Accurate design of bridge piers over rivers requires a clear understanding of scour behavior and the surrounding flow patterns. The selection of span length, number of openings, and minimum pier depth must consider the region’s hydrological and hydraulic characteristics. In this study, the effects of flow discharge and river depth on scour depth around the Zanjanrud Bridge pier were investigated. Numerical methods and various empirical equations were employed to estimate the scour depth, and the results were compared with actual field data. A linear fit between observed and estimated scour depths, along with statistical analysis, showed that some empirical formulas provided higher accuracy than others. Additionally, the finite volume (FV) numerical method demonstrated good performance in predicting scour depth due to its ability to model complex flows while preserving conservation principles. The findings of this research can contribute to improved bridge pier design and help mitigate scour-related damages.