vachana pitamaha dr. p.g. halakatti college of engineering & technology, vijaypur...

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B.L.D.E.A’s

Vachana Pitamaha Dr. P.G. Halakatti

College of Engineering & Technology,

Vijaypur – 586 103

Course File

2017-2018

CHOICE BASED CREDIT SYSTEM

Semester – IV

Department of Civil Engineering

Name:

USN:

Roll No. : Division:

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Department Vision

To emerge as the premier department in Technical education and Research, to meet the

infrastructural needs and challenges of the Society.

Department Mission 1. To impart technical education to students by adopting innovative teaching/learning processes and

fostering soft skills for leading successful career.

2. To develop students tendency for innovation, leadership and aptitude to solve social concerns

ethically through curriculum, reinforced with co and extra-curricular activities.

Programme Educational Objectives (PEO’s)

1. Graduates will analyze, design and execute civil engineering projects by applying principles of

science and engineering.

2. Graduates will be actively engaged in higher studies and research work.

3. Graduates will be leaders in their chosen profession and personal endeavors.

4. Graduates will be able to solve the engineering problems that account for economical,

environmental, ethical and societal considerations by engaging in lifelong learning.

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Program Outcomes (POs)

Engineering Graduates will be able to:

1. Engineering knowledge: Apply the knowledge of mathematics, science, engineering fundamentals,

and an engineering specialization to the solution of complex engineering problems.

2. Problem analysis: Identify, formulate, review research literature, and analyze complex

engineering problems reaching substantiated conclusions using first principles of mathematics,

natural sciences, and engineering sciences.

3. Design/development of solutions: Design solutions for complex engineering problems and

design system components or processes that meet the specified needs with appropriate

consideration for the public health and safety, and the cultural, societal, and environmental

considerations.

4. Conduct investigations of complex problems: : Use research-based knowledge and research

methods including design of experiments, analysis and interpretation of data, and synthesis of the

information to provide valid conclusions.

5. Modern tool usage: Create, select, and apply appropriate techniques, resources, and modern

engineering and IT tools including prediction and modeling to complex engineering activities with

an understanding of the limitations.

6. The engineer and society: Apply reasoning informed by the contextual knowledge to assess

societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to the

professional engineering practice.

7. Environment and sustainability: Understand the impact of the professional engineering solutions

in societal and environmental contexts, and demonstrate the knowledge of, and need for

sustainable development.

8. Ethics: Apply ethical principles and commit to professional ethics and responsibilities and norms of

the engineering practice.

9. Individual and team work: Function effectively as an individual, and as a member or leader in

diverse teams, and in multidisciplinary settings.

10. Communication: Communicate effectively on complex engineering activities with the engineering

community and with society at large, such as, being able to comprehend and write effective reports

and design documentation, make effective presentations, and give and receive clear instructions.

11. Project management and finance: Demonstrate knowledge and understanding of the

engineering and management principles and apply these to one’s own work, as a member

and leader in a team, to manage projects and in multidisciplinary environments.

12. Life-long learning: Recognize the need for, and have the preparation and ability to engage

in independent and life-long learning in the broadest context of technological change.

Civil Engineering Program Specific Outcomes (PSO)

By the time of graduation, Civil Engineering students can

1. Apply knowledge of mathematics, science and basics of engineering in professional career.

2. Practice in the core areas of civil engineering and conduct laboratory and field tests.

3. Analyze and Design a component, system or establish process in civil engineering.

4. Build the managerial and professional skills in executing the engineering projects addressing the

social concerns.

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VISIVESVARAYA TECHNOLOGICAL UNIVERSITY, BELGAVI.

SCHEME OF TEACHING AND EXAMINATION

IV SEMESTER CIVIL ENGINEERING

Sl. No Name of Subject Subject Code Page No’s

1 Engineering Mathematics – IV 15CV41 05 to 26

2 Analysis of Determinate Structures 15CV42 27 to 46

3 Applied Hydraulics 15CV43 47 to 62

4 Concrete Technology 15CV44 63 to 75

5 Basic Geotechnical Engineering 15CV45 76 to 89

6 Advanced Surveying 15CV46 90 to 100

7 Fluid Mechanics and Hydraulic Machines

Laboratory 15CVL47 101 to 109

8 Engineering Geology Laboratory 15CVL48 110 to 116

NOTE: The syllabus of theory subjects has been divided into five modules.

Scheme of Examination for Theory Papers:

The question paper will have ten questions, each full question carrying 16 marks.

There will be two full questions (with a maximum three sub divisions, if necessary) from each

module.

Each full question shall cover the topics under a module.

The students shall answer five full questions selecting one full question from each

module.

If more than one question is answered in modules, best answer will be considered for the

award of marks limiting one full question answer in each module.

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COURSE: ENGINEERING MATHEMATICS - IV

Semester: IV Year: 2016-17 (Even Semester)

Subject Code: 15CV41 IA Marks: 20

Total Contact Hours: 50 hrs Hours per week: 4

VTU Exam Marks: 80 Exam: 03 Hours

1. Syllabus:

MODULE Levels No. of

hrs

MODULE-I

Numerical Methods: Numerical solution of ordinary differential equations of

first order and first degree, Taylor’s series method, modified Euler’s method,

Runge - Kutta method of fourth order.

Milne’s and Adams-Bashforth predictor and corrector methods (No derivations

of formulae).

L2 & L3 10

MODULE-II

Numerical Methods: Numerical solution of second order ordinary differential

equations, Runge- Kutta method and Milne’s method.

Special Functions: Series solution-Frobenious method. Series solution of

Bessel’s differential equation leading to 𝐽𝑛(𝑥)-Bessel’s function of first kind.

Basic properties, recurrence relations and Orthogonality. Series solution of

Legendre’s differential equation leading to 𝑃𝑛(𝑥)-Legendre Polynomials.

Rodrigue’s formula, problems

L2 & L3 10

MODULE-III

Complex Variables: Review of a function of a complex variable, limits,

continuity and differentiability. Analytic functions, Cauchy-Riemann equations in

Cartesian and polar forms. Properties and construction of analytic functions.

Complex line integrals-Cauchy’s theorem and Cauchy’s integral formula, Residue,

poles, Cauchy’s Residue theorem (without proof) and problems.

Transformations: Conformal transformations, discussion of transformations

W = Z2, W = ez, W = z + (1

z) (𝑧 ≠ 0) and bilinear transformations-

Problems

L2 & L3

L4

10

MODULE-IV

Probability Distributions: Random variables(discrete and continuous),

Probability mass/density functions. Binomial distribution, Poisson distribution,

Exponential and normal distributions, Problems.

Joint probability distribution: Joint Probability distribution for two discrete

random variables, expectation, covariance, correlation coefficient.

L3 10

MODULE-V

Sampling Theory: Sampling, Sampling distributions, standard error, test of

hypothesis for means and proportions, confidence limits for means, student’s t-

distribution, Chi-square distribution as a test of goodness of fit.

Stochastic process: Stochastic process, probability vector, stochastic matrices,

fixed points, regular stochastic matrices, Markov chains, higher transition

probability simple problems.

L3 & L4 10

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Course Outcomes:

1. Use appropriate single step and multi-step numerical methods to solve first and second order

ordinary differential equations arising in flow data design problems.

2. Explain the idea of analyticity, potential field’s residues and poles of complex potentials in field

theory and Electromagnetic theory.

3. Employ Bessel's functions and Legendre's polynomials for tackling problems arising in continuum

mechanics, hydrodynamics and heat conduction.

4. Describe random variables and probability distributions using rigorous statistical methods to

analyze problems associated with optimization of digital circuits, information, coding theory and

stability analysis of systems.

5. Apply the knowledge of joint probability distributions and Markov chains in attempting

engineering problems for feasible random events.

Graduate Attributes (as per NBA)

1. Engineering Knowledge

2. Problem Analysis

3. Life-Long Learning

4. Accomplishment of Complex Problems

Text Books:

1. B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 43rd Ed., 2015.

2. E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed., 2015.

Reference books:

1. N.P.Bali and Manish Goyal: A Text Book of Engineering Mathematics, Laxmi

Publishers, 7th Ed., 2010.

B.V.Ramana: "Higher Engineering Mathematics" Tata McGraw-Hill, 2006.

H. K. Dass and Er. RajnishVerma: "Higher Engineering Mathematics", S. Chand publishing, 1st

edition,2011.

2. Prerequisites of the course:

To learn this subject, the student must have the knowledge about differentiation integration, set

theory, permutation & combination and probability.

3. Overview of the course:

The primary goal of this course is to highlight the essential concepts of i) numerical methods

ii) complex variables iii) series solutions of differential equations iv) probability

Many differential equations of interest to engineers are not amenable to analytical solutions and

hence we must resort to numerical solutions. Also the rapid development of high speed digital

computers and the

Increasing desire for numerical answers to applied problems has led to the enhanced demands in the

methods and techniques of numerical analysis.

Complex variables are useful in the study of fluid mechanics, thermodynamics, electric fields,

aerodynamics, elasticity etc. Conformal mapping, which preserves angles in magnitude and sense, is

useful in solving boundary value problems in two dimensional potential theory by transforming a

complicated region to a simpler region.

The solutions to differential equations with variable co-efficient cannot be expressed as finite linear

combination of known elementary functions, however in such cases solutions can be obtained in the

form of infinite power series. In series solutions of differential equations with variable co-efficients

we use power series method.

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Probability is the measure of how frequently the same event occurs in an experiment. The study of

probability provides a mathematical frame work to asses the chances of the predictions coming true

and is essential in every decision making process.

Probability distribution is the theoretical counter part of frequency distribution, and plays an

important role in the theoretical study of populations. Ex: The shoes industry should know the sizes

of foot of the population. Sampling aims at gathering the maximum information about the population

with the minimum effort, time and cost.

Stochastic process: Stochastic process technique, probability vector, stochastic matrices, fixed points,

regular stochastic matrices, Markov chains, higher transition probability

4. Relevance of the course to this program:

Numerical Methods:

Numerical techniques are applicable for determining the motion of a body falling through a viscous

fluid arising in a wide variety of engineering contexts.

Complex variables:

In the theory of alternating current, the application of complex impedance involves functions having

complex numbers as independent variables. The theory of complex variables has made a significant

contribution in the design of aerofoil sections for aircraft and other lifting bodies. The strength of the

theory in such applications is its ability to generate mappings which transforms complicated shapes,

such as an aerofoil section into a simpler shape.

Complex Integration:

To express a complex function as a Taylor’s series is applicable in the field of Control and

communications theory

Series Solution of ordinary differential equations and special functions :

Heat equation, wave equation and Laplace’s equation with cylindrical symmetry can be solved in

terms of Bessel’s functions, with spherical symmetry by Legendre’s polynomials.

Probability distributions:

Probability distributions are applicable for problems concerning i) Radar detection ii) Number of

rounds fired from a gun hitting a target. iii) Defective vehicles in a workshop. iv) Telephone calls.

v) Errors made by chance in experimental measurements. vi) Reliability and queuing theory.

Joint Probability: Problems in Economics, Biology or social science needs statistical method

analyzing two or more variables in such cases the concept of joint probability required.

Sampling:

It is quite often necessary to draw some valid conclusions concerning a large mass of population

which is practically impossible and therefore it is preferred to examine a small part of the population

called Sample with the motive of drawing some conclusion about the entire population.

Stochastic Process: Stochastic process can be used to analyze and solve diver’s range of problems

arising in production and inventory control, resource planning, service systems computer networks

and many other.

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5. Course Outcomes:

1. On completion of this course, students are able to use appropriate numerical methods to solve

first and second order ordinary differential equations.

2. Use Bessel's and Legendre's function which often arises when a problem possesses axial and

spherical symmetry, such as in quantum mechanics, electromagnetic theory, hydrodynamics

and heat conduction.

3. State and prove Cauchy's theorem and its consequences including Cauchy's integral formula

compute residues and apply the residue theorem to evaluate integrals.

4. Analyze, interpret, and evaluate scientific hypotheses and theories using rigorous statistical

methods

5. Application area: Computer science, Psychology, Agriculture, Geography, Radar detection and

Thermodynamics.

6. Module wise plan:

Learning Objectives: At the end of this chapter student should be able to

1. Recall the various formulae

2. Apply the appropriate formulas to solve the differential equations with initial conditions.

3. Interpret the one step methods to solve the differential equations with one initial condition and using

successive integrations.

4. Interpret the multistep methods to solve the differential equations with more than one initial condition.

5.Apply Milne’s and Adams-Bashforth’s methods to solve the differential equations with one initial

condition after using one step method to get the required number of initial conditions.

6. Evaluate the predicted value of y at xn+1 and then correct it using the corrector formula.

Lesson Plan:

Module - 1 Title : Numerical Methods Planned Hours: 08

Lecture

no. Topics covered

Teaching

Method PSO’s

PO’s

Attained

COs

Attained Ref Book/

Chapter no.

L1

Numerical solution of ordinary

differential equations of first

order and first degree. Examples

on Taylor’s series method

Chalk and

Board

1

1, 2, 4, 5

& 11

1

T1/32,

T2/21

L2 Some more examples on

Taylor’s series method

L3 Euler’s formula & Modified

Euler’s formula- examples

L4 Some more examples on

Modified Euler’s method

L5 Runge-Kutta method of fourth

order-examples

L6 Milne’s predictor and corrector

method-examples

L7 Some more examples on Milne’s

method

L8 Adams-Bashforth predictor and

corrector method-examples

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Assignment questions

1. Using Taylor’s series method, compute the solution of:

a) yxdx

dy , y(0) = 1 at the point x = 0.2 correct to three decimal places.

b) 2yx

dx

dy , y(0) = 1 at the point x = 0.1

c) the initial value problem xey

dx

dy32 , y(0)=0, at x = 0.1 and x = 0.2

d) dxxydy )1( , y = 2 at x =1 at the point x = 1.02

e) yxy 2 in the range 2.00 x by taking step size h= 0.1 ,given that

y = 10 at x = 0, initially considering terms up to the fourth degree.

f) 22 yx

dx

dy , y(0) = 0 at the point x = 0.4 correct to three decimal places.

2. Using Euler’s modified method, obtain a solution of the equation

a) yxdx

dy , with initial conditions y =1 at x = 0 , for the range 0<x<0.6

in steps of 0.2.

b) 2xy

dx

dy y = 2 at x = 0 Obtain ‘y’ at x = 0.2 in two stages of 0.1 each.

c) 2yx

dx

dy , y(0) = 1 taking h = 0.1, find y(0.2) correct to four decimal

places

d) yx

dx

dy10log , with y(20) = 5 ,taking h = 0.2. Find y(20.2) and y(20.4)

e) yxdx

dy 2

, y(0) = 1 taking h = 0.05, find y(0.1) considering the accuracy

up to two approximations in each step.

3. Employ Runge-Kutta method of fourth order to solve the equation

a) 2

3y

xdx

dy , y(0) = 1 at x = 0.2 taking step length h = 0.2.

b) 1022 yx

dx

dy , and y(0)=1 , compute y(0.2) (Take h=0.2)

c) xy

xy

dx

dy

y(0)=1 , compute y(0.2) (Take h=0.2)

d) 1dx

dyyx y(0.4) = 1 at x = 0.5

4. Using Milne’s method and Adams–Bashforth’s predictor- corrector method, solve

X: 0 0.2 0.4 0.6

Y: 0 0.02 0.0795 0.1762

a) Given 2yx

dx

dy and the data

Find y(0.8)

b) Given that 2

2 yx

dx

dy , and y(1)=2,

COs

Attained

1

10


1. Recall the various formulae

2. Apply the appropriate formulas to solve the second order ordinary differential equations with initial

conditions.

3. Solve the Bessel differential equation in series, Recurrence relations

4. Solve the Legendre differential equation in series.

5. Apply Rodrigue’s formula to evaluate Legendre polynomials.

Lesson Plan:

y(1.1)=2.2156, y(1.2)=2.4649 and

y(1.3)=2.7514. compute y(1.4) ,correct to three decimal places.

X: 0 0.1 0.2 0.3

Y: 2 2.010 2.040 2.090

c) Given yedx

dy x 2 and the data

Find y(0.4)

d) Given that2yx

dx

dy & the data.

Compute y(0.4)

e) Given 1 y(0) ,2 yxdx

dy and the starting values y(0.1) = 0.90516,

X: 0 0.1 0.2 0.3

Y: 1 1.1 1.231 1.402

Y (0.2)=0.82127, y(0.3) = 0.74918 evaluate y(0.4).

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Module - 2 Title : Numerical Methods Planned Hours: 12

Lecture

no. Topics covered

Teaching

Method PSO’s

PO’s

attained

COs

attained Ref Book/

Chapter no.

L09 Numerical solution of second order

ordinary Differential equations-

Runge-Kutta method-examples

Chalk and

Board

1

1, 2, 4, 5

& 11

2

T1/32T2/

21,5

L10 Milne’s method- Examples

L11 Series solution –Frobenious method

L12 Series solution of Bessel

differential equation leading to

𝐽𝑛(𝑥)-Bessel’s function of first kind

L13 Basic properties, and examples

L14 Some more Examples

L15 Recurrence relations.

L16 Orthogonality

L17 Series solution of Legendre

Differential equation leading to 𝑃𝑛(𝑥)

L18 Legendre polynomials

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Assignment questions COs

Attained

1. Using Runge-Kutta method find third approximation to the values

a) y″ = xy′ 2 – y2 for x = 0.2 correct to four decimal places. Initial conditions are

x = 0, y = 1, y’ = 0

b) yxdx

dyx

dx

yd 33

2

2

, given y(0) = 1 , y′ (0) = ½

c) ydx

dyx

dx

yd

2

2

given that y = 1, 0dx

dy when x = 0

d) 2

2

2

2

ydx

dyx

dx

yd

given that y = 1, 0

dx

dy when x = 0

2. The angular displacement of θ of a simple pendulum is given by the equation

0sin2

2

l

g

dt

d, where l = 98 cm and g = 980 cm/sec2, if θ = 0

and 472.4dt

d at t = 0, use Runge-Kutta method to find θ.

3. Given y″ + xy′ + y = 0, y(0) = 1 , y′(0) = 0, obtain y for x = 0(0.1)0.3 by any

method. Further, continue the solution by Milne’s method to calculate y (0.4).

4. Applying Milne’s method compute 𝑦(0.8) given that y satisfies the equation

𝑦′′ = 2𝑦𝑦′ and 𝑦 & 𝑦′ are governed by the fallowing values

𝑥 0 0.2 0.4 0.6

𝑦 0 0.20

27

0.422

8

0.68

41

𝑦′ 1 1.04

1

1.179 1.46

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5. Apply Milne’s method to compute y (0.4) given the equation 𝑦′′ + 𝑦′ = 2𝑒𝑥

And the following table of initial values.

𝑥 0 0.1 0.2 0.3

𝑦 2 2.01 2.04 2.09

𝑦′ 0 0.2 0.4 0.6

6. Use Frobenius method to solve the equations

a) 3xy″ + 2y′ + y = 0 b) 4xy″ + 2(1-x)y′ - y = 0

7. Solve Bessel’s differential equation leading to Jn(x).

8. Prove

a)

)()]([

1 xJxdx

xJxdn

nn

n

b)

)()]([

1 xJxdx

xJxdn

nn

n

c)

xx

xJ sin2

)(2

1

d) xx

xJ cos2

)(2

1

9. Prove 2𝑛𝐽𝑛(𝑥) = 𝑥[𝐽𝑛+1(𝑥) + 𝐽𝑛−1(𝑥)]

10. Prove 𝑑

𝑑𝑥[𝑥𝑛𝐽𝑛(𝑥)] = 𝑥𝑛𝐽𝑛−1(𝑥)

2

L19 Examples

L20 Rodrigue’s formula

12

11.

Prove that

)(

0)()(

2

121

1

0 n

nnJ

dxxJxxJ where , are the roots of

0)( xJ n

12. Solve the Legendre’s differential equation 0)1(2)1(2

22 ynn

dx

dyx

dx

ydx

13. Prove the Rodrigue’s Formula Pn(x) = n

n

n

nx

dx

d

n1

!2

1 2

14. Express the following polynomials in terms of Legendre polynomials

a ) f(x) = 5x3 + x b) f(x) = 4x3 – 2x2 - 3x + 8

c ) f(x) = 2x3 – x2 - 3x + 2 d ) f(x) = x4 + 3x3 – x2 + 5x – 2

e ) f(x) = x3 + 2x2 - 4x + 5 f ) f(x) = x3 – 5x2 + 6x + 1

g ) f(x) = x3 + 2x2 - x + 3 h ) f(x) = x4 + x3 + 2x2 – x – 3

2


1. Identify the analytic functions

2. Apply the C-R equations to show the complex functions are analytic.

3. Recall the properties of analytic functions.

4. Construct the analytic functions given real or imaginary part using Milne Thompson method

5. Evaluate Complex Line Integrals by using Cauchy’s theorem and formula

6. Study of Residue, Poles, Cauchy’ Residue Theorem

7. Interpret the conformal mapping from z-plane to w-plane under some standard transformation

8. Find the Bilinear transformation and the corresponding invariant points

Lesson plan:

Lecture

no. Topics covered

Teaching

Method PSOs

POs

attained

COs

attained

Ref Book/

Chapter

No.

L21

Introduction to function of a complex

variable.Limit,continuity,differentiability

and analytic function

Chalk and

Board

1

1, 2, 4,

5 & 11

3

T1/20T2/

13,14,16,

17

L22 Cauchy-Riemann equations in Cartesian

form and polar form

L23 Properties of analytic functions and

construction of analytic function f(z) given

its real or imaginary parts

L24 Line integral of Complex valued functions,

Examples

L25 Cauchy’s theorem and related examples.

L26 Cauchy’s integral formula and Generalized

Cauchy’s integral formula -examples

L27 Residues, Poles, Cauchy’s Residue theorem

with proof and problem

L28 Problems.

Module : 3 Title : Complex variables Planned Hours: 12

13

L29 Discuss the conformal transformation w =

z2, ,w = ez - examples

L30 Discuss the transformation 𝑤 = 𝑧 +

1

𝑧

Examples

L31 Bilinear transformations

L32 Problems

Assignment questions COs

Attained

1. Derive Cauchy – Riemann equations in Cartesian form and Polar form.

2. Define harmonic function. Prove that real and imaginary parts of an analytic function are

harmonic in Cartesian and polar form

3. Show that the following functions are harmonic and find their harmonic conjugate. Also find

the corresponding analytic function

a) 𝑢 = 𝑒2𝑥(𝑥𝑐𝑜𝑠𝑦 − 𝑦𝑠𝑖𝑛2𝑦) b) 𝑢 =2 cos 𝑥𝑐𝑜𝑠ℎ𝑦

𝑐𝑜𝑠2𝑥+𝑐𝑜𝑠ℎ2𝑦

c) 𝑣 = (𝑟 −1

𝑟) 𝑠𝑖𝑛𝜃 d) 𝑣 =

−𝑠𝑖𝑛𝜃

𝑟

e) 𝑣 = 𝑒−𝑥(𝑥𝑐𝑜𝑠𝑦 + 𝑦𝑠𝑖𝑛𝑦) f) 𝑢 =1

𝑟𝑐𝑜𝑠𝜃

g) 𝑣 = −𝑠𝑖𝑛𝑥𝑠𝑖𝑛ℎ𝑦 h) 𝑢 = 𝑒𝑥cosy + 𝑥𝑦

i) 𝑣 = 𝑒−2𝑦𝑠𝑖𝑛𝑥 j) 𝑢 = (𝑥 − 1)3 − 3𝑥𝑦2 + 3𝑦2

4.Construct analytic function f(z) = u + iv as a function of z using the following data

a) 𝑢 − 𝑣 = 𝑒𝑥(𝑐𝑜𝑠𝑦 − 𝑠𝑖𝑛𝑦) b) 𝑢 − 𝑣 =𝑐𝑜𝑠𝑥+𝑠𝑖𝑛𝑥−𝑒−𝑦

2𝑐𝑜𝑠𝑥−𝑒𝑦−𝑒−𝑦 when 𝑓 (𝜋

2) = 0

c) 𝑢 − 𝑣 = (𝑥 − 𝑦)(𝑥2 + 4𝑥𝑦 + 𝑦2) d) 𝑢 + 𝑣 =2𝑠𝑖𝑛2𝑥

𝑒2𝑦−𝑒−2𝑦−2𝑐𝑜𝑠2𝑥

e) 𝑢 + 𝑣 =1

𝑟2 (𝑐𝑜𝑠2𝜃 − 𝑠𝑖𝑛2𝜃)

5.If f(z) = u + iv is an analytic function of z, then prove that

a) [𝜕2

𝜕𝑥2 +𝜕2

𝜕𝑦2] |𝑓(𝑧)|2 = 4|𝑓 ′(𝑧)|2 b) {

𝜕

𝜕𝑥|𝑓(𝑧)|}

2+ {

𝜕

𝜕𝑦|𝑓(𝑧)|}

2= |𝑓 ′(𝑧)|

2

c) (𝜕𝑓

𝜕𝑥)

2+ (

𝜕𝑓

𝜕𝑦)

2= [(

𝜕𝑓

𝜕𝑢)

2+ (

𝜕𝑓

𝜕𝑣)

2] |𝑓 ′(𝑧)|

2.

6. Show that 𝑣 = 𝑐𝑜𝑠𝑥𝑠𝑖𝑛ℎ𝑦 is harmonic and find its harmonic conjugate.

7. Find the harmonic conjugate of 𝑣 = 𝑙𝑜𝑔√𝑥 + 𝑦 and find its analytic function.

8. Evaluate ∫ 𝑧𝐶

dz where c is the i)straight line from i to i. ii)right half of the unit

circle lzl = 1

9. Evaluate ∫ (𝑧2 + 𝑧)𝑑𝑧2+3𝑖

1−𝑖 along the line joining the points ( 1, -1 ) & ( 2,3 )

10. Prove that ∫𝑑𝑧

𝑧−𝑎= 2i

𝐶 , where C is the circle: z – a = r.

11.Prove that ∫ (𝑧 − 𝑎)𝑛𝑑𝑧 = 0𝐶

, (n, any integer ≠ -1),

where C is the circle :z – a = r.

12. Evaluate ∫ (2𝑥 + 𝑖𝑦 + 1)𝑑𝑧2+𝑖

1−𝑖 along the two paths

a) x = t + 1 , y = 2t2 – 1 b) the straight line joining (1 - i ) & (2 + i)

3

3

14

13. Verify Cauchy’s theorem for f(z) = z2 taken over the boundary of a square

with vertices at 1, i in counter clockwise direction.

14. Verify Cauchy’s theorem for the function f(z) = 3z2 + iz – 4 , where c is the

Square having vertices 1 i,-1 i.

15. Verify Cauchy’s theorem for the function f(z) = ze−z over the unit circle with

Origin as the centre.

16. Verify Cauchy’s theorem for the integral of z3 taken over the boundary of the

Rectangle with vertices -1, 1, 1 + i , -1 + i .

17. Evaluate ∫𝑒2𝑧

𝑧−2𝐶𝑑𝑧 where C is the circle C: z = 1.

18. Evaluate ∫𝑧2+1

𝑧−3𝐶𝑑𝑧 where C is the circle C : z -1= 1

19. Verify Cauchy’s theorem for the function f(z) = 2 sin 5z , where c is the

Square with vertices 1 i,-1 i.

20. Evaluate ∫𝑧2−𝑧+1

𝑧−1𝐶 𝑑𝑧 where C is the circle a) C : z = 1 b) C : z =

2

1

21. Evaluate ∫𝑒𝑧

𝑧(1−𝑧)3𝐶 where C is

a) C : z = 2

1 b) C : z -1 =

2

1 c) C : z = 2

22. Evaluate ∫𝑑𝑧

𝑧2−4𝐶 over a) C : z = 1 b) C: z = 3 c) C:z + 2 = 1

23. Evaluate ∫𝑒𝑧

𝑧−𝑖𝑑𝑧

𝐶 where C is the circle a) C : z = 2 b) C : z = 2

24.Evaluate ∫𝑒2𝑧

(𝑧−1)(𝑧−2)𝑑𝑧

𝐶 where C is the circle z = 3

25. Evaluate ∫𝑠𝑖𝑛z2+𝑐𝑜𝑠z2

(𝑧−1)2(𝑧−2)𝑑𝑧

𝐶 where C is the circle z = 3.

26.If 𝑓(𝑧) has a simple pole at 𝑧 = 𝑎,then 𝑅𝑒𝑠 𝑓(𝑎) = lim𝑧→𝑎

[(𝑧 − 𝑎) 𝑓(𝑧)]

27.Find the sum of the residues of

𝑓(𝑧) =𝑠𝑖𝑛𝑧

𝑧𝑐𝑜𝑠𝑧 𝑎𝑡 𝑖𝑡𝑠 𝑝𝑜𝑙𝑒𝑠 𝑖𝑛𝑠𝑖𝑑𝑒 𝑡ℎ𝑒 𝑐𝑖𝑟𝑐𝑙𝑒 |𝑧| = 2

28.Determine the poles of the function 𝑓(𝑧) = 𝑧2

(𝑧 − 1)2(𝑧 + 2)⁄

And the residue at each pole. Hence evaluate

∮ 𝑓(𝑧)𝑑𝑧, 𝑤ℎ𝑒𝑟𝑒 𝐶 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑖𝑟𝑐𝑙𝑒 |𝑧| = 2.5

29.Evaluate ∮𝑧−3

𝑧2+2𝑧+5𝑑𝑧 where C is the circle

i)|𝑧| = 1 ii)|𝑧 + 1 − 𝑖| = 2 iii) |𝑧 + 1 + 𝑖| = 2

30.Evaluate ∮𝑠𝑖𝑛𝜋𝑧2+𝑐𝑜𝑠𝜋𝑧2

(𝑧−1)2 (𝑧−2) 𝑑𝑧 where C is the circle |𝑧| = 3

31. Find the transformation of the straight lines parallel to the axes under the

Transformation w = z2.

15

32.Show that the transformation w = z2 transforms

a) The circle |𝑧| = 𝑎 to a circle |𝑤| = 𝑎2

b) The first quadrant in the z-plane to the upper half of the w-plane

c) The upper half of the z-plane to the entire w-plane.

33. Under the transformation w = z2, find

a) The image of the square region bounded by the lines x = 1,x = 2, y = 1 ,

y = 2.

b) The image of the triangular region bounded by the lines x = 1, y = 1 ,

x + y = 1.

c) The image of the region bounded by ½ x 1 and ½ y 1.

34. Show that the transformation w = ez transforms lines parallel to the

a) y axis into concentric circles centered at the origin in the w- plane.

b) x axis into radial lines in the w-plane .

35.Show that under the transformation w = ez

a) y axis is mapped onto the unit circle at the origin in the w-plane.

b) x axis is mapped onto the positive u-axis in the w-plane .

36. Find & draw the image of the rectangular region -1 x 3, - y in the z-plane under

the transformation w = ez

37.Find the images of the circles lzl = 1 and lzl = 2 under the conformal transformation

w = z + z

1 and sketch the region.

38.Discuss the transformation w = ez and show that it transforms the region between

the real axis and the line parallel to the real axis at y = , into the upper half the w- Plane.

39. Define bilinear transformation. Find the Bilinear transformation which maps the given

points and the corresponding invariant points.

a) z = 1, i, -1 into w = i, 0, -i b) z = -1,0,1 into w = 0, i, 3i

c) z = 1, i, -1 into w = 0, 1, d) z = 0,-i ,2i into w = 5i, ∞, -i/3

e) z = 0,-1, into w = -1,-2-i , i f) z = 2,1,0 into w = 1, 0, i,

g) z = -1,i,1 into w = 1, i, -1 h) z = 1, i, -1 into w = 2,i,-2

i) z = i,1, -1 into w = 1, 0, ∞, j) z = 0, i, ∞ into w = 1, -i, -1

3

16


1. Identify Random variables, Discrete and continuous probability distributions.

2. Apply the concept based on pdf & cdf and evaluate various problems based on it.

3. Interpret mean, variance in Binomial, Poisson, Normal distributions, classify and

evaluate and make certain judgments.

Lesson Plan:

Module - 4 Title Probability Distributions Planned Hours: 09

Lecture

no. Topics covered

Teaching

Method PSO’s

PO’s

attained

COs

attained

Ref Book/

Chapter no.

L33 Random variables, Discrete and

continuous probability

mass/density functions

Chalk

and

Board

1 1, 2, 4, 5

& 11

4

T1/26,

T2/22

L34 Examples on Probability

functions.

L35 Binomial distributions, mean and

variance and examples

L36 Poisson distributions, mean and


L37 Exponential distributions, mean

and variance and examples

L38 Normal distributions, mean and


L39 Joint probability distribution for

two discrete random variables,

examples.

L40 Expectation, covariance,

correlation coefficient.

L41 Examples

Assignment questions

COs

Attained

1. A random variable ‘x’ has the following function values of ‘x’

x 0 1 2 3 4 5 6 7

y 0 k 2k 2k 3k k2 2k2 7k2 + 7

a) Find k b) Evaluate P(x < 6) c) Evaluate P(x 6) d) P (3< x 6)

2. A coin is tossed twice. A random variable X represents the number of heads

turning up. Find the discrete probability distribution for X. Also find its mean and

variance.

3. Find the value of ‘k’ such that the following represents a finite probability

4

17

distribution. Hence find its mean and standard deviation.

x -3 -2 -1 0 1 2 3

y k 2k 3k 4k 3k 2k k

4. Prove that the mean & S. D of the Binomial distribution are np & npq

respectively

5. Prove that the mean & S.D of the Poisson distribution are m & m

respectively.

6. Six coins are tossed. Find the probability of getting

a) Exactly 3 heads b) At least 3 heads c) At least one head

7. A travel agency has 2 cars which it hires daily. The number of demands for a car

on each day is distributed as a Poisson variate with mean 1.5. Find the

probability

that on a particular day a) there was no demand b) a demand is refused.

8. In a consignment of electric lamps 5% are defective. If a random sample of 8

lamps is inspected, what is the probability that one or more lamps are defective?

9. The probability of a shooter hitting a target is1/3. How many times he should

shoot so that the probability of hitting the target at least once is more than ¾.

10. Show that mean & standard deviation of exponential distribution are equal.

11. Find the mean & standard deviation of normal distribution.

12. The length of telephone conversation has been an exponential

distribution& found on an average to be 5 minutes. Find the probability that a

random call made from this booth a) ends in less than 5 minutes b) between 5 & 10

minutes.

13. The probability that a man aged 60 will live up to 70 is 0.65.Out of 10 persons

aged 60, what is the probability that a) at least 7 of them will live up to 70

b) exactly 9 will live up to 70 c) at most 9 will live up to 70.

14. In a quiz contest of answering ‘Yes’ or ‘No’ ,what is the probability of

guessing at least 6 answers correctly out of 10 questions asked? Also find the

probability of the same if there are 4 options for a correct answer.

15. The probability that a news reader commits no mistake in reading the news

is1/e3.

Find the probability that on a particular news broadcast he commits

i)only 2 mistakes ii) more than 3 mistakes iii)at most 3 mistakes.

16. If the probability of a bad reaction from a certain injection is 0.001, determine

the chance that out of 2000 individuals, more than two will get a bad reaction.

17. The marks of 1000 students in an examination follows a normal distribution

with mean 70 & standard deviation 5. Find the number of students whose marks

will bea) less than 65 b) more than 75

18. In an examination 7% of students score less than 35%, marks & 89% of

4

18

students score less than 63% marks. Find the mean & standard deviation if the

marks are normally distributed.

19. In a normal distribution 31% of the items are under 45 and 8% are over 64.

find the mean and standard deviation of the distribution.

20. The increase in sales per day in a shop is exponentially distributed with Rs.800 as

the average. If sales tax is levied at the rate of 6%, find the probability that the

increase in sales tax return from that shop will exceed Rs.30 per day.

21. The joint distribution of two random variables X and Y is as follows.

y

x -4 2 7

1 1/8 1/4 1/8

5 1/4 1/8 1/8

Compute the following.

(a) 𝐸(𝑋) 𝑎𝑛𝑑 𝐸(𝑌) (𝑏) 𝐸(𝑋𝑌) (𝑐) 𝜎𝑋 𝑎𝑛𝑑 𝜎𝑌 (𝑑) 𝐶𝑂𝑉(𝑋, 𝑌) (𝑒) 𝜌(𝑋, 𝑌)

22. X and Y are independent random variables. X take values 2, 5, 7 with probability

1/2, 1/4, 1/4, respectively. Y takes values 3, 4, 5 with the probability 1/3, 1/3,

1/3

(a) Find the joint probability distribution of X and Y.

c) Show that the covariance of X and Y is equal to zero.

23. Find the joint distribution of X and Y, which are independent random variables with the

following respective distributions;

𝑥𝑖: 1 2

𝑓(𝑥𝑖): 0.7 0.3

𝑦𝑖: -2 5 8

𝑔(𝑦𝑖): 0.3 0.5 0.2

And

Show that Cov (𝑋, 𝑌) = 0.

24. Determine (a) marginal distributions of 𝑋 and 𝑌 (b) Cov(𝑋, 𝑌), for the following joint

distribution. Determine whether 𝑋 and 𝑌 are independent.

𝑌

𝑋

-3 2 4

1 0.1 0.2 0.2

3 0.3 0.1 0.1

25. A fair coin is tossed three times. Let 𝑋 denote 0 to 1 according as a head or tail occurs on

the first toss. Let 𝑌 denote the number of heads which occur.

(a) Find the marginal distribution of 𝑋 and 𝑌, (b) Determine the joint distribution of 𝑋 and 𝑌 and Cov(𝑋, 𝑌).

4

MODULE:5 Title: SAMPLING THEORY & Planned Hours: 09

19


1. Outline the process of sampling made in daily life.

2. Distinguish between standard error, null and alternate hypothesis and Type I,II errors.

3. Classify and calculate the above said errors and apply known procedure to solve

problems.

4. Interpret level of significance for means.

5. Interpret and explain confidence limits for means of large and small samples.

6. Apply known technique and solve the examples.

7. Interpret and evaluate scientific hypotheses

8. Outline the random process that undergoes transitions from one state to another on

a state space.

Lesson Plan:

STOCHASTIC PROCESS

Lecture

no. Topics covered

Teaching

Method

PSOs POs

attained

COs

attained

Ref Book/

Chapter no.

L42 Introduction to sampling and

sampling distribution and simple

examples

Chalk

and

Board

1

1, 2, 4, 5

& 11

5

T1/27,

T2/23

L43 Standard error, test of hypothesis

for mean and proportions and

examples

L44 Confidence limits for means of

large and small samples.

L45 Student’s t-distribution with

examples.

L46 Chi-square distribution as test of

goodness of fit.

L47 Introduction to Stochastic process.

L48 Probability vector, stochastic

matrices.

L49 Fixed points, regular stochastic

matrices.

L50 Markov chains, higher transition

probability.

https://en.wikipedia.org/wiki/Stochastic_process

https://en.wikipedia.org/wiki/State_space

20

Assignment Questions

COs

Attained

1. Explain the following terms a) Null hypothesis b) Confidence limits

c) Type I & Type II errors d) students’‘t’ distribution. e) level of significance.

2. A die was thrown 9000 times & a throw of 5 or 6 was obtained 3240 times,

on the assumption of random throwing, do the data indicate that the die is

unbiased.

3. A random sample of 400 items chosen from an infinite population is found to

have a mean of 82 and a standard deviation of 18. Find the 95% confidence

limits for the mean of the population from which the sample is drawn.

4. In a city ‘A’ 20 % of a random sample of 900 school boys had a certain

Slight Physical defect. In another city ‘B’ 18.5% of a random sample of 1600

school boys had the same defect. Is the difference between the proportions

significant?

4. One type of aircraft is found to develop engine trouble in 5 flights out of

total of 100 & another type in 7 flights out of a total 200 flights. Is there a

significant difference in the two types of aircrafts so for as engine defects are

concerned?

6. A survey was conducted in a slum locality of 2000 families by selecting a

sample of size 800. It was revealed that 180 families were illiterates. Find

the probable limits of the illiterate families in the population of 2000.

7. In an examination given to students at a large number of different schools

the mean grade was 74.5 & S.D grade was 8. At one particular school where

200 students took the examination the mean grade 75.9. Discuss the

significance of this result from the view point of a) one tailed test b) two

tailed test at both 5 % & 1% level of significance.

8. Random sample of 1000 engineering students from a city A and 800 from

city B were taken. It was found that 400 students in each of the sample

were from payment quota. Does the data reveal the significant difference

between the two cities in respect of payment quota students.

9. A sample of 400 items is taken from a normal population whose mean is 4

& variance 4. If the sample mean is 4.45, Can the samples be regarded as a

simple sample .

10. The mean of two large samples of 1000 & 2000 members are 168.75 cms

and 170 cms respectively. Can the samples be regarded as drawn from the

same population of standard deviation of 6.25 cms

11. Balls are drawn from a bag containing equal number of black & white balls ,

each ball being replaced before drawing another . In 2250 drawings 1018

black & 1232 white balls have been drawn. Do you suspect some bias on the

part of the drawer?

12. A coin is tossed 400 times and it turns up head 216 times. Discuss whether the

coin may be an unbiased one at 5% level of significance.

13. It is required to test whether the proportion of smokers among students is less

than that among the lectures. Among 60 randomly picked students, 2 were

smokers. Among 17 randomly picked lectures, 5 were smokers. What would be

your conclusion?

14. From a random sample of 10 pigs fed on diet A, The increase in weight in

the certain period were 10, 6,16,17,13,12,8,14,15,9 lbs. For another sample of

5

5

21

12 pigs fed on diet B, the increase in the same period were

7,13,22,15,12,14,18,8,21,23,10,17 lbs. Test whether diets A & B differ

significantly as regards their effect on increase in weight.(Given t 0.05 for 20 d.f =

2.09)

15. A group of 10 boys fed on a diet A and another group of 8 boys fed on a

different diet B for a period of 6 months recorded the following increases in

weights (lbs)

Diet A : 5, 6, 8, 1, 12, 4, 3, 9, 6, 10

Diet B : 2, 3, 6, 8, 10, 1, 2, 8

Test weather diet A and B differ significantly regarding their effect on increases

in weight.

16. A group of boys and girls are given an intelligence test. The mean score, S.D

score

Boys Girls

Mean 124 121

SD 12 10

n 18 14

and numbers in each group are as follows.

Is the mean score of boys significantly different from that of girls?

(Given t 0.05 for 30 d.f = 1.960)

17. Eleven school boys were given a test in drawing. They were given a months

further tuition and a second test of equal difficulty was held at the end of it. Do

the marks give evidence that the students have benefitted by extra coaching?

Boys 1 2 3 4 5 6 7 8 9 10 11

Marks Test I 23 20 19 21 18 20 18 17 23 16 19

Marks Test II 24 19 22 18 20 22 20 20 23 20 17

18. The nine items of a sample have the following values:

45,47,50,52,48,47,49,53,51

Does the mean of these differ significantly from the assumed mean of 47.5.

Apply student’s t- distribution at 5% l.o.s.(t 0.05 for 8 d.f = 2.31)

19. A certain stimulus administrated to each of the 12 patients result at

in the following change in blood pressure, 5,2,8,-1,3,0,6,-2,1,5,0,4. Can it be

concluded that the stimulus will increase blood pressure. Use t 0.05 for 11

d.f = 2.201

20. A set of five similar coins is tossed 320 times and the result is

Test the hypothesis that the data follows a Binomial distribution.

(x 2 0.05 ,at d.f 5 = 11.07.)

No of heads 0 1 2 3 4 5

Frequency 6 27 72 112 71 32

5

22

21. Fit a binomial distribution to the data and test for goodness of fit at the

level of significance 0.05

x 0 1 2 3 4 5

f(x) 38 144 342 287 164 25

22. Fit a poission distribution to the data and test for goodness of fit at the

level of

x 0 1 2 3 4

f(x) 419 352 154 56 19

Significance 0.05

23. A die is thrown 60 times and the frequency distribution for the number

appearing on the face x is given by the following table. Test the hypothesis that

the die is unbiased.

x 1 2 3 4 5 6

f(x) 15 6 4 7 11 17

24. In an experiment on pea breeding , the following frequencies of seeds were

obtained. Theory predicts that the frequencies should be in proportion 9 : 3:

3: 1 Examine the correspondence between theory and experiment.

(x 2 0.05 ,at d.f 3= 7.815)

Round and

yellow

wrinkled

and

yellow

Round

and

green

wrinkled

and

green

total

315 101 108 32 556

25. Define probability vector .If A =

21

21

bb

aa is a stochastic matrix and

V = 21 vv is a probability vector show that VA is also a probability

vector.

26. Define stochastic matrix. Find the unique fixed probability vector of the

regular

Stochastic matrix A =

21

21

41

43

27. Define regular stochastic matrix. Find the unique fixed probability vector of

the regular stochastic matrix P =

010

0 21

21

41

41

21

5

23

8. Portion for I.A. Test:

28. Show that P =

0

100

010

21

21

is a regular stochastic matrix. Also find the

associate unique fixed probability vector.

29. Prove that the Markov chain whose transition probability matrix is

P =

0

0

0

21

21

21

21

32

32

is irreducible.

30. Assume that a computer system is in one of the three states :busy, idle or

undergoing repair denoted by states 0,1,2 . Observing its state at a certain

specified time on each day, it is found that the system approximately behaves like

a Markov chain with the transition probability matrix

4.006.0

1.08.01.0

2.02.06.0

.

Prove that the chain is irreducible and determine the study state probabilities.

31. A software engineer goes to his office everyday by motorbike or by car. He

never goes by bike on two consecutive days. But if he goes by car on a day then

he is equally likely to go by car or by bike on the next day. Find the transition

probability matrix of the Markov chain. If a car is used on the first day of the

week find the prob that after 4 days a) Bike is used b) Car is used

32. Each year a man trades his car for a new car in 3 brands of the popular

company Maruti Udyog limited. If he has a ‘standard’ he trades it for ‘zen’. If he

has a ‘zen’ he trades it for a‘Esteem’. If he has a ‘Esteem’ he is just as likely to

trade it for a new ‘Esteem’ or for a‘Zen’ or a ‘standard’ one. In 1996 he bought

his first ca which was Esteem. Find the probability that he has a) 1998 Esteem

b) 1999 Zen

33. A salesman’s territory consists of 3 cities A,B,C. He never sells in the same

city for 2 consecutive days. If he sells in city A then the next day he sells in next

city B. However if he sells in either B or C, then the next day he is twice as

likely to sell in city A as in the other city. In the long run how often does he sell

in each of the cities.

34. Define i) probability vector ii) stochastic matrix iii) regular stochastic

matrix iv) absorbing state of a Markov chain v) recurrent state of a Markov

chain . vi) transient state of a Markov chain

35. A students study habits are as follows .If he studies one night he is 70%sure

not to study the next night. On the other hand if he does not study one night he is

60%sure not to study the next night also. Supposing that he studies on Monday

night, find the probability that he does not study on Friday night.

5

5

I. A. Test No. Modules

I I and II or I and IV

24

II III and IV or II and IV

27

COURSE : ANALYSIS OF DETERMINATE STRUCTURES

SEMESTER – IV

Subject Code 15CV42 IA Marks 20

Number of Lecture Hours/Week

04 Exam Marks 80

Total Number of Lecture Hours

50 Exam Hours 03

CREDITS – 04

Course objectives: This course will enable students to

1. Ability to apply knowledge of mathematics and engineering in calculating slope,

definitions,

2. bending moment and shearing force using various methods of approach.

3. Ability to identify, formulate and solve engineering problems.

4. Ability to analyse structural system and interpret data.

5. Ability to communicate effectively in design of structural elements.

6. Ability to engage in lifelong learning with the advances in structural problems.

Modules

Teaching

Hours

Revised

Bloom’s

Taxonomy

(RBT) Level

Module -1

Introduction and Analysis Of Plane Trusses Structural forms, Conditions of equilibrium-Degree of freedom- Linear and non linear analysis-Static and kinematic

indeterminacies of structural systems-Types of trusses-

Assumptions in analysis-Analysis of determinate trusses by

method of joints and method of sections.

10 L2,L4,L5

Module -2

Deflection of Beams Introduction and definitions of slope, Deflection and moment curvature, Sign conventions, Derivation of differential equations

of flexure, Double integration method, Use of discontinuity.

Function: Macaulay’s method, slope and deflection for standard

loading cases using Macaulay’s

Method for basically determinate prismatic beams subjected to

point loads, udl, uvl and couple,

Moment area method-Deviation, Deflectance and Deflection,

Mohrs theorems, Sign conventions, Application of moment area

method for determinate prismatic beams, Beams of varying

section, Use of moment diagram by parts, Conjugate beam

method, Real beam and conjugate beam, Application of

conjugate beam method of determinate beam of variable cross

Sections.

10 L2,L4,L5

28

Module -3

Energy Principles And Energy Theorems Principle of virtual displacements, Principle of virtual forces,

Strain energy and complimentary energy, Strain energy due to

direct force, Strain energy due to bending, Deflection of

determinate beams and trusses using total strain energy,

Deflection at the point of application of single load, Castiglianos

theorems and its application to estimate the deflections of trusses,

bent frames, Special applications-Dummy unit load method.

10 L2,L4,L5

Module -4

Arches And Cable Structures

Three hinged parabolic arches with supports at the same and

different levels. Determination of normal thrust, radial shear and

bending moment. Analysis of cables under point loads and udl.

Length of cables for supports at same and at different levels-

Stiffening trusses for suspension cables.

10 L2,L4,L5

Module -5

INFLUENCE LINES AND MOVING LOADS Concepts of influence lines-ILD for reactions, SF and BM for

determinate beams-ILD for axial forces in determinate trusses-

BM,SF and axial forces in determinate beams using rolling loads

concepts.

10 L2,L4,L6

Course outcomes: After studying this course, students will be able to:

1. Evaluate the forces in determinate trusses by method of joints and sections.

2. Evaluate the deflection of beams-cantilever, simply supported and overhanging

beams by different methods and also evaluations using moment diagram by parts.

3. Understand the energy principles and energy theorems and its applications to

determine the deflections of trussess and bent frames.

4. Determine the stress resultants in arches and cables.

5. Understand the concept of influence lines and construct the ILD diagram for the

moving loads.

Program Objectives (as per NBA)

o Engineering Knowledge. o Problem Analysis. o Interpretation of data.

Text Books:

1. Reddy C S, Basic structural Analysis , Tata McGraw Hill, New Delhi.

2. Muthu K U.et al,Basic structural Analysis,2nd

edition, IK International Pvt. Ltd., New

Delhi,2015.

3. Bhavikatti, Structual Analysis, Vikas Publishing House Pvt. Ltd,New Delhi,2002

Reference Books: 1. Prakash Rao D S, Structual Analysis, Universities Press Pvt. Ltd,2007.

2. Hibbetlr R C,Structual Analysis, Prentice Hall, 9th

edition,2014

3. Devadoss Menon, Structual Anlysis, Narosa Publishing House,New Delhi,2008.

29

1. Prerequisites

Engineering Mechanics and Strength of Materials.

2. Over view of the course:

This Course deals with the introduction to structural systems, analysis of plane trusses,

deflection of beams by different methods, strain energy, principle of virtual work, Castigliano’s

theorems, deflection of beams and trusses. Deflection of beams and trusses using strain energy

and unit load methods. Determination of thrust, shear and bending moment for three hinged

parabolic arches, analysis of cables. Concepts of influence lines-ILD for reactions, SF and BM for

determinate beams-ILD for axial forces in determinate trusses- BM,SF and axial forces in

determinate beams using rolling loads concepts.

3. Course outcomes

After studying this course, students will be able to:

1. Evaluate the forces in determinate trusses by method of joints and sections.

2. Evaluate the deflection of beams-cantilever, simply supported and overhanging beams

by different methods and also evaluations using moment diagram by parts.

3. Understand the energy principles and energy theorems and its applications to

determine the deflections of trusses and bent frames.

4. Determine the stress resultants in arches and cables.

5. Understand the concept of influence lines and construct the ILD diagram for the moving

loads.

4. Relevance of the course

In the design of structural components determination of axial forces, shear forces and Bending

Moments are very much essential and to check the stability of structure it necessary to calculate

the deflection. Hence this course provides opportunity to learn analysis of frames, beams, Arches,

Cables and determination of deflection of beams and fames.

5. Application

Design of structures.

6. Module wise Plan

30

Module 1

Introduction and Analysis Of Plane Trusses

No. of hours : 10

Learning Objectives: At the end of this chapter student will be able to

1. Explain Forms of structures, linear and nonlinear structures, Degrees of freedom.

2. Determine the static and kinematic indeterminacies of structural systems.

3. Determine the forces in the members of trusses by method of joints and sections

Lesson Plan :

Lecture

No. Topics covered

Teaching

Method

PSOs

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter No.

L1 Forms of structures. Chalk and

Board

1 & 3 1,2 & 12 1

T1/2,3,

T2/1,2, T3/1

R1/1,2

L2 Conditions of equilibrium,

degrees of freedom, linear

and nonlinear Structures

Chalk and

Board

L3 Determination of Static

indeterminacy of

structures.

Chalk and

Board

L4 Determination of

Kinematic indeterminacy

of structures.

Chalk and

Board

L5 Problems on Static and

Kinematic indeterminacies.

Chalk and

Board

L6

Types of trusses,

assumptions in analysis

and analysis of trusses by

method of joints

Chalk and

Board

L7 Analysis of trusses by

method of joints

Chalk and

Board


method of joints

Chalk and

Board


method of sections

Chalk and

Board


method of sections

Chalk and

Board

31

Assignment Problems:

1. What are the various forms of structures?

2. What are the conditions of equilibrium?

3. What do you mean by degree of freedom?

4. Define: Static indeterminacy ii) Kinematic indeterminacy of structures.

Give examples.

5. What do you understand by statically determinate structure?

6. Define Linear and non linear structures

7. Determine the forces in the members of trusses shown below

90KN 100kN 80kN

All panels 3m each.

100

kN

32

MODULE 2

Deflection of Beams

No. of hours : 10


1. Define slope, deviation, deflectunce and deflection

2. Derive differential equation of flexure.

3. Determine slope and deflection for prismatic and varying sections of beam for

defferent loadings by different methods like double integration, Macaulay;s, moment

area and conjugate beam methods.

Lesson Plan:

Lecture

No. Topics covered

Teaching

Method

PSOs

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter No.

L11

Introduction and

definitions of slope,

Deflection and moment

curvature, Sign conventions,

Derivation of differential

equations of flexure

Chalk and

Board

1 & 3

1,2 & 12

2

T1/6,T2/3,4

, T3/2 ,

R1/3

L12 Determination of slope and

deflection byDouble

integration method

Chalk and

Board


deflection by Macaulay’s

method

Chalk and

Board


deflection by Macaulay’s

method

Chalk and

Board

L15 Derivation of Mohr;s

theorems and sign

conventions.

Chalk and

Board


deflection by Moment area

method

Chalk and

Board


deflection by Moment area

method

Chalk and

Board

L19 Introduction to conjugate

method.

Chalk and

Board


deflection by Conjugate

beam method.

Chalk and

Board


deflection by Conjugate

beam method.

Chalk and

Board

33


1. State and prove Mohr’s theorem.

2. Calculate maximum slope and deflection for the following beams by double

integration and Moment area methods

i) Simply supported beam carrying point load W at centre.

ii) Simply supported beam carrying UDL over the whole length.

iii) Cantilever carrying point load W at end.

iv) Cantilever carrying UDL over the whole length

3. A cantilever of length 2m carries a point load of 20kN at the free end and another

load of 20kN at its centre. If E= 105N/mm² and I=108 , then determine by

moment area method, the slope and deflection at free end.

4. Calculate slope at A and deflection at the centre point of Simply supported beam of

span 4m carrying UDL on 2 kN/m over the whole length and a point load of 10kN

at the centre by moment area method.

5. Find the slope and deflection at free end for the beam shown using moment area

theorem

Take EI= 40000kN𝑚−2

6. Find the slope and deflection at free end for the beam shown using moment area

theorem

Take E=2x105 and I=20x106

7. What is conjugate beam?

34

8. A S.S beam of length 5m carries a point load of 5kN at a distance of 3m from left

end. If E= 2x105 and I=108 determine the slope at the left support and

deflection underthe point load using conjugate beam method. [Ans;

slope=0.00035rad, defl=0.6mm]

9. A S.S beam is shown in fig. Calculate slope at end A and B and the deflection at

the centre C using conjugate beam method.

10. Using conjugate beam method determine the slope and deflection at C of beam

ABC loaded as shown, Given E= 200GPa and I= 3x108

11. Determine the slope at A,B,C and find the deflection at C for the beam shown by

conjugate beam method.

35

12. Calculate the deflection at B and the slope at C for the beam shown

13.Calculate the maximum slope and maximum deflection of a cantilever beam

shown in fig by conjugate beam method. And also calculate deflection at C

Module -3

Energy Principles And EnergyTheorems

No. of hours : 10

Learning Objectives : At the end of this chapter student will be able to

1. Define Principle of virtual displacements, Principle of virtual forces, Strain energy

and complimentary energy.

2. Derive expression for strain energy due to direct force and bending.

3. Determine deflection for determinate beams and trusses by strain energy method and

unit load method.

4. Apply Castigliano’s theorems to estimate the deflections of trusses, bent frames.

36

Lesson Plan:

Lecture

No. Topics covered

Teaching

Method

PSOs

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L21

Principle of virtual

displacements, Principle of

virtual forces, Strain energy

and complimentary energy,

Strain energy due to direct

force, Strain energy due to

bending,

Chalk and

Board

1 & 3 1,2 & 12 3

T1/6, T2/5,

T3/3,4

R1/2

L22

Deflection of determinate

beams using total strain

energy

Chalk and

Board

L23


trusses using total strain

energy

Chalk and

Board

L24 Derivation of Castiglion;s

theorems.

Chalk and

Board

L25 Application Castiglion;s

theorem to determine

deflection of bent frames.

Chalk and

Board



deflection of trusses.

Chalk and

Board



deflection of trusses.

Chalk and

Board

L28


beams using unit load

method

Chalk and

Board

L29


trusses using unit load

method.

Chalk and

Board

L30


trusses using unit load

method.

Chalk and

Board

37


1) State and prove castigliano first theorem.

2) Determine the vertical and horizontal deflection at C of the beam shown in fig. Take E=

200GPa and I= 80x106

3) Using strain energy concept, compute the deflection at A of the bent ABCD in fig located

as shown. Assume E= 2x105 N/mm and I=2.8x108

4) Calculate the deflection under point load and slope at left hand support of S.S beam loaded

as shown in fig. by strain energy method. Take E= 200x106 and I=25x10−6𝑚4.

i.

38

5) Compute vertical displacement at centre Taking E= 2x105 N/mm and I=825x107

for a cantilever of span 12m carrying UDL of 25 kN/m over the whole span.

6) For the truss shown in fig. calculate the change in length of diagonal BE due to the applied

load. The area of upper chords=400mm², web members=300mm² and E= 200kN/mm².

i.

7) The members of the truss shown in fig are so proportioned that under the given loading, all

compression members are stressed to 80 Mpa and all tension members are stressed to 10

Mpa. Find vertical displacement at F using E= 200GPa.

39

8) The frame shown in fig, consists of 4 panels each 2.5m and c/s areas are such that when

the frame carries equal loads at the panel points of the lower chord, the stresses in all

tension members is 100N/mm² and the stresses in all compression members is 80N/mm².

Determine the relative moment between joints C and K in the direction CK. Take E=

200kN/mm².

Module 4

Arches and Cable Structures

No. of hours : 10


1. To determine normal thrust, radial shear and bending moment for Three hinged

parabolic arches with supports at the same and at different levels.

2. To analyse Cables under point loads and udl and to calculate length of cables.

3. To determine S.F and B.M in Stiffening Girdres.

Lesson Plan:

Lecture

No. Topics covered

Teaching

Method

PSOs

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L31

Introduction to three hinged

parabolic arches with supports

at same and different levels

Chalk and

Board

1,2 & 12 4

T1/2,8 ,

T2/7,8,

T3/7,8,R1/1

2

L32

Determination of normal

thrust, radial shear and

bending moment for Three

hinged parabolic arches with

supports at the same levels.

Chalk and

Board

40

L33





supports at the same levels

with different loadings.

Chalk and

Board

1 & 3

L34





supports at different levels

with different loadings.

Chalk and

Board

L35





supports at different levels

with different loadings

Chalk and

Board

L36 Analysis of cables under point

loads

Chalk and

Board

L37 Analysis of cables under point

loads and udl.

Chalk and

Board

L38 Length of cables for supports

at same and at different levels

Chalk and

Board

L39 Stiffening trusses for

suspension cables.

Chalk and

Board

L40 Stiffening trusses for

suspension cables.

Chalk and

Board


1. A symmetrical three hinged parabolic arch of span 40m and rise 8m carries on UDL of 30

kN/m over the left half of the span. The hinges are provided at the supports& at the centre

of arch. Calculate the reaction at the supports. Also calculate the B.M, radial shear and

normal thrust at a distance of 10m from left support.

(Ans. VA = 450kN, H=375 kN, Y10= 6m,

B.M.= 750 kN/m, Q=210 48’ F=0, N=403.89kN).

2. A three hinged circular arch, 25m in span with a central rise of 5m. It is loaded with a

concentrated load of 10 kN at 7.5m from the left hand hinge. Find the a) Horizontal thrust,

b) Reaction at each end hinge, c)B.M. under the load. (Ans. VA= 7kN, VB =3 kN, H= 7.5

kN, Y7.5=4.3m R = 18.125m, B.M. = 20.25kN/m)

41

3. Show that for a three hinged parabolic arch of span 1 and rise h, carrying UDL over the

entire span, The B.M. at any point on the arch is zero.

4. A three hinged parabolic arch of span 30m has its supports at depths 4m and 16m below

crown C. The arch carries a load of 80 kN at a distance of 5m to the left of C and a second

load of 100 kN at 10m to the right of C. Determine the reactions at supports and B.M.

under the loads.

(Ans. L1 =10m, L2=20m, VA =70kN, VB=110kN, H2 =75kN B.M. 80

= 125kN/m, Y5 =3, Y10 =12m B.M.02 =200kNm. )

5. A three hinged parabolic arch is of 60m span and 15m rise and carries a dead load of

15kN/m. A live load of 30kN/m is also applied over the right half portion of the span.

Determine the moment, shear and thrust at sections 10m from the ends and magnitude and

position of maximum sagging and hogging moments in the arch.

6. A rope is hanging from two points A and B, 30m. apart horizontally, B being 3m lower

than A. It supports a UDL of 10kN/m of horizontal length. Determine the position of the

lower point, if the rope has sag of 3m below B, length of the rope and the horizontal

tension and the maximum tension at two ends of the rope.

7. A suspension cable of horizontal span 95m is supported at two different levels. The right

support is higher than left support by 4m. The dip to the lowest pint of the cable is 5m. The

C/S area of the cable is 3500 𝑚𝑚2. Find the UDL that can be carried by the cable if the

maximum stress is limited to 600 N/𝑚𝑚2.

(Ans. L1= 40.56m, L2= 54.44m, H= 164.65m, Tmax =TB= 173.417w,

W=212.109 kN/m.)

8. A suspension bridge is 50m. Span with a 16m wide roadway. It is subjected to a load of

25kN/𝑚2 including dead loads. The bridge is supported by a pair of cable haring a central

dip of 4.2m. Find the cross sectional area of the cable necessary if the maximum

permissible stress in the cable material is not exceed 600N/𝑚𝑚2.

(Ans. W= 200 kN/m, VA= VB= 5000kn H= 14881kN Tmax = 15698.5 kN,

A= 26164 𝑚𝑚2)

42

Module 5 INFLUENCE LINES AND MOVING LOADS

No. of hours : 10

Learning Objectives : At the end of this chapter student will be able to

1. Draw ILD for reactions, SF and BM for determinate beams and ILD for axial forces

in determinate trusses.

2. To determine BM,SF and axial forces in determinate beams and trusses using rolling loads concept.

Lesson Plan:

Lecture

No. Topics covered

Teaching

Method

PSOs

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L41 Introduction to Influence lines.

ILD for reactions. Chalk and

Board

1 & 3 1,2 & 12 5

T1/7,

T2/6,

T3/5,6,

R1/13

L42 ILD for SF and BM for

determinate beams and problems Chalk and

Board

L43

Determination of reactions, SF

and BM using ILD for

determinate beams for different

loadings.

Chalk and

Board

L44




loadings.

Chalk and

Board

L45




loadings.

Chalk and

Board

L46 ILD for axial forces in

determinate trusses.

Chalk and

Board

L47 Determination of SF and BM in

beams for rolling loads Chalk and

Board

L48 Determination of SF and BM in

beams for rolling loads Chalk and

Board

L49 Determination of axial forces in

trusses for rolling loads Chalk and

Board

L50 Determination of axial forces in

trusses for rolling loads Chalk and

Board

43

Assignment Questions :

1. Using analytical method find i) the maximum bending moment, ii) the maximum positive

shear force and iii) the maximum negative shear force at a section 4m from left support A of

simply supported girder of 10m span when 4 wheel loads 10 kN, 15kN , 30 kN , 30 kN spaced

at 2m , 3m , and 3m respectively with 10 kN load leading the span.

2. In a simply supported girder AB of span 20m , determine the maximum bending moment and

maximum shear force at a section 5m from A , due to the passage of a uniformly distributed

load of intensity 20kN/m , longer than the span.

3. A uniform load of 40kN /m run , 6m long crosses a girder of 30m span, calculate the

maximum shear force and maximum bending moment at sections 5m , 10m, 15m from the left

hand support.

4. Draw the ILD for shear force and bending moment for a section at 5m from the left hand

support of a simply supported beam 20m long. Hence calculate the maximum bending

moment and shear force at the section , due to an uniformly distributed rolling load of length

of 8m and intensity 10kN/m run.

5. A train of 5 wheel loads 120kN,160 kN , 400kN , 260 kN , 240 kN spaced at 2.5m with 240kN

load leading crosses a simply supported beam of span 22.5m. Using influence line diagrams

calculate the maximum positive and negative shear forces at mid span and absolute bending

moment any where in the span.

6. Develop IL for members 1,2 and 3

7 .Portion for I.A. Test:


I I and II

II III and IV

1

2

3

6 x 5.0m = 30m

4m

47

COURSE: APPLIED HYDRAULICS SEMESTER – IV


Number of Lecture 04 Exam Marks 80 Hours/Week

Total Number of Lecture 50 Exam Hours 03 Hours

CREDITS – 04 COURSE OBJECTIVES

The objectives of this course is to make students to learn: 1. Principles of dimensional analysis to design hydraulic models and Design of various

models. 2. Design the open channels of various cross sections including optimum design sections. 3. Energy concepts of fluid in open channel, Energy dissipation, Water profiles at different

conditions Analysis of the performance of Turbines and Pumps for various design data and to know their corresponding operation characteristics, including designing the required hydraulic

machines for the given data

Revised Bloom’s

Modules Teaching Taxonomy

Hours (RBT) Level

Module 1: Dimensional and Model analysis 10

Dimensional analysis 03 L1,L2,L3 Dimensional analysis and similitude: Dimensional

homogeneity, Non Dimensional parameter, Buckingham π

theorem, dimensional analysis‐choice of variables, Rayleigh

methods, examples ‐ Rise in capillary tube, head

characteristics of a pump, drag on a ship, velocity in an open

channel, pipe orifice, discharge over a sharp edge weir, celerity

of a gravity wave.

Model analysis: Model analysis‐similitude, types of 04

similarities, force ratios, similarity laws, model classification,

Reynolds model, Froude’s model, Eulers Model, Webber’s

model, Mach model, scale effects, problems involving

Reynolds, Froudes and Eulers Model.

Distorted models, Numerical problems

Buoyancy and Flotation 03

Buoyancy, Force and Centre of Buoyancy, Metacentre and

Metacentric height, Stability of submerged bodies,

Determination of Metacentric height – Experimental and

theoretical method, Numerical problems

Module 2: Open Channel Flow Hydraulics 10

Uniform Flow L3,L4 Introduction, Classification of flow through channels, Chezys

and Manning’s equation for flow through open channel, Most 06

economical sections, Uniform flow through Open channels,

Numerical Problems.

Specific Energy and Specific energy curve, Critical flow and 04

48

corresponding critical parameters, Numerical Problems

Module 3: Non-Uniform Flow 10

Hydraulic Jump, Expressions for conjugate depths and Energy 03 L2,L3

loss, Numerical Problems

Gradually varied flow, Equation, Back water curve and afflux, 04 L2,L3

Length of back water curve, Numerical Problems 03

Description of water curves or profiles, Mild, steep, critical,

horizontal and adverse slope profiles, Numerical problems

Module 4: Hydraulic Machines 10

Introduction, Impulse-Momentum equation. Direct impact of a 05 L2,L3 jet on a stationary and moving curved vanes, Introduction to

concept of velocity triangles, impact of jet on a series of curved

vanes- Problems

Turbines – Impulse Turbines

Introduction to turbines, General lay out of a hydro-electric 05

plant, Properties of turbines, classification of turbines. Pelton

wheel-components, working principle and velocity triangles.

Maximum power, efficiency, working proportions – Nu merical

problems

Module 5: Reaction Turbines and Miscellaneous 10

Introduction, Radial flow reaction turbines, Numerical 05 L1,L2 problems, Francis Turbine, Numerical problems.

Introduction and description of Axial Flow turbines, Centrifugal

pump, Draft tube theory (No problems) 03

Specific speed, Unit quantities, Numerical problems

02

COURSE OUTCOMES After a successful completion of the course, the student will be able to:

1. Apply dimensional analysis to develop mathematical modeling and compute the

parametric values in prototype by analyzing the corresponding model

parameters[L3,L4][PO2,PO3]

2. Design the open channels of various cross sections including optimum design sections

[L4][PO3]

3. Apply Energy concepts of fluid in open channel, calculate Energy dissipation, compute

Water profiles at different conditions [L1][L2][PO3]

4. Analyze the performance of Turbines and Pumps for various design data and to know

their corresponding operation characteristics, including designing the required hydraulic

machines for the given data[L2][L3][PO2]

49

Program Objectives

1. PO1: Engineering Knowledge

2. PO2: Problem analysis

3. PO3: Design/Development of Solutions

Text Books: 1. R.K. Bansal, “ Fluid mechanics and hydraulic machines”, Laxmi Publishing (P) Ltd.,

India.- 2011.

2. Shesha Prakash M N, Hydraulics and Hydraulic Machines, Wiley India Pvt Ltd., New

Delhi (2015)

3. Naryan Pillai, Principals of Fluid Mechanics & Fluid Machines, Universities Press 4. Jagadish Lal, Hydraulic Machines, Metropolitan Book Co Pvt Ltd., New Delhi

Reference Books:

1. C.S.P. Ojha, R. Berndtsson, and P.N. Chandramouli, “Fluid Mechanics and Machinery” , Oxford University Publication - 2010.

2. K.Subramanya, “ Fluid mechanics” Tata McGraw-Hill publishing company limited.

3. Modi and Seth, Hydraulics and Fluid Mechanics, including Hydraulic Machines, 20th

edition,

4. J.B. Evett, and C. Liu, “Fluid mechanics and Hydraulics ”, McGraw-Hill Book

Company.- 2009

50

Course Plan

Semester: III Year: 2016– 17

Course : Applied Hydraulics. Subject Code: 15CV43

Total no. of lecture hours : 50 Duration of Exam. : 3 Hrs.

1.Prerequisites: This subject requires the student to have knowledge of Basic Mathematics,

Elements of civil engineering and Fluid Mechanics.

2. Over view of the course: This course covers the dimensional analysis and Model Studies, uniform

and non uniform flow in open channels. It includes hydraulic jump in open channel and its

importance in the design of hydraulic structures. Discussion of the impact of jet on different types of

vanes such as curved vane and flat vanes are included in this course Finally this course contents the

hydraulic machine study includes turbines (Pelton wheel and Kaplan turbine) and pumps

(centrifugal).

3. Course outcomes: By the end of the course the student will be able to:

a. Apply dimensional analysis to develop mathematical modeling and compute the parametric

values in prototype by analyzing the corresponding model parameters.

b. Design the open channels of various cross sections including optimum design sections.

c. Apply Energy concepts of fluid in open channel, calculate Energy dissipation, compute.

Water profiles at different conditions.

d. Analyze the performance of Turbines and Pumps for various design data and to know their

corresponding operation characteristics, including designing the required hydraulic machines for the

given data.

4. Relevance of the course to the programme: Civil engineer is involved in the analysis and design

of irrigation systems which include dams, weir, barrages, canals, drains and other supporting systems,

for which good knowledge of hydraulics and hydraulic machines is very much essential.

5.Application areas: The widespread applications of hydraulics in civil engineering include

transportation of fluids in open channels, as well as flow measurement in open channels. These areas

of application use a variety of calculations for design and for analysis. Hydraulic machines study

helps in designing pumps and turbines for lifting of water from source to the destination.

51

Module wise Plan

Module 1 Teaching Hours Revised Bloom’s taxonomy

Dimensional and Model analysis. 10 L1, L2, L3

Learning Objectives: At the end of this Module, student will be able to

1. To study and concept of dimensional analysis, units and dimensions of physical quantities

2. Dimensionally homogeneous equations and dimensional analysis techniques

3. Expressing physical problem in mathematical form and establishing the functional

relationship among physical variables using dimensional analysis techniques.

4. Model laws and application of model laws to analyze the prototype structure.

Lesson Plan:

Lecture

No. Topics covered

Teaching

Method

POS’s

Attained

PO’s

Attained

CO’s

Attained

Reference or

Text Book/

Chapter No.

L1 Introduction, Systems of

units, Dimensions of

quantities,

PPT

1 1, 5, 8 &

9 1, 2 & 6

T1/1, T3/1-3,

R4/1

L2

Dimensional

Homogeneity of an

equation. Analysis-

Raleigh’s method,

PPT

L3 Buckingham’s Π

theorem- problems.

PPT

L4 Buckingham’s Π

theorem- problems.

PPT

L5

Model Studies,

Similitude, Non-

dimensional numbers:

Froude models-

Undistorted and

Distorted models.

Chalk and

Board

T1/2, T3/4,

R4/2-3

L6

Model Studies,

Similitude, Non-

dimensional numbers:

Froude models-

Undistorted and

Distorted models.

Chalk and

Board

L7 Reynold’s models-

Problems

Chalk and

Board

52

L8

Buoyancy, Force and

Centre of Buoyancy,

Metacentre and

Metacentric height,

Stability of submerged

bodies,

Chalk and

Board

L9

Determination of

Metacentric height –

Experimental and

theoretical method,

Chalk and

Board

L10 Numerical problems Chalk and

Board

Assignment Questions:

Q.1. Define dimensional homogenous, non-homogenous and dimensionless equations with examples.

Q.2. Explain the uses of dimensional analysis in the study of fluid mechanics.

Q.3. What are the two methods of dimensional analysis and explain Rayleigh method.

Q.4. Explain the outline of procedure for Buckingham -method.

Q.5. Describe the model and prototype, list and explain model similitudes.

Q.6. List the dimensionless numbers and explain Froude and Reynolds number.


Open Channel Flow Hydraulics. 10 L3, L4


1. To define open channel flow and its importance in civil engineering

2. Importance of computation of uniform flow in open channels

3. To study the concept and derivation of optimum channel sections.

4. To study and concept of critical flow in open channels.

53

Lesson Plan:

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained

PO’s

Attained

CO’s

Attained

Reference or

Text Book/

Chapter No.

L11

Introduction, Geometric

properties of

Rectangular and

Triangular

Chalk and

Board

1 1, 5,& 9 2 & 6 T1/3, T3/5,

R4/4

L12 Trapezoidal and

Circular channels.

Chalk and

Board

L13 Chezy’s equation,

Manning’s equation-

problems.

Chalk and

Board

L14 Chezy’s equation,

Manning’s equation-

problems.

Chalk and

Board

L15

Most economical open

channels-Rectangular,

Triangular, Trapezoidal

and Circular channeles-

problems.

Chalk and

Board

1 1, 5,& 9 2, 3 & 6

T1/5-6, T3/8-

9, R4/6

L16

Most economical open

channels-Rectangular,

Triangular, Trapezoidal

and Circular channeles-

problems.

Chalk and

Board

L17 Introduction, Specific

energy, Specific energy

diagram, Critical depth,

Chalk and

Board

1 1, 5& 9 2, 3 & 6

T1/10, T3/10,

R4/9

L18 Conditions for Critical

flow- rectangular

section.

Chalk and

Board


flow- Theory &

problems.

Chalk and

Board


flow- Theory &

problems.

Chalk and

Board

54

Assignment questions:

Q.1. Distinguish between open channel flow and pipe flow.

Q.2. Explain the geometric properties of open channel.

Q.3. Derive chezzy’s equation.

Q.4. Define most economical channel section and derive the conditions of most economical

rectangular channel section.

Q.5. Derive the conditions of most economical trapezoidal and triangular channel section.

Q.6. List the classification of channel flow and explain types of uniform and non-uniform flow.

Q.7. Explain specific energy and critical depth in uniform flow channel section.

Q.8. Draw and explain specific energy curve.

Q.9. Derive the condition for minimum specific energy for a given discharge.

Q.10. What are the characteristics of the critical state of flow through a channel section?


Non-Uniform Flow. 10 L2, L3


1. To study the difference between gradually and rapidly varied flow in a prisimatic channel.

2. To study hydraulic jump in open channel and its importance in the design of hydraulic

structures.

3. To study dynamic equation for gradually varied flow.

4. To study the application of dynamic equation for understanding various slopes of prisimatic

channel.

5. To study the water curves in prisimatic channel to different slope condition.

55

Lesson Plan:

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained

PO’s

Attained

CO’s

Attained

Reference or

Text Book/

Chapter No.

L21

Introduction to rapidly

varied flow (hydraulic

jump).

Chalk and

Board

1 1, 5, 9 2 & 6 T1/3, T3/5, R4/4

L22 Expressions for conjugate

depths and Energy loss.

PPT

L23

Hydraulic jump in a

Horizontal Rectangular

Channel- Theory and

problems.

Chalk and

Board

L24 Introduction to Gradually

varied flow.

PPT

L25

Dynamic equation for Non-

Uniform flow in an Open

channel.

Chalk and

Board

1 1, 5, 9

2, 3 & 6

T1/5-6, T3/8-9,

R4/6

L26

Back water curve and

afflux,

Length of back water curve,

Numerical Problems

Chalk and

Board

L27

Description of water curves

or profiles, Mild, steep,

critical,

horizontal and adverse

slope profiles, Numerical

problems

PPT

1 1, 5, 9 2, 3 & 6 T1/10, T3/10,

R4/9

L28



critical, horizontal and

adverse slope profiles,

Numerical problems

PPT

L29





Numerical problems

PPT

L30





Numerical problems

PPT

56


Hydraulic Machines. 10 L2, L3

Learning Objectives: At the end of this Module, student will be able to.

1. To study and concept of impulse momentum principle and its application

2. Application of Impulse momentum principle to determine force exerted by moving gets on

stationary plate. Keeping flat plate in vertical inclined and curved surface.

3. Application of impulse momentum principle to find force exerted by jet On series of curved

vanes.

4. Introduction of Hydraulic machines and working principle of turbines.

5. Pelton wheel working principle and design.

Lesson Plan:

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained

PO’s

Attained

CO’s

Attained

Reference or

Text Book/

Chapter No.

L31 Introduction, Impulse-

Momentum equation.

Chalk and

Board

1 1, 5, 9 4 & 6 T1/8, T3/7,

R4/5

L32

Introduction, Force

exerted by a jet on a

fixed curved vane,

moving curved vane.

Chalk and

Board

L33 Introduction to concept

of velocity triangles.

Chalk and

Board

L34

Impact of jet on a series

of curved vanes-

problems.

Chalk and

Board

L35 Numerical problems. Chalk and

Board

L36 Introduction to

Turbines.

Chalk and

Board

1 1, 5, 9 4 & 6 T1/9, T3/11,

R4/10

L37 Classification of

Turbines.

Chalk and

Board

L38 Pelton wheel-

components.

Chalk and

Board

L39

Pelton wheel working

and velocity triangles.

Maximum power,

efficiency, working

proportions.

Chalk and

Board

L40 Numerical problems.

Chalk and

Board

57


1. A jet of water impinges a curved plate with a velocity of 20 m/s making an angle of 20o with

the direction of motion of vane at inlet and leaves at 130o to the direction of motion at outlet. The

vane is moving with a velocity of 10 m/s. Compute. i) Vane angles, so that water enters and leaves

without shock. ii) Work done/s

2. A jet of water having a velocity of 35 m/s strikes a series of radial curved vanes mounted on a

wheel. The wheel has 200 rpm. The jet makes 20o with the tangent to wheel at inlet and leaves the

wheel with a velocity of 5 m/s at 130o to tangent to the wheel at outlet. The diameters of wheel are 1

m and 0.5 m. Find i) Vane angles at inlet and outlet for radially outward flow turbine. ii) Work done

iii) Efficiency of the system

3. To show that efficiency of impact of jet on radially mounted flat vanes is 50% when the jet

strikes normally on the vane.

4. A jet of water of diameter 50 mm strikes a stationary, symmetrical curved plate with a velocity

of 40 m/s. Find the force extended by the jet at the centre of plate along its axis if the jet is deflected

through 120o at the outlet of the curved plate

5. A jet of water strikes a stationery curved plate tangentially at one end at an angle of 30o . The jet

of 75 mm diameter has a velocity of 30 m/s. The jet leaves at the other end at angle of 20o to the

horizontal. Determine the magnitude of force exerted along ‘x’ and ‘y’ directions.

6. With a neat sketch explain the layout of a hydro-electric plant

7. Classify the turbines based on head, specific speed and hydraulic actions. Give examples for

each.

8. Design a Pelton wheel for a head of 80m. and speed of 300 RPM. The Pelton wheel develops

110 kW. Take co-eficient of velocity= 0.98, speed ratio= 0.48 and overall efficiency = 80%.

9. A Pelton wheel has to develop 13230 kW under a net head of 800 m while running at a speed of

600 rpm. If the coefficient of Jet Cy = 0.97, speed ratio f = 0.46 and the ratio of the Jet diameter is 1

/16 of wheel diameter. Calculate i) Pitch circle diameter ii) the diameter of jet iii) the quantity of

water supplied to the wheel iv) the number of Jets required.

Assume over all efficiency as 85%.

10. The head at the base of the nozzle of a Pelton wheel is 640 m. The outlet vane angle of the

bucket is 15o . The relative velocity at the outlet is reduced by 15% due to friction along the vanes. If

the discharge at outlet is without whirl find the ratio of bucket speed to the jet speed. If the jet

diameter is 100 mm while the wheel diameter is 1.2 m, find the speed of the turbine in rpm, the force

exerted by the jet on the wheel, the Power developed and the hydraulic efficiency. Take Cv=0.97.

58


Reaction Turbines and Miscellaneous. 10 L1, L2


1. To study and analase the difference between impluse and reaction turbines.

2. Application of Impulse momentum principle to find force exerted by jet, work done and

efficiency of Francis turbine.

3. Application of Impulse momentum principle to find force exerted by jet, work done and

efficiency of Kaplan turbine.

Lesson Plan:

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained

PO’s

Attained

CO’s

Attained

Reference or

Text Book/

Chapter No.

L41 Introduction to

reaction turbine.

Chalk and

Board

1 1, 5, 9

5 & 6 T2/12

L42

Explaination to

Francis turbine and

its components.

Chalk and

Board

L43

velocity traingles,

work done and

efficiency for Francis

turbine.

Chalk and

Board


Board

L45

Explaination to

Kaplan turbine and

its components.

Chalk and

Board

L46

Explaination to

Kaplan turbine and

its components.

Chalk and

Board

L47

velocity traingles,

work done and

efficiency for Kaplan

turbine.

Chalk and

Board

L48 Introduction to

centrifugal pump.

Chalk and

Board

L49 Draft tube theory. Chalk and

Board

L50

Description of

specfic speed, unit

quantities, Numerical

problems.

Chalk and

Board

59


1. Difference between reaction turbine and impulse turbine.

2. What are all the types of draft tube

3. Define unit power, unit speed, unit discharge and specific speed with reference to hydraulic

turbines. Derive expressions for these terms.

4. A Kaplan turbine runner is to be designed to develop 10000 kw. The net head is 8.0m. The speed

ratio= 2.09, flow ratio=0.68, overall efficiency is 85% and diameter of the boss is 1/3 the diameter of

the runner. Find the diameter of the runner, its speed and the specific speed of the turbine.

5. Working principle of pumps and suitability of pumps in civil engineering application.

6. Working Principle of centrifugal pumps, work done and efficiency

5) Portion for IA tests:


I I and II

II III and IV

62

COURSE :CONCRETE TECHNOLOGY

SEMESTER – IV


Number of Lecture

Hours/Week

04 Exam Marks 80

Total Number of

Lecture Hours

50 Exam Hours 03

CREDITS – 04 Course objectives: This course will enable students to:

1. Recognize the importance of material characteristics and their contributions to strength development in

Concrete

2. Proportion ingredients of Concrete to arrive at most desirable mechanical properties of Concrete.

3. Ascertain and measure engineering properties of concrete in fresh and hardened state which meet the

requirement of real time structures.

Modules Teaching

Hours

Revised Bloom’s

Taxonomy

(RBT) Level Module-1: Concrete Ingredients

Cement – Cement manufacturing process, steps to reduce carbon

footprint, chemical composition and their importance, hydration of

cement, types of cement. Testing of cement.

Fine aggregate: Functions, requirement, Alternatives to River

sand, M-sand introduction and manufacturing.

Coarse aggregate: Importance of size, shape and texture. Grading

and blending of aggregate. Testing on aggregate, requirement.

Recycled aggregates

Water – qualities of water.

Chemical admixtures – plasticizers, accelerators, retarders and air

entraining agents.

Mineral admixtures – Pozzolanic and cementitious materials, Fly

ash, GGBS, silica fumes, Metakaolin and rice husk ash.

10 L1,L2,L3

Module -2: Fresh Concrete

Workability-factors affecting workability. Measurement of

workability–slump, Compaction factor and Vee-Bee

Consistometer tests, flow tests. Segregation and bleeding. Process

of manufacturing of concrete- Batching, Mixing, Transporting,

Placing and Compaction. Curing – Methods of curing – Water

curing, membrane curing, steam curing, accelerated curing,

selfcuring.

Good and Bad practices of making and using fresh concrete and

Effect of heat of hydration during mass concreting at project sites.

10 L1,L2,L3

63

Module -3: Hardened Concrete

Factors influencing strength, W/C ratio, gel/space ratio, Maturity

concept, Testing of hardened concrete, Creep –factors affecting

creep. Shrinkage of concrete – plastic shrinking and drying

shrinkage, Factors affecting shrinkage. Definition and significance

of durability. Internal and external factors influencing durability,

Mechanisms- Sulphate attack – chloride attack, carbonation,

freezing and thawing. Corrosion, Durability requirements as per

IS-456, Insitu testing of concrete- Penetration and pull out test,

rebound hammer test, ultrasonic pulse velocity, core extraction –

Principal, applications and limitations.

10 L1,L2,L3

Module -4: Concrete Mix Proportioning

Concept of Mix Design with and without admixtures, variables in

proportioning and Exposure conditions, Selection criteria of

ingredients used for mix design, Procedure of mix proportioning.

Numerical Examples of Mix Proportioning using IS-10262

10 L1,L2,L3,L4

Module -5: Special Concretes

RMC- manufacture and requirement as per QCI-RMCPCS,

properties, advantages and disadvantages. Self-Compacting

concrete- concept, materials, tests, properties, application and

typical mixFiber reinforced concrete - Fibers types, properties,

application of

FRC. Light weight concrete-material properties and types. Typical

light weight concrete mix and application

Fiber reinforced concrete - Fibers types, properties, application of

FRC.

Light weight concrete-material properties and types. Typical light

weight concrete mix and applications

10 L1,L2, L3,L4

64

TEXT BOOKS

1. Neville A.M. “Properties of Concrete”-4th Ed., Longman.

2. M.S. Shetty, Concrete Technology - Theory and Practice Published by S. Chand and

Company, New Delhi.

3. Kumar Mehta. P and Paulo J.M. Monteiro “Concrete-Microstructure, Property and

Materials”, 4th Edition, McGraw Hill Education, 2014

4. A.R. Santha Kumar, “Concrete Technology”, Oxford University Press, New Delhi (New

Edition)

REFERENCE BOOKS

1. M L Gambir, “Concrete Technology”, McGraw Hill Education, 2014.

2. N. V. Nayak, A. K. Jain Handbook on Advanced Concrete Technology, ISBN: 978-81-

8487-186-9

3. Job Thomas, “Concrete Technology”, CENGAGE Learning, 2015

4. IS 4926 (2003): Code of Practice Ready-Mixed Concrete [CED 2: Cement and Concrete]

5. Criteria for RMC Production Control, Basic Level Certification for Production Control

of Ready Mixed Concrete-BMTPC

6. Specification and Guidelines for Self-Compacting Concrete, EFNARC, Association

House

65

COURSE PLAN

1. Prerequisites

This course requires the student to know about the basic of civil engineering fundamentals of

chemistry, building materials etc.

2. Over view of the course

With the ever expanding body of knowledge related to concrete, the gap between what is

knowable and what the practicing engineers know is widening. While all the new knowledge that

is getting added to the knowledge bank is not necessarily required at the work front, a major portion

of it is quite relevant. In this context, it is natural to explore various avenues that practicing engineers

have of acquiring concrete related knowledge.

Almost every concrete engineer without exception gets his first bit of knowledge about this

subject in the Engineering College. After graduation, the engineer is left to the mercy of his/her

employer, his own personal initiative and the experience and exposure that he gets with regard

to concrete construction to add on to the basic knowledge acquired in the college.

3. Course outcomes:

After studying this course, students will be able to:

1: Relate material characteristics and their influence on microstructure of concrete.

(L2,L3)(PO1)

2: Distinguish concrete behaviour based on its fresh and hardened properties.

[L2, L4] (PO1, PO2)

3: Illustrate proportioning of different types of concrete mixes for required fresh and

hardened properties using professional codes. [L3] (PO1, PO2, PO3)

4. Program Objectives (as per NBA)

. Engineering Knowledge (PO1)

· Problem Analysis (PO2)

· Design / development of solutions (PO3)

66

5. Relevance of the course

It is an undisputed fact that concrete is amongst the most widely used construction materials

today. In most of the construction projects, the largest quantum of work both in physical and financial

terms is some form of concrete. Thus a majority of contractors, Design consultants, PMCs and

engineers owe their livelihood to concrete in great measure. It is therefore natural to expect that in

the Civil Engineering curriculum, concrete technology should have a lion’s share.

6. Application.

The concrete technology has wide spread use in the field civil engineering construction. The

subject knowledge leads to improve the quality of concrete, in turn minimizing the repair and

rehabilitation work.

Module wise Plan

Module.1 Teaching

Hours

Revised Bloom’s Taxonomy

(RBT) Level

Concrete Ingredients 10 L1,L2,L3

Learning Objectives: At the end of this chapter student will understand

1. To study the physical and chemical properties of cement & types.

2. To study the properties of FA and CA

3. To understand the importance of uses of mineral and chemical admixtures & types.

Lecture

No. Topics covered

Teaching

Method

PSO’S

Attained PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter No.

L1

Cement – Cement

manufacturing

process, steps to

reduce carbon

footprint,

Chalk and

Board

1

1

1 T2/1 R1/2

L2

chemical composition

and their importance,

hydration of cement,.

Chalk and

Board 1

T2/2 R1/2

L3 types of cement.

Testing of cement

Chalk and

Board 1

T2/2 R1/2

L4

Fine aggregate:

Functions,

requirement,

Alternatives to River

sand, M-sand

introduction and

manufacturing.

Chalk and

Board 1

T2/3 R1/3

67

L5

Coarse aggregate: Importance of size,

shape and texture.

Grading and blending

of aggregate.

Chalk and

Board 1

T2/3 R1/3

L6

Testing on aggregate,

requirement.

Recycled aggregates

Chalk and

Board 1

T2/3 R1/3

L7

Water – qualities of

water.

Chemical

admixtures –

plasticizers,

accelerators,

Chalk and

Board

1 T2/5 R1/5

L8

retarders and air,

entraining agents.

Chalk and

Board 1 T2/5 R1/5

L9

Mineral admixtures – Pozzolanic and

cementitious

materials, Fly ash,

GGBS,

Chalk and

Board 1

T2/5 R1/5

L10

silica fumes,

Metakaolin and rice

husk ash.

Chalk and

Board

1 T2/5 R1/5

Assignment Question: CO’s

Attained

1)Briefly explain the hydration of cement 1

2)List the equation used to find the percentages of compounds with numerical

example

1

3)List the different types of cement 1

4) Explain the role of FA and CA in manufacture of concrete 1

5) Collect samples of aggregate and test their properties 1

6)Explain the process of deflocculation 1

7)Differentiate the plasticizer and Super plasticizer 1

8)List the suppliers names and corresponding admixtures 1

9)Write the physical properties of different mineral admixtures 1

68

Module.2 Teaching

Hours


(RBT) Level

Fresh Concrete 10 Hours L1, L2, L3


1. To study types of admixtures.

2. To know the chemistry of action of admixtures

3. To understand the importance of uses of mineral admixtures.

Lecture

No. Topics covered

Teaching

Method

PSO’S

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L21 Definition of workability and

factors affecting it Chalk and

Board

1,2,4

1,2

2 T2/6 R1/6

L22 Definition of workability and

factors affecting it continued

Chalk and

Board 2 T2/6 R1/6

L23

Measurement of workability

Slump test, Compaction

factor

Chalk and

Board 2 T2/6 R1/6

L24

Measurement of workability

vee-bee consistometer, flow

test

Chalk and

Board 2 T2/6 R1/6

L25

Segregation and bleeding and

its effect on quality of

concrete

Chalk and

Board 2 T2/6 R1/6

L26

Segregation and bleeding and

its effect on quality of

concrete continued

Chalk and

Board 2 T2/6 R1/6

L27 Process of manufacture of

concrete- Batching & Mixing Chalk and

Board 2

T2/6

R1/11

L28

Process of manufacture of

concrete Mixing

&Transporting Chalk and

Board 2

T2/6

R1/11

L29


concrete Transporting

&Placing Chalk and

Board 2

T2/6

R1/11

L30


concrete Compaction

&Curing

Chalk and

Board 2

T2/6

R1/11

69

Assignment Question: CO’s Attained

1 2 Explain different types of experiments to measure workability 2

3 4 Prepare a concrete mix and test and comment on its workability 2

5 6 Visit the site of construction and present a report 2

7 8 What are the ingredients of concrete? Explain their functions? 2

9 10 Write a note on following

a. Batching b. Mixing c. Placing d. curing 2

Module.3 Teaching

Hours


(RBT) Level

Hardened Concrete. 10 Hours L1, L2, L3


1. To have complete knowledge of concrete properties in hardened state

2. To study stress-strain characteristic of concrete

3. To study different types of deformations in the concrete

4. Importance of durability of concrete and factors affecting it.

5. Factors promoting the permeability of concrete, corrosion of reinforcement, Alkali aggregate

reaction.

6. The methods of tests of hardened concrete

Lecture

No. Topics covered

Teaching

Method

PSO’S

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L31

Factors affecting strength,

w/c ratio, gel/space ratio,

maturity concept.

Chalk and

Board

2,4

1,2

2 T2/7 R1/8

L32 Maturity concept, Testing of hardened concrete

Chalk and

Board 2 T2/7 R3/8

L33

Creep –factors affecting creep. Shrinkage of concrete – plastic shrinking and drying shrinkage,

Chalk and

Board 2 T2/8 R3/8

L34

Factors affecting

shrinkage. Definition and

significance of durability

Chalk and

Board 2 T2/8 R3/8

70

L35

Definition of durability and different factors contributing to deterioration of concrete

Chalk and

Board 2 T2/9 R3/8

L36

Chemical attack, acid

attack, efflorescence ,

Sulphate attack

Chalk and

Board 2 T2/9 R3/8

L37 chloride attack Chalk and

Board 2 T2/9 R3/8

L38

Carbonation of concrete

and Freezing and Thawing

effect

Chalk and

Board 2 T2/9 R3/8

L39

In-situ testing of

concrete- Penetration and

pull out test

Chalk and

Board 2 T2/10

R3/13

L40

Rebound hammer test,

ultrasonic pulse velocity,

core extraction

Chalk and

Board 2

T2/10

R3/13


Attained

1. Explain how, w/c, gel/space and maturity affect the strength of concrete 2

2. Solve some numerical examples on maturity concept and gel/space ratio 2

3. Explain the tests conducted on hardened concrete as per IS standards 2

4.Write a short note on

a. creep b. shrinkage c. modulus of elasticity 2

5. Explain the factor affecting modulus of elasticity of concrete and relation between

the modulus of elasticity and strength 2

6. What is durability of concrete? explain factors affecting the durability of concrete 2

7. Explain Sulphate attack and chloride attack. 2

8. Study the different types of deteriorated structures 2

71

Module.4 Teaching

Hours


(RBT) Level

Concrete Mix Proportioning 10 Hours L1, L2, L3, L4


1. Factors affecting the design mix

2. Different types of Mix design

3. IS Method with reference to IS 10262-2009

Lecture

No. Topics covered

Teaching

Method

PSO’S

Attained PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter No.

L41 Definition of mix design

and terminologies

Chalk and

Board

3,4

1,2,3

3 T2/11 R3/10

L42 Factors affecting mix design Chalk and

Board 3 T2/11 R3/10

L43

variables in

proportioning and Exposure conditions

Chalk and

Board 3 T2/11 R3/10

L44

Procedure of mix

proportioning (includes

flowchart).

Chalk and

Board 3 T2/11 R3/10

L45 IS Method 10262, Design examples

Chalk and

Board 3 T2/11 R3/10

L46 IS Method 10262, Design

examples

Chalk and

Board 3 T2/11 R3/10


examples

Chalk and

Board 3 T2/11 R3/10


examples with flyash

Chalk and

Board 3 T2/11 R3/10



Chalk and

Board 3 T2/11 R3/10



Chalk and

Board 3 T2/11 R3/10

72


Attained

1. Carry out design mix for M20, M40 and M50 by ACI, BS and IS Methods and

compare 3

Module.5 Teaching

Hours


(RBT) Level

Special Concretes 10 Hours L1,L2, L3,L4


1. Knowledge of use of RMC, SCC.

2. Properties and uses of FRC, Light weight concrete

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L41

RMC- manufacture and

requirement as per QCI-

RMCPCS,

Chalk and

Board

4,5&7 1,2&3

2,3

T2/12

L42 properties, advantages and

disadvantages

Chalk and

Board 2,3

T2/12

L43 . Self-Compacting

concrete- concept,

Chalk and

Board 2,3

T2/12

L44 materials, tests, Chalk and

Board 2,3

T2/12

L45

properties, application and

typical mix

Chalk and

Board 2,3

T2/12

L46 Fiber reinforced concrete -

Fibers types,

Chalk and

Board 2,3

T2/12

L47

properties, application of

FRC.

Chalk and

Board 2,3

T2/12

L48 Light weight concrete-

material

Chalk and

Board 2,3

T2/12

L49 properties and types.

Chalk and

Board 2,3

T2/12

L50

Typical light

weight concrete mix and

applications

Chalk and

Board 2,3

T2/12

73


Attained

1) List the type of accessories required for RMC 2,3

2) Write the typical tests conducted for SCC 2,3

3) List the various fibers used for FRC 2,3

4) List the Fibers available in the market 2,3

5) Different types of light weight concretes 2,3

6) Physical properties and application of LWC 2,3

7). Portion for I.A. Test:


I I and II

II III, IV and V

76

COURSE TITLE: BASIC GEOTECHNICAL ENGINEERING

SEMESTER – IV Subject Code 15CV45 IA Marks 20 Number of Lecture Hours/Week 04 Exam Marks 80 Total Number of Lecture Hours 50 Exam Hours 03

CREDITS – 04 Course objectives: This course will enable students

The objectives of this course is to make students to learn:

1. To appreciate basic concepts of soil mechanics as an integral part in the knowledge of civil

engineering. Also to become familiar broadly with geotechnical engineering problems such as,

foundation engineering, flow of water through soil medium and terminologies associated with

geotechnical engineering.

2. To know the basic engineering properties and the mechanical behaviour of different types of soil. This

includes strength-deformation characteristics under shearing stresses. Also consolidation properties of

clayey soils.

3. To determine the improvement in mechanical behaviour by densification of soil deposits using

compaction.

To know how the properties of soils that can be measured in the lab

Modules

Teaching

Hours

Revised Bloom’s Taxonomy (RBT)

Level

Module -1: Introduction: Introduction, origin and formation of soil, Phase Diagram, phase relationships, definitions and their inter relationships. Determination of Index properties-Specific gravity, water content, in-situ density and particle size analysis (sieve and sedimentation analysis) Atterberg’s Limits, consistency indices, relative density, activity of clay, Plasticity chart, unified and BIS soil classification.

10

L1, L2

Module -2 : Soil Structure and Clay Mineralogy

Single grained, honey combed, flocculent and dispersed structures, Valence bonds, Soil-Water system, Electrical diffuse double layer, adsorbed water, base-exchange capacity, Isomorphous substitution. Common clay minerals in soil and their structures- Kaolinite, Illite and Montmorillonite and their application in EngineeringCompaction of Soils: Definition, Principle of compaction, Standard and Modified proctor’s compaction tests, factors affecting compaction, effect of compaction on soil properties, Field compaction control - compactive effort & method of compaction, lift thickness and number of passes, Proctor’s needle, Compacting equipments and their suitability.

10 L1, L2

Module -3: Flow through Soils: Darcy’s law- assumption and validity, coefficient of permeability and its determination (laboratory and field), factors affecting permeability, permeability of stratified soils, Seepage velocity,

10 L1, L2, L3

77

superficial velocity and coefficient of percolation, Capillary

Phenomena

Seepage Analysis: Laplace equation, assumptions, limitations

and its derivation. Flow nets- characteristics and applications.

Flow nets for sheet piles and below the dam section.

Unconfined flow, phreatic line (Casagrande’s method –with and

without toe filter), flow through dams, design of dam filters.

Effective Stress Analysis:

Geostatic stresses, Effective stress concept-total stress, effective

stress and Neutral stress and impact of the effective stress in

construction of structures, quick sand phenomena

Module -4: Consolidation of Soil:

Definition, Mass-spring analogy, Terzaghi’s one dimensional

consolidation theory - assumption and limitations. Derivation of

Governing differential Equation

Pre-consolidation pressure and its determination by Casagrande’s method. Over consolidation ratio, normally consolidated, under consolidated and over consolidated soils. Consolidation characteristics of soil (Cc, av, mv and Cv. Laboratory one dimensional consolidation test, characteristics of e-log(σ’) curve, Determination of consolidation characteristics of soils- compression index and coefficient of consolidation (square root of time fitting method, logarithmic time fitting method). Primary and secondary consolidation.

10 L1, L2, L3,

L4

Module -5: Shear Strength of Soil:

Concept of shear strength, Mohr–Coulomb Failure Criterion,

Modified Mohr–Coulomb Criterion

Concept of pore pressure, Total and effective shear strength

parameters, factors affecting shear strength of soils. Thixotrophy

and sensitivity,

Measurement of shear strength parameters - Direct shear test,

unconfined compression test, triaxial compression test and field

Vane shear test, Test under different drainage conditions. Total

and effective stress paths.

10 L2, L3

78

Course outcomes:

On the completion of this course students are expected to attain the following outcomes;

1. Will acquire an understanding of the procedures to determine index properties of any type of soil,

classify the soil based on its index properties

2. Will be able to determine compaction characteristics of soil and apply that knowledge to assess

field compaction procedures

3. Will be able to determine permeability property of soils and acquires conceptual knowledge about

stresses due to seepage and effective stress; Also acquire ability to estimate seepage losses across

hydraulic structure

4. Will be able to estimate shear strength parameters of different types of soils using the data of

different shear tests and comprehend Mohr-Coulomb failure theory.

5. Ability to solve practical problems related to estimation of consolidation settlement of soil deposits

also time required for the same.

Program Objectives (as per NBA):

o Engineering Knowledge.

o Problem Analysis.

o Design / development of solutions (partly).

o Interpretation of data.

Text Books:

1. Gopal Ranjan and Rao A.S.R., Basic and Applied Soil Mechanics- (2000), New Age

International (P) Ltd., Newe Delhi.

2. Punmia B C, Soil Mechanics and Foundation Engineering- (2012) , Laxmi Pulications.

3. Murthy V.N.S., Principles of Soil Mechanics and Foundation Engineering- (1996), 4th

Edition, UBS Publishers and Distributors, New Delhi.

4. Braja, M. Das, Geotechnical Engineering; (2002), Fifth Edition, Thomson Business

Information India (P) Ltd., India

Reference Books:

1. T.W. Lambe and R.V. Whitman, Soil Mechanics, John Wiley & Sons, 1969.

2. Donold P Coduto, Geotechnical Engineering- Phi Learning Private Limited, New Delhi

3. Shashi K. Gulathi & Manoj Datta, Geotechnical Engineering-. (2009), “Tata Mc Graw Hill.

4. Narasimha Rao A. V. & Venkatrahmaiah C, Numerical Problems, Examples and objective

questions in Geotechnical Engineering-. (2000), Universities Press., Hyderabad.

5. Muni Budhu ,Soil Mechanics and Foundation Engg.- (2010), 3rd

Edition, John Wiely & Sons

79

1. Pre requisites of the course

This course requires an understanding of the principles of Engg Mechanics to the

study of soil mechanics.The knowledge and application of the principles of other basic

sciences such as Physics and Chemistry would also be helpful in the understanding of soil

behavior.Basics of the fluid mechanics and strength of materials is equally essential.

2. Overview of the course

The course is divided into two parts. First part deals with the physical and mechanical

properties of undisturbed and remolded soils. It discusses those properties in detail which

serves as convenient criteria for distinguishing between different soils and provides

instructions for describing soils adequately. It also deals with those soil properties that have

which have a direct bearing on the behavior of soil masses during and after construction

operations. It provides an elementary knowledge of theories required for solving problems

involving the stability of a soils and interaction between soil and water.

Second part deals with the application of a knowledge of soil behavior and theories of

soil mechanics to design and construction in the field of foundation and earth work

engineering by studying in detail compaction consolidation and shearing strength of soil.

3. Course outcome (co’s)

At the end of course the student will be able to

1. Will acquire an understanding of the procedures to determine index properties of any type of

soil, classify the soil based on its index properties.

2. Will be able to determine compaction characteristics of soil and apply that knowledge to

assess field compaction procedures.

3. Will be able to determine permeability property of soils and acquires conceptual knowledge

about stresses due to seepage and effective stress; also acquire ability to estimate seepage

losses across hydraulic structure.

4. Will be able to estimate shear strength parameters of different types of soils using the data of

different shear tests and comprehend Mohr-Coulomb failure theory.

5. Ability to solve practical problems related to estimation of consolidation settlement of soil

deposits also time required for the same.

80

4. APPLICATIONS

The field of geotechnical engineering is very vast.The knowledge of geotechnical engineering

is particularly helpful in the following problems in civil engineering.

1. Foundation design and construction

2. Pavement design

3. Design of underground and earth retaining structures

4. Design of embankments and excavations

5. Design of earth dams.

6.Module wise lesson plan

Module 1 - Introduction No. of hours : 10


1) History of soil mechanics, origin and formation of soil and various soil deposits available in India.

2) Phase diagram of a soil in bulk, dry, saturated states and determination of index properties.

3) Determinations of Atterberg’s Limits

4) Explain theSoil classifications

Lesson Plan

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained PO’s

Attained CO’s

Attained

Reference

Book/

Chapter No.

L1 Introduction, origin and

formation of soil

Chalk and

Board

1 & 2

1&2

1 T2/1, T3/1 &

R1/1

L2 Phase diagram,

definitions

Chalk and

Board 1

T2/2, T3/3 &

R1/3

L3 Phase relationships and

their interrelationships

Chalk and

Board 1

T2/1, 2, T3/3,4

& R1/3,4

L4 Phase relationships and

their interrelationships

Chalk and

Board 1

T2/1, 2, T3/3,4

& R1/3,4

L5 Determination of Index

properties, Specific

Gravity

Chalk and

Board 1

T2/3,4 T3/3,4

& R1/3,4

L6 Water content , in-situ

density

Chalk &

Board, PPT 1

T2/3,4 T3/3,4

& R1/3,4

81

L7 Partical sieve analysis

(Sieve and

Sedimentation analysis)

Chalk &

Board, PPT 1

T2/4 T3/4,5 &

R1/3,4

L8 Atterberg’s Limits,

consistency indices Chalk &

Board, PPT 1

T2/4 T3/4,5 &

R1/3,4

L9 Relative density activity

of clay and problems Chalk and

Board 1

T2/4 T3/4,5 &

R1/3,4

L10 Plasticity chart, unified

and BIS soil

classification

Chalk &

Board, PPT 1

T2/4 T3/4,5 &

R1/3,4

Assignment Questions: CO’s Attained

1. Explain in brief the formation of a soil. 1

2. With the help of three phase diagram define the following termsw, γd , γsat

, γb, n, na, e , Sr, ac 1

3. Derive the following from first principles

a. e= w G/Sr

b. na= e(1-Sr)/ 1+e

c. γd= G γw/1+e , γb=(G+eSr) γw/(1+e), γsat=(G+e ) γw/(1+e)

d. γd=(1- na)G γw/(1+wG)

1

4. A saturated specimen of undisturbed inorganic clay has a volume of 19.2

cm3 and mass 32.5 g. After oven-drying at 1050 C for 24 hours, the mass

reduces to 20.9 g. for the soil in the natural state, find w, G, e, γsat , γd. 1

5. In a Jodhpur-Mini-Compactor test, 612 g of wet soil occupies a colume of

300 cm3 at a moisture content of 12.6%. Determine γ ,γd, e, n and S in the

compacted soil if the specific gravity of soil is 2.68. 1

6. Explain in detail consistency limits of soil with the help of a sketch and

explain plasticity chart 1

7. The Atterberg limits of a soil sample are wl =50%,wp=30% and ws=15%.

If the specimen of this soil shrinks from a volume of 10 cm3 at liquid limit

to 5.94 cm3 when it is a oven-dried calculate. 1. Shrinkage ratio 2. Specific

gravity of soil solids.

1

8. Explain the laboratory methods of determination of moisture content and

specific gravity and field dry density 1

9. Define liquid limit, liquidity index and consistency index. Determine the

value of the liquid limit of a soil from the following test data.

N: 38,34,20,12 & w: 16,17,20,22 1

10. Draw neatly the IS plasticity chart and label the symbol of various soils 1

82

Module 2–Soil structure and Clay mineralogy No. of hours : 10


1) To define & explain with a neat sketch different soil structure and clay mineralogy.

2) To explain base exchange capacity isomorphs substitution electrical diffused double layer absorbed

water.

3)Factors affecting compaction and effect of compaction and soil properties.

4) Methods of compaction and compacting equipment’s.

Lesson Plan

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained PO’s

Attained CO’s

Attained

Reference

Book/

Chapter No.

L11

Single grained, honey

combed, flocculent &

dispersed structures Valence

bonds

Chalk &

Board, PPT

1 & 2

1,2 & 4

1 T2/5, T3/2 &

R1/2

L12

Soil-Water system, Electrical

diffuse double layer,

adsorbed water, base-

exchange capacity

Chalk &

Board, PPT 1

T2/5, T3/2 &

R1/2

L13

Isomorphous substitution.

Common clay minerals in

soil and their structures-

Kaolinite, Illite

Chalk &

Board, PPT 1

T2/5, T3/2 &

R1/2

L14 Montmorillonite and their

application in Engineering Chalk &

Board, PPT 1

T2/5, T3/2 &

R1/2

L15 Compaction of Soils:

Definition, Principle of

compaction

Chalk &

Board, PPT 1

T2/17, T3/13

& R1/5

L16 Standard and Modified

proctor’s compaction tests

Chalk &

Board, PPT 1

T2/17, T3/13

& R1/5

L17

Factors affecting

compaction, effect of

compaction on soil

properties

Chalk &

Board, PPT 1

T2/17, T3/13

& R1/5

L18

Field compaction control -

compactive effort &

method of compaction, lift

thickness and number of

passes,

Chalk &

Board, PPT 1

T2/17, T3/13

& R1/5

L19 Proctor’s needle Compacting

equipments and their

suitability

Chalk &

Board, PPT 1

T2/17, T3/13

& R1/5

L20 Problems on compaction of

soil

Chalk and

Board 1

T2/17, T3/13

& R1/5

83

Assignment Questions CO’s

Attained 1. With a neat sketches, describe single grained honey combed flocculent and dispersed

structures. 1

2. Define defused double layer and exchangable ions with a neat sketch. 1

3. Distinguish between std and Modified proctor tests and factors affecting compaction. 1

4. The following are results of standard compaction test performed on a sample of soil,

Plot the water content-dry density curve and obtain the optimum water content and

max dry density. Calculate the water content necessary to completely saturate the

sample at its max dry density, assuming no change in the volume. Take G-=2.7. Water content % 5 10 14 20 25

Bulk density (g/cm3) 1.77 1.98 2.1 2.18 2.16

1

5. Write a note on compaction control in field. 1

Module 3–Flow through Soil No. of hours : 10


1) Explain the importance of Flow through Soil.

2) Explain the importance of Seepage Analysis of soil

3) Explain the importance of an Effective Stress Analysis of Soil.

Lesson Plan

Lecture

No. Topics covered

Teaching

Method

PSO

Attained PO’s

Attained CO’s

Attained

Reference

Book/

Chapter

No.

L21

Darcy’s law- assumption and

validity, determination of

coefficient of permeability (Lab

& Field)

Chalk &

Board, PPT

1 & 2

1,2, & 4

1 & 2 T2/7, T3/6

& R1/6

L22 Factor affecting permeability,

permeability of stratified soils,

Seepage velocity

Chalk &

Board, PPT 1 & 2

T2/7, T3/6

& R1/6

L23 Superficial velocity and

coefficient of percolation,

Capillary Phenomena

Chalk &

Board, PPT 1 & 2

T2/7, T3/6

& R1/6

L24 Seepage Analysis: Laplace

equation, assumptions,

limitations& Its derivation

Chalk &

Board, PPT 1 & 2

T2/9, T3/7

& R1/7

L25 Flow nets- characteristics and

applications flow nets for sheet

Chalk &

Board, PPT 1 & 2

T2/9, T3/7

& R1/7

84

piles and below the dam section

L26

Unconfined flow, phreatic line

(Casagrande’s method –with

and without toe filter), flow

through dams, design of dam

filters.

Chalk &

Board, PPT 1 & 2

T2/9, T3/7

& R1/7

L27 Effective Stress Analysis:

Geostatic stresses, Effective

stress concept-total stress,

Chalk &

Board, PPT

1 & 2 T2/13,

T3/10 &

R1/9

L28

effective stress & Neutral stress,

impact of the effective stress in

construction of structures, quick

sand phenomena

Chalk &

Board, PPT

1 & 2 T2/13,

T3/10 &

R1/9

L29 Problems on seepage analysis Chalk and

Board

1 & 2

T2/9, T3/7&

R1/7

L30 Problems on effective stress

analysis

Chalk and

Board

1 & 2 T2/13,

T3/10 &

R1/9


Attained

1. Explain Darcy’s law , assumptions and its validity. 1 & 2

2. Explain factors affecting permeability 1 & 2

3. Derive Laplace equation, mention its assumptions 1 & 2

4. What is flow net? Explain characteristic and applications. 1 & 2

5. Explain Geodetic, Effective, Total, and Neutral stresses. 1 & 2

6. Explain the impact of effective stress in construction of structures. 1 & 2

Module 4 – Consolidation of Soil No. of hours : 10


1) To explain consolidation process through mass-spring analogy.

2) Explain normally consolidated , under consolidated and over consolidated soils

3) Explain Consolidation characteristics of a soil such as Cc, av,mvand Cv

4) Explain Primary and Secondary consolidations.

85

Lesson Plan

Lecture

No. Topics covered

Teaching

Method

PSO’

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter No.

L31

Definition, Mass-spring

analogy, Terzaghi’s one

dimensional consolidation

theory - assumption and

limitations.

Chalk &

Board, PPT

1,2 & 3

1,2 & 3

3 T2/15, 16,

T3/11 & R1/10

L32

Derivation of Governing

differential Equation Pre-

consolidation pressure and its

determination by

Casagrande’s method.

Chalk &

Board, PPT 3

T2/15, 16,

T3/11 & R1/10

L33

Over consolidation ratio,

normally consolidated, under

consolidated and over

consolidated soils

Chalk &

Board, PPT 3

T2/15, 16,

T3/11 & R1/10

L34

Consolidation

characteristics of soil (Cc, av,

mv and Cv. Laboratory one

dimensional consolidation

test,

Chalk &

Board, PPT 3

T2/15, 16,

T3/11 & R1/10

L35 characteristics of e-log(σ’)

curve

Chalk &

Board, PPT 3

T2/15, 16,

T3/11 & R1/10

L36

Determination of

consolidation characteristics

of soils compression index

and coefficient of

consolidation by square root

of time fitting method,

Chalk &

Board, PPT 3

T2/15, 16,

T3/11 & R1/10

L37

Determination of

consolidation characteristics

of soils compression index

and coefficient of

consolidation by logarithmic

time fitting method,

Chalk &

Board, PPT 3

T2/15, 16,

T3/11 & R1/10

L38 Primary consolidation Chalk &

Board, PPT 3

T2/15, 16,

T3/11 & R1/10

L39 secondary consolidation Chalk &

Board, PPT 3

T2/15, 16,

T3/11 & R1/10

L40 Problems on Consolidation of

soil

Chalk &

Board 3

T2/15, 16,

T3/11 & R1/10

86


Attained

1. Explain the mechanism of consolidation with the help of mass-spring

analogy 3

2. Explain Terzaghi’s theory of one dimensional consolidation.List the

assumptions that are made in this theory 3

3. Define co-efficient of compressibility(av),co-efficient of volume

change(mv),compression index(Cc) and co-efficient of consolidation (Cv). 3

4. An undistributed sample of clay 24 mm thick, consolidated 50% in 20 min,

when tested in the laboratory with drainage allowed at the top and bottom.

The clay layer, from which the sample was obtained, is 4 m thick in the field.

How much time will it take to consolidate 50% with double drainage? If the

clay stratum has only single drainage , calculate the time to consolidate 50%.

Assume uniform distribution of consolidation pressure

3

5. Two clay specimens A and B of thickness 2 cm and 3 cm, have equilibrium voids

ratio 0.68 and 0.72 respectively under a pressure of 200 kN/m2. If the equilibrium

voids ratio of the soils reduced to 0.50 and 0.62 respectively. When the pressure was

increased to 400kN/m2, find the ratio of co-efficients of permeability of the two

specimens. The time required by the specimen A to reach 40 per cent degree of

consolidation is ¼ of that required B for reaching 40% degree of consolidation

3

Module 5–Shear Strength of Soil No. of hours : 10


1) Different laboratory tests on shear strength of soil

2) Determination of shear strength parameters under different drainage conditions

3) Determination sensitivity by Vane shear test and unconfined compression test

87

Lesson Plan

Lecture

No. Topics covered

Teaching

Method

PSO’

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L41 Concept of shear strength,

Mohr–Coulomb Failure criterion

Chalk &

Board,

PPT

1,2 & 3

1,2,3 & 4

4

T2/18,

T3/12 &

R1/11

L42 Modified Mohr–Coulomb

Criterion

Chalk &

Board,

PPT

4 T2/18,

T3/12 &

R1/11

L43 Concept of pore pressure Chalk &

Board,

PPT

4 T2/18,

T3/12 &

R1/11

L44 Total and effective shear strength

parameters

Chalk &

Board,

PPT

4 T2/18,

T3/12 &

R1/11

L45 factors affecting shear strength of

soils Thixotrophy and sensitivity

Chalk &

Board,

PPT

4 T2/18,

T3/12 &

R1/11

L46 Measurement of shear strength

parameters - Direct shear test

Chalk &

Board,

PPT

4

T2/18,

T3/12 &

R1/11

L47 Measurement of shear strength

parameters - unconfined

compression test

Chalk &

Board,

PPT

4 T2/18,

T3/12 &

R1/11

L48 Triaxial compression test & field

Vane shear test

Chalk &

Board,

PPT

4 T2/18,

T3/12 &

R1/11

L49 Test under different drainage

conditions

Chalk &

Board,

PPT

4 T2/18,

T3/12 &

R1/11

L50 Total and effective stress paths Chalk &

Board,

PPT

4 T2/18,

T3/12 &

R1/11

Assignment Questions CO’s Attained

1. Explain Mohr-Coulomb theory of shear strength and pore water in pressure. 4

2. Compare the merits and demerits of Triaxial shear test and Direct shear test. 4

3. With a neat sketch explain the vane shear test and obtain the expression for shear strength. 4

4. In a direct shear test on sand, the normal stress was 2.0 kg/cm2 and shear stress at failure was 0.8 kN/cm2 .

Determine the orientations of the principle planes at failure. 4

5. A lateral pressure in a trixial compression test in a cohesive soil gave the following results: angle of shearing

resistance 0=17.5 deg:cohesion=3.0kg/cm2:total axial stress at failure =18 kg/cm2. Determine the lateral

pressure.

4

5) Portion for IA tests:


I I and II

II III and IV

90

COURSE : ADVANCED SURVEYING SEMESTER – IV


Number of Lecture Hours/Week 04 Exam Marks 80

Total Number of Lecture hours 50 Exam Hours 03

CREDITS – 04

Course objectives: This course will enable students to:

1. Apply geometric principles to arrive at solutions to surveying problems.

2. Analyze spatial data using appropriate computational and analytical techniques.

3. Design proper types of curves for deviating type of alignments.

4. Use the concepts of advanced data capturing methods necessary for engineering practice

Modules Teaching

Hours

Revised Bloom’s

Taxonomy

(RBT) Level Module -1: Curve Surveying

Curves – Necessity – Types, Simple curves, Elements, Designation of curves, Setting out simple curves by linear

methods (numerical problems on offsets from long chord

& chord produced method), Setting out curves by

Rankines deflection angle method (numerical problems).

Compound curves, Elements, Design of compound

curves, Setting out of compound curves (numerical

problems). Reverse curve between two parallel straights

(numerical problems on Equal radius and unequal radius).

Transition curves Characteristics , numerical problems on

Length of Transition curve, 7.5 Vertical curves –Types –

(theory).

10 L1,L3,L5

Module -2: Geodetic Surveying and Theory of Errors Geodetic Surveying: Principle and Classification of triangulation system, Selection of base line and stations,

Orders of triangulation, Triangulation figures, Reduction

to Centre, Selection and marking of stations Theory of

Errors: Introduction, types of errors, definitions, laws of

accidental errors, laws of weights, theory of least squares,

rules for giving weights and distribution of errors to the

field observations, determination of the most

probable values of quantities.

10 L1,L2, L3

Module -3: Introduction to Field Astronomy: Earth, celestial sphere, earth and celestial coordinate systems, spherical triangle, astronomical triangle,

Napier’s rule

10 L4,L5

Module -4: Aerial Photogrammetry Introduction, Uses, Aerial photographs, Definitions, Scale of vertical and tilted photograph (simple problems),

Ground Co-ordinates (simple problems), Relief

Displacements (Derivation), Ground control, Procedure

of aerial survey, overlaps and mosaics,

10 L2,L3, L5

91

Stereoscopes, Derivation Parallax(Derivation) .

Module -5: Modern Surveying Instruments

Introduction, Electromagnetic spectrum, Electromagnetic distance measurement, Total station,

Lidar scanners for topographical survey. Remote

Sensing: Introduction, Principles of energy interaction

in atmosphere and earth surface features, Image

interpretation techniques, visual interpretation. Digital

image processing, Global Positioning system

Geographical Information System: Definition of GIS,

Key Components of GIS, Functions of GIS, Spatial

data, spatial information system Geospatial analysis,

Integration of Remote sensing and GIS and

Applications in Civil Engineering(transportation, town

planning).

10 Hours L2,L3, L5

Course outcomes: After a successful completion of the course, the student will be able to: 1. Apply the knowledge of geometric principles to arrive at surveying problems

2. Use modern instruments to obtain geo-spatial data and analyse the same to appropriate

engineering problems.

3. Capture geodetic data to process and perform analysis for survey problems with the use of

electronic instruments;

4. Design and implement the different types of curves for deviating type of alignments.

Program Objectives (as per NBA)

Engineering Knowledge.

Problem Analysis.

Interpretation of data.

Text Books: 1. B.C. Punmia, “Surveying Vol.2”, Laxmi Publications pvt. Ltd., New Delhi. 2. Kanetkar T P and S V Kulkarni , Surveying and Levelling Part 2, Pune Vidyarthi Griha

Prakashan,

3. K.R. Arora, “Surveying Vol. 1” Standard Book House, New Delhi.

4. Sateesh Gopi, Global Positioning System, Tata McGraw Hill Publishing Co. Ltd. New Delhi

Reference Books: 1. S.K. Duggal, “Surveying Vol.I & II”, Tata McGraw Hill Publishing Co. Ltd. New Delhi. 2. R Subramanian, Surveying and Leveling, Second edition, Oxford University Press, New

Delhi.

3. David Clerk, Plane and Geodetic Surveying Vol1 and Vol2, CBS publishers

4. B Bhatia, Remote Sensing and GIS , Oxford University Press, New Delhi.

5. T.M Lillesand,. R.W Kiefer,. and J.W Chipman, Remote sensing and Image interpretation ,

5th edition, John Wiley and Sons India

6. James M Anderson and Adward M Mikhail, Surveying theory and practice, 7th Edition, Tata

McGraw Hill Publication.

7. Kang-tsung Chang, Introduction to geographic information systems, McGraw Hill Higher

Education

1) Pre requisites of the course

The subject requires the student to know about the fundamentals of surveying and basics of previous

topics learnt in the earlier semester

2) Overview of the course

The subject focuses on setting out of curves (horizontal and vertical). This course is also includes

Advanced Surveying and Mapping Systems i.e. aerial photogrammetry, Global Positioning Systems

& Total station, its advantages and applications which is important and essential for all civil

engineers engaged in field work.

Course Outcome

After a successful completion of the course, the student will be able to:

1. Apply the knowledge of geometric principles to arrive at surveying problems

2. Use modern instruments to obtain geo-spatial data and analyse the same to appropriate

engineering problems.

3. Capture geodetic data to process and perform analysis for survey problems with the use of

electronic instruments;

4. Design and implement the different types of curves for deviating type of alignments.

Relevance of the Course

Civil Engineer should have basics of surveying and the knowledge of Modern instruments so that he

can handle all the practical situations efficiently and economically. The course is more relevant to

precise instruments like Tacheometer, Total Station and GPS. These instruments help in

ascertaining heights, distances, difference in elevations, curve settings, areas and volumes necessary

for all types of civil engineering works.

3) Applications

Survey work is involved in all civil engineering projects, like

1. Setting out of the railway and highway curves

2. Estimation of areas, volumes of the regular irregular shapes by various methods

3. Preparation of contour maps

4. Total stations are mainly used by land surveyors. They are also used by archaeologists to

record excavations and by police, crime investigators and insurance companies to take

measurements of scenes.

83

4) Module wise lesson plan


1) Define curves, types, requirements & various elements of different types of curves.

2) The linear and angular method of setting out of different types of curves

Lesson Plan

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L1

Definition of a curve, types of

curves, necessity of curves,

notation and definitions used

in curves.

Chalk and

Board 1

1&2

4 T1/1, R1/11

L2 Setting out the simple curves

by linear methods and

Numerical problems

Chalk and

Board 1

4 T1/1, R1/11

L3 Setting out the simple curves

Numerical problems

Chalk and

Board 1

4 T1/1, R1/11

L4 Setting out of curves by

Rankines deflection method

Chalk and

Board 1

4 T1/1, R1/11

L5 Introduction of compound

curve and elements of

compound curve.

Chalk and

Board 1

4 T1/2, R1/11

L6 Setting of compound curve &

Numerical problems

Chalk and

Board 1

4 T1/2, R1/11

L7

Introduction and elements of

reverse curves (reverse curve

between two parallel straights)

& Numerical problems

Chalk and

Board 1

4 T1/2, R1/11

L8 Reverse curves (reverse curve

between two parallel straights)

Numerical problems

Chalk and

Board 1

4 T1/2, R1/11

L9 Introduction, necessity,

functions and characteristics

of transition curves

Chalk and

Board 1

4 T1/3, R1/11

L10 Introduction to Vertical curve

and its types.

Chalk and

Board 1

4 T1/4, R1/11

Module-1: Curve Surveying No. of hours : 10

83



Attained

1) Define the following terms: External distance, Mid-ordinate, Point of curvature,

Point of tangent 4

2) Derive the relationship between various elements of simple curve. 4

3) Two tangents intersect at the chainage 1190, the deflection angle being 360

Calculate all the data necessary for setting out a curve with radius of 300 m by

chords produced method. The peg interval is 30 m.

4

1. Define the following terms: Point of compound curvature & Point of reverse

curvature 4

2. With a sketch, explain the various elements of a compound curve. Derive the

relations for calculating the chainages of tangents points. 4

3. Derive the relationship between various elements of a reverse curve for parallel

straight. 4

4. Two straight lines with a total deflection angle of 720 30’ are to be connected by a

compound curve of two branches of Equal length. The radius of the first arc is

350m and that of second arc is 500m and the chainage at vertex point is 1525m.

Find the chainages of two tangent point and that of point of compound curvature.

4

5. Two Parallel railway lines are to be connected by a reverse curve, each section

having same radius. If the lines are 12m apart and the maximum distance between

tangent points measured parallel to the straights is 48m, find the maximum

allowable radius. If however both the radii are different, calculate the radius of

second branch if that of first branch is 60m. Also calculate the length of both the

branches.

4

6. What is a transition curve? What are the advantages of a transition curve? 4

7. What are basic criteria for the design of a transition curve? Derive an expression

for super-elevation. 4

8. How would you decide the length of a transition curve? Discuss the various

methods. Which method is preferred and why? 4

Module-2: Geodetic Surveying and Theory of Errors No. of hours : 10


1) Define Geodetic surveying & triangulation

2) Principle and Classification of triangulation system,

3) Define laws of accidental errors, laws of weights, theory of least squares, rules for giving

weights and distribution of errors to the field observations

4) Determine the most probable values of quantities.

83

Lesson Plan

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L11 Geodetic Surveying: Principle and Classification of triangulation system,

Chalk and

Board 1

1 & 2

1 T1/8

L12 Selection of base line and

stations, Orders of

triangulation

Chalk and

Board 1 1 T1/8

L13 Triangulation figures,

Reduction to Centre,

Chalk and

Board 1 1 T1/8

L14 Selection and marking of

stations

Chalk and

Board 1 1 T1/8

L15 Theory of Errors: Introduction Chalk and

Board 1 1 T1/8

L16 Types of errors, definitions,

laws of accidental errors

Chalk and

Board 1 1 T1/8

L17 laws of weights, theory of

least squares

Chalk and

Board 1 1 T1/8

L18

Rules for giving weights and

distribution of errors to the

field observations,

Chalk and

Board 1 1 T1/8

L19

Determination of the most

probable values of

quantities.

Chalk and

Board 1 1 T1/8

L20

Determination of the most

probable values of

quantities.

Chalk and

Board 1 1 T1/8



Attained

1. In a triangulation survey, four triangulations stations A, B, C, and D were tied using

a braced quadrilateral ABCD. The length of the diagonal AC was measured and

found to be 1116.40 m long. The measured angles are as below: α = 44°40′59″ γ =

63°19′28″ β = 67°43′55″ δ = 29°38′50″. Calculate the length of BD.

1

2. Compute the value of R for the desired maximum probable error of 1 in 25000 if

the probable error of direction measurement is 1.20″. 1

3. Compute the strength of figure ABCD (Fig. 6.13) for all the routes by which the

length CD can be determined from the known side AB assuming that all the

stations have been occupied, and find the strongest route.

1

4. In a triangulation survey, the altitudes of two stations A and B, 110 km apart,

are respectively 440 m and 725 m. The elevation of a peak P situated at 65 km from

A has an elevation of 410 m. Ascertain if A and B are intervisible, and if necessary,

find by how much B should be raised so that the line of sight nowhere be less than

3 m above the surface of ground. Take earth’s mean radius as 6400 km and the

mean coefficient of refraction as 0.07.

1

83

Module-3: Introduction to Field Astronomy No. of hours : 10


1) Define Astronomical terms & Coordinate Systems

2) Describe Earth and celestial coordinate systems, spherical triangle, astronomical triangle, Napier’s rule.

Lesson Plan

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L21 Definitions of Astronomical terms.

Chalk and

Board 1

1, 2,&3

3 T1/13

L22 Earth, celestial sphere, earth and celestial coordinate systems

Chalk and

Board 1

3 T1/13

L23 Spherical triangle, Properties

& Formulae in Spherical

triangle

Chalk and

Board 1

3 T1/13

L24 Simple numerical problems Chalk and

Board 1

3 T1/13

L25 Astronomical triangle Chalk and

Board 1

3 T1/13

L26 Simple numerical problems. Chalk and

Board 1

3 T1/13


Board 1

3 T1/13

L28 Napier’s rule. Chalk and

Board 1

3 T1/13


Board 1

3 T1/13


Board 1

3 T1/13

83



Attained

1) Define the following terms: Equation of Time, Celestial Sphere, Parallax,

Sidereal Time, Zenith & Nadir, celestial Horizon, Terrestrial Poles & Equator. 2

2. What are the coordinates systems employed to locate position of Heavenly

bodies? Is it necessary to have several systems instead of one? 2

3. Find the shortest distance between two places A & B, given that the longitudes of

A & B are 150 N & 120 6’ N & their longitudes are 500 12’ E and 540 E

respectively. Find also the direction of B on the great circle route. Radius of

Earth= 6370 Km

2


1) Define aerial photogrammetry, advantages & applications.

2) Ground control, Procedure of aerial survey, overlaps and mosaics

Lesson Plan

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L31 Introduction, Uses, Aerial photographs

Chalk and

Board 1

1 & 2

3 T1/14

L32 Definitions, Scale of vertical and tilted photograph (simple problems),

Chalk and

Board 1 3 T1/14


Board 1 3 T1/14

L34 Ground Co-ordinates (simple

problems)

Chalk and

Board 1 3 T1/14


Board 1 3 T1/14

L36 Relief Displacements

(Derivation)

Chalk and

Board 1 3 T1/14

L37 Ground control, Procedure of

aerial survey

Chalk and

Board 1 3 T1/14

L38 Overlaps and mosaics , Chalk and

Board 1 3 T1/14

L39 Stereoscopes, Derivation Chalk and

Board 1 3 T1/14

L40 Parallax(Derivation) Chalk and

Board 1 3 T1/14

Module-4: Aerial Photogrammetry No. of hours : 10

83

Module-5 Modern Surveying Instruments No. of hours: 10


1) Define Electromagnetic spectrum, Electromagnetic distance measurement

2) Global Positioning Systems, segments of GPS & working principle.

3) Methods of GPS surveying, errors and accuracy, applications of GPS.

Lesson Plan

Lecture

No. Topics covered

Teaching

Method

PSO’s

Attained

PO’s

Attained

CO’s

Attained

Reference

Book/

Chapter

No.

L41 Introduction, Electromagnetic spectrum, Electromagnetic distance measurement,

Chalk and

Board 1

1, 2 & 3

2 T1/14

L42 Total station Chalk and

Board 1

2 T1/15

L43 Lidar scanners for topographical survey

Chalk and

Board 1

2 T1/15

L44

Remote Sensing: Introduction, Principles of energy interaction in atmosphere and earth surface features

Chalk and

Board 1

2 T1/16

L45 Image interpretation

techniques, visual

interpretation.

Chalk and

Board 1

2 T1/16

L46 Digital image processing Chalk and

Board 1

2 T1/16

L47 Global Positioning system Chalk and

Board 1

2 T1/16

L48 Geographical Information

System: Definition of GIS,

Key Components of GIS,

Chalk and

Board 1

2 T1/16

L49 Functions of GIS, Spatial data,

spatial information system

Chalk and

Board 1

2 T1/16

L50

Geospatial analysis,

Integration of Remote sensing

and GIS and Applications in

Civil Engineering

(transportation, town planning)

Chalk and

Board 1

2 T1/16

5) Portion for IA tests: I. A. Test No. Modules

I I and II

II III and IV

83

COURSE : FLUID MECHANICS AND HYDRAULIC MACHINES LABORATORY

SEMESTER – IV

Subject Code 15CVL47 IA Marks 20


Total Number of Lecture Hours 42 Exam Hours 3

CREDITS – 02

Course objectives: This course will enable students to;

1. Calibrate flow measuring devices

2. Determine the force exerted by jet of water on vanes

3. Measure discharge and head losses in pipes

4. Understand the fluid flow pattern

Modules Teaching

Hours

Revised Bloom’s

Taxonomy (RBT) Level

1. Verification of Bernoulli’s equation 3 L1, L2

2. Determination of Cd for Venturimeter and Orifice

meter 3 L1, L2

3. Determination of hydraulic coefficients of small

vertical orifice 3 L1, L2

4. Calibration of Rectangular and Triangular notch 3 L1, L2

5. Calibration of Ogee and Broad crested weir 3 L1, L2

6. Determination of Cd for Venturiflume 3 L1, L2

7. Experimental determination of force exerted by a jet

on flat and curved plates (Hemispherical Vane). 3 L1, L2

8. Experimental determination of operating

characteristics of Pelton turbine 3 L1, L2

9. Determination of efficiency of Francis turbine 3 L1, L2

10. Determination of efficiency of Kaplan turbine 3 L1, L2

11. Determination of efficiency of centrifugal pump. 3 L1, L2

12. Determination of Major and Minor Losses in Pipes 3 L1, L2

13. Demonstration Experiments:

a. Reynold’s experiment to understand laminar and

turbulent flow

b. Flow Visualization

c. Calibration of Sutro-weir

6 L1, L2

Course outcomes: During the course of study students will develop understanding:

Properties of fluids and the use of various instruments for fluid flow measurement.

Working of hydraulic machines under various conditions of working and their characteristics



o Problem Analysis.


o Interpretation of data

83

Text Books:

1. Sarbjit Singh , Experiments in Fluid Mechanics - PHI Pvt. Ltd.- New Delhi

2. Mohd. Kaleem Khan, “Fluid Mechanics and Machinery”, Oxford University Press

Reference Books:

1. Hydraulics and Fluid Mechanics’ – Dr. P.N. Modi & Dr S.M. Seth, Standard Book House- New

Delhi. 2009 Edition

Prerequisites:

Preliminary concepts of fluid mechanics and Applied Hydraulics studied in theory subject.

Applications:

1. To find the discharge in closed and open channel.

2. To find the efficiency of hydraulic machinery.

3. To find the losses in closed pipe.

LESSON PLAN

Week Experiment Name of the Experiment PSO’s

Attained

PO’s

Attained

CO’s

Attained

I

1 1. Verification of Bernoulli’s equation

1,2&4 1,4,5,6,9,

10,11&12

1&2

2 2. Determination of Cd for Venturimeter and

Orifice meter

II 3 3. Determination of hydraulic coefficients of

small vertical orifice

III 4 4. Calibration of Rectangular and Triangular

notch

IV 5 5. Calibration of Ogee and Broad crested weir

6 6. Determination of Cd for Venturiflume

V 7

7. Experimental determination of force

exerted by a jet on flat and curved plates

(Hemispherical Vane).

VI 8 8. Experimental determination of operating

characteristics of Pelton turbine

VII 9 9. Determination of efficiency of Francis

turbine

VIII 10 10. Determination of efficiency of Kaplan

turbine

IX 11 11. Determination of efficiency of centrifugal

pump.

X 12 12. Determination of Major and Minor Losses

in Pipes

XI 13

13. Demonstration Experiments:

d. Reynold’s experiment to understand

laminar and turbulent flow

e. Flow Visualization

f. Calibration of Sutro-weir

Portion for I.A. Test Experiment

Final I.A. Test Experiment 1 to 12

83

VIVA QUESTIONS & ANSWERS

1. Define Bernoulli's theorem

Ans: It is defined as total head include pressure head, velocity head and datum line is equal to

constant.

2. Application of Bernoulli's equation

Ans: It is used in venturemeter and orifice meter to determine the discharge through pipe.

3. Define notch and explain its classifications

Ans: Notch is an opening provided in the side of a tank or channel to measure the rate of flow. The

surface of the liquid will be below the top edge of the notch.

i. Based on the shape – Rectangular, Triangular (V), Trapezoidal, Cipolletti, Parabolic, stepped

notches.

ii. Based on the end condition – Notch with end contraction and notch without end contraction.

iii. Based on the crest – Sharp crested and beveled notch.

4. Define the co-efficient of discharge, Cd. what is its significance?

Ans: Cd is defined as the ratio of actual discharge to the theoretical discharge. The value of Cd is

always less than 1 as actual discharge will be less than theoretical discharge due to losses. Hence, Cd

expresses the amount of loss.

5. Why a triangular notch is preferred over a rectangular notch for measuring low discharge.

Ans: For low discharge, the head over the triangular notch is considerable than a rectangular notch,

which gives the accurate measurement of discharge.

6. Explain the advantages of triangular notch over rectangular notch.

Ans: For low discharges, the head over the triangular notch is considerable than a rectangular notch,

which gives the accurate measurement of head and discharge and reduce the measurement error.

i. The formula for V-notch is simpler as it involves the measurement of head only (if it is a

right angled notch).

ii. The coefficient of discharge is fairly constant.

iii. The ventilation is not required.

iv. The head due to velocity of approach may be ignored without much error.

7. Under what conditions you prefer triangular notch?

Ans: For low discharges, the triangular notch is preferred than a rectangular notch.

8. If 10% of error is made in the measurement of head over the triangular notch, what is the

corresponding error in computed discharge?

Ans: The error in discharge corresponding to 10% error in the measurement of head is 25%.

9. What is the meaning of calibration?

Ans: Calibration indicates the determination of coefficient of discharge, Cd, of a measuring device.

It also represents the standardization of the device.

10. When do you use rectangular notch?

Ans: Rectangular notch is used when the discharge to be measured is larger.

83

11. What is the end contraction? What are its effects?

Ans: In the case of a rectangular notch, the nappe width is reduced due to contraction at the two

ends, which is called end contraction. The end contraction reduces the discharge over the notch.

12. What is the meaning of suppressed notch?

Ans: A notch is called suppressed notch when the effect of end contraction on the notch width does

not exist. In such a case, the crest length of notch will be equal to the width of the channel.

13. Explain the end contraction of a rectangular notch.

Ans: In case of a rectangular notch the crest width is reduced by contracted nappe by an amount

equal to 0.1H at each end as per Francis. Hence, the net nappe length becomes (L — 0.2H).

14. What is the effect of velocity of approach on the discharge?

Ans: The velocity with which water approaches or reaches the weir or notch before it passes over it,

is called velocity of approach, Va. It is computed by dividing the discharge by the approaching flow

area. It will give an additional head to the flowing water givenby ha = Va2/2g. The discharge

estimated considering the velocity of approach will be larger than that without the velocity of

approach.

15. If 12% of error is made in the measurement of head over the notch, what is the

corresponding error in computed discharge?

Ans:The error in discharge corresponding to 12% error made in the measurement of head is 18%.

16. Define the nappe.

Ans: The sheet of water flowing over the notch or weir is called nappe or vein.

17. Define the term weir

Ans: a weir is a concrete or masonry structure constructed across the river to measure the discharge.

The crest width of weir may be sharp, narrow or broad

18. How is weirs classified

Ans:the weirs are classified as given below:

1. Based on the head over the crest:- Sharp-crested, narrow-crested, broad-crested, and long-

crested weirs

2. Based on shape: -Rectangular, triangular (V), trapezoidal, cippoletti, parabolic and stepped

notch.

3. Based on end condition: - Weir without end contraction and weir with end contraction.

4. Based on the corner shape at the upstream end:- Sharp cornered and rounded end.

5. Based on the discharge condition:- Freely discharging and submerged

19. What is the difference between a notch and weir?

Notch is a metal plate fixed in small laboratory channel, whereas the weir is a concrete

structure constructed across the river to measure the discharge.

Notch is always sharp crested, whereas the weir may be sharp, narrow, broad or long crested

based on the crested width.

20. Define the venturi flume.

Ans: A venturi flume is gauging flume used in the open channels to measure the discharge.

83

21. What is the use of a venturi flume?

Ans. The venturi flume is used to measure the discharge in open channels.

22. What is the difference between venturi flume and Venturi meter.

Ans.The venturi flume is used in open channels, whereas Venturi meter has application in pipes,

both are employed to measure the discharge.

23. What are the different methods of fluming a channel?

Ans. The flurning is done by one of the following ways:

(a) By reducing the width of channel in the direction of flow, called channel contraction.

(b) By raising the bed level of the flume with the provision of hump

(c) By combining both channel contraction and hump.

24. Define the specific energy.

Ans: The energy of flowing fluid per unit weight with reference to the channel bottom taken as

datum is called specific energy.

The specific energy E is given by: E = y +V2/2g

where, y is the depth of flow, V the velocity of flow and g the gravitational acceleration.

25. What is the difference between specific energy and total energy?

Ans: Specific energy is the sum of pressure head (y) and kinetic head (V2/2g), whereas total energy

is the sum of datum head, pressure head and kinetic head.

Specific energy: E = y+ V2/2g

Total energy: E = Z + p/γ +V2/2g

26. What do you mean by standing wave?

Ans: A standing wave is nothing but a hydraulic jump formed when supercritical flow meets the

subcritical flow hump.

27. What is the use of Venturi meter?

Ans: A Venturi meter is the device used to measure or determine the rate of flow or discharge of

fluid through a pipe.

28. What is the basic principle on which Venturi meter works?

Ans: The Venturi meter works on the principle of developing the pressure difference in the

direction of flow by decreasing the cross-sectional area of the flow and the measurement of this

pressure difference enables the determination of the flow through the pipe.

29. Explain the construction of Venturi meter.

Ans: The venturi meter consists of convergent cone of smaller length, cylindrical throat and the

larger divergent cone. Convergent cone tapers from the original pipe diameter to the throat size,

whereas the divergent cone enlarges from throat size to the original pipe size.

30. What is the range of included angle of the convergent and divergent cones?

Ans: Convergent angle = 21° ± 1° and divergent angle = 5' to 15°.

83

31. What is the length of the convergent cone?

Ans:Length of convergent cone approximately equal to 2.7(D — d) where D is the diameter of pipe

and d the diameter of throat.

32. Whether the convergent cone is longer or divergent cone? Why?

Ans:The convergent cone is shorter than the divergent cone. The convergent cone is made shorter to

reduce the loss of energy due to acceleration. Similarly the divergent cone is made longer so as to

cause the gradual retardation of the fluid and eliminate flow separation. This decreases the energy

loss due to formation of eddies.

33. At what distance from the throat and convergent cone pressure taps are prodded?

Ans: The pressure tappings are made one at just upstream of the inlet section and the other in the

middle of the throat.

34. Can pressure taps be provided between throat and divergent cone? Why?

Ans: No. Because in the divergent cone flow separation occurs and pressure measurers will not

yield the discharge measurement.

35. What is meant by flow separation?

Ans:Flow separation is the departure of the flow from the boundary due to sudden divergence and

increase in the flow area or due to deviation.

36. Why there is no pressure tapping in the divergent cone of the Venturi meter?

Ans: Because in the divergent cone flow separation occurs and pressure measurement will not yield

the discharge measurement.

37. What should be the diameter of throat in terms of inlet diameter?

Ans: The throat diameter will be commonly 1/2 of the inlet diameter.

38. What is venturi head?

Ans: The difference in pressure heads at inlet and throat sections is called venturi head.

((P1/w) – (P2/w)) = h

39. What is the limit for reduction in throat diameter and why?

Ans: Diameter of throat may vary from 1/3 to 3/4 of pipe diameter (commonly 1/2 of the pipe

diameter) to avoid cavitation.

40. Explain the phenomena of cavitation.

Ans: Due to larger reduction in pressure, the liquid particles are converted into vapour bubbles at

throat portion. When these bubbles reach the location of high pressure, they burst due to

condensation. This bursting causes the removal or erosion of pipe material, which is called

cavitation.

41. Can Venturi meter be used in inclined and vertical pipes? Ans: Yes.

42. Define the coefficient of discharge.

Ans: The coefficient of discharge is defined as the ratio of actual discharge to the theoretical

discharge, represented by Cd, and is given by

Cd= Qact/Qth

83

43. What is the value of Cd of the Venturi meter for fluids of low viscosity?

Ans: Cd value for low viscous fluids is 0.98. The Cd value generally ranges between flow 0.97 and

0.99 for Venturi meter.

44. What is an orifice? Explain its classifications.

Ans: An orifice is an opening provided in the side or at the bottom of a tank through which the fluid

is discharged.

Classification:

(i) Based on the shape - Circular, rectangular and triangular.

(ii) Based on the discharging jet - Free, and submerged (partially/fully submerged).

(iii) Based on the upstream edge - Sharp edged, and bell mouthed.

(iv) Based on the ratio of size of the orifice (d) to the constant head (H) - Small (d < H/5) and

large (d> H/5).

45. What is the range of Cy for different orifices?

Ans: Range of C,, is 0.95 to 0.99.

46. What are the different methods of finding Cv and Cc.?

Ans: Methods of finding Cv - Jet distance measurement method, velocity measurement method, and

momentum method.

Methods of finding Cc - Micrometer contraction gage, ratio of Cd to Cv.

47. Explain the jet distance measurement method of finding Cv.

Ans: The coordinates (x, y) of the discharging jet with respect to the vena contracta are measured

and used to find the Cv with the help of principles of projectiles.

Cv, = 𝑥

2√𝐻𝑦

Where, H is the constant head over the orifice.

48. Explain the velocity measurement method of finding Cv.

Ans: The actual velocity of the jet at vena contracta is measured using the pitot tube. The theoretical

velocity is computed from the measured head (√2𝑔𝐻). Then Cv = Vact/Vth.

49. Explain the momentum method of finding Cv.

Ans: In this method, the actual velocity of jet at vena contracta is determined using the impulse-

momentum equation.

50. What is the theoretical value of Cc. for a sharp edged orifice?

Ans: The theoretical value of coefficient of contraction for a sharp edged orifice is

Cc = 𝜋

𝜋 + 2 = 0.611

51 What is the general value of coefficient of contraction used?

Ans: 0.64 to 0.65 is the value of coefficient of contraction used for an orifice(the range 0.61-0.69)

52. Explain the significance of micrometer contraction gauge when determining the coefficient

of contraction of an orifice.

83

Ans: The micrometer contraction gauge measures the diameter of the jet at vena contracta along two

perpendicular directions. The average of the two values gives the jet diameter at vena contracta.

Hence, the coefficient of contraction can be computed by the ratio of jet area at vena contracta to the

orifice area.

53. How do you determine the Cd of an orifice?

Ans: The actual discharge is measured by volumetric method. The known volume of water is

collected in a measuring tank and dividing it by the time required, the actual discharge is obtained.

The theoretical discharge is calculated by a√2𝑔𝐻 (where,a is the area of the orifice).

Therefore, Cd = Qact/Qth.

54. Differentiate between a large and small orifice.

Ans: An orifice is called small if d < H/5 and large if d >H/5, where, d is the size of the orifice and

H is the head over the orifice.

55. What is the value of Cd that can be assumed when the width of the rectangular or the

diameter of the circular orifice is about 0.3 m or more?

Ans: As an approximation, Cd = 0.6 is used.

56. Define the coefficient of resistance.

Ans: The coefficient of resistance is the ratio of the loss of kinetic energy as the liquid flows

through the orifice to the actual kinetic energy possessed by the flowing fluid. It is given by

Cr = (1

𝐶𝑣2− 1)

57. State the impulse-momentum equation.

Ans: The impulse of the resultant force is equal to the change in momentum of the body. It is given

by ΣF = ρQ(V2 - V1), where ΣF is the sum of the forces, ρ the mass density of fluid, Q the discharge,

V2 the final velocity of flow and V1 the initial velocity of flow.

58. Define the impulse and momentum.

Ans: Impulse is defined as the product of force and time. Momentum is the product of mass and

velocity.

VIVA QUESTIONS

1. What is meant by a Roto-dynamic machine?

2. What is meant by priming of a pump?

3. What energy is converted in a pump?

4. What types of fluids are pumped by centrifugal pumps?

5. What are the pumping characteristics of a centrifugal pump?

6. What is meant by efficiency of a pump?

7. On what principle the Pelton wheel turbine works?

8. What is the shape of buckets in Pelton wheel turbine?

9. What is the clearance angle of the buckets? State why it is not 1800?

10. Define unit quantities and specific speed.

11. Why multiple jets are used in Pelton wheel turbine?

12. What is the main aim of the experiment?

13. What is meant by a positive displacement pump?

14. What types of fluids are pumped by Reciprocating pumps?

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15. What are the pumping characteristics of a Reciprocating pump?

16. What is the normal efficiency of a Reciprocating pump?

17. What are the normal precautions to be taken when operating a pump?

18. What is the function of air vessel?

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COURSE : ENGINEERING GEOLOGY LABORATORY

SEMESTER – IV

Subject Code 15CVL48 IA Marks 20


Total Number of Lecture Hours 42 Exam Hours 3

CREDITS – 02

Course objectives: This course will enable students

1. To identify the minerals and rocks based on their inherent properties and uses in civil

engineering

2. To interpret the geological maps related to civil engineering projects.

3. To learn the dip and strike, borehole problems, thickness of geological formation related to

foundation, tunnels, reservoirs and mining.

4. To understand subsurface geological conditions through a geophysical techniques and

watershed management.

5. To visit the civil engineering projects like dams, reservoirs, tunnels, quarry sites etc.

Modules Teaching

Hours

Revised Bloom’s

Taxonomy (RBT) Level

1. Identification of minerals as mentioned in

theory,their properties, uses and manufacturing

ofconstruction materials.

6 L1 L2

2. Identification of rocks as mentioned in theory,

theirengineering properties and uses in

construction anddecorative purposes

6 L2, L3

3. Dip and Strike problems: Determination of dip

andstrike direction in Civil Engineering projects

(Railway lines, tunnels, dams, reservoirs) –

graphical or any other method.

6 L4

4. Bore hole problems: Determination of

subsurface behavior of rocks, their attitude

related to foundation, tunnels, reservoirs and

mining. Triangular and Square land, assuming

ground is horizontal.

6 L3, L4, L5

5. Calculation of Vertical, True thickness and

width of the outcrops 6 , L4, L5

6. Interpretation of Electrical resistivity curves to

find out subsurface information such as thickness

of soil ,weathered zone, depth of hard rock and

saturated zone

4 L3, L4

7. Interpretation of Toposheets and geological

maps related to Civil Engineering projects 8

L5, L6

Course outcomes:

During this course, students will develop expertise in;

1. Identifying the minerals and rocks and utilize them effectively in civil engineering practices.

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2. Understanding and interpreting the geological conditions of the area for the implementation of civil

engineering projects.

3. Interpreting subsurface information such as thickness of soil, weathered zone, depth of

hard rock and saturated zone by using geophysical methods.

4. The techniques of drawing the curves of electrical resistivity data and its interpretation for

geotechnical and aquifer boundaries



o Problem Analysis.


o Interpretation of data.

Question paper pattern:

All are individual experiments

Instructions as printed on the cover page of answer script for split up of marks to be strictly

followed.

All exercises are to be included for practical examination.

Reference Books:

1. M P Billings, Structural Geology , CBS Publishers and Distributors, New Delhi

2. B.S.Satyanarayana Swamy , Engineering Geology Laboratory Manual , Dhanpat Rai Sons,

New Delhi.

3. L R A Narayan, Remote sensing and its applications, University Press.

4. P.K.MUKERJEE, Text book of Geology , World Press Pvt. Ltd., Kolkatta

5. John I Platt and John Challinor, Simple Geological Structures, Thomas Murthy & Co, London

Question Paper Pattern

Qn.

No. EXPERIMENT MARKS MARKS (80 )

1 Identification of Minerals by giving their physical properties and civil

engineering applications (5minerals) 20 (5 x 4)

2 Identification of rocks by giving their physical properties, classification

and their civil engineering applications (5 rocks) 20 (5 x 4)

3 Dip and strike problems 6

4 Bore hole problems (3 point method) 10

5 Thickness of strata problems including calculation of vertical, true

thickness and its width of outcrop. 4

6 Electrical resistivity curves drawing and its

interpretation for Geotechnical and Aquifer investigations 6

7 Interpretation of Toposheets 5

8 Geological maps, their cross sections and

description 10

9 Viva voce 5

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LESSON PLAN

WEEK EXperiment Name of the Experiment PO,

Attained

CO,

Attained

I 1

Mineral properties, composition and uses, Use in the

manufacture of construction materials Quartz Group

(Glass);

1,2,,5,9,10

1,2,3,4,6,7

II 2

Feldspar Group (Ceramic wares and Flooring tiles);

Kaolin (Paper, paint and textile);Asbestos (ACsheets);

Carbonate Group ( Cement);Gypsum (POP, gypsum

sheets, cement); Mica group(Electrical industries); Ore

minerals - Iron ores(Steel); Chromite (Alloy);

Bauxite(aluminum); Chalcopyrite

III 3

Identification of rocks based on their Geological

properties Igneous rocks : Granite, Gabbro,Dolerite, ,

Basalt

IV 4 Sedimentary Roaks :Sandstone,Lime stone,Shale,

Laterite Metamorphic Rocks

V 5 . Dip and Strike problems: Determination of dip and

strike direction in Civil Engineering projects

VI 6 (Railwaylines, tunnels, dams, reservoirs) –graphical or

anyother method

VII 7 Bore hole problems: Determination of subsurface

behavior of rocks, their attitude related to foundation,

VIII 8 tunnels, reservoirs and mining. Triangular and Square

land land, assuming ground is horizontal

IX 9 Calculation of Vertical, True thickness and width of the

outcrops

X 10 Calculation of Vertical, True thickness and width of the

outcrops

XI 11

Interpretation of Electrical resistivity curves to find out

subsurface information such as thickness of

soil,weathered zone, depth of hard rock and saturated

zone

XII 12 Interpretation of Toposheets and geological maps

related to Civil Engineering projects.

XIII 13 Interpretation of Toposheets and geological maps

related to Civil Engineering projects.

Portion for I.A. Test Experiment

I I.A. Test Experiment 1 to 13

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QUESTIONS (Viva)

1. What is a Mineral ?

2. Name or list the index properties that are helpful in the identification f minerals ?

3. What are rock forming minerals and economic minerals ?

4. What do you mean by the term habit as applied to minerals ? Give a few examples.

5. How do you distinguish crystalline and amorphous minerals ?

6. Define (1) Luster (2) Fracture (3) Cleavage. Name any three important types in

each with mineral examples.

7. What is the difference between cleavages and fracture ?

8. What is conchoidal fracture. Give example ?

9. In what types of minerals cleavages are possible ? Explain why. Which mineral is an exception ?

10. In what types of minerals cleavages are absent and why ?

11. Explain rhombohedral cleavages, prismatic cleavage, basal cleavage. Give example.

12. What is Hardness of minerals ?

13. Name Mohs’ standard hardness points (minerals).

14. Name the tools required to determine hardness of minerals.

15. How do you determine hardness of minerals.

16. What is streak, state its importance? Give examples.

17. How do you determine streak ?

18. What for a pen knife is used in testing a mineral ?

19. How do you estimate specific gravity of minerals ?

20. What do you mean by low Sp.Gr. and high Sp. Gr. ?

21. Name special properties of minerals ?

22. Explain paramagnetism. Give example.

23. What is acid test ? For what type of minerals it is applied ?

24. Explain how you would conduct an acid test.

25. Define taste, odour and feel of minerals. Give examples.

26. How would you identify or distinguish.

a) Quartz and calcite l) Chromite and hematite

b) Gypsum and calcite m) Talk and gypsum

c) Opal and magnesite n) Olivine and serpentine

d) Orthoclase and plagioclase o) Amphiboleasbestosandchrysotle asbestos

e) Calcite and plagioclage p) Iron pyrites and gold

f) Biotite and chlorite q) Agate and jasper

g) Biotite and vermiculite r) Calcite and selenite

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h) Muscovite and selenite s) Pyrolusite and limonite

i) Hornblende and augite t) Hornblende and tourmaline

j) Magnetite and hematite u) Pyrites and cbalcopyrite

k) Magnetite and chromite

27. Give chemical composition of

a) Quartz h) Galena o) Talc

b) Calcite i) Bauxite p) Beryl

c) Gypsum j) Pyrolusite q) Biotite mica

d) Pyrite k) Orthoclase r) Vermiculite

e) Magnetite l) Olivine s) Tourmaline

f) Hematite m) Hornblende t) Magnesite

g) Chromite n) Augite u) Chalcopyrite

28. Name the important minerals with their chemical composition required for as in

i) a) Ore of iron

b) Ore of manganese

c) Ore of aluminium

d) Ore of lead

e) Ore of chromium

f )Ore of copper

ii) Regractory

iii) Abrasive

iv) Dye stuffs

v) Fillers

vi) Insecticide

vii Cement and plaster

viii) Insulator (heat and sound)

ix) Electronics

29. What is a rock ?

30 Name the three major groups of rocks. Give examples.

31 List the index properties of rocks that help their identification.

32 Name the important textures of igneous rocks. Give examples.

33 What are volcanic rocks and how do they differ from plutonic and hypabyssal

igneous rocks.

34 What are plutonic igneous rocks ? Give examples.

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35 What are hypabyssal igneous rocks ? Give examples.

36 What do you mean by mineral composition of rocks.

37 What are essential minerals ? Name them.

38. What are mechanically formed sedimentary rocks ?

39. What is cementation ? Give two examples of cemented rocks.

40. What are fossils ?

41. Name two organically formed (biochemical) sedimentary rocks.

42. What is lamination ? In which rock you notice this and why ?

43. What are ripple marks and sun crack polygons ?

44. Which sedimentary rocks answer acid test and why ?

45. What is a conglomerate ?

46 What is laterite ? What are its special characters ?

47 What is metamorphism ? Explain thermal metamorphism. Why it is also called contact

metamorphism ?

48 Name the metamorphic agents.

49. List the textures of sedimentary and metamorphic rocks.

50 What is augen gneiss ?

51 What are rocks cleavages ? How are they utilized ?

52 What is a porphyry ?

53. How do you distinguish

a) Granite and syenite b) Granite and gneiss

c) Quartzite and marble d) Gneiss and schist

e) Gabbro and dolerite f) Conglomerate and breccia

g) Compact basalt and slate h) Syenite porphyry and diorite porphyry

i) Pegmatite and granite porphyry j) Sandstone and quartzite

k) Limestone and marble l) Slate and schist

m) Shale and slate n) Granite and diorite

o) Rhyolite and sandstone p) Dlerite and basalt

54 Name the important rocks suitable as/for

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i) Building stones ii) Ornamental stones

iii) Chip carpeting (paving stones) iv) Concrete aggregate

v) Road metal vi) Railway ballast

vii) Flooring and roofing viii) Monumental/memorial stone

ix) Plastic goods x) Sculpturing

xi) Fertilizer

vachana pitamaha dr. p.g. halakatti college of engineering & technology, vijaypur...

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