Further note, that unlike the mathematical concept of a fluid parcel which can be uniquely identified as well as exclusively distinguished from its direct neighbouring parcels in a real fluid such a parcel would not always consist of the same particles.
22.
Fluid animations are typically focused on emulating the qualitative visual behavior of a fluid, with less emphasis placed on rigorously correct physical results, although they often still rely on approximate solutions to the Euler equations or Navier-Stokes equations that govern real fluid physics.
23.
Part two of the question ( assuming there is a relatively easy answer to part 1 ) is : If I wanted to approximate the density of a real fluid-what kinds of density functions over the unit sphere produce relatively, simple functions for the line integral?
24.
The "'momentum thickness "', "'? "'or "'? 2 "', is the distance by which a surface would have to be moved parallel to itself towards the reference plane in an inviscid fluid stream of velocity u _ 0 to give the same total momentum as exists between the surface and the reference plane in a real fluid.
25.
The "'displacement thickness "', "'? * "'or "'? 1 "'is the distance by which a surface would have to be moved in the direction perpendicular to its normal vector away from the reference plane in an inviscid fluid stream of velocity u _ 0 to give the same flow rate as occurs between the surface and the reference plane in a real fluid.
26.
It is available via its traditional derivation ( a mechanical equation of state ), or via a derivation based in statistical thermodynamics, the latter of which provides the equal area rule, and related but distinct theoretical models, e . g ., based on the principle of corresponding states, have been developed to achieve better fits to real fluid behaviour in equations of comparable complexity.
27.
For example, if " n " were less than one, the power law predicts that the effective viscosity would decrease with increasing shear rate indefinitely, requiring a fluid with infinite viscosity at rest and zero viscosity as the shear rate approaches infinity, but a real fluid has both a minimum and a maximum effective viscosity that depend on the physical chemistry at the molecular level.
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