# INVISCID FLUID DYNAMICS - 2024/5

Module code: MAT2050

## Module Overview

This module introduces students to inviscid fluid flows including surface waves. 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 & Physics

### Module Leader

DUNLOP Carina (Maths & Phys)

## Overall student workload

Independent Learning Hours: 69

Lecture Hours: 33

Guided Learning: 15

Captured Content: 33

Semester 2

None.

## Module content

Indicative content includes:

• 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.

• 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
School-timetabled exam/test In-semester test (50 minutes) 20
Examination End-of-Semester Examination (2 hours) 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 in-semester test (50 minutes), worth 20% of the module mark, corresponding to Learning Outcomes 1 to 4.

• A synoptic examination (2 hours), worth 80% of the module mark, corresponding to Learning Outcomes 1 to 6.

Formative assessment
There are two formative unassessed courseworks over an 11 week period, designed to consolidate student learning.

Feedback
Students receive individual written feedback on the formative unassessed coursework and the in-semester test. The feedback is timed so that feedback from the first unassessed coursework assists students with preparation for the in-semester test. The feedback from both unassessed courseworks and the in-semester test assists students with preparation for the end-of-semester examination. This written feedback is complemented by verbal and written feedback given in tutorials. Students also receive verbal and written feedback in office hours.

## Module aims

• Introduce students to inviscid fluid problems including real world applications.
• Introduce key techniques required to solve such problems including flow visualisation.
• Enable students to solve complex problems using a variety of approaches, such as the velocity potential, the complex potential and the stream function.
• Introduce conformal mapping as a technique (used in conjunction with complex potentials) to solve fluid dynamics problems in complex geometries.
• Introduce the Euler equations of motion and their use.
• Introduce the theory of surface water waves and the concepts of group and phase velocity.

## Learning outcomes

 Attributes Developed 001 Students will understand and be able to quote definitions related to fluids such as inviscid, irrotational, incompressible, pressure, velocity field etc. KC 002 Students will recognize that a velocity potential can be introduced to describe the flow for an irrotational incompressible fluid. They will be able to calculate the velocity field from the velocity potential and vice versa. KCT 003 Students will be able to apply Bernoulli¿s equation to find the pressure field given a particular flow field, and will recognize 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 004 Given the velocity potential for a particular flow field, students will be able to calculate the stream function, and vice versa. Further, they will be able to calculate the streamlines for the flow and plot them successfully. KCT 005 Students will be able to define the complex potential and calculate the velocity field and streamlines from this potential. Students will be able to understand how the complex potential can be used in conjunction with conformal mappings to calculate flow properties in complex geometries. KC 006 Students will be able to calculate the dispersion relation for linear water waves and calculate group and phase velocities. 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:

• Three one-hour lectures per week for eleven weeks, with typeset notes to complement the lectures. The lectures provide a structured learning environment with opportunities for students to ask questions and to practice methods taught.

• Students will reinforce lectures by tackling a wide range of problems.

• There are two unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive individual written feedback on these as guidance on their progress and understanding.

• Lectures may be recorded. Lecture recordings are intended to give students the opportunity to review parts of the session that they might not have understood fully and should not be seen as an alternative to attendance at lectures.

Students should also use the books listed as background reading on the subject.

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.

## Reading list

https://readinglists.surrey.ac.uk
Upon accessing the reading list, please search for the module using the module code: MAT2050

## Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourceness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills and capabilities in the following areas:

Digital Capabilities: The SurreyLearn page for MAT2050 features a dynamic discussion forum where students can pose questions and engage with others using e.g. LaTeX and MathML tools. This enhances their digital competencies while facilitating collaborative learning and information sharing.

Employability: The mathematical proficiency gained by taking MAT2050 hones critical thinking and problem-solving abilities. Students learn to evaluate complex problems, break them into manageable components, and apply logical reasoning to arrive at solutions — these skills are highly sought after by employers.

Global and Cultural Capabilities: Students enrolled in MAT2050 originate from various countries and possess a wide range of cultural backgrounds. During problem solving sessions in lectures, student engagement in discussions naturally cultivates the sharing of different cultures.

Resourcefulness and Resilience: Students taking MAT2050 gain skills in solving complex problems involving fluid flow using a variety of techniques. The practice gained in identifying an appropriate approach for a problem and then solving the problem promotes resourcefulness and resilience.

Sustainability: MAT2050 equips students with valuable knowledge and skills to address critical challenges in sustainability. For example, fluid dynamics plays a vital role in the design and optimization of wind turbines and other renewable energy systems. Further, inviscid fluid dynamics is essential in improving the aerodynamics of vehicles, reducing drag and fuel consumption. Sustainable transportation relies on efficient, eco-friendly vehicles, and the principles of fluid dynamics are fundamental to achieving these goals.

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Physics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Nuclear Astrophysics BSc (Hons) 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 with Statistics MMath 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
Physics with Nuclear Astrophysics MPhys 2 Optional A weighted aggregate mark of 40% is required to pass the module
Physics MPhys 2 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Quantum Computing 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 and Physics BSc (Hons) 2 Optional A weighted aggregate mark of 40% 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 and Physics MMath 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 2024/5 academic year.