## MAS320 Fluid Mechanics I

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 Nils Mole 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 module builds on Level 2 work (MAS280 Mechanics and Fluids; MAS222 Differential Equations). The first step is to derive the equation (Navier-Stokes) governing the motions of most common fluids. This serves as a basis for the remainder of MAS320, with the main addition to MAS280 being that it covers viscous (frictional) fluids.

Prerequisites: MAS222 (Differential Equations); MAS280 (Mechanics and Fluids)
No other modules have this module as a prerequisite.

## Outline syllabus

• Rate of strain tensor, constitutive equation, Navier-Stokes equation.
• The stress vector.
• Exact solutions of the Navier-Stokes equations: simple shear flow, Poiseuille flow, steady flow under gravity down an inclined plane, flow between rotating cylinders, infinite plate impulsively started into motion.
• Reynolds number and the vorticity equation. The Burgers vortex.
• Small Reynolds number flow, the flow past a sphere, flow through a tube with slowly varying radius.
• Boundary layer theory: flow past a flat plate, skin friction, displacement thickness, momentum thickness, the Blasius solution, the Kármán-Pohlhausen approximation method.

## Aims

• To broaden the students' knowledge of Fluid Mechanics, in particular by introducing them to viscous fluids.
• To introduce students to the mathematical and physical concepts used in the area of Fluid Dynamics.

## Learning outcomes

By the end of the unit students should be able to demonstrate a knowledge of Fluid Mechanics, and have an awareness of 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. Format: 4 compulsory questions.