What is Continuum and Fluid Mechanics?
Continuum Mechanics is a means of studying the behaviour of materials by ignoring its particulate nature. A continuum is an area that can keep being divided and divided infinitely; no individual particles. It is a simplification that makes it possible to investigate the movement of matter on scales larger than the distances between particles. So when studying the movement of the atmosphere the fact that is it made up of atoms is ignored. It would, in any case, be impossible to predict the motion of each atom. Fortunately, when asking questions such as "How warm will it be tomorrow?" we are only interested in the average behaviour of large numbers of atoms, not in their individual motion. At larger scales the evolution of galaxies can also be described using continuum models instead of trying to predict the movement of every planet, asteroid, and star.
This approach is used to study a huge range of phenomena, including the flow of air and water as well as in studies of rock slides (the individual particles being large rocks), snow avalanches, blood flow, and even galaxy evolution.
Fluid Mechanics is a subdiscipline of Continuum Mechanics which focuses on the behaviour of fluids which include liquids and gases. Important examples for our everyday lives are water and air.
Beautiful photos of fluids in motion can be found in the Physics of Fluid gallery.
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Continuum and Fluid Mechanics and Applied Mathematics
Have you ever wondered how airplanes fly (mathematicians 'proved' they could not around the turn of the 19th century!) or how weather predictions are made? Why dimples on a golf ball increase the distance it travels? Why curve balls curve? Do toilets really flush counterclockwise in the northern hemisphere and clockwise in the southern hemisphere? Why are surface water waves almost always nearly parallel to the beach?
These are questions you can learn answers to if you study Applied Mathematics at Waterloo.