6 points, SCA Band 2, 0.125 EFTSL
Undergraduate - Unit
Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
School of Mathematical Sciences
- First semester 2017 (Day)
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:
- Explain the scope of fluid dynamics in the physical sciences;
- Articulate the mathematical description of fluid motion;
- Summarise the derivation of the equations of incompressible fluid motion;
- Apply the process of scaling to simplify the governing equations for viscous and inertia dominated flows;
- Apply the process of scaling to lubrication and boundary layer flows;
- Solve the governing and reduced equations in simple situations and understand the physical implications of the solutions and their limitations.
Examination (3 hours): 60% + Assignments and tutorial work: 22.5% + Tests: 17.5%
Three 1-hour lectures and one 2-hour support class per week
See also Unit timetable information