The average gas velocity, u(g), is widely used as a measure of bubble swarm velocity in a column. However, it is only correct in the ideal case : i.e. uniform distribution of uni-sized bubbles. Under real conditions, i.e. a non-uniform distribution of multi-sized bubbles, the hindered velocity, u(h), obtained by interpolating the interface rise velocity, was identified with the real bubble swarm velocity by the authors (Shen and Finch, 1996, Chem. Engng Sci. 51, 3665-3674). The ideal case is akin to a one-dimensional domain. In the two-dimensional domain, with a knowledge of the radial gas holdup profile and liquid circulation velocity over the cross section of the column, u(h) was Simulated using the model of Richardson and Zaki with the coefficient m(c) describing the system characteristics. The observation that u(h) less than or equal to u(g) was mathematically proved by an inequality assuming a parabolic gas holdup profile of order n = 2.