units

MTH3360

Faculty of Science

# Undergraduate - UnitMTH3360 - Fluid dynamics

This unit entry is for students who completed this unit in 2015 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. print version

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

 Level Undergraduate Faculty Faculty of Science Organisational Unit School of Mathematical Sciences Offered Clayton First semester 2015 (Day) Coordinator(s) Dr Anja Slim and Professor Phil Hall

### Synopsis

The basic equations of fluid dynamics; Cartesian tensors, the viscous stress tensor; equations of state; linearisation, sound and internal gravity waves; phase and group velocity; non-linear evolution; shocks; computational methods; exact solutions of the full equations: plane Poiseuille flow, impulsively started plate; overview of numerical methods and analog experiments, dimensional analysis, scaling; low Reynolds number flow: properties, flow around a sphere, Hele-Shaw flow, Saffman-Taylor instability, viscous gravity currents; high Reynolds number flows; Bernoulli's Theorem and streamlines, vorticity and the vorticity equation, line vortices, circulation and Kelvin's theorem, potential flow; boundary layers: flow past a flat plate, flow past bluff bodies and separation.

### Outcomes

On completion of this unit students should be able to:

1. Explain the scope of fluid dynamics in the physical sciences;
2. Summarise the derivation of the equations of fluid motion, including manipulating Cartesian tensors;
3. Solve those equations in simple situations for compressible and incompressible flows, and simplify those equations using the methods of linearization, dimensional analysis and scaling;
4. Explain the dynamics of linear waves in fluids, the physical reasons why waves may form shocks, and the nature of the developed shocks after they do;
5. Summarise the properties of the Stokes equations for low Reynolds number flows;
6. Apply Bernoulli's theorem to simple problems;
7. Explain the concept of vorticity, apply that to irrotational flows and appreciate the role of boundary layers.

### Assessment

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

Three 1-hour lectures and an average of two 1-hour support classes per week 