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Mathematical methods and fluid mechanics
| Start | End |
|---|---|
| 03 Oct 2026 | Jun 2027 |
What you will study
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Unit 1 Properties of a fluid introduces the continuum model and many of the properties of a fluid, such as density, pressure and viscosity. The basic equation of fluid statics is formulated and used to find the pressure distribution in a liquid and to provide a model for the atmosphere. -
Unit 2 Ordinary differential equations starts by showing how changes of variables (involving use of the Chain Rule) can be applied to solve certain non-constant-coefficient differential equations, and leads on to the topics of boundary-value and eigenvalue problems. It concludes with an introduction to the method of power-series for solving initial-value problems. -
Unit 3 First-order partial differential equations extends the earlier version of the Chain Rule to cover a change of variables for functions of two variables, and shows how this leads to the method of characteristics for solving first-order partial differential equations. -
Unit 4 Vector field theory relates line, surface and volume integrals through two important theorems – Gauss’ theorem and Stokes’ theorem – and formulates the mass continuity equation for a fluid in motion.
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Unit 5 Kinematics of fluids introduces the equations of streamlines and pathlines, develops the concept of a stream function to describe fluid flows, and formulates Euler’s equation of motion for an inviscid fluid. -
Unit 6 Bernoulli’s equation analyses an important equation arising from integrals of Euler’s equation for the flow of an inviscid fluid. It relates pressure, speed and potential energy, and is presented in various forms. Bernoulli’s equation investigates phenomena such as flows through pipes and apertures, channels and over weirs. -
Unit 7 Vorticity discusses two important mathematical tools for modelling fluid flow, the vorticity vector (describing local angular velocity) and circulation. The effects of viscosity on the flow of a real (viscous) fluid past an obstacle are described. -
Unit 8 The flow of a viscous fluid establishes the Navier–Stokes equations of motion for a viscous fluid. It investigates some of their exact solutions and simplifications that can be made by applying dimensional arguments.
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Unit 9 Second-order partial differential equations shows how a second-order partial differential equation can be classified as one of three standard types, and how to reduce an equation to its standard form. Some general solutions (including d’Alembert’s solution to the wave equation) are found. -
Unit 10 Fourier series reviews and develops an important method of approximating a function. The early sections refer to trigonometric Fourier series, and it is shown how these series, together with the separation of variables, can be used to represent the solutions of initial-boundary value problems involving the diffusion equation and the wave equation. Later sections generalise to the Fourier series that arise from Sturm–Liouville problems (eigenvalue problems with the differential equation put into a certain standard format), including Legendre series. -
Unit 11 Laplace’s equation is a particular second-order partial differential equation that can be used to model the flow of an irrotational, inviscid fluid past a rigid boundary. Solutions to Laplace’s equation are found and interpreted in the context of fluid flow problems, for example, fluid flow past a cylinder and a sphere.
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Unit 12 Water waves uses some of the theory developed in Block 3 to investigate various types of water waves, and discusses several practical examples of these waves. -
Unit 13 Boundary layers and turbulence looks at the effects of turbulence (chaotic fluid flow) and the nature of boundary layers within a flow, introducing models to describe these phenomena.
Entry requirements
Preparatory work
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functions, graphs and coordinate systems -
differentiation and functions of several variable -
linear algebra -
differential equations -
mechanics -
numerical methods and practical applications -
Fourier series.
Teaching and assessment
Support from your tutor
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marking your assignments and offering detailed feedback to help you improve -
providing individual guidance, whether that’s for general study skills or specific module content -
guiding you to additional learning resources -
facilitating online discussions between your fellow students in the dedicated forums.
Assessment
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4 Tutor-marked assignments (TMAs) -
Examination
What's included
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a week-by-week study planner -
course-specific module materials -
audio and video content -
assessment details and submission section -
online tutorial access -
access to student forums.
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supplementary items.
You will need
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a scientific calculator.
Computing requirements
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Primary device – A desktop or laptop computer with at least 8 GB of RAM and a quad-core processor (2.4 GHz minimum speed). It’s possible to access some materials on a mobile phone, tablet or Chromebook; however, they will not be suitable as your primary device. -
Peripheral device – Headphones/earphones with a built-in microphone for online tutorials. -
Operating systems – Windows 11 or the latest supported macOS. -
Internet access – Broadband or mobile connection. -
Browser – Google Chrome and Microsoft Edge are recommended; Mozilla Firefox and Safari may be suitable. -
Our OU Study app operates on supported versions of Android and iOS. -
Software – Any additional software will be provided or is generally available for free.