The performance of pipe culverts on steep slopes with tapered inlets is, in general, sensitive to the presence of air-carrying vortices over the inlet. Under such conditions, an area of operation is defined. The minimum bound of the performance is shown to approximate inlet control operation of the inlet with atmospheric pressure over a free surface flow immediately downstream of the inlet control section. The performance of pipe culvert inlets is presented in terms of a discharge coefficient that closely approximates commonly used values of the discharge coefficient for orifices of similar edge geometry. The significance of various aspects of the inlet geometry with respect to the operation of the culvert, as well as to the location of the applicable control section, is explored. At small model sizes, the performance of pipe culverts with tapered inlets is shown to be subject to significant scale effects.