A self-consistent solution of genaralized, quasi-one dimensional non-ideal fluid equations describing the steady state critical plasma flows in high pressure capillary discharges is presented. All three equations used (continuity, momentum and energy) include ablative effects. No limitation to the case of ideal equation of state or to the spatial uniformity of the ionization degree is imposed. A numerical algorithm enabling the determination of self-consistent boundary conditions required for the integration of the differential equations is used. Illustrative results for typical physical parameters, namely, electrical current and radius and length of the capillary are presented for polyethylene capillaries. The effects of changes in the geometrical characteristics of the capillary as well as in the electrical and radiative characteristics of the discharge on the plasma parameters are also considered.