Within the framework of a program devoted to complex research on electric arcs and near-electrode processes, a simplified 2-dimensional mathematical model of electric
arc with self-settled length in a cylindrical cooled channel with axial injection of working gas was developed. To find electric arc length in the channel it was supposed that the arc moves downwards on a flow and makes casual wandering on cross section of the channel under action of whirlwinds, which each bent site of an arc generates in a flow behind itself. Within these assumptions the equation for mean arc length was obtained. Created model of an electric
arc complemented by a condition of short circuit quite satisfactorily describe known experimental data.