| Unit name | Fluid Dynamics 3 |
|---|---|
| Unit code | MATH33200 |
| Credit points | 20 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Eggers |
| Open unit status | Not open |
| Pre-requisites |
MATH20900, MATH 20100, Level 1 Mechanics. |
| Co-requisites |
MATH33000 is useful but not essential |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
The course starts with ways of describing fluids and their motion, e.g. streamlines and streaklines are distinguished. Consideration of vector-valued functions of position and time, such as velocity fields requires a full development of vector calculus, its operators (div,grad and curl) and its theorems. The equations of motion and mass conservation are derived for an inviscid fluid. Bernoulli's equation, the concept of vorticity and Kelvin's circulation theorem are introduced. These serve to clarify the circumstances in which the idealization of irrotational flow can be used. Except for some work on the motion of vortices the remainder of the course deals with solutions for irrotational flow. In large part this is a matter of finding solutions to Laplace's equation. This partial differential equation is one of the more important equations in mathematics. Its solutions can be useful in such diverse fields as topology, electromagnetism, and soil mechanics. This section and the preceding work on the calculus of vector fields are fundamental to deeper study of many areas of mathematics and applied mathematics, and to much of theoretical physics. Application is mainly to simple flows, but the course concludes with consideration of the lift and drag on an airfoil.
