MA-561 (Fluid Dynamics)

Course Contents:

Review of gradient, divergence and curl. Elementary idea of tensors.

Velocity of fluid, streamlines and pathlines, steady and unsteady flows, velocity potential, vorticity vector, conservation of mass, equation of continuity, equation of motion of a fluid, pressure at a point in fluid at rest, pressure at a point in a moving fluid, Euler’s equation of motion, Bernoulli’s equation.

Singularities of flow, source, sink, doublets, rectilinear vortices, complex variable method for two-dimensional problems, complex potentials for various singularities, circle theorem, Blasius theorem, theory of images and its applications to various singularities.

Three-dimensional flow, irrotational motion, Weiss’s theorem and its applications, viscous flow, vorticity dynamics, vorticity equation, Reynolds number, stress and strain analysis, Navier-Stokes equation, boundary layer equations.

Texts/References:

1. F. Chorlton, A Text Book of Fluid Dynamics.
2. G.K. Batchelor, An Introduction to Fluid Dynamics.
3. A. R. Paterson, A First Course in Fluid Dynamics.
4. L.M. Milne Thomson, Theoretical Hydrodynamics.

Exam Scheme: Mid-sem exam (25%), one assignment (10%), one class test (5%), one surprise class test (10%), numerical problem solution (10%) and end-sem exam(40%).

Problems and Solution Hints: Will be available from time to time.