Marine Hydrodynamics Lecture – 01 Introduction Md. Habibur Rahman Lecturer Department of Naval Architecture and Marine Engineering (NAME) Bangladesh University of Engineering and Technology (BUET), Dhaka – 1000

Student Assessment Conditions Frequency per semester Marks Class Attendance 14 weeks 30 Class Test & Assignment 3 out of 4 60 End Semester 1 210

Reference “Applied Hydrodynamics” – H. R. Vallentine (Prof. of Civil Engineering, University of Newcastle, New South Wales) “Applied Hydrodynamics” (An Introduction to Ideal and Real Fluid Flows) – Hubert Chanson

Course Content Flow of an ideal fluid: equation of continuity, streamlines, streak lines and path lines, two – dimensional flow patterns, rotational and irrotational flows, vorticity, velocity potential functions, stream functions, Euler’s equation of motion, Bernoulli’s equation, velocity and pressure distribution. Flow of a real fluid: Navier – Stokes equation, displacement, momentum and energy thickness of the boundary layer, and characteristics of flow around a ship hull. Standard patterns of flow: uniform flow, irrotational vortex, circulation, source, sink and doublet, flow past a half body, cylinder and Rankine body, virtual mass, and Magnus effect. Conformal transformation: analytic functions, singularities, Cauchy – Riemann equations, complex potential, application of conformal transformation to some flow cases, Joukowski’s hypothesis, lift of an infinite aerofoil. Appendix A: Theorems of Green, Stokes, Cauchy and Blasius and their application to some hydrodynamics problems.

Fluid Fluid: A fluid is a gas or liquid that, unlike a solid, flows to assume the shape of the container in which it is placed. This occurs because a fluid responds to a shear stress, or a force per unit area directed along the face of a cube of fluid, by flowing, rather than by an elastic displacement as in a solid. The term fluid refers to gases and liquids. Gases and liquids have more in common with each other than they do with solids, since gases and liquids both have atoms/ molecules that are free to move around. They are not locked in place as they are in a solid. The hotter the fluid, the faster its molecules move on average, and the more space the fluid will occupy (if its container allows for expansion.) Also, unlike solids, fluids can flow. Properties of Fluid: Density: Density of a fluid is defined as the ratio of the mass of a fluid to its volume. Specific Volume: Specific volume of a fluid is defined as the volume of a fluid occupied by a unit mass or volume per unit mass of a fluid. Viscosity of Liquid: Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of fluid.

Types of Fluids based on Viscosity Ideal Fluid A fluid that has no viscosity, no surface tension and incompressible is defined as an ideal fluid. For such a fluid, no resistance is encountered as it moves. Ideal fluid does not exist in nature, however fluids with low viscosity such as air, water may however be treated as ideal fluid, which is reasonable and well accepted assumption. Real Fluid A fluid that has viscosity, surface tension and is compressible which exists in nature is called real or practical fluid. The properties of real fluid are:- i. Property of viscosity; ii. Surface tension; iii. Capacity to vaporize.

Types of Fluids based on Viscosity Newtonian Fluid A Newtonian fluid is one in which the shear stress, in one-directional flow, is proportional to the rate of deformation as measured by the velocity gradient across the flow. The common fluids such as air, water and light petroleum oils, are Newtonian fluids. In other words, A real fluid in which the shear stress is directly proportional to rate of shear strain (or velocity gradient). – Newton’s Law of Viscosity Non – Newtonian Fluid A real fluid in which the shear stress is not directly proportional to rate of shear strain (or velocity gradient) that means a real fluid which does not obey the Newton’s law of Viscosity is called non – Newtonian fluid. 𝜏=constant× 𝜕𝑦 𝜕𝑥 𝑛