AMAT 42793: Fluid Dynamics

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Course Code  :           AMAT 42793

Title                :           Fluid Dynamics

Pre-requisites :           PMAT 41763

 

Learning Outcomes   :

At the end of this course the student will

  • recognize the difference between discrete mass-points and continuous matter in mechanics
  • define 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, conservation of momentum, conservation of energy, Euler’s equations of motion,  Bernoulli’s theorem, Vorticity, Irrotational motion under conservative forces, Kinetic energy in irrotational motion, Uniqueness theorems, Velocity circulation round a closed curve, Kelvin’s theorem, Vortex lines,  Helmholtz vorticity equation, Naviers stokes theorem, Cyclic and acyclic motions, Kinetic energy in irrotational motion, 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:  Irrotational motion, Laplace’s Equation, Spherical Harmonics, Flow of a stream past a fixed sphere, Motion of a sphere in a fluid, Impulsive motion.

 Method of Teaching and Learning : A combination of lectures, tutorial discussions and presentations.

 Assessment     : Based on tutorials, tests, presentations and end of course Examination.

 Recommended Reading       :

  1. Feistauer ,M. Mathematical Methods in Fluid Dynamics, chapman and Hall/CRC,1993.
  2. A. J. Chorin, J. E. Marsden. A Mathematical Introduction to Fluid Mechanics, Springer Science & Business Media, 2012.
  3. Dan, H. , Martin, B. Fluid Dynamics Theory and Computation, Stokholm 2005.
  4. Chorlton, F. Textbook of Fluid Dynamics, CBS Publishers & Distributors, 2005
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