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Mechanics & Stress Analysis*
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Fundamentals of Fluid Mechanics

In fluid mechanics, ‘flow’ is what we call a fluid’s tendency to deform continuously under a shear force. This response to tangential forces and not normal forces is what differentiates fluids from solids:

Both the solid and the fluid will deform slightly under the uniform normal force, but then resist any further compression.

When a shear (tangential) force is applied to a solid, it deforms slightly in the direction of the force, but then resists further deformation. When a shear force is applied to a fluid, however, it immediately begins to deform, and will continue to do so until the force is removed (it will then eventually come to rest due to the frictional force between the fluid and the container wall).

When acted on by a normal force, solids and fluids behave similarly. When acted on by a shear force, they behave very differently.

As well as differentiating solids and fluids, we must differentiate between liquids and gasses:

  • A gas will fill the whole space it is given, a liquid will fill the bottom

  • Gasses are far more compressible, as their density is dependent on pressure

The Continuum Viewpoint

Fluids, like solids, are made up of a vast number of molecules. If we really wanted to, we could therefore investigate the flow and deformation of fluids by looking at the motion of each individual molecule. This is called the molecular viewpoint and is the most fundamental viewpoint – it is used in the pure sciences, but in engineering it is far too complex.

Instead, we make the continuum assumption:

A body consists of infinitely many homogeneous elements, each one significantly smaller than the body itself, but significantly larger than the individual molecules.

We model the elements as homogeneous, as this allows us to define important properties, such as density, temperature etc. at the point of the element.

Assuming that the body is not homogenous on the whole, we can find the average density of the body:

If we define an element in the body to have mass δm and volume δV, where the volume tends towards zero, we can work out the density of the individual element: