Numerical simulations of the fully developed flow region in a cylindrical channel of the plasmatron are performed. As the results, temperature and velocity radial distributions, dependences of pressure and voltage gradients on operating parameters of the plasma torch are obtained for the argon arc burning in the laminar gas flow. Special attention was given to define and to calculate criteria for transition from the laminar to the turbulent regime of the gas flow in the fully developed flow region. For this purpose some experimental results of Frind, Damsky  and Runstadler  were employed. Using these experimental results we have calculated the value of the critical Reynolds number characterizing the onset of the turbulence for the arc flow.