SEMESTER: THIRD

3CE01 MATHEMATICS-III

**UNIT-I :**Ordinary Differential Equations. Complete solution, Operator D, rules for finding the complementary function, the inverse operator , Rules for finding particular integral. Method of variation of parameters, Cauchy's and Legendre's Linear Differential equations. Simultaneous linear differential equations with constant coefficients Applications to civil engineering.

**UNIT-II** Laplace transforms : Definition and elementary properties, Inverse L.T. by various methods, Convolution theorem, Solution of ordinary and simultaneous differential equation using Laplace transform of periodic functions. Application to problems of beams.

**UNIT-III**

aPartial Differential Equations. P.D.E. of first order and first degree of types i) f(p,q) = O ii) f(p,q,z)=0, iii) f(p,q,x,y)=O iv) f(p,q,x,y,z)=O i.e. (a) Lagrange's form Pp + Qq = R (b) Claivant's form z=px+qy+f(p,q) v) Equations reducible to above standard types linear Homogeneous P.D.E. of nth order with constant co-efficient.

**UNIT-IV** Numerical Methods :- (a) i) Solution of Algebraic and transcended Equations by Newton Raphson method and by method of False Position. ii) Solution of system of linear equations by Grout's method, Gauss Seidal method and Relaxation Method. (b) Numerical solution of differential equations by Picard's method, Taylor's series method, Euler's method, modified Euler's method and Rungekutta forth order method.

**UNIT-V**Complex variable : Analytic functions, C.R.conditions, Harmonic functions. harmonic conjugate functions, Milne's method, conformal mapping, Elementary conformal mapping w=z+c, w=cz, w+ Bilinear transformation.

**UNIT-VI** Statistics : Probability : Axioms, conditional probability, Bay’s theorem, Mathematical Expectation and probability distributions (Binomial, Poisson and Normal) Curve fitting by method of least square only for line and parabola, Correlation regression.

1) Text book on Applied Engineering Mathematics,Vol. II,J.N. Wartikar and P.N.Wartikar,Pune Vidyarthi Griha Prakashan,Pune.

2) Advance Mathematics for Engineers by Chandrika Prasad.

3) Method of Applied mathematics by F.B.Hildebran.

4.Introductory methods of Numerical Analysis by S.S.Sasby.

5. Computer Oriented Numerical Method by Raja Raman.

**Unit-I **

1. Mechanical properties : Concept of direct, bearing and shear stresses and strains, stress-strain relations, Biaxial and triaxle loading, elastic constants and their relationship, stress-strain diagrams and their characteristics for mild steel, tor steel and concrete, Generalized Hook’s law, factor of safety. 2. Uniaxial stresses and strains: Stresses and strains in compound bars in uniaxial tension and compression, temperature stresses in simple restrained bars and compound bars of two metals only.

**Unit-II**

1. Axial force, shear force & bending moment diagrams: Beams, loading and support conditions, bending moment, shear force and axial load diagrams for all types of loadings for simply supported beams, cantilevers and beams with overhangs, relation between shear forces, bending moment and loading intensity.**Unit-III **

1. Stresses in beams (Bending, Shear), i) Bending: Theory of simple bending, section modulus, moment of resistance, bending stresses in solid, hollow and built up section. ii) Shear : Distribution of shear stresses on beam cross sections, iii) Strain energy under uniaxial tension and compression, impact loads and instantaneous stresses.

**Unit-IV**

1.Torsion: Theory of torsion & assumptions, derivation of torsion equation, polar modulus, stresses in solid & hollow circular shaft, power transmitted by shaft, closed coiled helical spring with axial load. 2. Thin cylinders subjected to internal pressures.

**Unit –V **

1. 1. Principal stresses : Biaxial stress system, principal stresses, principal planes, Mohr's circle of stresses, principal strains. 2. Combined direct & bending stresses : Combined direct and bending stresses, applications to short columns with eccentric loads, retaining walls with horizontal lateral force.

**Unit-VI**

1. Slope & deflection of beams: Slope & deflection in statically determinate beams subjected to point loads, uniformly distributed loads, moments by a) Macaulay’s method b) Moment Area method c) Conjugate Beam method. 2. Theory of long columns, Euler, Rankine formula.

**Reference Books:**

1) E.P.Popov : Mechanics of Materials, Prentice Hall of India, New Delhi.

2) S. Timoshenko and O.H.Young: Elements of Strength of Materials, East West Press.

3) Shames, I. H. : Introduction to Solid Mechanics, Prentice Hall of India, New Delhi, 1990.

4) Beer and Johston : Mechanics of Materials, McGraw Hill.

5) Natarajan, Mahadeoappa, Strength of materials

**SECTION-A**

**UNIT-I :** 1) Introduction to the study of fluid motion. Mechanical properties of fluids and their influence on flow characteristics. 2) Fluid Statics:- Fluid pressure, pressure variation in fluids, manometers, forces on plane and curved surface buoyancy. (12 Hrs)

**UNIT-II:** Buoyancy, stability of floating bodies. Kinematics and dynamics of fluid flow: - Types of flows, Stream lines, potential lines, flow net, continuity equation. One and two dimensional motion, one dimensional method of flow analysis. Bernoulli’s equation. Venturimeter, Momentum equation for steady flow. Vortex motion. (8 Hrs)

**UNIT-III:** Dimensional analysis: Dimensional homogeneity and dimension less ratios. Dimensionless parameters. Similitude and model studies. (6 Hrs)

**SECTION-B**

**UNIT-IV: **Motion of viscous fluids:-Introduction to laminar and Turbulent flows. Boundary layer concept. Separation. Drag lift on immersed bodies. Reynolds number and its significance. (7 Hrs)

**UNIT V: **Darcy weisbach equation i.e. Equation of pipe flow, friction charts and its use, Minor losses in pipes and fittings, losses due to sudden enlargement and contraction, Hydraulic and energy gradient lines, pipes in series and parallel. Elementary concept of water hammer. (8 Hrs)

**UNIT VI: **1. Principles of fluid machinery: Dynamic action of fluid force exerted by fluid jet on plane, curved, stationary and moving vanes. Velocity diagrams, Work done by impact, pressure due to deviated flow. 2. General Theory of Hydrodynamic

**Machines:-** Euler’s equation, Degree of reaction, classification of machines according to degree of reaction. Efficiencies: Volumetric efficiency, Hydraulic efficiency, mechanical efficiency and overall efficiency. (7 Hrs)

**Text Book:**

1) CSP Ojha, R. Berndtsson, Fluid Mechanics and Machinery; Oxford University.

2) Bansal R.K., Fluid Mechanics and Fluid Machines; Laxmi publications.

1) R.K.Rajput; Engineering Fluid Mechanics; S. Chand publications.

2) Dr. Mody & Seth; Hydraulics and Fluid Mechanics; Standard book house

3) S. Ramamrutham, Hydraulic, Fluid Mechanics & Fluid Machines.

3ME04 ENGINEERING THERMODYNAMICS

**Unit-I** Introduction to basic concepts of thermodynamics, Macroscopic and microscopic approaches, properties of system, state and equilibrium, processes and cycle. Temperatures and Zeroth law of thermodynamics, Quasistatic process, Forms of energy and its conversion. Gas Laws and Ideal gas equation of states, difference between gases and vapours, equation of state, gas constant and universal gas constant. (08 hrs)

** Unit-II** Work and Heat: Definition of work, thermodynamic work, displacement work and other forms of work, Definition of Heat, Work and heat transfer as path function, comparison of work and heat, work done during various processes, P-V diagrams. First law of thermodynamics: Energy of a system, classification of energy, law of conservation of energy law applied to closed system undergoing a cycle, Joules experiment. Energy a property of system, internal energy-a function of temperature, Enthalpy, specific heat at constant volume and constant pressure. Change in internal energy and Heat transfer during various non-flow processes. (10 hrs)

**Unit-III** First Law applied to flow processes: Steady state, steady flow process, mass balance and energy balance in steady flow process, steady flow energy equation and its application to nozzles and diffusers, turbine and compressor pumps, heat exchangers, Throttle valve etc. work done and Heat transfer during steady flow processes. (9Hrs)

**Unit-IV **Second Law of thermodynamics: Limitations of Ist law, Thermal energy reservoir, heat engines refrigerator and heat pumps. Kelvin-Plank and Clausious statements, their equivalence, reversible and irreversible processes, Carnot cycle, two propositions regarding the efficiency of Carnot cycles. The thermodynamic temperature scale. Reverse Carnot cycle. COP of heat pump and refrigeration. Inequality of Clausius. (7 Hrs)

**Unit-V **Entropy: Entropy-a property of system, entropy change for ideal gases, entropy change of a system during irreversible process, lost work. Principle of increase of entropy. Availability and irreversibility:- Available energy referred to cycle, decrease in available energy with heat transfer through a finite temperature differences. The Helmholtz and Gibbs functions, Availability, Irreversibility and effectiveness. (8 Hrs)

**UnitVI**

a) Air Standard Cycles: Otto, diesel, semidiesel, sterling and joule cycles etc., their efficiencies and mean effective pressure.

b) Vapour Cycles:- Rankine and Modified Rankine Cycle. Comparison of Rankine and Carnot cycle, representation on P-V, T-S and H-S diagram. (No numerical on this unit) (8 Hrs)

**Text Book:**

1) Engineering Thermodynamic - by P.K.Nag.

2) Thermodynamics Volume: I & II; R. Yadav;

**Reference Books:**

1. Basic Engineering Thermodynamics - by Reyner Joel

2. Thermodynamics - by C.P. Arora.

3. Fundamentals of Classical Thermodynamics - by G.J.Vanwylen.

4. Engineering Thermodynamics; P. Chattopadhyay; Oxford

5. Engineering Thermodynamics; Gordon Rogers, Yon Mayhew; Pearson

**Objectives**

**SECTION-A**

**Unit-I :** Introduction to manufacturing processes & classification; Introduction to pattern making- Pattern materials, pattern making tools, allowances, Types of patterns, functions of patterns, General properties of moulding sands, Mold hardness. Preparation of sand moulds of different types, Moulding processes, core making, core prints, core boxes. Sand casting Processes - Basic principle and Terminology of sand casting, gating system, types of gate, risers, etc. (9Hrs)

**Unit-II: **Technology of melting and casting - Melting furnaces, crucibles, pit, open hearth, gas fired cupola, cupola operation and electric hearth furnaces, Electric furnaces - Direct Arc, Indirect arc and electric induction furnace. Defects in castings and its types, Causes and remedies of casting defects. Origin and classification of defects, shaping faults, Inclusion and sand defects, Gas defects, shrinkage defects, contraction defects, dimensional errors. Inspection and testing of castings:- Radiography, ultrasonic, Eddy current testing, fluorescent penetrate test. (7 Hrs)

**Unit III: **Casting processes and their principle of operation and applications permanent mold casting, slush casting, shell molding, Investment or lost wax casting, vacuum process, centrifugal casting, continuous casting, Die casting equipment and processes for Gravity, pressure and vacuum casting methods, cleaning of castings, Modernisation & Mechanisation of Foundries. (8 Hrs)

**SECTION-B**

**Unit IV : **Mechanical working of metals: Principle of hot and cold working process and its types, Extrusion, piercing, pipe and tube production, manufacture of seamless pipe and tubing. Shearing operations, tube drawing, wire drawing, spinning, embossing and coining, squeezing and bending operations, rotary swaging, rolling, types of rolling mills, forging operations, upset forging. (8 Hrs)

**Unit V: **Joining processes:- Mechanical joining processes, Mechanical fastening, riveting, soldering, brazing Welding, Types of welding processes-Arc welding: principle and working, Gas welding- principle and working Types and purpose of Electrodes, Electrode coatings(flux). TIG & MIG Processes – Working principles and its applications, shielding gases, MIG-Spray transfer and dip transfer processes. (6 Hrs.)

**Unit VI:** Submerged arc welding & resistance welding: - Heat generation in resistance welding, operational characteristics of resistance welding processes such as spot welding, projection welding, and butt welding. Principle of operation of friction welding, forge welding, plasma arc, Thermit welding. Welding defects, Testing and Inspection of welds, Ultrasonic, Electroslag, Electron Beam, laser welding, weldability. Surface Treatment-Electroplating, electroforming, and iodising, metal spraying, shot peening, polishing, mechanical cleaning. (9 Hrs)

**Text-Book:**

1) Workshop Technology Vol. I by Bawa, Tata McGraw Hill Publication.

2) Workshop Technology Vol I by Hajra Chaudhary, Dhanpat Rai & Sons 2001

**References:**

1) Workshop Technology Vol I by Raghuwanshi.

2) Manufacturing Processes by J.P. Kaushish; PHI

3) Processes and Materials of Manufacture by R.A.Lindberg, PHI Pub 2001.

4) Foundry Technology by Goel Sinha.

**Practicals:**

Minimum Six to Eight out of following:

1) Tension test on metals.

2) Compression test on materials.

3) Shear test on metals.

4) Impact test on metals.

5) Hardness test on metals.

6) Torsion test on metals.

7) Deflection of beams.

8) Modulus of rupture test.

9) Deflection of springs.

Practical examination shall be viva-voce based on above practical and the syllabus of the course.

**3ME07 FLUID POWER-I-LAB.**

**Practical Term Work:**

At least six practical’s (study/Trials) based on above syllabus, as given below shall be performed and a report there of submitted by the students.

1) Study of Manometers.

2) Measurement of fluid pressure by manometer.

3) Determination of metacentric height.

4) Verification of Bernoulli’s equation.

5) Flow measurement by Venturimeter.

6) Study of Venturimeter.

7) Determination of Reynolds number.

8) Velocity distribution in Boundary layer & thickness of B.L.

9) Determination of co-efficient of friction for pipes.

10) Determination of head loss due to sudden enlargement.

11) Determination of head loss due to sudden contraction.

12) Determination of losses in bends.

13) Determination of losses in elbows.

14) Study of flow through pipes in series & parallel.

15) Verification of momentum equation.

**Note: -** Practical examination shall consist of oral or Experimentation based on above term work.

**3ME08 MANUFACTURING PROCESSES-I –LAB.**

**Practice:**

1) Study of safety precautions in workshop practices.

2) Foundry: - Any two of the following jobs Sand preparation and practice in moulding of various types of patterns:

Pattern making 1 job, Moulding 1 job Casting 1 job.

3) Joining Processes:- 2 composite jobs involving electric welding, gas welding and resistance welding process.

A journal should be prepared and submitted on above term work. The practical examination shall consist of a job preparation and college assessment should be based upon the jobs, term work and viva examination.

CIVIL ENGINEERING

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