Second Semester 1999/2000
Lecturer: Dr G W Roberts
Recommended books:
Fluid mechanics, D Pneuli and C Gutfinger, C.U.P 1992,
ISBN 0-521-58797-2(pbk) (QA901.P58).
Elementary fluid mechanics, D J Acheson, Oxford University
Press, 1990, œ16.75, ISBN 019859660X, (TA357.A276).
Aims:
To give the student an understanding of the concepts and
theory involved in the modelling of the flow of fluids.
Objectives:
The students should be able to derive equations, state and
prove theorems and solve problems in the areas of continuum
mechanics, flow kinetics and inviscid fluid mechanics.
The student is expected to apply a variety of mathematical
techniques covered in Part 1 and H1 modules.
Summary:
This module introduces the basic concepts underlying the
modelling of fluid flows. The motion of inviscid fluids is
then studied in detail using complex potential methods which
culminates in the theory of two-dimensional aerofoils.
The Navier-Stokes equations for viscous fluids are derived,
analysed and applied to a variety of problems
including pipe flow and boundary layer theory.
Pre-requisites: G2M55, G2M56 and G2M70.
Syllabus:
Basic concepts:
Properties of fluids, continuum model, Eulerian and Lagrangian
descriptions, streamlines, particle pathlines and streak lines.
Discussion of internal stress and of
viscosity. Conservation of mass, incompressibility.
Inviscid flow:
Equation of motion (Euler equation) and boundary conditions;
2-D incompressible flow, stream function; vorticity.
Irrotational flows: complex variable method, 2-D aerofoil theory;
vortex motion.
Viscous flow
Equation of motion (Navier-Stokes equation) and boundary conditions.
Reynolds number - dynamical similarity;
some exact solutions of the N.-S. equation - pipe and channel flow.
Low Reynolds number flow (Stokes flow), lubrication theory.
High Reynolds number flow, boundary layers, separation.
Assessment: 2 hour end of semester closed book examination 100%
Latest modification to this page: 9/ 3/99
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