# (Syllabus) GATE 2011 : Examination Syllabus : (Mechanical Engineering)

**GATE 2011 : Examination Syllabus**

## :: ME-Mechanical Engineering ::

**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.

**APPLIED MECHANICS AND DESIGN**

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 over flat 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. irreversibility and availability; behaviour
of ideal and real gases, properties of pure substances, calculation of work and
heat in ideal processes; analysis of 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; moist air: 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, stressstrain diagrams for engineering materials.

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 of design 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, simple queuing models, PERT and
CPM.