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Continuum hypothesis, Newton‘s law of viscosity, some cartesian tensor notations. Stress
Analysis: Stress at a point, Stress in a fluid at rest, Stress in a fluid in motion, Relation between
stress and rate of strain components (Stokes‘ Law of Friction), Thermal conductivity, Generalized
law of heat conduction. Fundamental Equations of the flow of viscous fluids: Introduction,
Equation of State, Equation of continuity, Equations of motion (Navier-Stokes Equations),
Equation of energy, Vorticity and Circulation (Kelvin‘s Circulation Theorem).
UNIT-III (15 Hours)

Dynamical similarity (Reynolds law), Inspection analysis, Dimensional analysis, Buckingham π
theorem and its application, π product and coefficients, non-dimensional parameter and their
physical importance. Exact solution of the N-S Equations, Steady motion between the parallel
plates (a) velocity distribution, (b) Temperature distribution, Plane couette flow, Plane Poiseuille
flow, Generalized plane Couette flow. Flow in a circular pipe (Hagen-Poiseuille flow) (a)
Velocity distribution, (b) temperature distribution. Theory of very slow motion: Flow past a
sphere (Stokes‘ and Oseen‘ flow.

*TUTORIAL (15 Hours (1 Hour per week))

SUGGESTED READINGS:

1. J.L. Bansal, Viscous fluid dynamics, Oxford and IBH Publishing Company Pvt. Ltd.,
(1977).
2. F. Chorlton, Text book of fluid dynamics, CBS Publishers and distribution. (2000).
3. G.K. Batchelor, An introduction to fluid dynamics, Cambridge University press, (1970).
4. C.S. Yih, Fluid Mechanics, McGraw-Hill Book Company. 3. S.W. Yuan, Foundation of
Fluid Mechanics, PHI Pvt Ltd. New Delhi (1969).

Math.416 Mathematical Python 3+1

LEARNING OBJECTIVES:

TheObjectives of this course are as follows:

 To be able to model and solve mathematical problems using Python Programs.
 To experience utility of open-source resources for numerical and symbolic
28. mathematical software systems

LEARNING OUTCOMES:

This course will enable the students to use Python:
 For numerical and symbolic computation in mathematical problems from calculus,
algebra, and geometry.
 To tabulate and plot diverse graphs of functions and understand tracing of shapes,
geometries, and fractals.
 To prepare smart documents with LaTeX interface.

THEORY (45 Hours)

UNIT – I: Drawing Shapes, Graphing and Visualization (15 Hours)

Drawing diverse shapes using code and Turtle; Using matplotlib and NumPy for data
organization, Structuring and plotting lines, bars, markers, contours and fields, managing, subplots
and axes; Pyplot and subplots, Animations of decay, Bayes update, Random walk.
UNIT – II: Numerical and Symbolic Solutions of Mathematical Problems (18 Hours)

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