|Unit level:||Level 2|
|Teaching period(s):||Semester 2|
|Offered by||School of Mathematics|
|Available as a free choice unit?:||N
The primary aim of this course unit is to provide students with a first introduction to continuum mechanics in general and theoretical fluid mechanics in particular. The material provides the student with an essential background to many third and fourth level courses on physical applied mathematics.
Fluid mechanics is concerned with understanding, and hence predicting, the properties (pressure, density, velocity etc.) of liquids and gases under external forces. This subject provides one of the major modern areas for the successful practical application of mathematics. Water, blood, air are all examples of fluids; of the many diverse fields where an understanding of the motion of fluids is important, one can mention oceanography and meteorology (in particular the dynamics of ocean circulation and weather forecasting), biological fluid dynamics (for example, blood flows through arteries), and aerodynamics.
The main physical focus at the end of the course is to calculate the forces on a body moving in a fluid e.g. aeroplane wing; the same study also relates to the behaviour of balls in football, cricket and golf, and of boomerangs and frisbees.
On completion of this unit successful students will be able to:
- Derive and apply identities involving Grad, Div and Curl, and alternative forms of the Divergence Theorem and Stokes' Theorem.
- Solve for the streamlines, particle paths and streaklines of a suitable given fluid flow.
- Define and use the Material Derivative.
- Identify the different types of forces acting on a fluid particle, derive the equation for Hydrostatic Equilibrium and apply this in simple situations.
- Derive and apply the Conservation of Mass equation and Euler's Equations of Motion in a fluid flow.
- Recognise the vorticity and the circulation in a fluid flow, and use the simplifications resulting from irrotational motion.
- Derive different forms of Bernoulli's Equation, under suitable sets of assumptions, and apply them in simple flow situations.
- In the case of irrotational, incompressible two-dimensional fluid flows, derive the streamfunction, the velocity potential and the complex potential, and use these to solve for the streamlines and the velocity components in suitably simple situations.
- State the Circle Theorem and Blasius' Theorem and apply these to find the forces on a body in a suitable simple flow.
- Other - 20%
- Written exam - 80%
Assessment Further Information
- Coursework; Weighting within unit 20%
- 2 hours end of semester examination; Weighting within unit 80%
Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding. Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback. Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.
- Lectures - 22 hours
- Tutorials - 11 hours
- Independent study hours - 67 hours