For local exhaust ventilation systems to be capable of removing contaminants reliably, accurate data on the velocity field around local exhaust devices is needed. The boundaries of the separation airflow at its inlet must be determined as a prerequisite for shaping leading edges of the exhaust hood. This shaping technique makes it possible to reduce local resistance, improve acoustic properties, increase contaminant capture efficiency and reduce electricity costs associated with operating ventilation systems in buildings. The goal of our study is to develop a discrete mathematical model of three-dimensional stationary separated airflow at the inlet of a rectangular exhaust duct. A novel aspect in our study is the mathematical simulation technique developed by us for 3D separated airflow at inlet of an exhaust hood. The discrete model was constructed using quadrangular vortex clouds comprising straight and curved segments, straight and curved horseshoe vortices, and closed curved vortex polygonal lines. We traced out the flow separation surface at the inlet of a sharp-edged rectangular exhaust duct and determined the axial airflow velocity using a computational procedure and a computer program designed by us. We compared our findings with the specially conducted experiment and different researchers' reports as well as values computed using complex analysis techniques for slotted exhaust hoods and our past computational data using the discrete vortex method for a square exhaust opening in non-stationary and quasi-axisymmetric settings. We found the results to be adequate. Our method can be used to determine the boundaries of vortex zones and trace out the velocity field at inlet of local exhaust hoods in a fully three-dimensional setting.