Physics is made of 3 main branches: classical mechanics "point mass" including gravity, electromagnetism (80% of phenomena) & fluid mechanics.
The 1st and 3rd are so far conceptually the most incompatible.
Pressure is the primitive in fluid theory(and force a non prinitive) , force in the other .
So obviously the unified fluid-poin mass theory needs to find new primitives or reject one concept.
Although Hamiltonian formulation does this to a degree, we need a deeper, more physically insightful theorization.
Rationale& problems
The rationale
nature is unified.
The problem
Incompressibility and other properties that succesfully explain
fluids cannot be related to point mass mechanics properties.
This is a didision that is man made and not for nature
Laws
Bernoulli & Newtonian cannot be unified. A new theoretical entity needs to be invented, like when Faraday invented the field, to incorporate one in another.
First a key question must be established that is Meaningful and observational effects based, about the relation of point mass forsive andBernoulli fluid phenomena
Just an observation, using the incompressible flow model there is no longer a thermodynamics pressure. You have rather a Lagrange multiplier.
Fluid mechanics is fundamentally based on physics laws: conservation laws of mass, momentum, and energy (first principle). These laws are applied under the hypothesis of continuum medium. Constitutive laws needed to complete the description of the dynamics of the classical fluid must verify the fundamental inequality of thermodynamics (second principle of thermodynamics). In this regard, the hypothesis of the local state leads to the formulation of the Gibbs relation in terms of the material derivatives. Taking into account the equation of the rate of entropy production, this fundamental inequality indicates that the irreversibility in the fluid results from the processes of thermal conduction and the work of deformation of the medium by the viscous stresses; the rate of entropy production can be expressed as the sum of the rate of intrinsic dissipation and heat dissipation. The constitutive laws of the classical fluid formulation should ensure that this sum remains positive so that it does not contradict the second principle.
See for example in French
Chapter ECFM-Chapitre 2 : Lois de Conservation
Chapter ECFM-Chapitre 3 : Equations Générales du Fluide Classique
Mecanics is far from being based only on point particles.Fluid mechanics and gases are harder many body problems where a
Variety of different approximations are applied.
The ideal gas model wherr the particles are taken independent or independent electron model in solids may answer your question.
Fluids are in a sense the opposite case
And rely on high correlation of the constituants.
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