Applied Mathematics
MP365: Fluid Mechanics (5 ECTS)
(This course will be run every other year.) This course consists of an introduction to the theory of fluid mechanics. Topics covered include: a review of vector calculus, ideal fluids, irrotational flow, Laplace's equation and some potential theory, elementary viscous flow with examples, the stress tensor, Cauchy's equation of motion, the Navier-Stokes equations, very viscous flow, including thin film and lubrication theory.
Taught in Semester(s) II. Examined in Semester(s) II.
Workload: 36 hours (24 Lecture hours, 12 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- mathematically model the behaviour of an ideal fluid;
- solve some simple fluid problems for incompressible, irrotational flows using potential theory;
- construct some analytical solutions for some elementary viscous fluid flows;
- understand the role of the stress tensor in the modelling of continuum systems;
- understand the assumptions made in deriving the Navier-Stokes equations for fluid motion;
- construct some analytical solutions for very viscous flows using lubrication theory.
Indicative Content
- A review of vector calculus.
- Ideal fluids, irrotational flow, Laplace's equation and some potential theory.
- Elementary viscous flow with examples.
- The stress tensor, Cauchy's equation of motion, the Navier-Stokes equations.
- Very viscous flow, including thin film and lubrication theory.
Module Resources
- Elementary Fluid Dynamics, D.J . Acheson, Oxford University Press
- An Introduction to Fluid Dynamics, G.K. Batchelor, Cambridge University Press
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