The reason for making assumptions is to make the calculation
easier (or possible).
Although fluids like air are certainly not incompressible,
the variation in their density is often unimportant.
Usually, as long as the Mach number is small (<0.3 as a
rule of thumb) then compressibility isn't important.
Because assuming a liquid fluid (not gas fluid) incompressible is good
enough in 98% of situations. But perhaps you get some kind of
enjoyment out of solving PDEs with non-symmetric stress tensors? You
can keep the term if you really want or need it.
Maybe good enough in situations without a pressure like open flow channels.
Hydropower pressure pipes need a surge tank to regulate elastic energies
during valve closing!
I trie to give the answer found in most text books of elasticity. The bulk
modulus K becomes K=E/(3*(1-2*n)) . So the denominator vanishes for
materials with Poisson number n=0.5 and therefor K is becoming infinite
(incompressibel). This singularity backs on the assumption that the elastic
modulus E>0 which is not the case for materials with n=0.5 where E=0 and
G=0. The bulk modulus for fluids can be found better with K=L*(1+n)/(3*n)
where L is the lame constante which tend toward K=L for n=>0.5 !
Don't you think that the use of elastic modulus equations for solids is
a poor beginning to understand the flow of fluids?
Encountering singularities is often a good clue that your simplifying
assumptins are inapplicable.
I think that the use of solid elasticity to understand fluids is loaded
with inconsistencies. Such as what you describe above.
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