This course provides a fundamental understanding of fluid mechanics. Starting from the definition of a fluid, theory will be build up in order to describe, characterize, analyze and understand the behavior of fluids (gases, liquids) in motion or static. Mechanics of fluids is a fundamental subject and one that finds many applications in meteorology and in aeronautics. In engineering several industrial and technological applications are found from ship design to pipe modeling.
The following topics will be covered:
Introduction: Basic concepts of fluid mechanics Fundamental term; Physical value; Fluids and their properties; Forces inside fluid.
Fluid Statistics: Pascal’s law; Euler’s equation of fluid statics; Measurement of pressure; Relative statics of fluid-constant acceleration, rotation; Forces of hydrostatic pressure; Buoyancy; Flotation; Stability. Surface tension' Capillary Action and Cavitation.
Fluid Kinematics: Euler and Lagrangian specification of fluid flow; Streamlines; Pathlines; Stream surface; Stream tube; Mass/volume flow; Control volume.
Fluid Dynamics: Hydrodynamic limit - deriving fluid equations; Mass, momentum and energy conservation; Navier-Stokes’s equations; Euler’s and Bernoulli’s equations for Ideal fluid flow and applications; Streamfunctions for incompressible flows and exact solutions; Potential flow, irrotational flow and velocity potential formulation; Vorticity dynamics; Real fluid flow: Viscosity. Determination of losses; Reynolds experiment; Laminar and turbulent flow; Boundary layer and viscosity; Velocity profile; Losses in pipes; Frictional losses; Moody’s diagram; Local losses; Coefficients of resistance; Introduction to multi-scale turbulence. Transport in turbulent flows.
Analytical mechanics is the mathematically sophisticated reformulation of Newtonian mechanics and consists of Lagrangian mechanics and Hamiltonian mechanics. Not only does analytical mechanics enable us to solve problems efficiently, but it also opens up a route leading to quantum mechanics and Statistical Mechanics. Latterly the language and ideas of Lagrangian and Hamiltonian Mechanics have found fruit in the description of the behavior of certain Chaotic systems. The section of the module on the Calculus of Variations provides the formulation of Lagrangian and Hamiltonian mechanics, the d’Alembert’s Principle is also studied in the formulation of Equations of Lagrange.