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Fluid Mechanics-I: Course Outline (MAT 458)

Fluid mechanics is the branch of physics that studies the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.

Course Objective

At the end of this course the students will be able to understand the importance of  Fluid mechanics in mathematics, science and engineering. The course will increase the basic level of the students in the field of fluid mechanics and will grow their knowledge from both mathematical point of view and also from application point of view. Also this course will help to those students who wish to undertake advance studies in fluid mechanics.

Course Contents

  • Real fluids and ideal fluids, velocity of a fluid at a point, streamlines and pathlines, steady and unsteady flows, velocity potential, vorticity vector, local and particle rates of change, equation of continuity. Acceleration of a fluid, conditions at a rigid boundary, general analysis of fluid motion.
  • Euler’s equations of motion, Bernoulli’s equation steady motion under conservative body forces, some potential theorems, impulsive motion.
  • Sources, sinks and doublets, images in rigid infinite plane and solid spheres, axi-symmetric flows, Stokes’s stream function.
  • Stream function, complex potential for two-dimensional, irrotational, incompressible flow, complex velocity potential for uniform stream. Line sources and line sinks, line doublets and line vortices, image systems, Miline-Thomson circle theroem, Blasius’ theorem, the use of conformal transformation and the Schwarz-Christoffel transformation in solving problems, vortex rows.
  • Kelvin’ s minimum energy theorem, Uniqueness theorem, fluid streaming past a circular cylinder, irrotational motion produced by a vortex filament.
  • The Helmholtz vorticity equation, Karman’s vortex-street. 

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