Undergraduate Module Catalogue

AVIA2100 Mathematical Techniques for Aerodynamics

Module manager: Dr DC Peacock
Email: d.c.peacock@leeds.ac.uk

Taught: invalid View Timetable

This module is not approved as an Elective

Module summary

A knowledge of aerodynamics is key to successful aircraft design and operation. Anyone hoping to enter this field requires not only a grasp of the conceptual principles but also the mathematical knowledge and skills required to model the air flow around and the forces developed on the aircraft. This module aims to equip the student with the mathematical knowledge and skills required when they study aerodynamics in the level 3 module Aircraft 2.

Objectives

This module aims to equip the students with the mathematical knowledge and skills to support them in their study of aerodynamics in AVIA 3000.

Learning outcomes
On completion of this module, students should be able to:
1. Use vectors to represent three-dimensional space, including points, lines and planes and find intersections among these.
2. Differentiate and integrate vectors in the context of dynamics problems, and understand scalar and vector products.
3. Apply a series to approximate a function.
4. Use series to solve differential equations.
5. Apply the skills learnt in LO1-4 to fluid flow applications.

Skills outcomes
Students acquire the following competencies in the module. In each case, the means of acquiring the competency is shown. These competencies correspond with those specified in "The Accreditation of Higher Education Programmes", Third edition, Engineering Council, 2014. P = practiced ACTIVELY, F= Formatively Assessed, S = Summatively Assessed. Discussions refer to both in-class discussions of questions from broad to highly focused and semi-structured discussion centred around numerous case studies.

SM2: HOW MANIFESTED: P through weekly problems solved both in class and outside of class. F through tests at the end of each section. S by the final exam.
EA3: HOW MANIFESTED: P through weekly problems solved both in class and outside of class. F through tests at the end of each section. S by the final exam.

Syllabus

1. Vectors - Scalar/vector definitions, vector types, vector addition, unit vector, magnitude. Direction cosine, scalar product, vector product, angle between two vectors. Vector calculus: grad, div, curl & Laplacian; directional derivative, line, surface and volume integration.

2. Series - Series/sequences definition, arithmetic progressions, arithmetic mean, geometric progression, geometric mean, sum of 'n' numbers in series. Infinite series, limiting values approaching infinity, convergence, divergence. Power series, Maclaurin series, limiting values approaching 0, L'Hopital's rule, Taylor series. Fourier series.

3. Application to:
(a) fluid kinematics - velocity and acceleration fields, Reynolds transport theorem.
(b) finite control volume analysis - conservation of mass, Newton's second law, the energy equation.
(c) differential analysis of fluid flow - conservation of mass, conservation of momentum.

Private study

Students will review the lecture notes and work through weekly problem sheets which will be reviewed in the tutorial sessions.

Opportunities for Formative Feedback

Through marks given in weekly formative problem sheets and through the tutorial sessions.

Reading list

The reading list is available from the Library website

Last updated: 10/08/2020 08:43:52

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