Abstract: Because of the inability to calculate the free settling terminal velocity of particles by directly using the related formula, the mathematical model is developed on an exploratory basis, based on the calculated and test data of settling velocity of particles in this instance, and the reliability of the modelling is verified. Result of study shows that: the calculated and test data of free settling terminal velocity are close to each other and are well within the allowable error limit; and the mathematical model of hindered settling velocity of particles derived based these data may serve as a guidance for the design and selection of relevant parameters of TBS.