## MATH3501 Modelling with Fluids (10)

### 10 creditsClass Size: 100

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2005/06

### Pre-requisites

MATH2360 or MATH2420 or equivalent. Exclusion - not with MATH2620 or MATH3502.

This module is approved as an Elective

### Objectives

To develop the ideal fluid model. To derive the equations of motion, and to illustrate basic flows. On completion of this module, students should be able to: (a) state the difference between an ideal fluid model and a real fluid; (b) calculate and sketch streamlines for simple flows; (c) derive the continuity equation and Euler?s momentum equation; (d) explain forces on objects using Bernoulli?s equation; (e) construct solutions past two-dimensional and axi-symmetric bodies from combinations of streamfunctions for uniform stream, source, sink and dipole; (f) construct solutions past two-dimensional bodies from combinations of the velocity potential for uniform stream, source, sink and dipole; solve such problems using complex potential; (g) state why the addition of circulation into flow past a circular cylinder creates a lift on the cylinder; solve such a problem using the velocity potential or the stream function.

### Syllabus

Fluid mechanics deals with the motion of fluids such as water, air and blood. A different mathematical formulation is needed to treat fluids as distinct from 'rigid bodies', for fluids can change their shape as they move. This module sets up the basic equations of fluid mechanics and uses them to consider mathematical models for e.g. the pollution caused by a factory emitting waste into a river, and the forces which keep a 400 ton jumbo jet in the air. Topics covered include: 1. Ideal fluid model. Picturing flows using streamlines. 2. Continuity equation. Euler's momentum equation. 3. Solutions for spherically symmetric flows. Irrotational flows: Laplace's equation and Bernoulli's equation. 4. Flow of stream past cylinder and sphere. Stokes' stream function, Rankine solids. 5. Two-dimensional problems and complex potential.

### Teaching methods

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

Lectures: 20 hours. 6 examples classes.

### Methods of assessment

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

One 2 hour examination at end of semester (100%).