<p>The significant impacts of pressure-flow scour have emerged as a critical concern in recent decades, largely due to the severe environmental effects of climate change. Earlier research primarily concentrated on estimating the maximum pressure-flow scour depth around cylindrical bridge piers through dimensional analysis and theoretical approaches. However, the reliability of some previous equations for predicting the scour depth has been questioned. This paper introduces two new theoretical methods to enhance the predictive accuracy of pressure-flow scour depth around cylindrical piers. Using the existing equations for maximum scour depth along the vertical jet centerlines, the first method adapts these principles to develop an equation for the pressure-flow scour around cylindrical bridge piers. The second method is grounded in phenomenological turbulence theory. It employs two distinct equations for calculating the angle and velocity of the combined jet, as well as the effective depth under the bridge deck. The equations formulated in this research have been calibrated using datasets that span sufficiently long-time intervals. The results indicate that both methods can accurately predict the maximum pressure-flow scour depth at equilibrium time. Notably, statistical indicators suggest that the second method offers significantly better results compared to the first and previous equations.</p>