In fluid mechanics, one hears the term steady, incompressible flow. Steady flow refers to the fact that the overall flow pattern (the flow lines, which indicate the paths of individual particles within the fluid) do not change with time. Incompressible flow refers to the fact that the fluid density does not change with time (the mass of the fluid cannot be "compressed" into a smaller volume, for instance). My question regards the alternatives to this pair of conditions. I understand that unsteady flow is possible in an incompressible fluid (after all, why wouldn't it be?). More perplexing to me is whether steady flow is possible in a compressible fluid. If the density of the fluid changes with time, then it seems to me the flow is not steady, because the paths of particles (or fluid elements, if you like) passing a certain point could not be the same as their predecessors'. Is incompressibility a prerequisite for steady flow?