Kinematics of Hydrodynamics
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The goal of this chapter is to discuss the general frame of hydrodynamics, like particle trajectories (path lines), stream lines, streak lines, free surfaces, and fluid surfaces, and to compare their behavior in the Eulerian and Lagrangian frames. The following sections and chapters proceed on the assumption that the fluid is practically continuous and homogenous in structure. Of course, the concept of continuum is an abstraction that does not take into account the molecular and nuclear structure of matter. In that, we assume that the properties of the fluid do not change if we consider smaller and smaller amounts of matter 167]. May be the wisest point of view while we remain at the level of general laws of fluid dynamics (or fluid mechanics) is to keep the physical scales rather vague . This aspect is in direct relation with the fact that these laws can be made dimensionless in a large variety of situations.