MTH3360 · 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

Learning outcomes

1. Explain the scope of fluid dynamics in the physical sciences;
2. Articulate the mathematical description of fluid motion;
3. Summarise the derivation of the equations of incompressible fluid motion;
4. Apply the process of scaling to simplify the governing equations for 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 understand 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.