<p>Prediction of the maximum scour depth around cylindrical piers in pressure flow conditions has posed significant challenges due to the limitations of existing equations derived from previous researches. This study addresses these challenges by introducing a theoretical frame to derive a formula to estimate the maximum scour depth of a cylindrical pier beneath the bridge deck at equilibrium conditions. The analysis focuses on understanding the vortex formation and vertical jet flow mechanism in shaping the scour patterns on the upstream side of cylindrical piers. Experimental validation is conducted to support the theoretical predictions and bridge the gaps in the current understanding of flow dynamics around these structures. Furthermore, recognizing the limited understanding of flow patterns and mechanisms around cylindrical piers situated beneath bridge decks, this study seeks to enhance and broaden current knowledge using observational methods. The findings indicating that the maximum pressure-flow scour depth is positioned at the upstream side of the cylindrical pier for various hydraulic and sediment conditions. The derived equation demonstrated strong predictive performance, with a Nash–Sutcliffe efficiency of 0.81 and a relative root mean square error of 11.41%. These findings provide a robust tool for engineers addressing scour risks under pressure-flow conditions.</p>