Experiments were carried out in geometrically similar vessels with diameters of 0.287, 0.495 and 1.1m respectively. Bubble diameter distribution was measured with a dual electric conductivity probe placed in the tanks. Gas holdup was measured by spillover method. Considering the coalescence of bubbles in the upper circulation region of the aeration stirred tank, introducing the concepts of turbulence decay and effective viscosity of gas-liquid system into this work, and taking into account the equilibrium between the surface energy of the bubbles and the energy supplied by agitation, mathematical models for bubble diameter and mean gas holdup were derived. The mathematical models were confirmed by experimental data.