units

MTH3360

Faculty of Science

18 September 2017 22 November 2024

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This unit entry is for students who completed this unit in 2016 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

Monash University

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.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Dr Anja Slim and Professor Phil Hall

Offered

Clayton

  • First semester 2016 (Day)

Synopsis

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.

Outcomes

On completion of this unit students will be able to:

  1. Explain the scope of fluid dynamics in the physical sciences;
  2. Understand the mathematical description of fluid motion;
  3. Summarise the derivation of the equations of incompressible fluid motion;
  4. Understand and apply the process of scaling to simplify the governing equations for viscous and inertia dominated flows;
  5. Understand and 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.

Assessment

Examination (3 hours): 60%
Assignments and tutorial work: 22.5%
Tests: 17.5%

Workload requirements

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

See also Unit timetable information

Chief examiner(s)

Professor Phil Hall

This unit applies to the following area(s) of study

Applied mathematics
Mathematical statistics
Mathematics

Prerequisites

MTH2010 or MTH2015, and MTH2032, or equivalent