One of the most important parameters in the fluidization process is to determine the minimum fluidization velocity. For this purpose, the conservation equation of momentum in the vertical transport of fluids and solids were used. In this study, the pressure drop term was replaced with Ergun's equation and the drag force was considered a linear function. The drag coefficient was extremized using the calculus of variations and the relationship between fluidization velocity and voidage was determined. Two test cases with their experimental data were used for validating the presented drag model. Drag functions obtained in previous studies did not match with the empirical data in the bed volume fraction range of 0.45-0.59. The present study reveals that the reason for this difference lies in the use of the Darcy pressure-drop and neglecting the importance of the linear velocity term in the drag model. For vessels of small diameter, the wall effect becomes important. The frictional pressure drop proposed by Ergun is appropriate because this correlation consists of a viscous term. Also, it is expected that by increasing the beds' voidage, the energy drop decreases. Contrary to Darcy's model, presented drag model predicts this behavior perfectly.