Marine Hydrodynamics

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.

Mod-01 Lec-01 Introduction to Marine Hydrodynamics.
Mod-02 Lec-02 Law of Conservation of Mass - Continuity of Equation.
Mod-03 Lec-03 Streamlines and Flow Direction.
Mod-04 Lec-04 Worked Examples on Various Types of Flow.
Mod-05 Lec-05 Equation of Motion (Law of Conservation of Momentum).
Mod-06 Lec-06 Applications of Equations of Motion.
Mod-06 Lec-07 Applications of Equations of Motion (Contd.).
Mod-07 Lec-08 Two Dimensional Flows.
Mod-07 Lec-09 Two Dimensional Flows (Contd.).
Mod-08 Lec-10 Source, Sink and Doublet.
Mod-09 Lec-11 Worked Examples on Two Dimensional Flows.
Mod-10 Lec-12 Conformal Mapping and Joukowsky Transformation.
Mod-11 Lec-13 Uniform Flow Past an Elliptic Cylinder.
Mod-12 Lec-14 Aerofoil theory.
Mod-12 Lec-15 Aerofoil theory (Contd.).
Mod-12 Lec-16 Aerofoil theory (Contd.).
Mod-13 Lec-17 Schwarz - Christoffel Transformation.
Mod-14 Lec-18 Motion of a cylinder.
Mod-15 Lec-19 Vertex Motion.
Mod-16 Lec-20 Irrotational Flow - A Bird's eyeview.
Mod-17 Lec-21 Introduction to Water Waves.
Mod-18 Lec-22 Basic Equation and Conditions of Water Waves.
Mod-19 Lec-23 Water particle kinematics in wave motion.
Mod-20 Lec-24 Capillary Gravity Waves.
Mod-21 Lec-25 Linearised Long Wave Equation.
Mod-21 Lec-26 Linearised Long Wave Equation (Contd.).
Mod-22 Lec-27 Wave motion in two layer fluids.
Mod-23 Lec-28 Worked Examples on Wave Motion.
Mod-23 Lec-29 Worked Examples on Wave Motion (Contd.).
Mod-24 Lec-30 Gravity wave transformation and energy rotation.
Mod-24 Lec-31 Gravity wave transformation and energy rotation (Contd.).
Mod-24 Lec-32 Gravity wave transformation and energy rotation (Contd.).
Mod-25 Lec-33 Navier - Stokes equation of motion.
Mod-26 Lec-34 Analysis of Basic Flow Problems.
Mod-26 Lec-35 Analysis of Basic Flow Problems (Contd.).
Mod-27 Lec-36 Unsteady unidirectional flows.
Mod-27 Lec-37 Unsteady unidirectional flows (Contd.).
Mod-28 Lec-38 An introduction to Boundary Layer Theory.
Mod-29 Lec-39 Solution methods for Boundary Layer Equations.
Mod-29 Lec-40 Solutions Methods for Boundary Layer Equations (Contd.).