The drag force on a sphere is described generally as the relation of the drag coefficient C_D and Reynolds number Re_N for a Newtonian fluid. In the case of a non-Newtonian fluid, it is desirable that the drag force is described as for a Newtonian fluid. Thus, a generalized Reynolds number Re^*, which can be expected to play the equivalent role of Re_N in Newtonian fluids, has been introduced from "similarity law of energy dissipation".
As was expected, a good correlation of C_D and Re^* has been obtained in the whole range of the experiment where the falling ball method was used with slurries of clay which could be assumed to be Bingham plastic fluids.