## MAS320 Fluid Mechanics I

 Semester 2, 2017/18 10 Credits Lecturer: Dr Eun-jin Kim Timetable Reading List Aims Outcomes Teaching Methods Assessment

The way in which fluids move is of immense practical importance; the most obvious examples of this are air and water, but there are many others such as lubricants in engines. Moreover, the scientific principles and mathematical techniques needed to explain fluid motion are of intrinsic interest. This half-module builds on Level 2 work (MAS280 Vectors and Fluid Mechanics; MAS222 Methods for Differential Equations). The first step is to derive the equation (Navier-Stokes equations) governing the motions of most common fluids. These serve as a basis for the remainder of MAS320.

Prerequisites: MAS222 (Differential Equations); MAS280 (Mechanics and Fluids)

The following modules have this module as a prerequisite:

 MAS411 Topics in Advanced Fluid Mechanics

## Outline syllabus

• Basic concepts of fluid mechanics
• Rate of strain tensor: Derivation and interpretation. Constitutive equation.
• Exact solutions of the Navier-Stokes equations: Simple shear flow. Poiseuille flow. Steady flow under gravity down an inclined plane. Flow with circular streamlines. Infinite plate impulsively started into motion.
• Vector and tensor identities: manipulation of Navier-Stokes equations. Stress tensor and stress vector.
• Flow past a sphere: Derivation of Stokes drag on a sphere for small Reynolds number.
• Vorticity: Reynolds number. Vorticity equation. Role of irrotational flow. Burgers vortex. Vortex lines. Lagrange's theorem.
• General description of turbulence: two-scale analysis

## Aims

• To broaden the students' knowledge of Fluid Mechanics.
• To introduce students to the mathematical and physical concepts used in the area of Fluid Dynamics.

## Teaching methods

Lectures, problem solving

20 lectures, no tutorials

## Assessment

One formal 2 hour written examination.