KC6027 - Fluid Dynamics

What will I learn on this module?

This module is designed to introduce fundamental concepts in the mathematical area of Fluid Dynamics. You will analyse the equations of continuity and momentum, and will investigate key concepts in this area. We will introduce the Navier-Stokes equations, and case studies will be used to visualise and analyse real-world problems (using appropriate software) as appropriate to delivery of the module. Initially, we will use the inviscid approximation and then utilise analytical and computational techniques to investigate flows. The second half of the module is a specialist course in laminar incompressible viscous flows, encompassing background mathematical theory allied to a case study approach, with solution to problems by both analytical and computational means.

Assessment of the module is by one individual assignment (30%) and one formal examination (70%).

The module is designed to provide you with a useful preparation for employment in an applied mathematical environment, physics environment or engineering environment.

Outline Syllabus
• Introduction of fluid dynamics, Navier-Stokes equations, equations of continuity and momentum for inviscid flow, unsteady one-dimensional flow along a pipe, irrotational flow, Bernouilli's equation, stream function formulation, flow past a cylinder, velocity potential.

• Low Reynolds Number Flow including: (i) lubrication theory, slider bearing, cylinder-plane, journal bearing, Reynolds equation, short bearing approximation; (ii) Flow in a corner, stream function formulation, solution of the biharmonic equation by separation of variables.

• High Reynolds Number Flow including boundary layer equations, skin friction, displacement and momentum thickness, similarity solutions, momentum integral equation, approximate solutions.

How will I learn on this module?

A wide range of learning and teaching approaches are used in this module. The module will be delivered using a combination of lectures and seminars in which students will be able to obtain help with problems associated with the module. Where deemed appropriate, computer laboratory sessions will be utilised to complement the taught material. Lectures allow students to experience and understand the formalism of the relevant mathematical techniques and include relevant examples. Seminars allow students to work through problems to develop their knowledge and skills, with the support of the tutor. Consequently, students have an opportunity to enhance their understanding of the subject through seminars which promote independent learning and tackle relevant problems. The mathematical rigour associated with this module naturally increases students’ employability and is a highly transferrable skill.

Students will be assessed by coursework (30%) and a formal examination (70%). The examination will cover all topics from the module. Written feedback will be provided on the coursework. Exam feedback will provided individually and also generically to indicate where the cohort has a strong or a weaker answer to examination questions.

How will I be supported academically on this module?

In addition to direct contact with the module team during lectures and seminars, students are encouraged to develop their curiosity by making direct contact with the module team either via email or the open door policy operated throughout the programme. Students will also be regularly referred to supporting resources including relevant texts and relevant multimedia materials.

References to these resources will be made available through the e-learning portal and in lectures and seminars.

What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk

What will I be expected to achieve?

Knowledge & Understanding:
1. Demonstrate critical knowledge and understanding of analytical techniques and fundamental concepts in fluid dynamics.
2. Demonstrate a systematic understanding of the stream function approach to analyse flow.
3. Demonstrate a systematic understanding of unsteady one-dimensional flow and irrotational flow problems, using the inviscid approximation.

Intellectual / Professional skills & abilities:
4. Apply and justify lubrication theory to analyse various bearing geometries.
5. Develop the boundary layer equations, obtain similarity solutions and obtain approximate solutions via the momentum integral equation, recognising the limitations of analytical approaches.

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):

How will I be assessed?

SUMMATIVE
• Coursework (30%) – 1
• Examination (70%) – 1, 2, 3, 4, 5

FORMATIVE
• Seminar problems – 1, 2, 3, 4, 5

Feedback is provided to students individually and in a plenary format both written and verbally to help students improve and promote dialogue around the assessment.

Informal feedback on work in progress is given continuously during seminars.

Formal feedback will be given directly after the coursework and the exam.

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None

Module abstract

This module is designed to introduce fundamental concepts in Fluid Dynamics - an important topic in Applied Mathematics – using both analytical and computational techniques. We will introduce the Navier-Stokes equations and case studies will be used to visualise and analyse real-world problems (using appropriate software) as appropriate to delivery of the module. The second half of the module is a specialist course in laminar incompressible viscous flows, specifically considering high and low Reynolds number flows, and encompassing background mathematical theory allied to a case study approach, with solution to problems by both analytical and computational means. Assessment of the module is by one individual assignment (30%) and one formal examination (70%). The module is designed to provide students with a useful preparation for employment or postgraduate study in an applied mathematical, physics or engineering environment.

Course info

UCAS Code G101

Credits 20

Mode of Study 4 years full-time or 5 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2022 or September 2023

Mathematics MMath (Hons)

All information on this course page is accurate at the time of viewing.

Our Campus based courses starting in 2022 and 2023 will be delivered on-campus with supporting online learning content. We continue to monitor government and local authority guidance in relation to Covid-19 and we are ready and able to adjust the delivery of our education accordingly to ensure the health and safety of our students and staff.

On-campus contact time is subject to increase or decrease in line with any additional restrictions, which may be imposed by the Government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors. This could potentially mean increased or fully online delivery, should such restrictions on in-person contact time be required.

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