| Lecture notes | OHPs in Lectures | Exercises sheets and answers | Summary of what was done | Miscellaneous |
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Main lecture notes for this part
A PDF of main lecture notes is available if you
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Exercises sheets and answers for this part
| Week: (PDFs of any OHPs used in a new window) | 16 | 17 | 18 | 19 | 20 | 21 | 29 |
| Week: (PDFs of any OHPs used in currrent window) | 16 | 17 | 18 | 19 | 20 | 21 | 29 |
Summary of what was done each week
| Week: | 16 | 17 | 18 | 19 | 20 | 21 | 29 |
Week 16:
OHPs used,
OHPs used.
print,
print.
Revision of gradient, divergence and curl.
The directional derivative.
Revision of the divergence theorem, Stokes' theorem and Green's theorem
in the plane.
The divergence and curl defined as limits based on the divergence
theorem and Stokes' theorem.
Divergence of a curl=0, the curl of a gradient is the zero vector
and the mention of potentials.
Week 17:
OHPs used,
OHPs used.
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print.
Gradient, divergence and curl in cylindrical polars.
Introduction to the continuum model.
A brief introduction of what stress is and the case of hydrostatic pressure
when we have an inviscid fluid.
Week 18:
OHPs used,
OHPs used.
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The equation of hydrostatic pressure for a fluid in equilibrium.
Describing fluid flow, the Lagrangian description and a Eulerian description.
The material time derivative.
The Lagrangian acceleration, the local acceleration and
the convective acceleration.
Examples of converting a Lagrangian description to a Eulerian description.
Classification of fluid flows -- 2D flows, steady flows, stagnation points
and particle paths.
Week 19:
OHPs used,
OHPs used.
print,
print.
Recap of the Lagrangian and Eulerian descriptions,
the material time derivative and terms such as Lagrangian acceleration,
local acceleration and convective acceleration.
Classification of fluid flows -- 2D flows, steady flows, stagnation points
and particle paths and streamlines.
Examples of determining particle paths and streamlines in unsteady flow
cases when they are different.
The equation of mass conservation linking density and velocity
and the condition for a flow to be incompressible.
A brief look at Euler's equations of motion for an inviscid fluid with
discussion as to why streamlines are considered and an introduction
to the term vorticity.
Brief discussion of the limitations of the inviscid model via showing
the solution of a model which includes viscous terms for the flow past
a cylinder at different speeds.
Week 20:
OHPs used,
OHPs used.
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Recap of material time derivative
and equation of mass conservation.
The condition on the velocity for a flow to be incompressible.
2D steady incompressible flow and the existence of a stream function
$\psi$. Streamlines are curves such that $\psi=const$.
The velocity components in both Cartesian and polar coordinates.
The definition of vorticity.
When the vorticity is zero we have irrotational flow and we have a
velocity potential as well as a stream function.
Interpretation of the vorticity as an average rotation.
Uniform flow and simple shear flow.
A brief introduction to flows to be considered in the next week.
Week 21:
OHPs used,
OHPs used.
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print.
Recap of the terminology: incompressibility, steady flow, stagnation points,
vorticity, irrotational flow, stream function, velocity potential
and that both functions satisfy Laplace's equation.
Recap of uniform flow and simple shear flow.
A line source with \psi=A\theta.
The strength of a source.
A line vortex involving \psi=(const)\ln r and the circulation.
Verification that the line source and line vortex are irrotational flows.
Derivation of the stream function for a dipole involving a line
source and a line sink of equal magnitudes moving together and the
strengths tending to infinity appropriately.
Combining a uniform flow and a dipole and showing that this gives the
flow round a cylinder in the inviscid model of fluid flow.
Comments about the case when a fluid has some viscosity as was
discussed at the end of chapter 2.
Week 29:
OHPs used,
OHPs used.
print,
print.
Revision session for the weeks 16-21 of ma2741.