Abstract: In order to study the critical speeds of the sand-water heterogeneous flow in the pipelines, through analysis of a large number of previous research results，at first with the aid of the data regression, a calculation model for deposition critical speeds of the sand-water heterogeneous flow in pipelines is developed; at the same time by the Durand resistance formula derivation, the calculation formula for the minimum head-loss critical speeds is put forward. Then several groups of related data from related scholars are used to verify and analyze the calculated values and experimental values of deposition critical speeds and the minimum head-loss critical speeds, and the calculated results indicate that the maximum deviation between the calculated results of the critical speeds and the minimum critical speeds and the related test results are not more than 15%. In the end, the relationships between the deposition critical speeds and the minimum head-loss critical speeds are given, and the change law of the deposition critical speeds and the minimum head-loss critical speeds with the particle size, the diameter of the pipelines and the slurry transport concentration are also analyzed, and it is found that with the decrease of the particle size, the gap between the deposition critical speeds and the minimum head-loss critical speeds becomes smaller gradually. As the diameter of the pipelines becomes larger, the gap between the two becomes larger gradually. With the increasing of the conveying concentration, the accumulation of the boundary speeds has a slight decrease trend, while the minimum head-loss critical speeds have a significant increase.