The destructive implication of pressure-flow scour during flood events is a critical issue for researchers throughout the world. The current paper presents two models to estimate the pressure-flow scour depth underneath a partially submerged bridge deck in the equilibrium phase based on the jet flow theory. An estimate of the submergence distance of the jet flow under the bridge deck is the base point of the first model. The second model uses the phenomenological theory of turbulence where the tangential component of jet velocity is scaled to the velocity of the eddy formed under the bridge deck. This theory has already been used by researchers to estimate the scour depth of the jet flow. Dimensionless parameters are constructed in the theoretical framework of both models. The angle and velocity of the combined jet under the bridge deck and the effective depth underneath the bridge deck have been obtained using the relations presented in the previous research. The application of the presented models is limited to cases where the relative opening height of the bridge deck is greater than 0.25. The derived equations of the current study are calibrated based on the data with sufficient time durations. The results show that both models predict fairly well the maximum pressure-flow scour depth. The values of Nash–Sutcliffe efficiency and relative root mean square errors of the second model predictions are more appropriate, compared to the estimates of the first model and estimates obtained by equations presented in the previous studies.
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