Scour is the leading cause of bridge collapse beneath any bridge pier located within the waterway. A numerical-based hydraulic model named the Hydrologic Engineering Centre River Analysis System and a mathematical model of the Florida Department of Transport were implemented to investigate their performance and accuracy in estimating the maximum scour depth beneath bridge piers where large and small-scale physical prototypes are used as a benchmark. The main findings are that a hydraulic model is an effective tool when employing the Colorado State University equation, which compares well with physical prototypes irrespective of the variation in piers' size and shape. Also, it has achieved more consistent results than the Froehlich and the Florida Department of Transport methodologies.