## MAS280 Mechanics and Fluids

Note: Information for future academic years is provisional. Timetable information and teaching staff are especially likely to change, but other details may also be altered, some courses may not run at all, and other courses may be added.

 Semester 2, 2022/23 10 Credits Lecturer: Dr Ashley Willis Timetable Reading List Aims Outcomes Assessment

This course extends the principles of Newtonian mechanics from the mechanics of particles to the mechanics of three-dimensional (3D) bodies, first to the motion of solids, then to the motion of fluids (e.g. air and water).

Mathematically, this course develops the vector calculus, the essential tool for describing a 3D world. The suffix notation and the Einstein summation convention are introduced as an alternative notation for the calculus.
Properties of the vector gradient operator are first seen as a natural description for potential forces. For more advanced use of the vector calculus, the most intuitive setting to comprehend its properties is through the study of fluid motion.
Topics include 3D extensions of the work-energy principle, planetary and satellite motion, elements of the motion of rigid bodies, and the motion of inviscid (frictionless) fluids.

Prerequisites: MAS112 (Vectors and Mechanics); MAS211 (Advanced Calculus and Linear Algebra) (Alternative prerequisite: PHY120 or PHY165)

The following modules have this module as a prerequisite:

 MAS320 Fluid Mechanics I MAS422 Magnetohydrodynamics

## Outline syllabus

• Suffix notation and a review of grad, div, curl and the integral theorems.
• Centre of mass and moment of inertia.
• The work-energy principle using the gradient operator.
• Planetary orbits.
• Motion of a rigid body.
• Integral theorems and coordinate systems.
• Kinematics of fluid motions.
• Euler's equations of motion for an inviscid fluid.
• Irrotational flows and Bernoulli's principle.

## Aims

• To extend a working knowledge of Newtonian mechanics to a broader range of contexts.
• To develop and expand ability to use the vector calculus.
• To extend an understanding of planetary motions and the motion of rigid bodies.
• To recognise and understand key features of fluids motion.

## Learning outcomes

• Recall and apply the basic operations of vector calculus in vector- and suffix-notation.
• Be able to mathematically express properties of point-, volume- and surface-forces.
• Be able to represent the above in different coordinate systems.
• Apply the above mathematics to calculate the motion of solids.
• Apply the above mathematics to calculate and analyse a fluid flow.

20 lectures, 5 tutorials

## Assessment

2 Assessed Homeworks at 5% each, 2-hour formal exam 90%.