Motion equation and its solution

For vertical impinging streams and under the assumptions of neglecting buoyancy force and the particle being spherical in form, the equation for the particle motion, Eq. (3.1), can be rewritten in the generalized form, applicable for various cases, as 

Due to various relationships of the drag coefficient, Parameter k, in Eq. (2.32) has different definitions for various flow regimes, as follows. 

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