A computational study of gas-liquid flows in micro/meso channels with characteristic dimensions of 100 mum to 1 mm has been conducted. The working fluids under investigation passing through the circular channel were air and water. Two phase flow patterns obtained from the computed results have been compared to those of the ones reported in literature and a reasonable agreement has been obtained. Also the frictional pressure drop values predicted during the computations were within the range of the measured ones. After the validation of the computational procedure, keeping the dimensionless numbers relevant to the small hydraulic diameters constant, the size of the channel has been changed to understand the transition to the flow regime in which the "conventional" governing equations fail.