MA40255: Viscous fluid dynamics
[Page last updated: 23 October 2023]
Academic Year: | 2023/24 |
Owning Department/School: | Department of Mathematical Sciences |
Credits: | 6 [equivalent to 12 CATS credits] |
Notional Study Hours: | 120 |
Level: | Masters UG & PG (FHEQ level 7) |
Period: |
- Semester 2
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Assessment Summary: | EX 100% |
Assessment Detail: | |
Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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Requisites: |
Before taking this module you must take MA30253
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Learning Outcomes: |
Students should be able to derive the Navier-Stokes equations for the flow of viscous fluids and analyse these in different flow situations using asymptotic analysis and partial differential equation theory.
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Aims: | To describe viscous flow phenomena and analyse these with the necessary mathematical theory.
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Skills: | Numeracy T/F, A
Problem Solving T/F, A
Written Communication F (on problem sheets).
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Content: | Review of Lagrangian and Eulerian descriptions: Jacobian, Euler's identity and Reynold's transport theorem. The continuity equation and incompressibility condition.
Cauchy's stress theorem and properties of the stress tensor. Cauchy's momentum equation.
Constitutive law for a Newtonian viscous fluid. The incompressible Navier-Stokes equations. Vorticity and Helmholtz's theorems. Energy. Exact solutions for unidirectional flows; Couette and Poiseuille flow.
Dimensional analysis, Reynolds number. Derivation of equations for high and low Reynolds number flows.
Further topics chosen from the following:
Boundary layer theory: thermal boundary layer on a semi-infinite flat plate. Derivation of Prandtl's boundary-layer equations and similarity solutions for flow past a semiinfinite flat plate. Discussion of separation and application to the theory of flight. Jeffrey-Hamel flows.
Slow flow: Slow flow past a cylinder and sphere. Non-uniformity of the two-dimensional approximation; Oseen's equation. Flow around corners and eddies.
Lubrication theory: bearings, squeeze films, thin films; Hele-Shaw cell and Saffman-Taylor instability.
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Course availability: |
MA40255 is Optional on the following courses:
Department of Mathematical Sciences
- RSMA-AFM16 : Integrated PhD Statistical Applied Mathematics
- TSMA-AFM17 : MRes Statistical Applied Mathematics
- TSMA-AFM19 : MSc Mathematics with Data Science for Industry
- TSMA-AWM19 : MSc Mathematics with Data Science for Industry
- TSMA-AFM16 : MSc Statistical Applied Mathematics
- USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
- USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
- USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
- USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
Department of Physics
- USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
- USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
- USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
- USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 4)
- USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
- USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)
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Notes: - This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24.
- Courses and units are subject to change in accordance with normal University procedures.
- Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
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