Abstract: An asymptotic expansion of compressible N-S equations werededuced via parametric expansion, and liquid flow characteristics under highdriven pressures in long micro-channels with arbitrary cross sections wereanalyzed by solving the zeroth order equations. The contributions due tocross section, length of the wall-slip, and other related factors were takeninto account by solving the Green's function over the cross section. A setof zeroth order solutions for circular cylinders of constant cross sectionwere presented, and the influences of the compressibility and viscosity ofthe liquids, and the slip length on the flow characteristics inmicro-channels under high pressure were studies.