MTH4360 · Fluid dynamics

Overview

The continuum hypothesis; notion of a fluid particle; pathlines and streamlines. Eulerian and Lagrangian frameworks; the material derivative. Conservation of mass; incompressibility; streamfunctions. Forces acting on a fluid; the stress tensor; conservation of momentum; the constitutive relation; the incompressible Navier-Stokes equations. Boundary conditions. Exact solutions of Navier-Stokes equations. Non-dimensionalization and dimensional analysis; Reynolds number. Low Reynolds number flows. Vorticity; circulation; Helmholtz' vorticity equation; properties of vorticity; Kelvin's circulation theorem. Lubrication theory. Inviscid flows; potential flows. Boundary layer equations and flows.

Areas of study: Applied mathematics Mathematical statistics Mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Critically evaluate and synthesise the extensive scope and applications of fluid dynamics within the physical sciences, demonstrating an advanced understanding of its interdisciplinary relevance
2. Articulate and analyse the mathematical description of fluid motion, showcasing proficiency in formulating and interpreting fluid dynamics equations
3. Summarise and critically evaluate the derivation of the equations governing incompressible fluid motion, demonstrating a deep understanding of the underlying principles.
4. Apply the process of scaling to simplify the governing equations for both viscous and inertia dominated flows.
5. Apply the process of scaling to lubrication and boundary layer flows.
6. Solve the governing and reduced equations in simple situations and demonstrate and in-depth understanding of the physical implications of the solutions and their limitations

Workload

2 hours of pre-recorded lectures; One 3-hour applied class and 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.