# INVISCID FLUID DYNAMICS - 2022/3

Module code: MAT2050

## Module Overview

This module introduces students to inviscid fluid flows. By the end of the module, students should be able to recognise dominant features of fluid motion, and to derive some simple solutions of the equations of motion. Students should also have an appreciation of the force balances that produce various classes of flows.

### Module provider

Mathematics

DUNLOP Carina (Maths)

## Overall student workload

Independent Learning Hours: 106

Lecture Hours: 11

Seminar Hours: 11

Guided Learning: 11

Captured Content: 11

Semester 2

## Prerequisites / Co-requisites

MAT1036 Classical Dynamics, MAT1005 Vector Calculus

## Module content

Background. Revision of Vector Calculus.

Introduction.  Density, hydrostatics, one-dimensional flow in tubes.

Kinematics. Velocity streamlines, particle paths, material derivative, mass conservation, velocity potential for irrotational flows.

Dynamics. Euler's equations of motion, boundary conditions, Bernoulli's equation.

Channel Flows. Flow under sluice gate, hydraulic jumps

Two-Dimensional flows.  Stream functions, line vortices, complex potentials, cylinder with circulation, image systems, conformal mappings.

Water waves. Potential flow with a free surface, small amplitude waves, phase velocity, group velocity.

## Assessment pattern

Assessment type Unit of assessment Weighting
Online Scheduled Summative Class Test ONLINE TEST 20
Examination Online ONLINE EXAM 80

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Understanding of the methods required to solve complex fluid flow problems.

• Subject knowledge through the recall of definitions as well as explaining the physical nature of flows, and explaining under what conditions certain approximations breakdown.

• Analytic ability through the solution of unseen and seen similar problems in the test and exam.

Thus, the summative assessment for this module consists of:

• One final examination worth 80% of the module mark.

• One in-semester test; worth 20% module mark

Formative assessment and feedback

Students receive written feedback via a number of marked, but unassessed, coursework assignments over an 11 week period.  In addition, verbal feedback is provided by lecturer in lectures and in office hours.

## Module aims

• Introduce students to inviscid fluid problems including the techniques required to solve such problems.
• Enable students to solve complex problems using a variety of approaches, such as the velocity potential, the complex potential and the stream function.
• Illustrate how the techniques of the module can be applied to more complex situations such as flow over aerofoils.

## Learning outcomes

 Attributes Developed 1 Understand and quote definitions related to fluids such as inviscid, irrotational, incompressible, pressure, velocity field etc. KC 2 Recognise that for an irrotational incompressible fluid that a velocity potential can be introduced to describe the flow and to be able to calculate the velocity field from the velocity potential and vice versa. KCT 3 Apply Bernoulli's equation to find the pressure field given a particular flow field, and recognise that this is only valid along a streamline. Students should also be able to calculate the pressure field using the unsteady version of Bernoulli's equation. KC 4 Calculate a stream function for a particular flow field given its velocity potential, and vice versa, and be able to calculate the streamlines for the flow and plot them successfully. KCT 5 Define the complex potential and calculate the velocity field and streamlines from this potential. Use conformal mappings to calculate streamlines and flow properties from simpler flow fields. KC 6 Calculate the dispersion relation for linear water waves. KC

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• A thorough account of inviscid flow techniques under a variety of simple situations, inside and outside simple geometries.

• Experience (through demonstration) of the methods and techniques used to solve problems in inviscid fluid mechanics.

The learning and teaching methods include:

Teaching will be by lectures and problem classes. In addition to reading the lecture notes, students will learn by tackling a wide range of problems. Students should also use the books listed as background reading on the subject.

Three hours per week (lectures and problem classes) over an 11 week period.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: MAT2050

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Physics BSc (Hons) 2 Optional A weighted aggregate of 40% overall and a pass on the pass/fail unit of assessment is required to pass the module
Mathematics and Physics BSc (Hons) 2 Optional A weighted aggregate of 40% overall and a pass on the pass/fail unit of assessment is required to pass the module
Physics MPhys 2 Optional A weighted aggregate of 40% overall and a pass on the pass/fail unit of assessment is required to pass the module
Mathematics and Physics MPhys 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2022/3 academic year.