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...Notes of fluid mechanics piero olla isac cnr and infn sez cagliari i monserrato italy june contents continuous limit suggested reading kinematics lagrangian eulerian description a ow transport vector eld vorticity rate strain compression application to hamiltonian dynamics conservation mass momentum constitutive laws the navier stokes equation condition local thermodynamic equilibrium digression into plasma physics microscopic interpretation pressure viscosity non newtonian uids energy kinetic balance heat isoentropic propagation sound bernoulli s hydrostatics stability under convection compressible ows boussinesq approximation burgers viscous method characteristics ideal potential inertia gravity waves corrections kelvin theorem helicity two dimensional invariance relabeling turbulence homogeneous isotropic time structure inertial range passive scalar weare interested in at macroscopic scales such that eects from discrete nature medium can be disregarded other words we are focusing on...