High energy dissipation of the free falling jet from the flip-bucket in the plunge pools will cause downstream river erosion. While simple and economic implementation of such structures has attracted the attention of most designers. Scour due to falling jet incidence with the river bed will threaten the stability of the dam and related structures, and hence determination of the plunge pool dimensions was an important design consideration. The purpose of this study is to develop empirical exponential relations using the principles of statistics and dimensionless relations by applying dimensional analysis in order to estimate the scour depth due to falling jets considering the effective parameters such as discharge per unit width, the difference between water levels in the reservoir and tailwater (jet fall height), tailwater depth, the mean diameter of bed particles and flip-bucket jet angle. By comparing the results of the suggested relations in this study with other investigator results it can be indicated that the developed relations have the maximum correlation coefficient and minimum computational error in an appropriate standard deviation range. Also, the accuracy and dispersion of the 139 collected data series that were used for the proposed relations was higher than the previous studies.