# MTH3360 - Fluid dynamics - 2019

## 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.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Coordinator(s)

Unit guides

Offered

Clayton

• First semester 2019 (On-campus)

Prerequisites

One of MTH2010, MTH2015, ENG2005 and one of MTH2032, MTH2040

## 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. 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.

## Assessment

End of semester examination (3 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

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