AMAT 42044

>< Type/ Status : Core
>< Title : Fluid Dynamics
>< Pre-requisites : AMAT 11015
>< Co-requisites : PMAT 42044
>< Objectives :
At the end of this course, the student will recognize the difference between discrete mass-points and continuous matter in mechanics and understand the fundamental properties of two-dimensional and Axi-symmetric motion, three dimensional motion of a perfect fluid, and motion of a viscous fluid.
>< Course Content :

Further Vector Analysis: Orthogonal curvilinear coordinates, Gradient, divergence and curl.

Basic Principles of Dynamics: Fluid pressure, Velocity, Acceleration, Stream lines, Equation of continuity, Euler’s equation of motion, Vorticity, Irrotational motion under conservative forces, Bernoulli’s equation, Helmholtz vorticity equation, Vortex lines, Velocity circulation round a closed curve, Cyclic and acyclic motions, Kinetic energy in irrotational motion, Kelvin’s theorem, Uniqueness theorems.

Two Dimensional Motion: Stream function and plotting stream lines, Complex potential, Sources and sinks, Vortices, Doublets and image systems, Milne-Thompson theorem, Flow past a cylinder, Applications of conformal transformations including Schwarz-Christoeffel transformation, Blassius theorem.

Axi-symmetric Motion: Stokes’ stream function (3D).

Three Dimensional Motion : Irrotaional motion, Laplace’s Equation, Spherical Harmonics, Flow of a stream past a fixed sphere, Motion of a sphere in a fluid,Impulsive motion.

Compressible Fluids: Sound waves in gasses.

Viscous fluids: Naviers -Stokes theorem, Motion of viscous fluids

>< Methodology : A combination of lectures, tutorial discussions and presentations
>< Scheme of Evaluation : Based on tutorials, tests, presentations and end of course Examination
>< Recommended Reading :
1. Raisinghania, M.D. (1995). Hydrodynamics, Schaum’s.
2. Thompson, L.E.M. (1949). Theoretical Hydrodynamics, Macmillon.
3. Chorlton, F. (1985). Textbook of Fluid Dynamics, CBS, India.
4. Bachelor G.K. (1977). An Introduction to Fluid Dynamics, Cambridge University Press.

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