Industrial turbomachines, such as fans and blowers for drying, venting, cooling or conveying tasks, are often used in industrial applications and frequently are large energy consumers. Thus, there is a need for further optimization and efficiency increase. For fans and blowers, gaps between moving parts are unavoidable due to manufacturing tolerances and possible thermal expansion. In this work, the radial gap and axial overlap between the inlet nozzle and the impeller and its impact on the performance characteristics have been investigated, because detailed knowledge of the losses due to the gap is important for the design of more efficient fans. The presented analysis was performed with the Navier–Stokes-solver ansyscfx. After a detailed grid study, the quantitative effect of the gaps on the performance of the centrifugal fan has been investigated by a variation of the radial gap and axial overlap. It was found, that at the best efficiency point (BEP) the efficiency drops between 1 and 6% depending on the gap width and at partial load it might drop fast also depending on the gap width, up to 50–60%. At overload the drop in efficiency is smaller than at partial load, dropping between 1 and 10%, depending on the gap width and the flowrate. In addition, a metamodel based on a dimensional and regression analysis was developed for partial and overload to predict the gap flowrate without additional computational fluid dynamics (CFD) simulations. The prediction accuracy between the CFD results and the dimensional analysis based metamodel is about 5–10%.