MAS2803 : Fluid Dynamics
- Offered for Year: 2019/20
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semester 2 Credit Value:
To introduce the fundamental concepts and governing equations of fluid mechanics, using mathematical techniques to analyse simple flow problems for an inviscid (frictionless) fluid.
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). Many of the ideas that were introduced in that module, including the differential operators and integral theorems, will be used extensively.
Outline Of Syllabus
• 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.
|Scheduled Learning And Teaching Activities||Lecture||25||1:00||25:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||1||6:00||6:00||Revision for class test|
|Guided Independent Study||Assessment preparation and completion||1||13:00||13:00||Revision for unseen exam|
|Guided Independent Study||Assessment preparation and completion||1||2:00||2:00||Unseen exam|
|Scheduled Learning And Teaching Activities||Lecture||1||1:00||1:00||Class test|
|Scheduled Learning And Teaching Activities||Lecture||3||1:00||3:00||Problem classes|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||4||1:00||4:00||Tutorials in the lecture room|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||12||0:10||2:00||Office hours|
|Guided Independent Study||Independent study||1||21:00||21:00||Studying, practising and gaining understanding of course material|
|Guided Independent Study||Independent study||3||3:00||9:00||Review of coursework assignments and class test|
|Guided Independent Study||Independent study||2||6:00||12:00||Preparation for coursework assignments|
Jointly Taught With
Teaching Rationale And Relationship
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. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.
The format of resits will be determined by the Board of Examiners
|Written Examination||40||2||M||10||Class test|
|Prob solv exercises||2||M||5||Coursework assignments|
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments will consist of two written assignment of approximately equal weight. The coursework assignments and the (in class, therefore 40 minute) coursework test 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.