Aims

To introduce the fundamental concepts and governing equations of fluid mechanics, using mathematical techniques to analyse simple flow problems for an inviscid (frictionless) fluid.

Module Summary

Fluid dynamics plays a central role in many natural phenomena. As we breathe, gas flows in and out of our lungs, whilst our heart pumps blood around the body. Without a proper understanding of large-scale fluid flows in the Earth’s atmosphere and oceans, it would be impossible for meteorologists to produce reliable weather forecasts. On yet larger scales, the complex motions in the Earth’s molten iron core are responsible for sustaining the terrestrial magnetic field. The principles of fluid dynamics can also be used to explain aerodynamic lift, whilst engineers need to be able to model fluid flows around solid bodies (like tall buildings) and along pipes.

This module will introduce the concept of a fluid, and the ways in which the motions of such a system can be described. The main focus of this module will be on the dynamics of inviscid (frictionless) fluids. Even with such an assumption, it is not possible to write down a general solution of the governing equations, but it is possible to make certain simplifying assumptions to deduce the properties of certain flows. In many respects, this module is a sequel to vector calculus (MAS2801/PHY2026). Many of the ideas that were introduced in that module, including the differential operators and integral theorems, will be used extensively.

Outline Of Syllabus

Continuum approximation.
•       Kinematics: Streamlines, pathlines, steady and time-dependent flows, convective derivative, vorticity and circulation.
•       Governing equations and elementary dynamics: Conservation of mass, the continuity equation and incompressibility, Euler’s equation, Bernoulli’s streamline theorem.
•       Irrotational flows and potential theory: Laplace’s equation, principle of superposition, simple examples including sources, sinks and line vortices, flow around a cylinder and sphere.
•       Linear water waves: Surface waves (deep and shallow), dispersive waves, group velocity.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.