MTH3360 - Fluid dynamics - 2018

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.

On completion of this unit students will be able to:

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.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Three 1-hour lectures and one 2-hour support class per week

See also Unit timetable information

Applied mathematics

Mathematical statistics

Mathematics