Equations for calculation of the terminal velocity and drag coefficient of solid spheres and gas bubbles

An analysis of the correlations proposed in the literature for calculation of the drag coefficient (C-D) and the terminal velocity of a falling rigid sphere has been made. Among the correlations describing C-D vs. Re, that of Turton and Levenspiel fits the experimental data almost perfectly. However, it is not explicit in the terminal velocity. The available explicit correlations do not fit the experimental data well. The present paper shows that a simple and precise explicit correlation can be developed if C-D is related to the Archimedes instead of the Reynolds number. The precision of the correlation proposed is similar to that of the Turton and Levenspiel (1986), while it is explicit in the terminal velocity. On the basis of this correlation, a model is proposed to calculate the drag coefficients and the terminal velocities of free falling or rising spherical particles in an infinite fluid as well as gas bubbles with any volume and shape rising in a contaminated liquid.