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Hmmm..I was hoping you wouldn't talk about reduced density: the word
"Incompressible" is often specified in this Bernoulli connection, after all.
The key idea is to consider the difference between the total pressure
along a stream line, and
the total pressure across streamlines - where dynamic pressure is not
available?
Dynamics does not allow us the luxury of supposing as we often can in
statics, that
" pressure is the same everywhere."