Development of new empirical equations for estimation of drag coefficient, shape deformation, and rising velocity of gas bubbles or liquid drops

Some new correlations are derived to estimate the drag coefficient, the shape deformation, and the rising velocity of particles moving in an infinite liquid medium. The correlations are derived in terms of the dimensionless groups such as Reynolds number (Re), Morton number (Mo), and Weber number (We). The derivations are based on the experimental data or some other correlations given in the literature. A single statement is proposed to estimate the drag coefficient for the spherical solid particles that may be applicable in the range of 0.5 < Re < 10(5). Similarly, some other equations are also derived to estimate the drag coefficient, the shape deformation, or the rising velocity for gas bubbles or liquid drops. The drag equation is applicable in the range of 0.5 < Re < 100 and 9 x 10(-7) <= Mo <= 7; the shape deformation equation is applicable in the range of 0.5 < Re < 100 and 1.1 x 10(-5) <= Mo <= 7; and the rising velocity equation is applicable in the range of 0.1 < Re < 100 and 9 x 10(-7) <= Mo <= 80. The model predictions are compared with the experimental data and with the other correlations given in the literature. The results indicated that the model predictions are in a good agreement with the literature data.