On-line materials
 Summary Written description Animated description (with sound) Application to the Fluid Mechanics course Creation of the animations

This page contains the audio-visual animations that go with the first four lectures of the second year Fluid Mechanics course.

# Lecture 1 - Picturing fluids

## Particles vs. Continuum

We know that fluids are made up of atoms and molecules so why do we model them as if they are continuous materials with no gaps? This clip explains why and may be useful for the starter questions on examples paper 4.

Flash
Windows Media (right click and choose 'save target as', then run stand-alone.)

## Ordinary vs. Partial Derivatives

Fluid mechanics usually involves partial derivatives rather than ordinary derivatives. This is because we model fluids as continuous materials in three-dimensional space. This clip explains why and may be useful for the starter questions on examples paper 4.

Flash
Windows Media (right click and choose 'save target as', then run stand-alone.)

# Lecture 2 - Euler's Equation and Bernoulli

## The Material Derivative

Although we model fluids as if they are continuous materials, we can still identify blobs of fluid within that field. For example, we could drop a blob of ink into water and follow the ink as it moves around. If we knew the velocity field in the fluid, we could use the material derivative to calculate the velocity of that blob of fluid.

This clip explains the material derivative by using the example of a punt drifting down the river next to the Mill pub, opposite Queen's College. It may be useful for Q7 of examples paper 4.

Flash
Windows Media (right click and choose 'save target as', then run stand-alone.)

## Euler's Equation

Euler's equation is simily f=ma written for an inviscid fluid. In this clip, Euler's equation is derived by considering the forces on a fluid blob and its resultant acceleration. At the end of the clip, Euler's equation is linked to Bernoulli's equation and to streamline curvature.

Flash
Windows Media (right click and choose 'save target as', then run stand-alone.)

## Worked example: flow over a river bed

This worked example concerns the flow over a wavy river bed. In the first part of the example, the velocity field is sketched. It is not relevant to questions in the examples paper but is useful background knowledge. The second and third parts are applicable to Q8 of Examples Paper 4. This worked example also contains step-by-step instructions on how to handle the Del operator (the upside-down triangle).

Flash
Windows Media (right click and choose 'save target as', then run stand-alone.)

## Worked example: point source in 2D

This worked example uses the material derivative to find the acceleration of a fluid blob in a velocity field. The worked example is in polar coordinates, which means that we have to be careful about the directions of the unit vectors when using the Del operator. This makes it more complicated than Q8 in examples paper 4, which is in Cartesian coordinates.

Flash
Windows Media (right click and choose 'save target as', then run stand-alone.)

# Lecture 3 - Viscous Fluids

## Random Collisions, Momentum Transfer and Viscosity

By jostling around randomly, the molecules in a fluid transfer momentum from one part of the fluid to another. In a continuum model, the ability of a fluid to transfer momentum is measured by the viscosity. This clip explains the link between viscosity and molecular motion.

Flash
Windows Media (right click and choose 'save target as', then run stand-alone.)

## Viscosity and Irreversibility

The molecules in a fluid do not lose kinetic energy when they jostle around and bump into each other. If they did, gases would cool down all by themselves. However, when one group of molecules with one bulk velocity exchanges momentum with another group of molecules with another bulk velocity, the total kinetic energy of ordered motion decreases and the total kinetic energy of disordered motion increases. This clip shows how this relates to the steady flow energy equation, to the entropy of a fluid and to irreversibility.

Flash
Windows Media (right click and choose 'save target as', then run stand-alone.)

## Laminar Viscous Flow between Flat Plates

When a fluid is laminar (i.e. sheets of fluid slide over each other) and is confined between flat plates, some properties (such as velocity and shear stress) only vary in one direction while other properties (such as pressure) only vary in the perpendicular direction. This means that the partial derivatives collapse to ordinary derivatives and the velocity profiles can be found by hand. This clip confirms this and also shows how to derive the governing equation for Couette and Poiseuille flow.

Flash
Windows Media (right click and choose 'save target as', then run stand-alone.)

# Lecture 4 - Boundary Layers

## Worked example: flow reversal between flat plates

This worked example examies combined Couette/Poiseuille flow and calculates the pressure gradient at which the flow will reverse. The techniques are useful for questions 2 and 3 in Examples paper 5.

Flash
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## Boundary Layers

Whenever a solid moves through a fluid, boundary layers form along the edge of the solid. This clip explains the shape of the velocity profile in these boundary layers.

Flash
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## Boundary Layer Separation

This clip explains why boundary layers separate and compares boundary layers with the Couette and Poiseuille flow studied in lecture 3. It then explains some of the consequences for flow around wings and other objects.

Flash
Windows Media (right click and choose 'save target as', then run stand-alone.)

 © 2007 Department of Engineering, University of Cambridge Information provided by mpj1001@eng.cam.ac.uk.