A steady-state submerged arc discharge stabilized by a water stream is modelled as a plasma bubble water. On the upstream boundary of the bubble, the water is evaporated, and the water vapour is dissociated and ionized. With a directed water velocity of ∼ 1 m s-1, the convective heat flux in the water stream direction is much more than the conducted flux. For a discharge power of ∼ 100 kW, the plasma bubble will have a length of ≈0.115 m and a radius of ≈0.018 m; the maximum plasma temperature will be ≈3800 K and the minimum plasma to water density ratio will be ≈5 × 10-5. The flow of plasma and water through a tube was considered using conservation laws. A criterion for tube chocking was obtained: pressure in the water upstream of the plasma bubble is determined by the discharge power and bubble cross-section. The plasma radiation is approximately black body in the core of the bubble, but on the boundary with the liquid water it is depressed in the ultraviolet region due to a strong absorption by the neutral hydrogen and oxygen atoms.