# 2022/23 Undergraduate Module Catalogue

## MATH3620 Fluid Dynamics 2

### 15 creditsClass Size: 81

**Module manager:** Dr Cedric Beaume**Email:** C.M.L.Beaume@leeds.ac.uk

**Taught:** Semester 1 (Sep to Jan) View Timetable

**Year running** 2022/23

### Pre-requisite qualifications

MATH2620 or equivalent. Some knowledge of vector calculus and PDEs is useful but not required.**This module is approved as a discovery module**

### Module summary

This module furthers the modelling of fluids started in MATH2620 by introducing the effects of fluid viscosity.### Objectives

At the end of this module students should be able to:- Write and use the Navier-Stokes equations;

- Understand the Reynolds number;

- Solve simple viscous flow problems analytically;

- Use lubrication theory to solve flows in narrow gaps;

- Calculate the simple boundary layer flows;

- Use complex variable techniques to solve for potential flows.

### Syllabus

-Stress tensor and Velocity Gradient. What is fluid viscosity? Stress and strain-rate tensors;

- Navier Stokes Equations. Derivation of the equations of motion for a viscous fluid. Simple one-dimensional flow solutions such as flow along pipes and channels. Definition of the Reynolds number describing the relative importance of inertia and viscosity. Discussion of high and low Reynolds number approximations;

- Lubrication Theory. Flows in narrow gaps such as in a slider bearing or squeezing flows between two plates;

- Boundary layers. Flows near boundaries at high Reynolds numbers. The vorticity equation for a viscous fluid. The flow above impulsively moving plate and diffusion of a vortex sheet. Discussion of boundary layers and separation;

- Complex Potential. Description of planar inviscid flows using the complex potential. Using conformal transformations to find the flow around an ellipse or flat plate. Calculating forces and torques from Blasius' theorem. The lift on an aerofoil.

### Teaching methods

Delivery type | Number | Length hours | Student hours |

Lecture | 33 | 1.00 | 33.00 |

Private study hours | 117.00 | ||

Total Contact hours | 33.00 | ||

Total hours (100hr per 10 credits) | 150.00 |

### Private study

Studying and revising of course material. Reading as directed. Completing of assignment and assessments.### Opportunities for Formative Feedback

Regular example sheets.### Methods of assessment

**Exams**

Exam type | Exam duration | % of formal assessment |

Standard exam (closed essays, MCQs etc) | 2 hr 30 mins | 100.00 |

Total percentage (Assessment Exams) | 100.00 |

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 websiteLast updated: 09/05/2022 09:13:04

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- Undergraduate module catalogue
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- Taught Postgraduate programme catalogue

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