. Journal of Complex Analysis.

6. DELIVERY METHODOLOGIES

(Depending on the suitability to the delivery of concept, one or more among the following delivery methodologies are

adopted to engage the student in learning)

DM1: Chalk and Talk DM5: Open The Box

DM2: Learning by doing

DM3: Collaborative Learning (Think Pair Share, POGIL, etc.) DM6: Group Project

DM4: Demonstration (Physical / Laboratory / Audio Visuals)

7. PROPOSED FIELD VISITS/ GUEST LECTURE BY INDUSTRY EXPERT

(To be added for the courses as directed by the department.)

Guest Lecture: "Application of Fourier Series & Fourier Transforms in Engineerings" on

8. ASSESSMENT (As per Regulations, AM1 and AM2 are compulsory for assessment. Whereas, any two or more

assessment methodologies can be considered from AM3 to AM9 under assignment towards continuous assessment of

the performance of students.)

AM1: Semester End Examination . AM2: Mid Term Examination

AM3: Home Assignments

AM6: Quizzes

AM7: Course Projects**

** (To be added for the courses as directed by the department. The no. of course projects is left to the liberty of faculty)

9. WEIGHTAGES FOR PROPOSED ASSESSMENT METHODOLOGIES

(The allotted marks for home assignments, quizzes and etc., except course projects are left to the liberty of faculty. But

for the finalisation of assignment marks, the following weightages can be considered.)

R15

S. No. Assessment Methodology Weightages in marks for the

courses with Course project

Weightages in marks for

the courses without

Course project

1. Home Assignments (AM3) 3%

10

5% 10

2. Quizzes (AM6) 3% 5%

3. Course project (AM7) 4% -

4. Mid Term Examination (AM2) 30 30

5. Semester End Examination (AM1) 60 60

(i) HOME ASSIGNMENTS

On the beginning day of each unit, home assignment sheet is given to the students and the solution sheet for the same is expected after

two days of the completion of unit.

(ii) QUIZZES

Two quizzes are conducted in the course duration. One is scheduled on 29/08/2017 and the second one is scheduled on 04/11/2017.

10. SIMULATION SOFTWARES (If any)

1. MATLAB

2. MATHEMATICA

11. DETAILED COURSE DELIVERY PLAN

(Detailed syllabus mentioning its learning outcomes, teaching plan, tutorial questions and home assignment questions

for each unit can be given. Heads under teaching plan is given below. Model Academic plan can be taken as reference.)

UNIT -I

Fourier series: Fourier series -- Fourier series of periodic functions, Euler’s formulae, Fourier series of even and odd functions having arbitrary periods, Half - range Fourier series. LEARNING OUTCOMES

After completion of this unit the student will be able to

• Express the function in terms of sine and cosine series in the given interval.

• Find the Fourier coefficients for a given function and express it in terms of sine/cosine series.

• Solve even and odd functions in terms of Fourier series.

• Evaluate the given function in terms of either half range Fourier sine series (or) cosine series.

TEACHING PLAN

S.

No. Contents of syllabus to be taught

No. of

Lecture

Periods

Lecture

Dates

Proposed Delivery

Methodologies

Learning Resources /

References

(Text Books /

Journals /

Publications/ Open

Learning Resources)

Course

Outcomes

1) Introduction and Applications of Fourier

series 1 5-07-17

DM1. Chalk and Talk (along

with PPT)

DM4. Demonstration of

one example.

T.1& T.2

L.3

CO 1

2)

Calculation of Euler’s coefficients.

1 6-07-17

DM1. Chalk and Talk

DM4. Detailed analysis with

the help of simulation

model

T.1 & T.2 CO 1

3) Problems on fourier series 1 7-07-17

DM1. Chalk and Talk



model

T.1 & T.2 CO 1

4) Points of discontinuity 1 7-07-17

DM1. Chalk and Talk



model

T.1, T.2 & L1 CO 1

5) Problems on discontinuity 1 12-07-17 DM1. Chalk and Talk. T.1& T.2 CO 1

6) Problems on even & odd function 1 13-07-17 DM1. Chalk and Talk. T.1& T.2 CO 1

7) Half range fourier series 1 14-07-17

DM1. Chalk and Talk



model

T.1 & T.2

L.3

CO 1

8) Problems 1 14-07-17

DM1. Chalk and Talk



model

T.1 & T.2 CO 1

9) Change of interval 1 19-07-17

DM1. Chalk and Talk



model

T.1& T.2 CO 1

10)

Problems on change of interval

1 20-07-17 DM1. Chalk and Talk T.1, T.2 & L.1 CO 1

TUTORIAL QUESTIONS

1.Write Dirichlet’s conditions for Fourier Expansion.

2. Find the Fourier series to represent the function −= xxxf ,sin)( .

3.Find the Fourier coefficient nb for the function f(x) = x.

4. Find half range cosine series for f(x) =

−

xforxlk

xforkx

2/)(

2/0

5. Expand 2)( 2 −= xxf as a Fourier series in the interval (-2,2).

UNIT- II

Fourier Transforms -- Fourier transform, Sine and Cosine transforms, properties and its applications.

LEARNING OUTCOMES


• Find Fourier transforms of given functions.

• Find Fourier sine and cosine transforms.

• Find finite Fourier sine/cosine transform in the given interval.

TEACHING PLAN

S.


No. of

Lecture

Periods

Lecture

Dates

Proposed Delivery

Methodologies


References

(Text Books /

Journals /

Course

Outcomes

Publications/ Open

Learning Resources)

1)

Introduction to Fourier transforms. 1 9-08-17

DM1. Chalk and Talk



model.

T.1 & L.2 CO2

2) problems on Fourier sine/cosine intregal 1 10-08-17

DM1. Chalk and Talk

(along with PPT)

T.1 CO2

3) Fourier integral in complex form

Fourier sine/cosine transform 1 11-08-17

DM1. Chalk and Talk

(along with PPT)

DM3. Collaborative

Learning (Think Pair Share)

T.1& T.2 CO2

4) Properties of Fourier transforms

1 16-08-17 DM1. Chalk and Talk

T.1, T.2 &L2. CO2

5)

Problems on Fourier transform

1 17-08-17

DM1. Chalk and Talk

DM3. Collaborative


T.1 & L.2 CO2

6)

Problems 1 18-08-17

DM1. Chalk and Talk

DM3. Collaborative


T.1 & L.2 CO2

7) Problems on Inverse Fourier transform 1 19-08-17

DM1. Chalk and Talk

DM3. Collaborative


T.1 & L.2 CO2

8) Problems on Fourier sine/cosine

transforms 1 21-08-17

DM1. Chalk and Talk

DM3. Collaborative


T.1 & L.2 CO2

9) Problems 1 23-08-17

DM1. Chalk and Talk

DM3. Collaborative


T.1 & L.2 CO2

10) Problems on inverse Fourier

sine/cosine transform 1 24-08-17

DM1. Chalk and Talk

DM3. Collaborative


T.1 & L.2 CO2

11) Problems 1 25-08-17

DM1. Chalk and Talk

DM3. Collaborative


T.1 & T.2 CO2

12) Finite fourier sine/cosine transforms 1 28-08-17

DM1. Chalk and Talk

DM3. Collaborative


T.1 & T.2 CO2

13) Problems 1 30-08-17

DM1. Chalk and Talk

DM3. Collaborative


T.1 & L.2 CO2

TUTORIAL QUESTIONS

1. Write Dirichlet’s conditions for Fourier transform.

2.If F(s) is the complex Fourier Transform of f(x), then prove that )())(( sFeaxfF isa=− .

3. Find the Fourier Transform of f(x) defined by

f(x) =

−

10

11 2

xfor

xforx hence evaluate

dxx

x

xxx)

2cos(

)sin()cos(

0

3

−

4. Find Fourier transform of f(x) defined by f(x) = 22 xae−

5. Find the Fourier sine transform ofx

exf

ax−

=)( .

UNIT- III

Standard Partial Differential Equations:

Method of seperation of variables, Applications: Problems of vibrating string- wave equation, Problems of one-dimensional heat equation,

Problems of steady state two dimensional heat flow-Laplace equation.

LEARNING OUTCOMES


• Solve the second order linear partial differential equations by method of separation of variables and Fourier series.

• Solve the first order wave equation by using the method of separation of variables and get the solution of wave equation.

• Find the solution of one dimensional heat equation in steady state and transient state.

• Solve Laplace equation by using the method of separation of variables.

TEACHING PLAN

S.


No. of

Lecture

Periods

Lecture

Dates

Proposed Delivery

Methodologies


References

(Text Books /

Journals /

Publications/ Open

Learning Resources)

Course

Outcomes

1)

Introduction to partial differential

equations

1 21/07/17

DM1. Chalk and Talk



model

T.1, T.2 & L4 CO 3

2) Elimination of arbitrary functions &

arbitrary constants 1 21/07/17

Tutorial

DM1. Chalk and Talk T.1, T.2 CO 3

3) Method of separation of variables 1 24/07/17

DM1. Chalk and Talk



model

T.1 & T.2 CO 3

4) one dimensional wave equation 1 26/07/17

DM1. Chalk and Talk



model

T.1 & T.5 CO 3

5) Problems 1 27/07/17

Tutorial

DM3: Collaborative

Learning -Think Pair Share

T.1, T.2 CO 3

6) one dimensional heat flow equation 1 28/07/17

DM1. Chalk and Talk



model

T.1, T.2& L5 CO 3

7) Problems on steady state heat flow 1 31/07/17

DM1. Chalk and Talk



model

T.1, T.2 CO 3

8) Problems on heat flow equation 1 2/08/17

Tutorial

DM3: Collaborative


T.1, T.2 & L5 CO 3

9) Laplace equation 1 3/08/17 DM1. Chalk and Talk

T.1, T.2 & L5 CO 3

10) Problems 1 7/08/17

Tutorial

DM3: Collaborative


T.1, T.2 CO 3

11) Problems on all above topics

1 7/08/17

Tutorial

DM3: Collaborative


T.1, T.2 CO 3

TUTORIAL QUESTIONS

1. Write one dimensional heat conduction equation.

2. Solve 022 =

+

y

uy

x

ux

3. The bounding diameter of a semi-circular plate of radius ‘a’ cm is kept at 0°c and temperature along the semi circular boundary is given by

−

=

)2/()(50

)2/(0,50),(

when

whenaT Find the steady state temperature T(r, θ).

4. A tightly stretched string with fixed end points x=0 and x=l is initially in a position given by

=

l

xyy

3

0 sin . If it is released from rest from this

position, find the displacement y(x ,t).

5 .Find the solution of Laplace equation.

UNIT- IV

Functions of a Complex variable: Functions of a complex variable, Continuity, Differentiability, Analyticity, Cauchy-Riemann equations in Cartesian

and polar coordinates, Harmonic and conjugate harmonic functions, Milne – Thompson method.

LEARNING OUTCOMES

• Define complex number with real and imaginary parts, limit of a function, continuity and differentiability of a function.

• Distinguish limit of a real and a complex function.

• Calculate the continuity, differentiability and analyticity of various functions at various points.

• Explain the Cauchy’s – Riemann equations in Cartesian and polar form.

• Test analyticity, Harmonic and Conjugate Harmonic of functions.

• Solve problems on analyticity by – Milne – Thompson method.

TEACHING PLAN

S.


No. of

Lecture

Periods

Lecture

Dates

Proposed Delivery

Methodologies


References

(Text Books /

Journals /

Publications/ Open

Learning Resources)

Course

Outcomes

1 Complex variable 1 31-08-17

DM1. Chalk and Talk



model

T.1,T.3 & T.4 CO 4

2 Analyticity. 1 01/09/17

DM1. Chalk and Talk



model

T.1,T.3 & T.4 CO 4

3 Cauchy- Riemann equations in

Cartesian form. 1 11/09/17

DM1. Chalk and Talk



model

T.1,T.3 & T.4 CO 4

4 C-R equations in polar form 1 13/09/17

Tutorial

DM3: Collaborative


T.1,T.3 & T.4 CO 4

5 Problems on analytic function 1 14/09/17 Tutorial T.1,T.3 & T.4 CO 4

DM3: Collaborative


6 Harmonic and conjugate Harmonic

functions. 1 15/09/17

Tutorial

DM3: Collaborative


T.1,T.3 & T.4 CO 4

7 Milne Thompson Method 1 18/09/17 DM1.Power point

presentation. T.1,T.3 & T.4 CO 4

8 Problems on Milne Thompson method 1 18/09/17 DM1. Chalk and Talk

T.1,T.3 & T.4 CO 4

9 Calculation of Harmonic functions

using Milne Thomson Method 1 20/09/17

DM1. Chalk and Talk

T.1,T.3 & T.4 CO 4

10 Problems 1 21/09/17 DM1. Chalk and Talk

T.1,T.3 & T.4 CO 4

TUTORIAL QUESTIONS

1.Derive C-R equations in polar form?

2.If a function is analytic, show that it is independent of z

3.Find the analytic function w= U+iV, if U= e-x [ (x2-y2)cos(y) + 2xy sin(y)]

4.If U and V are harmonic functions, show that Uy-Vx + i(Uy+Vx) is analytic function of z.

5.Show that 2

22 )()1()( zfuppu pp −−=

UNIT- V

Integration of Complex function, Power series and Residues:

Line integral, evaluation along a path and by indefinite integration. Cauchy’s integral theorem, Cauchy’s integral formula. Expansion of Taylor’s

series and Laurent series (without proofs). Singular point, Isolated singular point, pole of order m , essential singularity. Residues – Evaluation of

residue by formulae, Residue theorem, Evaluation of real integrals.

LEARNING OUTCOMES


• Define a Closed Curve , multiple curve, contour , simply connected region ,multiply connected region and Observe the properties of Integrals.

• Estimate the line Integral along a given path .

• Distinguish Cauchy’s integral theorem and Cauchy’s integral formula.

• Apply Cauchy’s Integral theorem to find the integral of a closed cur.

• Recognize Sequence , Infinite series , power series,region of convergence of a series.

• Describe Taylor’s Series Maclaurin’s series and Laurent series

• Apply Taylor’s Series and Laurent series to expand the function.

• Explain Singular point –Isolated singular point, essential singularity and pole.

• Calculate Residues by formulae and by Laurent series.

• Evaluate real integrals by contour integration.

TEACHING PLAN

S.


No. of

Lecture

Periods

Lecture

Dates

Proposed Delivery

Methodologies


References

(Text Books /

Journals /

Course

Outcomes

Publications/ Open

Learning Resources)

1) Complex Integration: Line Integral 1 21/09/17

DM1. Chalk and Talk



model

DM3: Collaborative

Learning -Think Pair Share.

T.1,T.3 & T.4 CO 4

2) Cauchy’s theorem 1 22/09/17

DM1. Chalk and Talk

Tutorial

DM3: Collaborative


T.1,T.3 & T.4 CO 4

3) Problems on Cauchy’s Theorem 1 27/09/17

DM1. Chalk and Talk

Tutorial

DM3: Collaborative


T.1,T.3 & T.4 CO 4

4) Cauchy’s integral formula 1 4/10/17 DM3: Collaborative

Learning -Think Pair Share T.1,T.3 & T.4 CO 4

5) Problems on Cauchy’s integral formula 1 5/10/17 DM1. Chalk and Talk

Tutorial T.1,T.3 & T.4 CO 4

6) Expansion in Taylor’s series 1 6/10/17

DM1. Chalk and Talk

DM3. Collaborative


T.1,T.3 & T.4 CO 4

7) Laurent series 1 9/10/17 DM1. Chalk and Talk T.1,T.3 & T.4 CO 4

DM3. Collaborative


8 Problems on expansions 1 11/10/17

DM1. Chalk and Talk

DM3. Collaborative


T.1,T.3 & T.4 CO 4

9 Singular point, Isolated singular

point,essential singularity 1 12/10/17

DM1. Chalk and Talk

DM3: Collaborative


T.1,T.3 & T.4 CO 4

10 Poles of different orders 1 13/10/17 DM1. Chalk and Talk

T.1,T.3 & T.4 CO 4

11 Residue formula 1 16/10/17

DM1. Chalk and Talk

DM3. Collaborative


T.1,T.3 & T.4 CO 4

12 Problems on residues 1 18/10/17

DM1. Chalk and Talk

DM3. Collaborative


T.1,T.3 & T.4 CO 4

13 Evaluation of residues by residue

formula 1 20/10/17

DM1. Chalk and Talk

DM3. Collaborative


T.1,T.3 & T.4 CO 4

14 Residue theorem 1 23/10/17

DM1. Chalk and Talk



T.1,T.3 & T.4 CO 4

model

15 Problems on residue theorem 1 26/10/17

DM1. Chalk and Talk

DM3. Collaborative


T.1,T.3 & T.4 CO 4

16 Evaluation of integrals using Residues 1 27/10/17

DM1. Chalk and Talk

DM3. Collaborative


T.1,T.3 & T.4 CO 4

17 Problems 1 02/11/17

DM1. Chalk and Talk

DM3. Collaborative


T.1,T.3 & T.4 CO 4

18 Problems 1 03/11/17

DM1. Chalk and Talk

DM3. Collaborative


T.1,T.3 & T.4 CO 4

TUTORIAL QUESTIONS

1. Find the Residues of 1

)(2 +

=z

zzf at each pole.

2. Find the Laurents series expansion of the function: )2)(3)(1(

162

+−−

−−

zzz

zz in the region 23 + z 5 .

3. Show by the method of residues, )0(5cos53

0

=+ ba

d

by contour integration in the complex plane.

4. Evaluate

+0

222 )(

cosdx

ax

mx.

HOME ASSIGNMENT-I

Issue date: 22/07/2017 Submission date: 28/08/2017

a) 1. Express 2)( xxf = as half – Range sine series in 20 x

b) Express 2)( xxxf −= as Fourier series in the interval − x

c) Find the Fourier Transform of = − xexxf x 0,)(

d) Find the Fourier cosine transform of f(x)=

−

2,0

21,2

10,

x

xx

xx

e) Find F.T of (a) f(x) =

−

10

11 2

xfor

xforx hence evaluate dx

x

x

xxx)

2cos(

)sin()cos(

0

3

−

HOME ASSIGNMENT-II

Issue date: 9 /10/2017 Submission date: 21/10/2017

1. Evaluate: +c

z

z

dze

)( 22 where c: z =4

2. Evaluate +i

dzz

1

0

2 along y=x2

3 .Prove that −c az

dz.= i2 where c: az − = r

4 . Evaluate −

+

c

z

iz

dzze2)(

)sinh(2

where c: z =4 using Cauchy’s Integral formula.

. 5. Evaluate +

2

0

2

))cos((

)(sind

ba

6. Evaluate −

+0

1

)1(dx

x

x p

7. Evaluate

+0

222 )(

cosdx

ax

mx

12. MODEL QUESTION PAPER

VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING & TECHNOLOGY

(AN AUTONOMOUS INSTITUTE)

II B.TECH. I SEMESTER REGULAR EXAMINATION-2017

SUBJECT: PDE WITH APPLICATIONS & COMPLEX ANALYSIS

(MECHANICAL & AME)

Time: 3 Hours Max. Marks: 60

------------------------------------------------------------------------------------------------------------------------------------------------------------------

PART-A

1. Answer the following 10×2 =20 Marks

a) Define periodic function with an example.

b) Find the Fourier coefficient 0a for the function −= xinxxf )( .

Subject Code

5BS14

R15

c) Write Dirichlet’s conditions for Fourier transform.

d) If F(s) is the complex Fourier Transform of f(x), then prove that )())(( sFeaxfF isa=− .

e) Find all possible solutions of Uxx+Uyy=0 using variable separable method?

f) Find the solution of one dimensional wave equation.

g) Write Cauchy-Riemann equations in polar form?

h) Verify whether u(x,y)= ex.cos(y) is harmonic (or) not.

i) Evaluate dzz

zz

C

−

+−

1

12

where C:|z|=1

j) Find the residue at poles of)1(

)(3

34

zz

zzzf

−

+= ?

PART- B 5x8 = 40 Marks

UNIT- I

1) Obtain the Fourier series expansion of f(x)= |x| in (- π, π) and hence deduce that ..............5

1

3

1

1

1

8 222

2

+++=

.

(or)

2) Find the Fourier series of f(x)=

−

xx

x

0,sin

0,0 ; hence show that )2(

4

1............

75

1

53

1

31

1−=+

•+

•+

• .

UNIT- II

3) Find the Fourier transform of ( ) )2/( 2xexf −= , -< x < .

(or)

4) Find the Fourier transform of f(x) =

−

10

11 2

xfor

xforx hence evaluate dx

x

x

xxx)

2cos(

)sin()cos(

0

3

−

UNIT- III

5) The bounding diameter of a semi-circular plate of radius ‘a’ cm is kept at 0°c and temperature along the semi circular

boundary is given by

−

=

)2/()(50

)2/(0,50),(

when

whenaT Find the steady state temperature T(r, θ).

(or)

6) A tightly stretched string with fixed end points x=0 and x=l is initially in a position given by

=

l

xyy

3

0 sin . If it is released from rest

from this position, find the displacement y(x ,t).

UNIT- IV

7. a) If f(z)=u+iv is an analytic function and u-v= ex(cos(y)- sin(y)) find f(z) in terms of f(z).

b) Find the orthogonal trajectories of the family of curves: x4+y4-6x2y2 = C

(or)

8) Evaluate ++

+

C

dzzz

z

52

42

where c is the circle (i) 1=z (ii) 21 =−+ iz (iii) 21 =++ iz using Cauchy’s integral formula.

UNIT- V

9) Evaluate by the method of residues +

2

0cosba

d

(or)

10)Evaluate

0,0))(( 2222

2

++

−

badxbxax

x









(II/IV) B. Tech :(I/II) Sem : (Automobile) L T/P/D C

Course Name: Mechanics of solids Course Code: 5ME01

Names of the Faculty Member : T. Raju

Number of working days : 90

Number of Hours/week : 4 + 1

Total number of periods planned : 80

1. PREREQUISITES

(This information helps the student to refer to the required topics before undergoing the course. This builds confidence

in a student.)

Engineering Mechanics, Basic Engineering Mathematics and Physics





• List and define the material properties and show the relationships between them.

• Describe principles of mechanics, stress and strain.

• Demonstrate thoroughly the concepts of principal stresses applied to solid structural

members and mohr’s circle diagram.

• Analyse various types of mechanical engineering problems concern to bending of beams,

torsion of shafts etc.




Upon completion of this course, students should be able to:

CO-1 : Show basic stress strain equations with appropriate assumptions

CO-2 : Interpret model and analyze solid mechanics problems on bars, beams and shafts.

CO-3 : Apply the concepts of principal stresses in real life design issues

CO-4 : Analyse and develop beams, shafts for various applications


Course

Outcomes

(COs)


A b c d E f g h i j k l

CO 1

3

CO 2

2

CO 3

2

CO 4

1


5. LEARNING RESOURCES:

(i) TEXT BOOKS

1. Mechanics of Materials (SI units) by J.M.Gere and S.P.Timoshenko; Publisher: CBS Publishers.

2. Strength of Materials by S. S. Rattan, Publisher: Tata McGraw-Hill Education.


(Course delivery including latest trends brings good insight of the course in students and also inculcates the habit

of self learning among the students.


1. Engineering Mechanics of Solids by Popov; Publisher: Pearson Education.

2. Strength of Materials Schaum’s Series.

(a) Publications NA


1. https://onlinecourses.nptel.ac.in/noc17_ce17/preview

2. https://onlinecourses.nptel.ac.in/noc17_ce22/preview

(iii) JOURNALS

1. Acta Mechanica Solida Sinica

2. Design and Analysis

3. Design Engineering


https://onlinecourses.nptel.ac.in/noc17_ce17/preview


adopted to involve the student in learning)


DM2: Learning by doing DM6: Case Study (Work on real data)


DM4: Demonstration (Physical / Laboratory / Audio Visuals) DM8: Any Other (Please specify)



1. Dr. K. Veera Brahmam Scientist E (DRDO-ASL) in the month of September 2017

8. ASSESSMENT

(As per Regulations, AM1 and AM2 are compulsory for assessment. Whereas, any two or more assessment

methodologies can be considered from AM3 to AM9 under assignment towards continuous assessment of the

performance of students.)

AM1: Semester End Examination AM2: Mid Term Examination

AM3: Home Assignments AM4: Open Book Test

AM5: Objective Test AM6: Quizzes

AM7: Course Projects** AM8: Group Presentations

AM9: Any other (Specify)

** COURSE PROJECTS

(To be added for the courses as directed by the department. The no. of course projects is left to the liberty of

faculty.

One course project is assigned to each project batch of size three in the beginning of the course and assessed at

the end of the course. One midterm evaluation is carried out to monitor the progress of the project and the team

coherence.)

1. Characterization of Aluminium Alloy AA5052, AA6061 and AA7075 2. Impact analysis of ductile materials 3. Failure analysis of ductile and brittle materials under Torsion 4. Failure analysis of ductile and brittle materials under uniaxial loading 5. Analysis of plate with a hole at the centre under axial loading

6. Analysis of different cross sections of bars under axial loading

7. Measurement of deflection of square cross section beam in different orientations

8. Optimum material removal rate in log of wood


(The allotted marks for home assignments, quizzes, course projects and etc., are left to the liberty of faculty. But for the

finalisation of assignment marks, the following weightages can be considered.)

For R15

S. No. Assessment Methodology


the courses with Course

project


the courses without

Course project

1.

Assignment

3%

10

5% 10

2. 3% 5%

3. Course project 4% -

4. Internal Examination 30 30

5. External Examination 60 60

For R13

S. No. Assessment Methodology Weightages in marks for


Weightages in marks

for the courses without

project Course project

1.

Assignment

Home Assignment 2%

5

5

2. NPTEL certification 1%




10.SIMULATION SOFTWARES (If any)

Not applicable as they just entered into II Year I semester




UNIT I

Tension, compression, and shear

Introduction; Normal Stress and Strain; Stress-strain diagrams; Elasticity and plasticity; Linear

elasticity and Hooke’s law; Allowable stress and allowable loads.

Axially loaded members

Introduction; Deflections of axially loaded members; Strain energy; Dynamic loading;

Thermal stresses

Learning outcomes: after successful completion of unit - I the student must be able to

1. Understand Fundamental stresses and derived stresses.

2. Discuss different types of Properties of Engineering Materials.

3. Understand the terms allowable stress and allowable loads and its importance in design.

4. Discuss the factor of safety values adopted for various materials in design.

5. Develop Expressions for deflection of axially loaded members and draw displacement

diagrams.

6. Explain the concept of strain energy.

7. Explain the role of the dynamic loads for inducing stresses in Machine members.

8.Explane the concept of thermal stresses in structural mambers.

TEACHING PLAN

S.

No.

Contents of syllabus to

be taught

No. of Lecture

Periods Lecture Dates

Proposed Delivery

Methodologies

Learning Resources / References

(Text Books / Journals /

Publications/ Open Learning

Resources)

Course

Outcomes

1 Introduction 1 03/07

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2 CO 1

2

Normal stress and

strain, stress-strain

diagrams,

Elasticity and Plasticity

4

05/07

06/07

07/07

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2

3

Linear elasticity and

hooke’s law, Allowable

stress

and Allowable loads

1 12/07

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2

CO 1

4 Introduction,

deflections of axially

loaded members

3 13/07

14/07

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.


5 Strain energy; Dynamic

loading 3

19/07

20/7

21/7

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example


6 Thermal stresses 3

24/7

26/7

27/7

DM1. Chalk and

Talk DM4.

Demonstration of

one example

TEXT BOOKS 1 & 2

CO 1

TUTORIAL QUESTIONS

1)What is stress and strain ? Types of Stress and Strains ?

2)What is the difference between static loading and dynamic loading ?

3)Draw Stress Strain curve for ductile materials and brittle materials and note down various points in diagram?

4 )What is Hooke’s law?

5)What is factor of safety and allowable stress?

6)Define Elastic constants and relation between elastic constants?

7)What is Impact loading?

UNIT 2

Shear force and bending moment diagrams

Types of beams; Types of loading; Shear force and bending moment; Relationship between load,

shear force and bending moment; Shear force and bending moment diagrams.

Torsion

Introduction; Torsion of circular bars; Non uniform torsion; Pure shear; Relationship between moduli

of elasticity E and G; Transmission of power by circular shafts;

Learning outcomes : after successful completion of unit - II the student must be able to

1. Understand the concept of shear stresses induced in a shaft due to the action of twisting.

2. Derive the Torsion formula.

3. Explain the concept of non-uniform torsion.

4. Discuss the concept of pure shear and develop the relation between moduli of elasticity E & G.

5. Explain the procedure to determining the power transmission by circular shafts.

6. Estimate the strain energy in case of pure shear and torsion.

7. Differentiate beam and bar. Understand types of loads and supports in case of beams.

8. Develop the relationship between shear force and bending moment.

9. Understand and draw the shear force and bending moment diagrams.

TEACHING PLAN

S.

No.


be taught

No. of Lecture


Proposed Delivery

Methodologies




Resources)

Course

Outcomes


DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2

CO2

2 Types of beams; Types

of loading; Shear force

and bending moment;

4

3/8

8/8

9/8

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2 CO2

3 Relationship between

load, shear force and

Bending moment

2 10/8

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.


4 Shear force and

bending moment

diagrams;

6

11/8

16/8

17/8

18/8

19/8

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.


5

Introduction; Torsion

of circular bars; Non

uniform

torsion;

6

21/8

23/8

24/8

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example


6

Pure shear;

Relationship between

modulus of

elasticity E and G;

Transmission of power

by

circular shafts

3 28/8

DM1. Chalk and

Talk DM4.

Demonstration of

one example

TEXT BOOKS 1 & 2

CO2

TUTORIAL QUESTIONS

1)What is shear force and Bending moment?

2)Relation between Load ,shear force ,Bending moment ?

3)Draw the SFD and BMD for cantilever and simply supported beams?

4)Derive torsion equation?

UNIT 3

Area moment of inertia of composite sections.

Stresses in beams

Introduction; Normal strains in beams; Normal stresses in beams; Cross-sectional shapes of beams;

Shear stresses in rectangular beams; Shear stress in webs of beams with flanges; Shear stress in

circular beams (solid and hollow sections);

Learning outcomes : after successful completion of unit - III the student must be able to

1. Calculate Moment of Inertia of different types of composite sections.

2. Derive a relation for flexure formula for a beam is under pure bending.

3. Determine normal stresses developed in a beam under the action of various types of loads.

4. Develop formulation from fundamentals for shear stresses induced in the beam on application

of loads.

TEACHING PLAN

S.

No.


be taught

No. of Lecture


Proposed Delivery

Methodologies




Resources)

Course

Outcomes


DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2

CO1 and

CO4

2 Area moment of inertia

of composite sections 2 13/9

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2 CO1 and

CO4

3

Introduction, Normal

strains in beams,

Normal

stresses in beams,

Cross-sectional shapes

of

beams-C, angular and

semicircle structures

5

14/9

15/9

18/9

21/9

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.


CO4

4

Shear stresses in

rectangular beams,

Shear

stress in webs of

beams with flanges,

Shear

stress in circular beams

(solid and hollow

sections); Concept of

shear center and shear

flow

6

22/9

25/9

27/9

04/10

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.


CO4

TUTORIAL QUESTIONS

1)Define Area moment of inertia and area Moment of inertia for different cross-sections ?

2)Normal stress in different cross-sections of a beams?

3)shear stresses in beams?

UNIT 4

Analysis of stress and strain

Introduction; Plane stress; Principal stresses and maximum shear stresses; Mohr’s circle for plane

stress; Hooke’s law for plane stress; Spherical and cylindrical pressure vessels (biaxial stress; Hoop

and longitudinal stresses); Combined loadings (plane stress); Principal stresses in beams;

Learning outcomes : after successful completion of unit - IV the student must be able to

1. Understand General stress element and plane stress condition.

2. Discuss the concept of principal stress and its significance in design of Materials.

3. Develop relations for normal stress and shear stress on any inclined plane of a given stress element.

4. Explain the types of stresses induced in spherical and cylindrical pressure vessels when

stored with high pressure fluids.

5. Estimate the resultant stresses when a component is subjected with various types of loads simultaneously.

TEACHING PLAN

S.

No.


be taught

No. of Lecture


Proposed Delivery

Methodologies




Resources)

Course

Outcomes

1

Introduction, Plane

stress, Principal

stresses and

maximum shear

stresses, Mohr’s circle

for plane stress

6

05/10

06/10

09/10

11/10

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2

CO3

2

Hooke’s law for plane

stress, Spherical and

cylindrical

pressure vessels

(biaxial stress, Hoop

and longitudinal

stresses);

4 12/10

13/10

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.


3

Combined loadings

(plane stress), Principal

stresses in

Beams

2

14/10

16/10

17/10

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.


TUTORIAL QUESTIONS

1) What do you mean by plane stress , principal stresses and maximum shear stresses?

2) Define Hooke’s law for plane stress ?

3) What are the stress inThin pressure vessels ?

4) For combined loadings what are the principal stress ?

UNIT 5

Deflections of beams

Introduction; Differential equations of the deflection curve; Deflections by integration of the bending

moment equation; Deflections by integration of the shear-force and load equations; Macaulay’s

method; Moment area method; Method of superposition;

Learning outcomes: after successful completion of unit - V the student must be able to

1. Derive differential equation of the deflection curve for beam under different types of loading.

2. Understand the deflection determined by integration of bending moment diagram.

3. Develop Expressions for deflection by integration of the shear-force and load equations.

4. Estimate the deflections in the beam on loading by Macaulay’s method.

5. Explain the concept of Moment area method for finding slope and deflection for a given loaded

beam.

6. Understand thoroughly concept of method of superposition.

7. Explain the concept of strain energy in bending.

TEACHING PLAN

S.

No.


be taught

No. of Lecture


Proposed Delivery

Methodologies




Resources)

Course

Outcomes

1

Introduction,

Differential equations

of the

deflection curve,

Deflections by

integration of the

bending moment

equation

4

20/10

21/10

23/10

24/10

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2

CO 1 and

CO4

2

Deflections by

integration of the

shear-force and

load equations,

Macaulay’s method,

Moment area

method

6

23/10

24/10

25/10

26/10

28/10

30/10

31/10

DM1. Chalk and

Talk (along with

PPT) DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2 CO 1 and

CO4

3 Method of

superposition; 2

01/11

02/11

03/11

DM1. Chalk and

Talk DM4.

Demonstration of

one example.

TEXT BOOKS 1 & 2

CO 1 and

CO4

TUTORIAL QUESTIONS

1) Derive differential equation of the deflection curve for beam under different types of loading?

2) Understand the deflection determined by integration of bending moment diagram.?

3) Develop Expressions for deflection by integration of the shear-force and load equations.?

4) Estimate the deflections in the beam on loading by Macaulay’s method.

5) Explain the concept of Moment area method for finding slope and deflection for a given loaded

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

HOME ASSIGNMENT - No.1


1. A steel tube 100mm internal dia., 125mm external dia. is surrounded by a brass tube of inner dia.

126mm and outer dia . 150mm. Both are rigidly connected. The compound tube is subjected to an axial

compressive load of 5KN.Find the stresses developed in each tube and the load carried by each tube.

Take Es =200GPa and E b =100GPa.

2. A specimen of dia. 13mm and gauge length 50mm was tested under tension. At20KN load, the

extension was observed to be 0.0315mm. Yielding occurred at a load of 35 KN and the ultimate load

was 60KN. The final gauge length at fracture was 70mm. calculate E, Yield stress, ultimate strength

and % elongation.

3. Two rods, one made of steel and the other of brass, hang vertically, 1.0m apart, from a rigid support.

Both are 1.0m long. The rods support a rigid bar horizontally. When a load of 25KN is placed at 400mm

from the steel rod on the horizontal bar, the extension of the two rods are found to be equal. If the area

of the steel rod is 300mm 2 , find the stresses and strains in the rods and the area of the brass rod. Take

E s = 200Ga and E b = 85Gpa

4. A steel wire 2.0m long and 3mm in dia. elongates by o.75mm, when a weight W is suspended from

the wire. If the same load is suspended from the brass wire 2.5m long and 2mm dia, it is elongated by

4.64mm. Find the modulus of elasticity of brass, if the modulus of elasticity of steel, E s = 200GPa

5. Find the Poisson’s Ratio and Bulk modulus of a material whose modulus of elasticity is 200 GPa and

modulus of rigidity is 80GPa. A 2.0m long rod of 40mm dia. made with the same material is stretched

by 2.5mm under some axial load. Find the lateral contraction.

6. Rails of 15m length were laid on the track when the temperature was 20 0 C. A gap of 1.8mm was

kept between two consecutive rails. At what maximum temperature the rails will remain stress free? If

the temperature is raised further by 15 0 C, what will be the magnitude and nature of stresses induced in

the rails? Take α s = 12×10 -6 /0C.

7. A flat steel bar 30mm wide and 5mm thick is placed between two bars of aluminum, each 30mm wide

and 8mm thick to form a compound bar at 10 0 C. Calculate the temperature stresses induced at55 o C,

taking.

E S =200 GPa , E al =67 GPa αs = 12× 10 -6 /0Cand α al = 24×10 -6 /0C.

8. A thin tyre is shrunk on a wheel of 1.0m diameter. Find the internal diameter of the tyre, if

circumferential stress is limited to 90N /mm 2 . Find also the least temperature to which the tyre must be

heated above that of the wheel, before it could be slipped on. For the tyre material take E= 200 GPa

and α =12×10 -6 /0C.

9. During a direct tension test on a 20mm dia. Rod 1.0m. long, the longitudinal strain was observed to

be 4 times the lateral strain. If its elastic modulus is 200GPa find the bulk modus and modulus of

rigidity. If the rod is subjected to hydrostatic pressure of 100 N/mm 2 , find the decrease in volume.

10. A bar of length 200mm tapers uniformly from 40mm dia to 35mm. calculate the change in its length

due to a an axial pull of 100KN, assuming E as 200 GPa .Derive the formula used in the calculation.

11. A steel bar of length 200mm and 50×50mm in section is connected at its end to an aluminum bar of

250mm length and 80×80mm in section, such that they have a common longitudinal axis. Find the load

which will reduce the total length by o.25mm. Find also the total work done. Take E s =200GPa And E al

=70GPa .

12. A uniform metal bar of 1.8m length and area of cross section 100mm 2 has an elastic limit of

160N/mm 2 . Find its proof resilience, if E=200GPa . Find also the maximum load which can be suddenly

applied without exceeding the elastic limit. Calculate the magnitude of the gradually applied load which

will produce the same extension.

13. A wagon of weight 25KN attached to wire rope is moving at a speed of 4Km ph. The cross sectional

area of the rope is 500mm 2 . Suddenly the rope jams and the wagon is brought to rest. If the length of

the rope is 10m at the time of sudden stoppage, find instantaneous stress and elongation of rope, if

E=200GPa and g =9.8m/sec 2 .

14. Two rods of same length same material are subjected to the same axial load. The first rod is of

uniform diameter D. The second bar has a diameter D for 1/3 of its length and 2D for the remaining

length, compare the strain energies of the two bars.

15. A steel wire of 2.5mm diameter is firmly held in a clamp from which it hangs vertically. An anvil is

secured to the wire 1.5m below the clamp. A weight bored to slide over the wire to drop freely, is

dropped freely onto the anvil from a height of 1m. Find the weight required to stress the wire to

900N/mm 2 , if E=200GPa. Neglect the weight of the anvil and assume the wire to be elastic



1.Sketch the S.F. &B.M. diagrams for an Overhanging beam ABCDE shown. Mark all the salient

points with respective values.

2. Draw SF and BM diagrams for the simply supported beam shown. Mark all the salient values

and points.

3. Draw SF& BM diagrams for the simply supported beam marking all the salient values.

4. An overhanging beam ABCD supported at Band D has an overhang AB of 3m on the left side. It

carries a load of 8KN at the point C, distance of C from D being 3m.Also there is a udl of 2KN/m over

AC of length 12m. Draw SF& BM diagrams marking all salient points.

5. A simply supported beam with overhanging ends is loaded as shown. If wx l=P, what is the ratio of a/l

for which the B.M. at the middle of the beam will be zero.

6. sketch SFD and BMD for the cantilever beam shown

7. Draw SFD& BMD for a simply supported beam subjected to a clock-wise couple M at L/4 from the left

support, where L is the span Also draw the Elastic curve.



1. An I – beam of 200mm depth is simply supported over an effective span of 8m. Find what max.

intensity of udl it can carry over entire length if the allowable bending stresses in tension and

compression are 30 and 45 N/mm 2 respectively. Take I NA = 5935.5×10 4 mm 4 . Distance of bottom fibre

from NA is 87.38mm.

2. Obtain the dimensions of the strongest rectangular section that can be cut from a circular log of wood

of 250mm diameter.

3. A T section with a flange of 200×20mm and web of 400mm×50mm is used as a cantilever with an

effective span of 2.75m. It is subjected to a couple of 50KNm clockwise at the free end. Sketchthe

variation in bending stress at midspan section and at the section carrying max. B.M.

4. If a hole of 20mm is made in the web, of the above section at a distance of 50mm from the junction

with flange, sketch the variation in bending stress across the depth.

5. Design a hollow circular section for a beam to carry a B.M .of 100kNm with internal external diameter

ratio of 0.75. Also sketch the variation in bending stress. Compare the economy with a solid section of

same material and same weight. Take allowable stress as 150N/mm 2 .



1.(a) A thin spherical shell of 1m internal diameter and 5mm thick is filled with a fluid under pressure

until its volume increases by 200cc.Taking E= 200 GPa and µ =0.3, calculate the internal pressure.

(b) What happens if the above spherical shell is subjected to a vacuum of same magnitude.?

(c) Are these volume changes the changes in the volume of the material of the shell or the volume of

the space inside the spherical shell.

2. (a) Show the probable crack pattern of failure of a thin cylinder when it fails due to (i)

maximum hoop stress, (ii) maximum longitudinal stress and (iii) maximum shear stress.

(b) A boiler of 2m diameter is made of 20mm thick plates. If the maximum tensile stress is not to

exceed 100 N/mm 2 , find the permissible steam pressure in the boiler, taking the efficiency of

longitudinal riveted joint as 75%. Calculate the longitudinal stress, if the efficiency of circumferential

joint is 65%.

3. A thin cylinder is laid in a vacuum of 3N/mm 2 . If the maximum tensile stress is limited to 50N/mm 2

with what maximum pressure, above atmosphere, a fluid can be introduced into the cylinder?

4. (a) A long boiler tube has to withstand an internal pressure of 6N/mm 2 above atmosphere. The

internal diameter of the tube is 60mm. Determine the thickness and mass/m of the tube if the maximum

tensile stress is not to exceed 130N/mm 2 . Mass density of steel is 7850kg/m 3 .

(b) A thick cylinder is designed using thin cylinder theory. Is it safe?

(c) A thin cylinder is designed using thick cylinder theory. Will it be safe?



1. A simply supported beam of span L carries a uniformly varying triangular load of intensity per unit

length at the right end and zero at the left end. Obtain the slope and Deflection at the left end and at the

position of max. B.M.

2.A simply supported beam of span 6m carries two point loads of 60KN and 50KN at 1m and 3m

respectively from the left end. Find the position and magnitude of max. deflection. Take E= as 200 GPa

and I =8500cm 4 . Also determine the value of deflection at the same point if one more load of 60KN is

placed over the left support.

3.A simply supported beam of 8m carries a partial u d l of intensity 5KN/m and length 2m, sarting from

2m from the left end. Find slope at left support and central deflection. Take E= 200Gpa and

I=8×10 8 mm 4

4.(a) A cantilever of 4m. Span carries a load of 40KN at its free end. If the defection at the free end is

not to exceed 8mm, what must be the moment of inertia of the cantilever section?

(b)If the above beam with that moment of inertia and the same span is subjected to a pure couple

acting at the free end and the maximum deflection is not to exceed 8mm, what maximum pure couple

can be applied?

5. A horizontal beam of uniform section is simply supported at its ends which are at the same level

and is loaded at the left support with an anti –clockwise moment ‘M’ and at the right support with a

clock –wise moment ‘2M’ both in the same vertical plane. The span of the beam is ‘l’ Find the angles of

the slope at each end, deflection of the mid point of the span in terms of M, L, and flexural rigidity.

-----------------------------------------------------------------------------------------------------------------------------------------------------------------


(END EXAMINATION)

Subject Code 13MED003

R13

VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING AND TECHNOLOGY (AUTONOMOUS)

B.Tech. II Year I Semester Adv. Supplementary Examinations, January, 2015 MECHANICS OF SOLIDS (Common to ME and AE)

Time: 3Hours Max. Marks: 70M

PART-A Answer ALL questions

1. Answer in ONE sentence 5X1=5M

a) What is yield stress?

b) What is significance of strain energy?

c) What is neutral plane?

d) What is hoop stress in a cylindrical vessel?

e) What is point of contraflexure?.

2. Answer the following very briefly. 5X2=10M

a) What is dynamic loading? In what way it is different from static loading?

b) Draw the shear force diagram for a cantilever beam loaded with a print load at its free end.

c) What is non-uniform torsion? Explain briefly.

d) Explain the concept of shear centre.

e) What is the significance of flexural rigidity? Explain.

3. Answer the following briefly. 5X3=15M

a) Draw the stress-strain diagram of a brittle material specimen subjected to tensile force and indicate salient points. b) Sketch the B.M diagram for a simply supported beam of spar ‘l’ subjected to a point load at the centre. c) A steel shaft 3cm diameter and 800cms i length is to transmit certain twisting torment such that angle of twist is not to

exceed 2.50. Determine the value of twisting moment and maximum shear stress. Take N=0.5 x105 N/mm2 d) State moment area theorems e) What is the concept of shear center? Briefly explain

PART-B Answer any FOUR questions 4X10=40M

4. a) Asteel bar 2m long, 2cm wide and 1cm thick is subjected to a pull of 2tonnes in the direction of its length. Find the changes in length, breadth and thickness. Take E=2.0x106kgf/cm2 and Poisson’s ratio=0.3. b) A short timber post of rectangular section has one side of section twice the other. When the post is loaded axially with 10,000N. It contracts by 0.0521 mm/meter length. Young’s modulus for this timber is 15kN/mm2, Calculate thesectional dimensions of the post.

5. A beam 6m long is simply supported at the ends, and carries a uniformly distributed load of 1500kg/m and three concentrated loads of 1000,2000 and 3000 kg acting respectively at the left quarter point, centre point and right quater point. Draw the S.F and B.M diagrams and determine the maximum bending moment.

6. A hollow shaft of diameter ratio 3/8 is required to transmit 500kW at 110rpm, the maximum torque being 20% greater than the mean .The shear stress is not to exceed 60N/mm2,and the twist in a length of 3m not to exceed 1.40. Calculate the maximum external diameter satisfying these conditions. Take C=84kN/mm2

7. a) A rectangular beam 300mm deep is simply supported over a span of 4 m. What uniformlydistributed load per meter, the beam may carry, if the bending stress is not to exceed 70kgf/cm2 , find the dimensions of the crosssection. b) A beam of triangular cross section having base width of 100mm and height of 150mm is subjected to a shear force of 15kN. Find the value of maximum shear stress, and sketch the shear stress distribution along the depth of beam.

8. Apoint in a stretched material is subjected to mutually perpendicular stresses of 6000 kgf/cm2tensile and 4000kgf/cm2 compressive. It is also subjected to a shear stress of 1000kgf/cm2. Draw the Mohr’s circle, and find the principle stresses and maximum shear.

9. A horizontal girder of steel having uniform section is 14mts long and is simply supported at its ends. It carries concentrated loads of 48kNand 40kN at two points 3mts and 4.5mts from two ends respectively. Moment of inertia for the section of the grider is 160x103 cm4 and E=2.1x106kg/cm2. Calculate the deflection of the girder at points under the two loads.

****

________________________________________________****The End*****_____________________________________________




II B. Tech : I Sem : AE L T/P/D C

3 1 4

Course Name: Thermodynamics Course Code: 5ME02

Names of the Faculty Member: R.RAMU




1. PREREQUISITES

Physics (5BS21), Ordinary Differential Equations and Laplace Transforms (5BS12).


(Objectives define the importance of course and how the course is helpful to the students in their career. Objectives must be defined

first and contents must be developed later.)


• To apply the basic concepts of thermodynamics and Thermodynamic Laws for various thermodynamic systems

• To evaluate the properties of pure substance and to analyse the concept of irreversibility and availability.

• To apply the basic concept of power cycles for External combustion engines and internal combustion engines.

• To evaluate the behavior of ideal gas mixtures and Thermodynamic properties.


(Outcomes define what the student will be able to do upon completion of the course. Course outcomes must be assessable. The

blooms taxonomy terms are used as reference in defining course outcomes)



• To apply the basic concepts of thermodynamics and Thermodynamic Laws for various thermodynamic systems

• To evaluate the properties of pure substance and to analyse the concept of irreversibility and availability.

• To apply the basic concept of power cycles for External combustion engines and internal combustion engines.

• Evaluate the behaviour of ideal gas mixtures and Thermodynamic properties of the given mixture of gases.


(This mapping represents the contribution of course in attaining the program outcomes and there by program educational

objectives. This also helps in strengthening the curriculum towards the improvement of program.)

Course

Outcomes

(COs)


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

CO 1 3 3 2 1 2

CO 2 3 3 1 3 3

CO 3 2 3 2 2 2 3 2 2 2 3

CO4 3 3 3 3 3 3 3 3 3

3



(i) TEXT BOOKS

T1. Engineering Thermodynamics by P.K. Nag, Publisher: McGraw-Hill

T2. Engineering Thermodynamics by P.Chattopadhyay,Oxford University Press

T3. Fundamentals of Thermodynamics by C. Borgnakke, R.E. Sonntag, and G.J. Van Wylen; Publisher John Wiley.

T4. Engineering Thermodynamics by Burgadt, Harper & Row Publication.

T5. Thermodynamics — An engineering approach by Yunus Cengel and Boles; Publisher: TMH.


(Course delivery including latest trends brings good insight of the course in students and also inculcates the habit of self learning

among the students.


(a) Open Learning Resources for self learning

L1. http://nptel.ac.in/courses/

(iii) JOURNALS

J1. Applied Thermal Engineering

J2. International Journal of Thermal Science

J3. Journal of Thermal Science and technology

J4. Journal of Thermal Analysis

J5. Journal of Thermal Insulation

J6. Journal of Thermal science

J7. Journal of Thermal Science and Applications

J8. Journal of Thermal Stress

J9. Fluid and Thermal Engineering

J10. Thermal Engineering

J11. Thermal Science

J12. Experimental Thermodynamics

J13. International Journal of Applied Thermodynamics

J14.Journal chemical Thermodynamics

J15. Journal of non Equilibrium Thermodynamics

J16. Journal of Thermodynamics


(Depending on the suitability to the delivery of concept, one or more among the following delivery methodologies are adopted to

engage the student in learning)

http://nptel.ac.in/courses/




DM4: Demonstration (Physical / Laboratory / Audio Visuals)



-Nil-

8. ASSESSMENT

(As per Regulations, AM1 and AM2 are compulsory for assessment. Whereas, any two or more assessment methodologies can be

considered from AM3 to AM9 under assignment towards continuous assessment of the performance of students.)



AM5: Objective Test



(The allotted marks for home assignments, quizzes and etc., except course projects are left to the liberty of faculty. But for the


R15




the courses without Course

project

1. Home Assignments (AM3) 10

4% 10

Objective Test (AM5) 3%

2. Open Book Test (AM4) 3%


5. Semester End Examination

(AM1) 60 60


On the beginning day of each unit, home assignment sheet is given to the students and the solution sheet for the same is expected after four

days of the completion of unit.

(ii) OBJECTIVE TEST

Two Objective Test are conducted in the course duration. One is scheduled on 19/08/2017 and the second one is scheduled on 14/10/2017.

(iii) OPEN BOOK TEST

One Open Book Test is conducted in the course duration. It is scheduled on 04/10/2017.


3. ANAYSIS

4. CFD


(Detailed syllabus mentioning its learning outcomes, teaching plan, tutorial questions and home assignment questions for each unit

can be given. Heads under teaching plan is given below. Model Academic plan can be taken as reference.)

UNIT -I

CONCEPTS AND DEFINITIONS

Thermodynamic system and control volume; Macroscopic versus microscopic point of view; Properties and state of a substance;

Processes and cycles, Energy, Specific volume and density, Equality of temperature; The Zeroth law of thermodynamics;

Temperature scales.

WORK AND HEAT

Definition of work; Units for work; Work done at the moving boundary of a simple compressible system; Other systems that involve

work; Definition of heat; Heat transfer modes; Comparison of heat and work.

THE FIRST LAW OF THERMODYNAMICS

The first law of thermodynamics for a control mass undergoing a cycle; The first law of thermodynamics for a change in state of a

control mass; Internal energy-a thermodynamic property; Problem analysis and solution technique; Enthalpy; The constant-volume

and constant-pressure specific heats; The internal energy, enthalpy, and specific heat of ideal gases; The first law as a rate equation.

FIRST LAW ANALYSIS FOR A CONTROL VOLUME

Conversion of mass and the control volume, the first law of thermodynamics for a control volume, The steady-state process;

Examples of steady-state processes.

LEARNING OUTCOMES


1. Distinguish different types Thermodynamic Systems.

2. Understand Thermodynamic Equilibrium.

3. Understand Irreversibility.

4. Distinguish Point and Path functions.

UNIT- II

THE SECOND LAW OF THERMODYNAMICS

Heat engines and refrigerators; The second law of thermodynamics; The reversible process; Factors that render processes

irreversible; The Carnot cycle; Two propositions regarding the efficiency of a Carnot cycle; The thermodynamic temperature scale;

The ideal-gas temperature scale; Ideal versus real machines.

ENTROPY FOR A CONTROL MASS

The inequality of Clausius; Entropy — a property of a system; The entropy of a pure substance; Entropy change in reversible

processes; The thermodynamic property relation; Entropy change of an ideal gas; The reversible polytropic process for an ideal gas;

Entropy change of a control mass during an irreversible process; Entropy generation; Principle of increase of entropy; Entropy as a

rate equation.

LEARNING OUTCOMES


1. Understand Limitations of the First Law.

2. Define Second law of Thermodynamics.

3. Prove the equivalence of two statements.

4. Define PMM II

5. Understand Carnot’s principle

6. Understand Carnot Cycle.

7. Understand the concept of Principle of Entropy Increase.

8. Understand the concept of Availability and Irreversibility.

UNIT- III

IRREVERSIBILITY AND AVAILABILITY

Available energy; Available energy Referred to a cycle; Quality of energy; Maximum work in a reversible process; reversible work

by an open system; Exchanging heat only with the surroundings; Useful work; Dead state; Availability; Availability in chemical

reaction; Irreversibility and Gouy-stodola Theorem; Availability or Exergy Balance; second law efficiency;

PROPERTIES OF A PURE SUBSTANCE

The pure substance; Vapor- liquid- solid- phase equilibrium in a pure substance; Independent properties of a pure substance; Steam

Tables; Thermodynamic surfaces; The compressibility factor; Equations of state.

LEARNING OUTCOMES


1. Understand the concept of Availability and Irreversibility. 2. Understand various properties of pure substances.

3. Construct Mollier Chart.

4. Define Dryness fraction

5. Find the dryness fraction of given sample of steam.

UNIT- IV

POWER CYCLES

Introduction to power systems; The Rankine cycle; Effect of pressure and temperature on the Rankine cycle; Air-standard power

cycles; Basic Brayton cycle; The air-standard cycle for jet propulsion; Reciprocating engine power cycles; The Otto cycle; The

Diesel cycle; The Dual cycle, The Sterling cycle; The Atkinson and Miller cycles.

LEARNING OUTCOMES


1. Represent various cycles on different coordinates.

2. Find the Mean Effective Pressures in various cycles.

3. Find the Thermal efficiency of various cycles.

4. Compare different cycles.

UNIT- V

IDEAL GAS REAL GAS

Ideal Gas;Real Gas; Internal Energy and Enthalpy of an Ideal Gas; Specific Heats of an ideal gas; Equations of state; Virial

Expansions; Law of Corresponding states; Boyle Temperature; Dalton’s Law of Partial Pressures; Thermodynamic Properties of Gas

Mixtures; Gibbs Function of Ideal Gas Mixtures

THERMODYNAMIC PROPERTY RELATIONS

Mathematical relations for a homogeneous phase; The Maxwell relations; Thermodynamic relations involving enthalpy, internal

energy, and entropy; The Clapeyron equation; Joule-Thompson coefficient; Real gas behavior and equations of state. LEARNING

OUTCOMES


1. Define perfect gas.

2. Understand – various Non-flow processes,

3. Understand Throttling and Free Expansion

4. Read Compressibility charts and Gas Tables

5. Understand Dalton’s Law of partial pressure & Avogadro’s Laws of additive volumes

TEACHING PLAN

S.


No. of

Lecture

Periods

Lecture

Dates

Proposed Delivery

Methodologies


References

(Text Books / Journals

/ Publications/ Open

Learning Resources)

Course

Outcomes

11)

Introduction of Thermodynamic and

Thermodynamic system and control

volume; Macroscopic versus microscopic

point of view;

2 03-07-17

DM1. Chalk and Talk

(along with PPT)

DM4. Demonstration of one

example.

L.1.

T.1, T.2& T.3 CO 1

12)

Properties and state of a substance;

Processes and cycles, Energy, Specific

volume and density,

2 04-07-17

DM1. Chalk and Talk

DM4. Detailed analysis

with the help of practical

examples

L.1.

T.1, T.2& T.3

CO 1

13)

Equality of temperature; The Zeroth

law of thermodynamics; Temperature

scales.

2 08-07-17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

14) Problems on the introduction topics 1 10-07-17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

15)

Definition of work; Units for work; Work

done at the moving boundary of a simple

compressible system; Other systems that

involve work;

3 11-07-17

&12-07-17

DM1. Chalk and Talk.



examples

L.1.

T.1, T.2& T.3

CO 1

16) Definition of heat; Heat transfer modes;

Comparison of heat and work. 1 15-07-17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

17) Problems on heat and work 2 17-07-17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

18)

The first law of thermodynamics for a

control mass undergoing a cycle; The

first law of thermodynamics for a

change in state of a control mass;

1 18-07-17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

19)

Internal energy-a thermodynamic

property; Problem analysis and solution

technique;

1 19-07-17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

20)

Enthalpy; The constant-volume and

constant-pressure specific heats; The

internal energy, enthalpy, and specific

heat of ideal gases; The first law as a

rate equation.

2 19/07/17 &

22/07/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

21) Problems on first law of

thermodynamics 2

24/07/17 &

25/07/17

Tutorial

DM1. Chalk and Talk

L.1.

T.1, T.2& T.3

CO 1

22)

Conversion of mass and the control

volume, the first law of

thermodynamics for a control volume,

The steady-state process;

1 07/08/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

23) Examples of steady-state processes. 1 08/08/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

24) Problems on first law applied to steady

flow process. 2 09/08/17

Tutorial

DM1. Chalk and Talk

L.1.

T.1, T.2& T.3

CO 1

25) Heat engines and refrigerators; The second

law of thermodynamics; 1 12/08/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

26) The reversible process; Factors that render

processes irreversible; 1

14/08/17&

15/08/17

DM1. Chalk and Talk



L.1.

T.1, T.2& T.3

CO 1

examples

27)

The Carnot cycle; Two propositions

regarding the efficiency of a Carnot

cycle; The thermodynamic temperature

scale; The ideal-gas temperature scale;

Ideal versus real machines.

2 16/08/17&

19/08/17

Tutorial



examples

L.1.

T.1, T.2& T.3

CO 1

28) Problems on second law of

thermodynamics 2 21/08/17

Tutorial

DM1. Chalk and Talk

L.1.

T.1, T.2& T.3

CO 1

29)

The inequality of Clausius; Entropy —

a property of a system; The entropy of a

pure substance;

1 22/08/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

30)

Entropy change in reversible processes;

The thermodynamic property relation;

Entropy change of an ideal gas;

2 23/08/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

31)

The reversible polytropic process for an

ideal gas; Entropy change of a control

mass during an irreversible process;

1 26/08/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

32)

Principle of increase of entropy;

Entropy as a rate equation.

1 28/08/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 1

33) Problems on entropy 2 29/08/17 Tutorial

DM1. Chalk and Talk

L.1.

T.1, T.2& T.3

CO 1

34)

Available energy; Available energy

Referred to a cycle; Quality of energy;

Maximum work in a reversible process;

1 30/08/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3 CO 2

35)

reversible work by an open system;

Exchanging heat only with the

surroundings;

1 31/08/17



examples

L.1.

T.1, T.2& T.3

CO 2

36) Useful work; Dead state; Availability;

Availability in chemical reaction; 1 02/08/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 2

37) Irreversibility and Gouy-stodola

Theorem; Availability or Exergy

Balance; second law efficiency;

1 11/09/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 2

38) Problems on Availability 3 18/09/17 &

19/09/17

Tutorial

DM1. Chalk and Talk

L.1.

T.1, T.2& T.3

CO 2

39)

The pure substance; Vapor- liquid-

solid- phase equilibrium in a pure

substance;

1 20/09/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 2

40)

Independent properties of a pure

substance; Steam Tables;

Thermodynamic surfaces;

1 23/09/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 2

41) The compressibility factor; Equations

of state 1 25/09/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 2

42) Problems on pure substance 2 26/09/17 Tutorial

DM1. Chalk and Talk

L.1.

T.1, T.2& T.3

CO 2

43)

Introduction to power systems; The

Rankine cycle; Effect of pressure and

temperature on the Rankine cycle;

problems.

6

03/10/17 &

04/10/17 &

07/10/17 &

09/10/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3 CO 3

44)

Air-standard power cycles; Basic Brayton

cycle; The air-standard cycle for jet

propulsion; problems

7

10/10/17 &

11/10/17 &

16/10/17 &

16/10/17&/

17/10/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 3

45)

Reciprocating engine power cycles; The

Otto cycle; The Diesel cycle; The Dual

cycle, The Sterling cycle; The Atkinson

and Miller cycles. Problems

7

18/10/17 &

21/10/17 &

23/10/17 &

24/10/17&

25/10/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 3

46)

Ideal Gas;Real Gas; Internal Energy and

Enthalpy of an Ideal Gas; Specific Heats of

an ideal gas; Equations of state;

1 28/10/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 4

47) Virial Expansions; Law of Corresponding

states; Boyle Temperature; 1 31/10/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 4

48)

Boyle Temperature; Dalton’s Law of

Partial Pressures; Thermodynamic

Properties of Gas Mixtures;

1 31/10/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 4

49) Gibbs Function of Ideal Gas Mixtures and

problems 2

01/11/17&

04/11/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 4

50) Mathematical relations for a homogeneous

phase; The Maxwell relations; 1 06/11/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 4

51)

Thermodynamic relations involving

enthalpy, internal energy, and entropy; The

Clapeyron equation; Joule-Thompson

coefficient;

1 07/11/17

DM1. Chalk and Talk



examples

L.1.

T.1, T.2& T.3

CO 4

52) Real gas behavior and equations of state.

And Problems 2 08/11/17

Tutorial

DM1. Chalk and Talk

L.1.

T.1, T.2& T.3

CO 4

TUTORIAL QUESTIONS

1. A mass of 1.5kg of air compressed in a quasi static process from 0.1 MPa to 0.7 MPa for which pv = constant. The initial density of

air is 1.16 kg/m3. Find the work done by the piston to compressed air.

2. A mass of gas is compressed in a quasi static process from 80 kPa, 0.1 m3 to 0.4 MPa, 0.03 m3. Assuming that the pressure and

volume are related by pvn = constant, find the work done by the gas system.

3. A system of volume V contains a mass m of gas at pressure p and temperature T. the macroscopic properties of the system obye the

following relationship: (𝑝 +𝑎

𝑉2) (𝑉 − 𝑏) = 𝑚𝑅𝑇 where a, b and R constants. Obtain an expression of the displacement work done

by the system during a constant temperature expansion from volume V1 to volume V2. Calculate the work done by a system which

contains 10 kg of this gas expanding from 1m3 to 10 m3 at a temperature of 293 K. use the values a = 15.7×104 Nm, b = 1.07×10-2

m3, and R= 0.287 kJ/kg K.

4. A gas of mass 1.5 kg undergoes a quasi static expansion which follows a relationship p = a+bV, where a and b are constants. The

initial and final pressure are 1000 kPa and 200 kPa respectively and the corresponding volumes are 0.2 m3 and 1.2 m3. The specific

internal energy of the gas is given by yhe relation 𝑢 = 1.5 𝑝𝑣 − 85 𝑘𝐽/𝑘𝑔 where p is the kPa and v is in m3/kg. calculate the net

heat transfer and the maximum internal energy of the gas attained during expansion.

5. A turbine operates under steady flow conditions, receiving steam at the following state; pressure 1.2 MPa, temperature 188°C,

enthalpy 2785 kJ/kg, velocity 33.3 m/s, and elevation 3 m. the steam leaves the turbine at the following state: pressure 20 kPa,

enthalpy 2512 kJ/kg, velocity 100 m/s and elevation 0m. heat is ost to the surroundings at the rate of 0.29 kJ/s. if the rate of steam

flow through turbine is 0.42kg/s. what is the power output of the turbine in kW?

6. A heat engine operating two reservoirs at 1000 K and 300 K is used to drive a heat pump which extracts heat from the reservoir at

300 K at a rate twice that at which the engine rejects heat to it. If the efficiency of the engine is 40% of the maximum possible and

the COP of the heat pump is 50% of the maximum possible, what is the temperature of the reservoir to which the het pump rejects

heat? What is the rate of heat rejection from the heat pump is the rate of heat supply to the engine is 50 kW?

7. A refrigerator plant for a food store operates as a reversed Carnot heat engine cycle. The store is to be maintained at a temperature of

-5°C and the heat transfer from the store to the cycle is at the rate of 5kW. If heat is transferred from the cycle to the atmosphere at

a temperature of 25°C, calculate the power required to drive the plant.

HOME ASSIGNMENT-II


Assignment-I

Q1. If a gas of volume 6000 cm3 and at pressure of 100 kPa is compressed quasistatically according to pV2 = constant until the volume becomes 2000

cm3, determine the final pressure and the work transfer.

Q2. A milk chilling unit can remove heat from the milk at the rate of 41.87 MJ/h. Heat leaks into the milk from the surroundings at an average rate of

4.187 MJ/h. Find the time required for cooling a batch of 500 kg of milk from 45°C to 5°C. Take the cp of milk to be 4.187 kJ/kg K.


Assignment-II

1. Two reversible heat engines are hooked up in a series so that the heat rejected by the first engine is absorbed by the second heat engine the upstream

engines receives 400 KW of heat from the source at 875K , while the downstream engine rejects heat to the sink at 275K.If the work output rate of the

upstream engine is twice as much as that of the downstream one, determine,

1. The thermal efficiency of both engines.

2. The heat rejected by the downstream engine.

3. The temperature of the intermediate reservoir.

2. Write the expression for COP of a heat pump and a refrigerator?

3. Show that violation of Kelvin Planck statement implies violation of Clausius statement


Assignment-III

Q1. In a steam generator, water is evaporated at 260°C, while the combustion gas (cp = 1.08 kJ/kg K) is cooled from 1300°C to 320°C. The

surroundings are at 30°C. Determine the loss in available energy due to the above heat transfer per kg of water evaporated (Latent heat of

vaporization of water at 260°C = 1662.5 kJ/kg).

Q2. 0.2 kg of air at 300°C is heated reversibly at constant pressure to 2066 K. Find the available and unavailable energies of the heat added. Take T0

=30°C and cp = 1.0047 kJ/kg K.


Assignment-IV

1.Calculate the state of a steam using steam table.

(a) Steam has a pressure of 15bar and specific volume of 0.12m3/kg

(b) Steam has a pressure of 10bar and temperature of 2000C.

(c) Steam has a pressure of 30bar and Enthalpy 2700kJ/kg.

2.Draw the p-V diagram of pure substance and explain its various regions of the diagram in details?

3. What is the effect of Rankine’s cycle efficiency when the steam is supplied at the inlet of the turbine is (a) Dry saturated (a) wet with dryness raction

‘x’ and (c) Superheated?


Assignment-V

1. From the basic principles prove that Cp-Cv=-T

T

v2p=

v

pT

2. A closed adiabatic cylinder of volume 1 m3 is divided by a partition into two compartments 1 and 2. Compartment 1 has a volume of 0.6 m3 and

contains methane at 0.4 MPa, 40°C, while compartment 2 has a volume of 0.4 m3 and contains propane at 0.4 MPa, 40°C. The partition is removed and

the gases are allowed to mix. (a) When the equilibrium state is reached, find the entropy change of the universe. (b) What are the molecular weight and

the specific heat ratio of the mixture? The mixture is now compressed reversibly and adiabatically to 1.2 MPa. Compute (c) the final temperature

of the mixture,(d) The work required per unit mass, and (e) The specific entropy change for each gas. Take p c of methane and propane as 35.72 and

74.56 kJ/kg mol K respectively.




III B.TECH. I SEMESTER REGULAR EXAMINATION-2017

SUBJECT: POWER ELECTRONICS

(COMMON TO ME &AE)


--------------------------------------------------------------------------------------------------------------------------------------------------------------

PART-A


a) Define Intensive and Extensive properties.

b) In a cold winter night you have switched on the heater .What kind of interaction it will be if the system is a)the heater b) air in the room

c) Heat is transferred from hot body to cold body .How do you interpret it in terms of entropy?

d) An automobile engine is heat engine. But it does not follow thermodynamic cycle. Justify

e) Define Wet steam and Dry Steam.

f) What do you mean by availability ? Explain

g) Lowering of condenser pressure is one way to enhance a Rankine cycle efficiency. Justify its limitations

h) Between vapour cycles and gas power cycle which one has low work ratios and Why?

i) What is a real gas? How does it differ from perfect gas?

j) Define Vander Waals equation and mention its limitations

Part-B

Answer the following questions 5×8=40 Marks

UNIT I

Q.1 a) Define with a neat sketch of P-V diagram an (a) isobaric process (b) isothermal process(c) isochoric process [3]

b) A system composed of 2 kg of the above fluid expands in a frictionless piston and cylinder machine from an initial state of 1 MPa, 100°C to a

final temperature of 30°C. If there is no heat transfer, find the net work for the process. [5]

Subject Code

5ME02

R15

OR

Q.2. a) A room for four persons has two fans, each consuming 0.18 kW power, and three 100 W lamps. Ventilation air at the rate of 80 kg/h enters

with an enthalpy of 84 kJ/kg and leaves with an enthalpy of 59 kJ/kg. If each person puts out heat at the rate of 630 kJ/h determine the rate at which heat

is to be removed by a room cooler, so that a steady state is maintained in the room. [8]

UNIT – II

Q.3. Using an engine of 30% thermal efficiency to drive a refrigerator having a COP of 5, what is the heat input into the engine for each MJ removed

from the cold body by the refrigerator? If this system is used as a heat pump, how many MJ of heat would be available for heating for each MJ of heat

input to the engine? [8]

OR

Q.4.Two kg of water at 80°C are mixed adiabatically with 3 kg of water at 30°C in a constant pressure process of 1 atmosphere. Find the increase in the

entropy of the total mass of water due to the mixing process (cp of water = 4.187 kJ/kg K). [8]

UNIT-III

Q.5. What is the maximum useful work which can be obtained when 100 kJ are abstracted from a heat reservoir at 675 K in an environment at

288 K? What is the loss of useful work if (a) A temperature drop of 50°C is introduced between the heat source and the heat engine, on the one hand,

and the heat engine and the heat sink, on the other (b) The source temperature drops by 50°C and the sink Temperature rises by 50°C during the

heat transfer process according to the linear law dQ/dT= ± constant? [8]

OR

Q.6. A rigid vessel contains 1 kg of a mixture of saturated water and saturated steam at a pressure of 0.15 MPa. When the mixture is heated, the state

passes through the critical point. Determine:(a) The volume of the vessel (b) The mass of liquid and vapour in the vessel initially (c) The temperature of

the mixture when the pressure has risen to 3 MPa (d) The heat transfer required to produce the final state. [8]

UNIT-IV

Q.7. An air standard dual cycle has a compression ratio of 15 and compression begins at 0.1 MPa, 40°C. The maximum pressure is limited to 6 MPa and

the heat added is 1.675 MJ/kg. Compute (a) the heat supplied at constant volume per kg of air, (b) the heat supplied at constant pressure per kg of

air, (c) the work done per kg of air, (d) the cycle efficiency, (e) the temperature at the end of the constant volume heating process, (f) the cut-off

ratio, and (g) the m.e.p. of the cycle. [8]

OR

Q.8. A simple steam power cycle uses solar energy for the heat input. Water in the cycle enters the pump as a saturated liquid at 40°C, and is pumped to

2 bar. It then evaporates in the boiler at this pressure, and enters the turbine as saturated vapour. At the turbine exhaust the conditions are 40°C and 10%

moisture. The flow rate is 150 kg/h. Determine (a) the turbine isentropic efficiency, (b) the net work output (c) the cycle efficiency, and (d) the area of

solar collector needed if the collectors pick up 0.58 kW/m2. [8]

UNIT-V

Q.9. A vessel is divided into three compartments (a), (b), and (c) by two partitions. Part (a) contains oxygen and has a volume of 0.1 m3 , (b) has a

volume of 0.2 m3 and contains nitrogen, while (c) is 0.05 m3and holds C O2 . All three parts are at a pressure of 2 bar and a temperature of 13°C.When

the partitions are removed and the gases mix, determine the change of entropy of each constituent, the final pressure in the vessel and the partial pressure

of each gas. The vessel may be taken as being completely isolated from its surroundings. [8]

OR

Q.10. Prove that Cp-Cv= -T

2

TT

V

TV

P

[8]









III B. Tech : I Sem : EEE-1 L T/P/D C

3 1 4

Course Name: Metallurgy and Material Science Course Code: 5ME03

Names of the Faculty Member: M. Venkateshwar Rao




1. PREREQUISITES

Maths, Physics, Chemistry





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

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

• Understand the different types of tools

• Able to understand the importance of Titanium & its alloys






1. Distinguish different types of metals and alloys

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

3. Analyze the failure of metals and alloys

4. Explain & justify the usage of Titanium & its alloys.


(This mapping represents the contribution of course in attaining the program outcomes and there by program

educational objectives. This also helps in strengthening the curriculum towards the improvement of program.)

Course

Outcomes

(COs)


a B C D e f g h i j k l

CO 1 3 3 2 1 2

CO 2 3 3 1 3 3

CO 3 2 3 2 2 2 3 2 2 2 3



(i) TEXT BOOKS

T1. Sidney H. Avner , Introduction to Physical Metallurgy, Mc Graw-Hill.

T2. William and Collister, " Materials Science and Engineering. Wiley India Pvt Ltd.

T3. V.Raghavan, Elements of Materials Science.


(Course delivery including latest trends brings good insight of the course in students and also inculcates the habit of self

learning among the students.


(a) Publications: NA


L1. http:// http://nptel.ac.in/courses/113105024/

L2. https://www.msm.cam.ac.uk/phase-trans/teaching.html

(iii) JOURNALS

J1. Science Direct Journal on Material secience.

J2. Science Direct Journal on physics of materials.



adopted to engage the student in learning)

DM1: Chalk and Talk



NO

8. ASSESSMENT




AM1: Semester End Examination . AM2: Mid Term Examination

AM3: Home Assignments



(The allotted marks for home assignments, quizzes and etc., except course projects are left to the liberty of faculty. But

for the finalisation of assignment marks, the following weightages can be considered.)

R15




the courses without

Course project

1. Home Assignments (AM3) 10%

10

10% 10

2. Quizzes (AM6)

3. Course project (AM7) -


5. Semester End Examination (AM1) 60 60


On the beginning day of each unit, home assignment sheet is given to the students and the solution sheet for the same is expected after

two days of the completion of unit.

(ii) QUIZZES

Two quizzes are conducted in the course duration. One is scheduled on 29/08/2017 and the second one is scheduled on 04/11/2017.

(iii) COURSE PROJECTS

One course project is assigned to each project batch of size three in the beginning of the course and assessed at the end of the course.

One midterm evaluation is carried out to monitor the progress of the project and the team coherence.


NOT APPLICABLE




UNIT –I

Metal Structure and Crystallization: Introduction, atom binding, ionic bond, covalent bond, metallic bond, and Vander Waals forces;

Crystal imperfections

Overview of Metal Structure and Crystallization. Constitution of alloys: Introduction, classification of alloys or compounds; Pure

metal; Intermediate alloy phase or compound -intermetallic compounds or valency compounds, interstitial compounds, and electron

compounds; Solid solutions; Substitution solid solution - factors that control the range of solubility in alloy system; Interstitial solid

solutions.

LEARNING OUTCOMES


1. Distinguish different types of metals and alloys

2. Analysis of solid solutions and rules to form a solid solutions.

3. Differentiate compound and alloy.

UNIT- II

Phase Diagrams: Introduction; Coordinates of phase diagrams; Experimental methods -construction of equilibrium diagrams by

thermal analysis, metallographic methods, and X-ray diffraction; Type-I-Two metals completely soluble in the liquid and solid states;

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

Nonequilibrium cooling; Homogenization; Properties of solid-solution alloys; Variation of Type I; Type II-Two metals completely

soluble in the liquid state and completely insoluble in the solid state; Type III-Two metals completely soluble in the liquid state but

only partly soluble in the solid state; Properties of eutectic alloy systems; Age hardening – solution treatment, and aging process;

Type IV-The congruent-melting intermediate phase; Type V-The peritectic reaction; Type VI-Two liquids partly soluble in the liquid

state: the monotectic reaction; Type VII-two metals insoluble in the liquid and solid states; Interrelation of basic types;

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

complex diagrams; Study of important binary phase diagrams of Cu-Ni, Al-Si, Sb-Pb, Pt-Ag, Bi-Cd, Cu-Pb, Cu-Sn and Fe- Fe3C.

LEARNING OUTCOMES


4. Understand microstructure of different metals and alloys.

5. Detail study of the microstructure of steels.

6. Distinguish different invariant reactions in various phase diagrams.

UNIT –III

The Heat Treatment of Steel: Introduction; Full Annealing; Spheroidizing; Stress-relief annealing; Process annealing; Normalizing;

Hardening; The isothermal transformation diagram; Transformation to Pearlite and Bainite; Cooling curves and I-T Diagram;

Transformation on continuous cooling; Position of the I-T curves; Hardening or austenitizing temperature; Homogeneity of austenite;

Mechanism of heat removal during quenching – vaporblanket cooling state (stage A), vapor transport cooling stage (stage B), Liquid

cooling stage (stage C); Quenching medium; Temperature of quenching medium; Surface condition -methods to minimize the formation of

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

Tempering; Austempering; Surface heat treatment or case hardening; Carburizing; Heat treatment after carburizing; Cyaniding and

Carbonitriding; Nitriding; Flame hardening; Induction Hardening; Residual Stresses; Hardenable carbon steels; Effect of cryogenic heat

treatment – A brief study.

LEARNING OUTCOMES


7. Understand microstructure of different metals and alloys in different heat treatment conditions.

8. Detail study of the case hardening process.

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

UNIT –IV

Alloy Steels: Introduction; Purpose of alloying; Effect of alloying elements upon Ferrite; Effect of alloying elements upon carbide; Influence

of alloying elements on the iron-iron carbide diagram; Effect of alloying elements in tampering; Classification of steels - nickel steel,

chromium steel, nickel-chromium steels, manganese steels, molybdenum steels, tungsten steels, vanadium steels, silicon steels, stainless

steels, martensitic stainless steels, ferritic stainless steels, austenitic stainless steels, precipitation-hardening stainless steels, maraging

steels, and ausforming.

Tool Steels: Classification of tool steels; Selection of tool steels; Comparative properties; Non-deforming properties; Depth of hardening;

Toughness; Wear resistance; Red-hardness; Machinability; Resistance to decarburization; Brand names; Water-hardening tool steels

(Group W); Shock resisting tool steels (Group S); Cold-work tool steels; Hot-work tool steels (Group H); High speed tool steels; Mold

Steels (Group P); Special purpose tool steels; Heat treatment of tool steels; Overview of tool failures; Special cutting materials – stellites,

cemented carbides, and ceramic tools.

LEARNING OUTCOMES


10. Analyze the failure of metals and alloys

11. Study of effect of alloying elements in steels.

12. Select suitable material for required applications.

UNIT –V

Cast Iron: Introduction; Types of cast iron; White cast iron; Malleable cast iron; Pearlitic malleable iron; Gray cast iron; Silicon in cast

iron; Sulfur in cast iron; Manganese in cast iron; Phosphorus in cast iron; Heat treatment of grey iron, Size and distribution of graphite

flakes; Mechanical properties and applications of grey cast iron; Chilled cast iron; Nodular cast iron; Alloy cast irons.

Non-Ferrous Metals and Alloys: Introduction; Copper and its alloys - Copper, temper designation of copper and copper alloys, and

copper alloys; Aluminum and its alloys -Aluminum, Alloy designation system, and temper designation; Titanium and Titanium alloys.

LEARNING OUTCOMES


13. Understand microstructure of different cast irons.

14. Suitable selection of material for required applications.

TEACHING PLAN

S.


No. of

Lecture

Periods

Lecture

Dates

Proposed Delivery

Methodologies


References

(Text Books /

Journals /

Publications/ Open

Learning Resources)

Course

Outcomes

53) Introduction to MMS 1 03-07-17 DM1. Chalk and Talk

T.1 CO 1

54)

Atomic bonding-covalent bond, ionic

bond, metallic bond, vander waals

forces .

1 04-07-17 DM1. Chalk and Talk

T.1 CO 1

55) Crystal imperfections-point defects,

line defects. 1 06-07-17

DM1. Chalk and Talk(along

with ppt)

T.1 CO 1

56) Crystal imperfections- surface defects,

volume defects 1 07-07-17

DM1. Chalk and Talk(along

with ppt)

T.1 CO 1

57) Metal crystal structure-SC, BCC, FCC,

HCP 1 10-07-17 DM1. Chalk and Talk. T.1 CO 1

58) Pure metal crystallization 1 11-07-17 DM1. Chalk and Talk

T.1 CO 1

59) Compounds- intermetallic, valency,

electron compounds 1 13-07-17

DM1. Chalk and Talk

T.1 CO 1

60) Solid solutions-humy rothery rules 1 14-07-17 DM1. Chalk and Talk

T.1 CO 1

61) Interstitial solid solutions 1 18-07-17 DM1. Chalk and Talk T.1 CO 1

62) Definition of phase and coordinates of

phase diagram 1 20/07/17

DM1. Chalk and Talk

T.1 CO 1

63)

Experimental methods for constructing

phase diagram- thermal analysis,

metallographic method

1 21/07/17 DM1. Chalk and Talk T.1 CO 1

64) Experimental methods for constructing

phase diagram- x-ray diffraction 1 24/07/17

DM1. Chalk and Talk

T.1 CO 1

65) Type-I-Two metals completely soluble

in the liquid and solid states 1 25/07/17

DM1. Chalk and Talk

T.1 CO 1

66) Equilibrium cooling of a solid solution

alloy 1 27/07/17

DM1. Chalk and Talk

T.1 CO 1

67) Diffusion; Nonequilibrium cooling;

Homogenization 1 28/07/17

DM1. Chalk and Talk

T.1 CO 1

68)

Type II-Two metals completely soluble

in the liquid state and completely

insoluble in the solid state

1 31/07/17 DM1. Chalk and Talk

T.1 CO 1

69)

Type II-Two metals completely soluble

in the liquid state and completely

insoluble in the solid state

1 01/08/17 DM1. Chalk and Talk

T.1 CO 1

70)

Type III-Two metals completely soluble

in the liquid state but only partly

soluble in the solid state

02/08/17 DM1. Chalk and Talk

T.1 CO 1

71) Numerical problems 03/08/17 DM1. Chalk and Talk

T.1 CO 1

72) The peritectic reaction 07/08/17 DM1. Chalk and Talk

T.1 CO 1

73) Age hardening 08/08/17 DM1. Chalk and Talk

T.1 CO 1

74) The eutectoid reaction, the peritectoid

reaction, and complex diagrams 10/08/17

DM1. Chalk and Talk

T.1 CO 1

75) Fe- Fe3C 11/08/17 DM1. Chalk and Talk

T.1 CO 1


T.1 CO 1


T.1 CO 1

78) Full Annealing 21/08/17 DM1. Chalk and Talk

T.1 CO 2


T.1 CO 2


T.1 CO 2

81) Normalizing; Hardening 28/08/17 DM1. Chalk and Talk

T.1 CO 2

82) The isothermal transformation

Diagram 29/08/17

DM1. Chalk and Talk

T.1 CO 2

83) Transformation to Pearlite and Bainite 31/08/17 DM1. Chalk and Talk

T.1 CO 2

84) Hardenability 01/09/17 DM1. Chalk and Talk

T.1 CO 2

85) case hardening- carburizing 11/09/17 DM1. Chalk and Talk

T.1 CO 2

86) Case hardening- Cyaniding and

Carbonitriding 12/09/17

DM1. Chalk and Talk

T.1 CO 2

87) Nitriding; Flame hardening; Induction

Hardening 14/09/17

DM1. Chalk and Talk

T.1 CO 2

88) Effect of cryogenic heat treatment 15/09/17 DM1. Chalk and Talk

T.1 CO 2

89) Effect of alloying elements upon Ferrite 18/09/17 DM1. Chalk and Talk

T.1 CO 3

90)

Influence of alloying elements on the

iron-iron carbide

Diagram


T.1 CO 3

91) Effect of alloying elements in tampering 21/09/17 DM1. Chalk and Talk

T.1 CO 3

92)

Classification of steels - nickel steel,

chromium steel, nickel-chromium

steels


T.1

CO 3

93)

manganese steels, molybdenum steels,

tungsten

steels, vanadium steels, silicon steels,

stainless steels


T.1 CO 3

94)

martensitic stainless steels, ferritic

stainless steels, austenitic stainless

steels, precipitation-hardening stainless

steels, maraging steels


T.1 CO 3

95) Classification of tool steels; Selection

of tool steels 03/10/17

DM1. Chalk and Talk

T.1 CO 3

96)

Comparative properties;

Non-deforming properties; Depth of

hardening; Toughness


T.1 CO 3

97)

Wear resistance; Red-hardness;

Machinability; Resistance to

decarburization; Brand names; Water-

hardening tool steels

(Group W); Shock resisting tool steels

(Group S)


T.1 CO 3

98) Cold-work tool steels; Hot-work tool

steels

(Group H); High speed tool steels


T.1 CO 3

99)

Mold Steels (Group P); Special purpose

tool steels; Heat

treatment of tool steels; Overview of

tool failures


T.1 CO 3

100) Special cutting materials – stellites,

cemented carbides, and ceramic tools 12/10/17

DM1. Chalk and Talk

T.1 CO 3

101) Types of cast iron 13/10/17 DM1. Chalk and Talk

T.1 CO 4

102) White cast iron 16/10/17 DM1. Chalk and Talk

T.1 CO 4

103) Malleable cast iron 17/10/17 DM1. Chalk and Talk

T.1 CO 4

104) Pearlitic

malleable iron 19/10/17

DM1. Chalk and Talk

T.1 CO 4

105) Gray cast iron; Silicon in cast iron 20/10/17 DM1. Chalk and Talk

T.1 CO 4

106)

Sulfur in cast iron; Manganese in cast

iron;

Phosphorus in cast iron


T.1 CO 4

107) Heat treatment of grey iron 24/10/17 DM1. Chalk and Talk

T.1

CO 4

108) Size and distribution of graphite flakes 26/10/17 DM1. Chalk and Talk

T.1

CO 4

109) Mechanical properties and applications

of grey cast iron 27/10/17

DM1. Chalk and Talk

T.1 CO 4

110) Nodular cast iron, Alloy cast irons 30/10/17 DM1. Chalk and Talk

T.1 CO 4

111) Copper and its alloys 31/10/17 DM1. Chalk and Talk

T.1 CO 4

112) Aluminum and its alloys 02/11/17 DM1. Chalk and Talk

T.1 CO 4

113) Alloy designation system 03/11/17 DM1. Chalk and Talk

T.1 CO 4

114) Titanium and Titanium alloys 06/11/17 DM1. Chalk and Talk

T.1 CO 4

115) Titanium and Titanium alloys 07/11/17 DM1. Chalk and Talk

T.1 CO 4

TUTORIAL& ASSIGNMENT QUESTIONS

1. How does the metallic bond differ from the ionic and covalent bonds?

2. Why is grain boundary irregular?

3. Explain various types of crystal imperfections?

4. Define APF? Find the APF for SC, BCC, FCC and HCP?

5. Explain hume-rothery rules in detail.?

6. Write short note on compounds?

7. Define phase and phase diagram? Explain importance of eutectic system with one example.

8. Write different reactions in equilibrium diagrams.

9. Discuss iron-iron carbide diagram in detail manner?

10. Evolution of microstructure of steels with help of iron-iron carbide diagram?

11. What are the types of Heat Treatment? And explain in detail about Annealing?

12. Describe the principle of flame hardening and induction hardening.

13. What is the effect of alloying elements upon ferrite and carbide?




II B.TECH. I SEMESTER REGULAR EXAMINATION-2017

SUBJECT: METALLURGY AND MATERIAL SCIENCE

(AE)


------------------------------------------------------------------------------------------------------------------------------------------------------------------

PART-A


i. Explain Hume-Rothery rules for Solid Solution CO1

ii. Write a brief note about atomic binding? CO3

iii. Explain Gibbs Phase Rule. CO3

iv. What is Coring? CO2

v. Define Heat Treatment? CO1

vi. Distinguish between Carburising and Nitriding CO1

vii. What is martensitic stainless steel? CO1

viii. Give the composition, properties and application of HSS CO1

ix. Why gray cast iron can be machined easily without the use of lubricant? CO1

Subject Code

5ME03

R15

x. Write short notes on Gun metal. CO1

Part-B

Answer the following questions 5×8=40 Marks

UNIT I

1. What is solid solution? Explain in detail about the types of solid solutions with Examples?

(OR)

2. What are point and surface defects found in solids? Illustrate these defects with suitable sketches.CO 1

UNIT II

3. Draw and Explain Fe-Fe3C phase diagram.

(OR)

4. a) Explain Isomorphous and Eutectoid system.

b) What is Coring? Explain.

UNIT III

5. What are the types of Heat Treatment? And explain in detail about Annealing?

(OR)

6. Describe the principle of flame hardening and induction hardening.

UNIT IV

7. What is the effect of alloying elements upon ferrite and carbide?

(OR)

8. What is stainless steel? How they are classified?

UNIT V

9. Write composition of malleable cast iron. Explain the malleabilizing treatment given to white cast iron.

(OR)

10. Describe the properties and applications of following

(a) Phosphorus bronze (b) brass (c) Duralumin (d) Titanium Alloys









II B. Tech : I Sem : Automobile Engineering L T/P/D C

3 3

Course Name: Fluid Mechanics and Hydraulic Machines Course Code: 5ME04

Names of the Faculty Member : Dr T. Srinivasa Rao

Number of working days : 90

Number of Hours/week : 5

Total number of periods planned : 67

1. PREREQUISITES

(This information helps the student to refer to the required topics before undergoing the course. This builds confidence

in a student.)

Maths, Physics and Engineering Mechanics




Understand the properties of fluids, principles of buoyancy, flow, force and head calculations

• Evaluation of types of fluid flow, Laminar and dynamic

• Knowledge on boundary layer principles applied to aerofoil

• Principles of operation of different types of hydraulic machinery





After completion of the course the student is able to

• Analyzing the fluid properties to solve flow, force and velocity problems

• Evaluating the flow characterizing in static and dynamic nature of flow

• Applying fluid flow and dynamics in solving problems in hydraulic machines

• Understanding the model analysis of hydraulic machinery and select appropriate machines for hydro power plant


Course

Outcomes

(COs)


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

CO 1

CO 2

CO 3

CO4


5. LEARNING RESOURCES:

(i) TEXT BOOKS

T1. Hydraulics and Fluid Mechanics Including Hydraulics Machines: Dr. P.N.Modi, Dr. S.M. Seth.

T2. Introduction to Fluid Mechanics, R. W. Fox, A. T. McDonald and P.J Pritchard.

T3. Fluid Mechanics, V. L. Streeter & E. B. Wylie.

T4. Fluid Mechanics, fundamentals & applications - Yunus A. Çengel, John M. Cimbala.

Fluid Mechanics: F. M. White .

T5. Fundamentals of Fluid Mechanics: Bruce Roy Munson, Donald F. Young, Theodore H. Okiishi, Wade W. Huebsch Wiley

Publication.


(Course delivery including latest trends brings good insight of the course in students and also inculcates the habit

of self learning among the students.


(a) Publications


(iii) JOURNALS



adopted to involve the student in learning)




DM4: Demonstration (Physical / Laboratory / Audio Visuals) DM8: Any Other (Please specify)



8. ASSESSMENT






AM5: Objective Test AM6: Quizzes

AM7: Course Projects** AM8: Group Presentations

AM9: Any other (Specify)

** COURSE PROJECTS

(To be added for the courses as directed by the department. The no. of course projects is left to the liberty of

faculty.

One course project is assigned to each project batch of size three in the beginning of the course and assessed at

the end of the course. One midterm evaluation is carried out to monitor the progress of the project and the team

coherence.)


(The allotted marks for home assignments, quizzes, course projects and etc., are left to the liberty of faculty. But for the


For R15




project


the courses without

Course project

1.

Assignment

10

10

2.




For R13




project

Weightages in marks

for the courses without

Course project

1.

Assignment

5

5

2.




10.SIMULATION SOFTWARES (If any)




UNIT No.: 1

Fluid Statics: Properties of fluid – specific gravity, viscosity, surface tension, vapor pressure and their influence on fluid motion, Pressure at

a point, measurement of pressure, Forces on immersed surfaces, Center of pressure, Buoyancy, Elements of stability of floating bodies.

Fluid Kinematics: Classification of flows, acceleration equations, Stream line, path line and streak lines and stream tube, continuity

equation, Stream function, velocity potential function.

LEARNING OUTCOMES

TEACHING PLAN

S.

No.


be taught

No. of Lecture


Proposed Delivery

Methodologies




Resources)

Course

Outcomes

1 Unit I Introduction 1 3/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

2 Properties of fluid 1 6/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

3

Specific gravity,

viscosity,

surface tension

2 7/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

4

vapor pressure and

their influence on fluid

motion

1 8/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

5

Pressure at a point,

measurement of

pressure

1 10/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

6 Forces on immersed

surfaces 1 13/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

7

Center of pressure,

Buoyancy, Elements of

stability of floating

bodies.

2 14/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

8 Fluid Kinematics:

Classification of flows, 1 15/7/17

DM1: Chalk and

Talk T1 CO1, CO2

acceleration equations, (along with PPT)

9 Stream line, path line

and streak lines 1 20/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

10 Stream tube 2 21/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

11 Continuity equation 1 22/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

12

Stream function,

velocity potential

function.

1 24/7/17

DM1: Chalk and

Talk

(along with PPT)

T1 CO1, CO2

TUTORIAL QUESTIONS

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

HOME ASSIGNMENT - No.

Issue date: dd/mm/yyyy Submission date: dd/mm/yyyy

-----------------------------------------------------------------------------------------------------------------------------------------------------------------

UNIT No. :2

Fluid Dynamics: Surface and body forces – Euler’s and Bernoulli’s equation, Venturimeter, Orifice meter, Pitot tube, Reynolds experiment

– Darcy Weisbach equation – Minor losses in pipes – pipes in series and pipes in parallel. Momentum equation, force on pipe bend.

LEARNING OUTCOMES

TEACHING PLAN

S.

No.


be taught

No. of Lecture


Proposed Delivery

Methodologies




Resources)

Course

Outcomes

1 27

2 28

3 29

4 31/7/17

5 3/8/17

6 7

7 10

8 11

9 12

10 17

11 18

12 19

TUTORIAL QUESTIONS

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



----------------------------------------------------------------------------------------------------------------------------------------------------------------- UNIT No. :3

Boundary Layer Theory: Development of boundary layer along a thin flat plate, Laminar boundary layer and turbulent boundary layer,

Laminar sub layer, boundary layer separation, Drag and lift forces - Aerofoils, pressure and form drags.

Impact of Jets: Hydrodynamic force of jets on flat, inclined and curved vanes - jet striking centrally and at tip, flow over radial vanes

LEARNING OUTCOMES

TEACHING PLAN

S.

No.


be taught

No. of Lecture


Proposed Delivery

Methodologies




Resources)

Course

Outcomes

1 21

2 24

3 26

4 28

5 31/8/17

6 1/9/17

7 11

8 14

9 15

10 16

11 18

TUTORIAL QUESTIONS

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



----------------------------------------------------------------------------------------------------------------------------------------------------------------- UNIT No. :4

Hydraulic Turbines: Classification of turbines, design of Pelton wheel, Francis turbine and Kaplan turbine – working proportion, work done,

efficiency, draft tube- theory, functions and efficiency. Geometric similarity, Unit and specific quantities, characteristic curves, governing of

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

LEARNING OUTCOMES

TEACHING PLAN

S.

No.


be taught

No. of Lecture


Proposed Delivery

Methodologies




Resources)

Course

Outcomes

1 21

2 22

3 23

4 25/9/17

5 5/10/17

6 6

7 9

8 12

9 13

10 14

TUTORIAL QUESTIONS

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



----------------------------------------------------------------------------------------------------------------------------------------------------------------- UNIT No. :5

Hydraulic Pumps: Classification, centrifugal pumps – types, working, work done, manometric head, losses and efficiency, specific speed –

pumps in series and parallel – performance characteristic curves, NPSH, Reciprocating Pump – types, Working, Discharge, slip, indicator

diagrams.

LEARNING OUTCOMES

TEACHING PLAN

S.

No.


be taught

No. of Lecture


Proposed Delivery

Methodologies




Resources)

Course

Outcomes

1 16

2 19

3 20

4 21

5 23

6 26

7 27

8 28

9 30

TUTORIAL QUESTIONS

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



-----------------------------------------------------------------------------------------------------------------------------------------------------------------


(END EXAMINATION)

________________________________________________****The End*****_____________________________________________

VNR VIGNANA JYOTHI INSTIYUTE OF ENGINEERING AND TECHNOLOGY

BACHUPALLY, NIZAMPET (S.O), HYDERABAD – 500 090

LABORATORY EXECUTION PLAN: 2017-18

II B. Tech : I Sem : AE-1 L T/P/D C

0 3 2

Course Name: Metallurgy and Material Science Laboratory Course Code: 5ME54

Names of the Faculty Members: M.Venkateshwar Rao, CH. Vamshi Krishna


Number of Sessions per week per batch: Batch: 1(3 lecture periods)

COURSE PREREQUISITES:

Maths, physics, chemistry

COURSE OBJECTIVES:


• Understand the need of proper simplification for different materials

• Understand the significance microstructure of different materials under microscopic testing.

• Understand the changes in microstructures after different treatments.

• Understand the microstructure of cutting tool.

COURSE OUTCOMES:

After completion of this course the student is able to

1. Identify materials for micro structure.

2. Test microstructure of any given material and predict properties.

VNR VJIET/ACADEMICS/2017/Formats/ II

3. Prepare appropriate heat treatment for a given material by checking its microstructure.

4. Examine the microstructure of cutting tool.

DETAILED SYLLABUS:

PART A

1. Preparation and study of the microstructure of metals like Iron, Cu and Al

2. Preparation and study of the microstructure of mild steels, low carbon steels, and high carbon steels

3. Study of the microstructures of cast irons

4. Study of the microstructures of non-ferrous alloys

5. Study of the microstructures of heat treated steels

6. Hardenability of steels by Jiminy end quench test

7. To find out the hardness of various treated and untreated steels

8. Study the microstructure of cutting tools

9. Study the micro structures of stainless steel

10. Study the different crystal structures of metals

LABORATORY EXECUTION PLAN

S. No. Topic Schedule Date

Batch-I

Schedule Date

Batch-II

1 Introduction (Story Board, Lab Protocol) 3/7/17 5/7/17

2

Preparation and study of the microstructure of mild

steels, low carbon steels, and high carbon steels

10/7/17 12/7/17

3

Preparation and study of the microstructure of mild

steels, low carbon steels, and high carbon steels

24/7/17 19/7/17

4 Study of the microstructures of cast irons

31/7/17 26/7/17


7/8/17 03/8/17


21/8/17 10/8/17

7 Study of the microstructures of non-ferrous alloys

28/8/17 17/8/17

8 Study of the microstructures of heat treated steels

04/9/17 24/8/17

9 Study of the microstructures of heat treated steels

11/9/17 4/9/17

10 Study the micro structures of stainless steel

18/9/17 11/9/17

11

To find out the hardness of various treated and

untreated steels

25/9/17 18/9/17

12 Hardenability of steels by Jiminy end quench test 09/10/17 25/09/17

13 Study the microstructure of cutting tools 16/10/17 04/10/17

14 Revision Session 23/10/17 11/10/17

Revision Session 30/10/17 18/10/17

15 Internal Lab Exam 06/11/17 01/11/17

Time Table

Monday : 10.00 a.m. to 12.30 p.m Thursday :

Tuesday : Friday :

Wednesday : 10.00 a.m. to 12.30 p.m Saturday :




II B. Tech : I Sem : AE-1 L T/P/D C

0 3 2

Course Name: MECHANICS OF SOLIDS LABORATORY Course Code: 5ME55

Names of the Faculty Members: T. Praveen Kumar, T. Raju, Rakesh




Mechanics of solids, Engineering Mechanics

COURSE OBJECTIVES:


• Analyze the various tests to be conducted on engineering materials

• The significance of tests in evaluating the corresponding mechanical properties

• Analyze the importance of technical parameters used during tests

• Applying the concepts learned in the real time

COURSE OUTCOMES:


• Apply the theoretical concepts by conducting the tests on different materials

• Evaluate the result of test and comment on the mechanical properties of materials

• Decide a material and an appropriate test suitable for given application


• Analyze the significance of the tests in different fields of engineering

DETAILED SYLLABUS:

PART A

1. Direct tension test

2. Bending tests:

a) Simple supported beam

b) Cantilever beam

3. Torsion test

4. Hardness test

a) Brinell hardness test

b) Rockwell hardness test

5. Test on springs

6. Compression test on a cube

7. Impact test

8. Punch shear test

9. Mechanical advantage:

(a) Simple screw jack

(b) Compound screw jack

10. Moment of Inertia of a fly wheel

11. To Study various types of Strain Gauges



Batch-I

Schedule Date

Batch-II

1 Experiment 1 completed as per cycle1 4/7/17 3/7/17

2 Experiment 2 completed as per cycle1

11/7/17 10/7/17




1/8/17 7/8/17




29/8/17 04/9/17



11 Experiment 11completed as per cycle2

26/9/17 25/9/17


10/10/17 09/10/17


14 Revision Session 24/10/17 23/10/17



Time Table

Monday : 10.00 a.m. to 12.30 p.m Thursday :

Tuesday : 1.20 p.m. to 3.50 p.m Friday :

Wednesday : Saturday :




II B. Tech : I Sem : AE L T/P/D C

0 3 2

Course Name: Fluid Mechanics and Hydraulic Machines

Course Code: 5ME56

Names of the Faculty Members: R.Ramu




Maths, physics

COURSE OBJECTIVES:

The student should be able to

• Analyzing the experiments to understand the concept, find the values and obtain the result of experiments

• Apply fundamental principles of fluid mechanics for the solution of practical mechanical engineering problems of water conveyance in

pipes, orifices, mouth pieces, notches & weirs

• Analyzing various pumps, water turbines, pipes and pressure measurement devices

• Evaluating efficiency for pumps and turbines

COURSE OUTCOMES:


5. Apply fundamental equations of fluid mechanics for turbines and pumps

6. Analyse fluid flow problems in mechanical engineering

7. Create a model of fluid flow equipments


8. Evaluate the experimental results with theoretical concepts

DETAILED SYLLABUS:

PART A

11. Verification of Bernoulli’s theorem 12. Calibration of Venturimeter / Orifice meter 13. Calibration of t notches 4 Determination of friction factor for a given pipe 9. Determination of Minor losses for the given equipment 10. Impact of jets on vanes 11. Performance test on Pelton wheel 12. Performance test on Francis turbine 13. Performance test on Kaplan turbine 14. Performance test on single stage centrifugal pump 15. Performance test on multi stage centrifugal pump 16. Performance test on reciprocating pump



Batch-I

Schedule Date

Batch-II

1 Introduction class 4/7/17 5/7/17

2 Lab Protocol 11/7/17 12/7/17

3

Experiment on Verification of Bernoulli’s theorem

18/7/17 19/7/17

4

Calibration of Venturimeter / Orifice meter 25/7/17 26/7/17

5

Calibration of t notches

1/8/17 2/8/17

6

Determination of friction factor for a given pipe

8/8/17 9/8/17

7

Determination of Minor losses for the given equipment

22/8/17 16/8/17

8

Impact of jets on vanes

29/8/17 23/8/17

9

Performance test on Pelton wheel

5/9/17 30/8/17

10

Performance test on Francis turbine

12/9/17 6/9/17

11

Performance test on Kaplan turbine

19/9/17 13/9/17

12

Performance test on single stage centrifugal pump

3/10/17 20/09/17

13

Performance test on multi stage centrifugal pump

10/10/17 4/10/17

14

Performance test on reciprocating pump

17/10/17 11/10/17




Time Table

Tuesday : 1.20 p.m to 3.50 p.m

Wednesday : 10.00 a.m. to 12.30 p.m

ACADEMIC HAND BOOK 2017-2018 II - vnr vjiet

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