General aspects of hydrodynamics

In hydrodynamics the description of fluid properties is based usually on a continuum hypothesis. Comprehensive treatments are given in Refs. [1-3] The elementary volumes have side lengths in the micrometer scale and hence are very large in comparison with the particle sizes. Such elementary volumes contain about 10 particles forming a continuum. 

Two methods are commonly used to study a fluid, the Lagrangian and the Eu-lerian picture. The Lagrangian description considers the trajectories v t) of fluid points as a function of time, which would be observed if very small iron filings particles were present in the fluid. Although intuitive, this description leads generally to a rather cumbersome analysis and is not the more appropriate one. In lieu of this approach the Eulerian method is preferred, investigating the motion of the fluid at fixed points of the space as a function of time. In this theory the velocity field v(r, /.) is the basic studied quantity. 

only incompressible fluids will be considered. This model is sufficiently close to real liquids and solutions. 

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