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The fluid is viewed as adjacent

fluid elements

The elements are taken as internally continuous, and surrounded by neighboring elements, or an external boundary.

The elements are analyzed in two ways:

  • The Eulerian view
  • The Lagrangian view

  • The first considers a spatially fixed well defined volume with respect to which fluid flow in and out. The latter considers a moving well-defined volume (attached to a given element of the fluid).

    In each case a respective element of fluid of given properties is associated with a three-dimensional velocity vector.

    Given a reference state where all fluid elements have a known velocity vector, and where all respective forces are well defined, and well quantified, Newtonian mechanics claims to be able to predict all future states in terms of the velocity and spatial attributes of the given fluid.

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