I am trying to understand Navier-Stokes fluid equations and I have two questions (these are very primitive questions, I am still trying to understand basic concepts)
1) all books say "assume that density is constant...assume fluid is incompressible", but this makes me confused: observing any smoke one can see some parts are completely opaque, some are particularly opaque and some are nearly transparent, so density does change in space and not constant as the books suggest?!
2) is pressure a function of density? I mean, the more you "compress" gas the more dense (i.e. density increases per unit volumes) hence the more pressure? so one can say pressure is just a function of density? Another way to ask my question: is it possible to increase pressure without increasing density? they "look" the same to me!!