In aerostatic bearing analysis, determining film pressure by solving the Reynolds equation in a numerical model is more effective than conducting bearing experiments or performing computational fluid dynamics (CFD) simulations. However, the discharge coefficient of an orifice-type restrictor is generally a given number that dominates model accuracy. This study investigated the influence of geometry and flow parameters on this discharge coefficient. The results indicate that this discharge coefficient is sensitive to the orifice diameter and film thickness and that the effects of the supply pressure, bearing radius, supply orifice length, supply passage diameter, conicity depth, and conicity angle can be disregarded. This study also built a surrogate model of this discharge coefficient based on the orifice diameter and film thickness by using artificial neural networks (ANNs).