MATH35001: Viscous Fluid Flow
This course is concerned with the mathematical theory of
viscous fluid flows. Fluid mechanics is one of the major areas
for the application of mathematics and has obvious practical applications in
many important disciplines (aeronautics, meteorology, geophysical
fluid mechanics, biofluid mechanics, and many others). Using a general
continuum mechanical approach, we will first derive the governing
equations (the famous Navier-Stokes equations) from first principles.
We will then apply these equations to a variety of practical problems
and examine appropriate simplifications and solution strategies.
Many members of staff in the department have research
interests in fluid mechanics and this course will also lay the foundations
for possible future postgraduate work in this discipline.
Vortex shedding caused by the flow past a flat plate (snapshot 1)
![[Vortex shedding 1]](vort1.gif)
This course is currently taught by
Prof Matthias Heil. This page provides online access to the lecture
notes, example sheets and other handouts and announcements.
Please note that the lecture notes only summarize the main results
and will generally be handed out
after the material has been covered in the lecture.
NOTE: The various links on this page (probably) won't
work from the mirrored version on the school's undergraduate
course pages. Please go to the original at
https://personalpages.manchester.ac.uk/staff/matthias.heil/Lectures/Fluids/index.html
before trying to download any of the handouts.
If you have any questions about the lecture, please see me in my
office (2.224 in the Alan Turing building), contact me by
email (
M.Heil@maths.man.ac.uk) or catch me after the lecture.
Vortex shedding caused by the flow past a flat plate (snapshot 2)
![[Vortex shedding 2]](vort2.gif)
Syllabus
- 1. Introduction; overview of the course; introduction to index
notation. [2]
- 2. The kinematics of fluid flow: The Eulerian velocity field; the rate of
strain tensor and the vorticity vector; the equation of
continuity. [3]
- 3. The Navier-Stokes equations: The substantial derivative; the
stress tensor; Cauchy's equation; the constitutive equations for
a Newtonian fluid. [4]
- 4. Boundary and initial conditions; surface traction and the conditions
at a free surface. [1].
- 5. One-dimensional flows: Couette/Poiseuille flow; flow down
an inclined plane; the vibrating plate. [3]
- 6. The equations in curvilinear coordinates; Hagen-Poiseuille
flow; circular Couette flow. [2]
- 7. Dimensional analysis and scaling; the dimensionless
Navier-Stokes equations and the importance of the Reynolds number;
limiting cases and their physical meaning; lubrication theory. [3]
- 8. The streamfunction/vorticity equations [2]
- 9. Stokes flow (zero Reynolds number flow); flow past a sphere. [2]
- 10. High-Reynolds number flow; boundary layers; the Blasius
boundary layer. [2]
Assessment:
The course will be examined in a two hour exam in January. Coursework
(you will be expected to hand in homework on a regular basis) will
account for 20% of the final mark.
Coursework:
Please hand in your coursework by Thursday 12 noon
of the week following the one in which the sheet was
covered in the examples class (so you'll have a second chance to
ask questions about a example sheet if you can't get all the coursework
done during the examples class). Please place your solutions
into the envelope at my office door (room 2.224 in the Alan Turing building).
I will return the marked homework (with solutions) in the following
week (or so....).
Handouts:
Please note a few corrections for previous
handouts (the files above have already been corrected).
Solutions:
For a short time only, the solutions to the example sheets (scanned
in and turned into pdf files) are available here
.
Old exams:
This course only used to be given every two years so there's only
a limited collection of previous exams available online. I believe
you are able to locate the most recent one (from 2006). I don't have
a copy of the actual exam paper from 2004 but here's the pdf version
of the final draft that I submitted to the exam office who filled
in dates etc.
...and, just in case you're about to send me an email: "No, you can't
have the solutions!".
Changes to timetable/coursework submission for the last few
weeks of term:
- Fri, Nov 16: Examples class (Example Sheet VII)
- Wed, Nov 21: Double lecture
- Fri, Nov 23: Examples class (Example Sheet VII)
- Mon, Nov 26: Example Sheet VII due
- Wed, Nov 28: Double lecture
- Fri, Nov 30: Examples class cancelled!
- Wed, Dec 05: Single lecture + examples class (Example Sheet VIII)
- Fri, Dec 07: Single lecture
- Wed, Dec 12: Single lecture + examples class (Example Sheet VIII)
- Thu, Dec 13: Example Sheet VIII due
- Fri, Dec 14: Single lecture
Page last modified: November 15, 2007
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