# Modules

### MAS2803 : Fluid Dynamics

• Offered for Year: 2019/20
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 2 Credit Value: 10 ECTS Credits: 5.0

#### 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). 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 Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Tutorials in the lecture room
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Guided Independent StudyIndependent study121:0021:00Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study33:009:00Review of coursework assignments and class test
Guided Independent StudyIndependent study26:0012:00Preparation for coursework assignments
Total100:00
##### Jointly Taught With
Code Title
PHY2033Fluid Dynamics
##### 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.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A85N/A
Written Examination402M10Class test
##### Exam Pairings
Module Code Module Title Semester Comment
PHY2033Fluid Dynamics2N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Coursework 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.