## 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 2020/21

### Pre-requisite qualifications

This module follows MATH2620, so having followed it is suitable. 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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Lecture 17 1.00 17.00 Private study hours 133.00 Total Contact hours 17.00 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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Exams
 Exam type Exam duration % of formal assessment Open Book exam 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