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 Sheet, Von Karman Vortex Sheet; 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, Reynolds Number; Boundary layer along 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.
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