COURSE OUTLINE: Introduction - ideal and viscous incompressible fluid; Kinematics of fluid; Lagrangian and Eulerian methods of description, velocity, acceleration, streamlines, pathlines, vorticity; Equation of continuity; Euler’s Equations of motion; Bernoulli's equation and its application, Two-dimensional motion - velocity potential, stream function, Sources, sinks, dipoles; Flow past a circular cylinder with and without circulation; Blasius Theorem; Problems on the motion of perfect fluids steady translation of a cylinder in an infinite fluid medium, unsteady translation; Added mass of cylinders; Spheres; The vortex system-circular vortex, two dimensional sources and vortex distributions, vortex sheets; Lifting Surfaces, Aerofoil theory - complex potential- Method of Conformal mapping- Joukowski profile; Flow past a Joukowski profile; Velocity and pressure distribution on aerofoils; Viscous fluids- Navier-Stokes equations, Laminar flow, Poiseuille flow, Couette flow, flow through a pipe; Boundary layer Theory-Reynolds Number; Boundary layer along with a flat plate; Blasius solution; Separation, Von Karman momentum integral method; Introduction to Turbulence; Gravity waves- Airy's wave; Free surface condition; Velocity potential- Dispersion relation; Surface tension effects; Orbital motion; Group velocity and its dynamical significance; Wave energy; Standing waves; Loops and nodes, Wave forces and Morison's equation, Long waves and waves in a canal; Tides.
COURSE DETAIL: The course content consists of five modules. Each module will have approximately 8-10 lectures. Apart from the basic theory, a large number of problems will be worked out to illustrate the utility of the theory. There will be a couple of problems at the end of each lecture/module as homework.