Backwashing of deep bed filters is achieved by fluidizing the filter media. A mathematical model for velocity gradient in two-dimensional turbulent flow that can also be applied to flow in fluidized beds in the transitional state was developed. The theory of fluidization in a circular cross-section column was presented. The existence of a viscous sublayer around each fluidized solid particle and the laminar sublayer thickness at the wall were neglected. To evaluate the theoretical expressions, numerical applications are carried out for filter-bed materials of two different types of sands and anthracite coal. An indirect verification of the existence of an optimum porosity around 0.70-0.75 during filter backwashing was observed in the laboratory experiments. The velocity gradient in backwashing of granular filters was found to be a function of power dissipation in a unit volume and coefficient C that indicates the effect of turbulence in total power dissipation. It was also found that turbulence intensity decreases with an increase of porosity, and the arithmetic mean shear stress has a maximum value between porosity values of 0.70 and 0.75.