A turbulent quasi-stabilized flow in a flat channel with uniform injection is considered. Results are presented from calculations carried out on the basis of equations from the theory of the Kutateladze and Leontiyev limiting Laws modified to include the effect of the longitudinal pressure gradient originating in such kind of flow. Based on these results a dependence of the relative friction factor on the injection parameter has been suggested. In addition, approximating formulae, that generalise the familiar solutions, are presented for calculating the longitudinal velocity profiles and longitudinal pressure distribution.