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2019/20 Undergraduate Module Catalogue

MATH2620 Fluid Dynamics 1

10 creditsClass Size: 130

Module manager: Prof Serguei Komissarov
Email: s.s.komissarov@leeds.ac.uk

Taught: Semester 2 View Timetable

Year running 2019/20

Pre-requisite qualifications

(MATH1010 and MATH1012 and MATH2365) or (MATH1050 and MATH1400 and MATH2365) or (PHYS1290 and PHYS1300 and PHYS2370) or (SOEE1301 and SOEE1311), or equivalent

This module is approved as a discovery module

Module summary

Fluid dynamics is the science of the motion of materials that flow, e.g. liquid or gas. Understanding fluid dynamics is a real mathematical challenge which has important implications in an enormous range of fields in science and engineering, from physiology, aerodynamics, climate, etc., to astrophysics.This course gives an introduction to fundamental concepts of fluid dynamics. It includes a formal mathematical description of fluid flows (e.g. in terms of ODEs) and the derivation of their governing equations (PDEs), using elementary techniques from calculus and vector calculus. This theoretical background is then applied to a series of simple flows (e.g. bath-plug vortex or stream past a sphere), giving the student a feel for how fluids behave, and experience in modelling everyday phenomena. A wide range of courses, addressing more advanced concepts in fluid dynamics, with a variety of applications (polymers, astrophysical and geophysical fluids, stability and turbulence), follows on naturally from this introductory course.

Objectives

This course demonstrates the importance of fluid dynamics and how interesting physical phenomena can be understood using rigorous, yet relatively simple, mathematics. But, it also provides students with a general framework to devise models of real-world problems, using relevant theories.

Students will learn how to use methods of applied mathematics to derive approximate solutions to a given problem and to have a critical view on these results.


Syllabus

This course gives an introduction to fundamental concepts of fluid dynamics. It presents elements of the theory of ideal fluids, completed with numerous real physical examples:
- Mathematical modelling of fluids: introduction to mathematical formalism, elementary kinematics, equation of mass conservation (including, e.g., representation of a physical system using mathematical objects such as functions and vector fields; characterisation of fluid flows in terms of ordinary differential equations; definition of streamfunctions; kinematic boundary conditions);
- Vorticity and potential flows: introduction to the concept of vorticity, flows solution to Laplace's equation (including, e.g., definitions of vorticity and circulation, elementary singular flows; elements of potential theory; methods of solutions of Laplace's equation);
- Dynamics: forces acting on fluids, momentum and vorticity evolution equations, Bernoulli's invariant, drag and lift forces (including, e.g., Euler's equation; conservation of vorticity and Kelvin's theorem; Archimedes' theorem; shape of the free surface of rotating fluids; aerodynamic forces on planes);
- Flows in open channels: steady waves over humps or through constrictions in channels (including, e.g., definition of the Froude number; sub- and supercritical one-dimensional flows);

Teaching methods

Delivery typeNumberLength hoursStudent hours
Workshop101.0010.00
Lecture221.0022.00
Private study hours68.00
Total Contact hours32.00
Total hours (100hr per 10 credits)100.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular problem solving assignments

Methods of assessment


Coursework
Assessment typeNotes% of formal assessment
In-course Assessment.15.00
Total percentage (Assessment Coursework)15.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.


Exams
Exam typeExam duration% of formal assessment
Standard exam (closed essays, MCQs etc)2 hr 00 mins85.00
Total percentage (Assessment Exams)85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 30/09/2019

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