Following a critical publication review on the expansion of fluidized bed with the fluid velocity, the well-known Richardson-Zaki equation is applied to develop a more accurate relationship linking the apparent drag force F-d, the effective gravitational force F-g and the voidage of fluidized beds under intermediate regime. A correcting constant a in the relationship is a function of Archimedes number which may provide a degree of flexibility for different systems covering a wide range of variables. With addition of the correlation developed in this work, equivalence correlations between equilibrium forces and the Richardson-Zaki equation can be found for a whole regime.