Abstract: A new theoretical analysis and corresponding mathematical modeling of the widely used type of one dimensional flow models and related characteristic flow parameters such as reversion point of flow, Reynolds shear stress, reversion flow position, and so on, were presented to detail the buoyancy - driven two - phase turbulence flow structures in bubble columns. Different relations between the said flow parameters and design parameters were obtained and compared with other mathematical modeling results. Based on the above analysis,a scale - up rule of such reactors was derived from hydrodynamic similarity , that is, with the local maximum Reynolds shear as the characteristic force scale , that is estimated by a theoretical relation provided in the present work, two bubble columns with different scales would have the same or approximate flow patterns and velocity distributions when the two columns have the same or approximate maximum Reynolds shear values. The said rule is verified through a comparison of the prediction results with experimental data available in literature, and good agreements were obtained.