Applied Mathematics III-
1 Laplace transform:
1.1 Introduction, Definition of Laplace transform, Laplace
transform of constant, trigonometrical, exponential functions.
1.2 Important properties of Laplace transform: First shifting
theorem, Laplace transform of L{ f (at) }, L{ t f (t) n }, L{
t
f (t)
}, L{ n
n
dt
d f (t)
}, L{
t
f u du
0
( ) }, without proof.
1.3 Unit step function, Heavi side function, Second shifting
theorem, Dirac-delta function, Periodic function and their
Laplace transforms without proof.
1.4 Inverse Laplace transform with Partial fraction and
Convolution theorem. (without proof)
1.5 Application to solve initial and boundary value problem
involving ordinary differential equations with one dependent
variable and constant coefficients.
2 Matrices:
2.1 Eigen values and eigen spaces of 2x2 and 3x3 matrices;
existence of a basis and finding the dimension of the eigen space
(no proofs); diagonalisable matrices.
2.2 Cayley - Hamilton theorem. (without proof)
2.3 Quadratic forms; orthogonal and congruent reduction of a
quadratic form in 2 or 3 variables; rank, index, signature;
definite and indefinite forms
3 Probability:
3.1 Random Variables:- discrete & continuous random variables,
expectation, Variance, Probability Density Function &
Cumulative Density Function.
3.2 Moments, Moment Generating Function.
3.3 Probability distribution: binomial distribution, Poisson &
normal distribution
4 Sampling Theory:
4.1 Test of Hypothesis, Level of significance, Critical region,
One Tailed and two Tailed test, Test of significant for Large
Samples:-Means of the samples and test of significant of means
of two large samples.
4.2 Test of significant of small samples:- Students t- distribution
for dependent and independent samples.
4.3 Chi square test:- Test of goodness of fit and independence of
attributes, Contingency table.
Correlation:
4.4 Karl Pearson’s coefficient of correlation, covariance,
Spearman’s Rank correlation.
4.5 Regression Lines.
5 Complex Variable:
5.1 Functions of a complex variable, Analytic functions,
Cauchy-Riemann equations in Cartesian co-ordinates, Polar coordinates.
(without proof)
5.2 Harmonic functions, Analytic method and Milne Thomson
methods to find f(z), Orthogonal trajectories. (without proof)
Mapping
5.3 Conformal Mapping, Linear, Bilinear transformations, Cross
ratio, fixed points and standard transformation such as rotation
and magnification, invertion, translation.
Engineering Chemistry– I
1 Basic Concepts of Chemistry and Molecular Structures-
Hydrogen bonding, Valence bond theory (application for H2
molecule). Molecular orbital theory, Bonding, Non-bonding and
anti-bonding orbitals, LCAO method, VSEPR theory .Structure
of BrF3, SF4, XeF4, and IF7. Molecular orbital diagrams of
homonuclear and hetero nuclear molecules H2, Be2, B2, C2, N2,
O2, F2,HF CO,NO and NO+ types etc, metallic bond
2 Co-ordination chemistry
Definitions- Co-ordination number or ligancy, Ligand, Complex
ion, Co-ordination or dative bond. Nomenclature and isomerism
(Only Geometrical and Structural) in co-ordination compounds
with respect to co-ordination number 4 and 6. Theories of
coordination compounds- Werner’s Co-ordination theory,
Valence bond theory, Crystal field theory (CFT), Ligand field
theory. Effective Atomic Number (EAN), Application of CFT to
tetrahedral and octahedral complexes, drawbacks of CFT.
Measurement of CFSE (10Dq), and Numericals based on EAN
and 10Dq measurement.
3 Organometallic compounds and Bio-inorganic chemistry
Chemistry of Fe-Carbonyls –Fe (CO)5,Fe2(CO)9 w.r.t
preparation, properties, structure and bonding. Biochemistry of
proteins containing Fe and Zn. O2 atom transfer reactions of bio
molecules containing Fe.
4 Reaction Mechanism & Reactive Intermediates
Transition state (T.S.), Intermediate, Difference between T.S. &
intermediate. Equilibrium (Thermodynamically) controlled & rate
(Kinetically) controlled reactions.
Explain w.r.t. Nitration of chlorobenzene, methylation of toluene
by Friedel-Craft’s reaction, sulphonation of naphthalene.
5 Reactive intermediates
Definition, carbocation, carbanion, carbon free radicals and
carbenes – their formation, structure & stability.
Reactive intermediate formation with mechanism and
applications-
Carbocation – Pinacol - Pinacolone reaction.
Carbanion – Michael reaction.
Free radical - Wohl-Ziegler bromaination reaction.
Carbene - Reimer-Tiemann reaction
6 Photochemistry
Introduction, difference between Photochemical and
thermo chemical reaction, laws of Photochemistry i) Grothus
Draper Law ii) Stark Einstein Law. Fluorescence and
phosphorescence. Jablonskii diagram, Quantum yield, reasons
for high quantum yield.
Photochemical reactions of carbonyl compounds-(i) Norrish
type- I cleavage (ii) Norrish type-II cleavage with mechanism
Fluid Flow Operation
1 Introduction and Basic Concepts:
Scope and Applications of fluid flow, Properties of fluids such
as Density, viscosity, surface tension, capillarity effect, vapour
pressure.
Pressure and Fluid Statics:
Fluid Pressure at a Point, Pascal’s Law, Pressure Variation
in a fluid at rest. Hydrostatic Equilibrium.
Measurement of Pressure, Manometers – Peizometers, UTube,
Single Column manometer, U – Tube differential
manometer, Inverted Differential U – tube manometer,
inclined manometer.
2 Fluid Kinematics:
Types of fluid flow namely steady and unsteady, Uniform
and non- uniform, laminar and turbulent, compressible and
incompressible internal and external, one, two dimensional
flow.
Newton’s Law of Viscosity, Rheological behaviour of
fluid, capillary viscometer.
3 Basic Equations of Fluid Flow:
Bernoulli’s equation Euler’s Equation, Modified
Bernoulli’s equation.
Major and Minor losses, Equivalent length, flow through
pipe in series, parallel, pipe network.
Practical Application of Bernoulli’s Equation:
Venturimeter: Horizontal and inclined, Orificemeter, Pitot
tube
Notches and Weirs: Introduction, classification, Derivation
for V – notch, Rectangular notch.
4 Flow through Pipes:
A] Incompressible flow:
Shear stress distribution and velocity distribution. Relationship
between Skin friction and wall shear, friction factor, Darcy-
Weisbach equation. Reynolds experiment and Reynolds no.,
Formation of Boundary.
Laminar Flow:
Shear stress, velocity distribution, Derivation of local velocity,
maximum velocity, average velocity, Kinetic Energy Correction
factor, Hagen – Poiseullie equation.
Turbulent Flow: Velocity distribution equations, Average
velocity, local velocity, maximum velocity, kinetic energy
correction factor (No Numericals on universal velocity). Von
Carmanequation and friction factors, Moody diagram.
Equivalent diameter for circular and non-circular ducts. Pipes in
series and parallel. Frictional Losses in different pipe fittings.
B] Compressible Fluids:
Introduction, Mach no, Sonic, supersonic and subsonic flow,
continuity equation and Bernoulli’s equation, stagnation
properties, Acoustic velocity. Adiabatic Flow. Isothermal Flow.
Isentropic Flow.
5 Flow past immersed bodies:
Drag forces, Coefficient of drag, Terminal settling velocity,
Stoke’s law.
6 Pumps, Valves and Agitators:
Classification and types, Centrifugal pumps – Construction and
working, Power required, Definitions of heads and efficiency,
NPSH, Priming, Cavitations, characteristic curves. Specific
speed, minimum speed.
Reciprocating Pump: Classifications and working.
Power Consumption in Agitation: Power curves, Power No.,
types of impellers.
Introduction to Compressors, Fans and Blowers.
Types of Valves: Globe valves, Gate valves, butterfly valves
and non – Return valves.
Chemical Engineering Thermodynamics I
01
First Law of Thermodynamics for flow and non-flow
processes
Calculation of heat and work for various types of processes
02
Second Law of Thermodynamics
Concepts of heat engine, heat pump and refrigerator
Carnot Cycle and Carnot Principle
Clausius Inequality
Concept of Entropy and estimation of Entropy change of
various processes
Third Law of Thermodynamics
03
Concept of Exergy, Exergy Balance
Steady flow Exergy equation and its application
04
Equations of State for non-ideal gases: Virial equation of
state, van der Waals equation of state, Redlich-Kwong,
Redlich-Kwong-Soave and Peng-Robinson equation of state
05
Maxwell Equation, Joule Thomson effect
Enthalpy and Entropy departure functions (vander Waals and
Redlich Kwong EOS)
Thermodynamic Charts, Diagrams and their applications
Fugacity and fugacity coefficient(vander Waals and Redlich
Kwong EOS)
Process Calculations
1
Introduction. Basic Chemical Calculations .Units And
Dimensions Various systems of units, conversion of units.
Density, specific volume, specific gravity, Concentration &
composition of mixtures and solutions. Ideal Gas law, Dalton’s
law, Amagat,s law, Raoult’s law, Henry’s law
06
2
Material Balance without chemical reactions. General material
balance equation, degree of freedom analysis for individual units,
solving material balance problems for various unit operations
using steady state equation, Material Balance for Unsteady
Processes. Recycle, Bypass and Purge Calculations.
3
Material Balance with chemical reactions. Concept of limiting
and excess reactants, conversion and yield, selectivity and degree
of completion of reaction, material balance problems related to
chemical reactions including recycle, bypass and purge
Calculations.
4
Energy Balance. Heat capacity, sensible heat, latent heat,
calculation of enthalpy changes. General energy balance
equation. Energy balances for process involving chemical
reaction including adiabatic reactions & combustion processes
(Orsat Analysis & Net, Gross Calorific Value determination).
5
Combined Material and Energy balance. Material and Energy
balance for binary distillation, combustion and evaporation.
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