GATE
2013
Mechanical
Engineering –ME
ENGINEERING
MATHEMATICS
Linear
Algebra:
Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Functions of single
variable, Limit, continuity and differentiability, Mean value theorems,
Evaluation of definite and improper integrals, Partial derivatives, Total derivative,
Maxima and minima, Gradient, Divergence and Curl, Vector identities,
Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and
Green’s theorems.
Differential
equations:
First order equations (linear and nonlinear), Higher order linear differential
equations with constant coefficients, Cauchy’s and Euler’s equations, Initial
and boundary value problems, Laplace transforms, Solutions of one dimensional
heat and wave equations and Laplace equation.
Complex
variables:
Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series.
Probability
and Statistics:
Definitions of probability and sampling theorems,Conditional probability, Mean,
median, mode and standard deviation, Random variables, Poisson, Normal and
Binomial distributions.
Numerical
Methods:
Numerical solutions of linear and non-linear algebraic equations Integration by
trapezoidal and Simpson’s rule, single and multi-step methods for differential
equations.
Engineering
Mechanics: Free
body diagrams and equilibrium; trusses and frames; virtual work; kinematics and
dynamics of particles and of rigid bodies in plane motion, including impulse
and momentum (linear and angular) and energy formulations; impact.
Strength
of Materials: Stress
and strain, stress-strain relationship and elastic constants, Mohr’s circle for
plane stress and plane strain, thin cylinders; shear force and bending moment
diagrams; bending and shear stresses; deflection of beams; torsion of circular
shafts;
Euler’s theory of columns;
strain energy methods; thermal stresses.
Theory
of Machines: Displacement,
velocity and acceleration analysis of plane mechanisms; dynamic analysis of
slider-crank mechanism; gear trains; flywheels.
Vibrations:
Free
and forced vibration of single degree of freedom systems; effect of damping;
vibration isolation; resonance, critical speeds of shafts.
Design:
Design
for static and dynamic loading; failure theories; fatigue strength and the S-N
diagram; principles of the design of machine elements
such as bolted, riveted and welded joints, shafts, spur gears, rolling and
sliding contact bearings, brakes and clutches.
FLUID
MECHANICS AND THERMAL SCIENCES
Fluid
Mechanics: Fluid
properties; fluid statics, manometry, buoyancy; control-volume analysis of
mass, momentum and energy; fluid acceleration; differential equations of
continuity and momentum; Bernoulli’s equation; viscous flow of incompressible
fluids; boundary layer; elementary turbulent flow; flow through pipes, head
losses in pipes, bends etc.
Heat-Transfer:
Modes
of heat transfer; one dimensional heat conduction, resistance concept,
electrical analogy, unsteady heat conduction, fins; dimensionless parameters in
free and forced convective heat transfer, various correlations for heat transfer
in flow overflat plates and through pipes; thermal boundary layer; effect of
turbulence; radiative heat transfer, black and grey surfaces, shape
factors,network analysis; heat exchanger performance, LMTD and NTU methods.
Thermodynamics:
Zeroth,
First and Second laws of thermodynamics; thermodynamic system and processes;
Carnot cycle. Irreversibilityand availability; behaviour of ideal and real
gases, properties of pure substances, calculation of work and heat in ideal
processes; analysisof thermodynamic cycles related to energy conversion.
Applications:
Power Engineering: Steam Tables, Rankine,
Brayton cycles with regeneration and reheat. I.C.
Engines:
air-standard Otto,Diesel cycles. Refrigeration
and air-conditioning: Vapour refrigeration cycle, heat pumps, gas
refrigeration, Reverse Brayton cycle; moistair: psychrometric chart, basic
psychrometric processes. Turbomachinery:
Pelton-wheel,
Francis and Kaplan turbines — impulse and
reaction principles, velocity
diagrams.
MANUFACTURING
AND INDUSTRIAL ENGINEERING
Engineering
Materials:
Structure and properties of engineering materials, heat treatment,
stress-strain diagrams for engineeringmaterials.
Metal
Casting: Design
of patterns, moulds and cores; solidification and cooling; riser and gating
design, design considerations.
Forming:
Plastic
deformation and yield criteria; fundamentals of hot and cold working processes;
load estimation for bulk (forging,rolling, extrusion, drawing) and sheet
(shearing, deep drawing, bending) metal forming processes; principles of powder
metallurgy.
Joining:
Physics
of welding, brazing and soldering; adhesive bonding; design considerations in
welding.
Machining
and Machine Tool Operations: Mechanics of machining, single and multi-point cutting
tools, tool geometry and materials,tool life and wear; economics of machining;
principles of non-traditional machining processes; principles of work holding,
principles ofdesign of jigs and fixtures
Metrology
and Inspection: Limits,
fits and tolerances; linear and angular measurements; comparators; gauge
design; interferometry;
form and finish measurement;
alignment and testing methods; tolerance analysis in manufacturing and
assembly.
Computer
Integrated Manufacturing: Basic concepts of CAD/CAM and their integration tools.
Production
Planning and Control: Forecasting models, aggregate production planning,
scheduling, materials requirement planning.
Inventory
Control: Deterministic
and probabilistic models; safety stock inventory control systems.
Operations
Research: Linear
programming, simplex and duplex method, transportation, assignment, network
flow models, simplequeuing models, PERT and CPM.
