Centrifugal pumps change their performance with respect to water when processing non-Newtonian fluids. Many aspects about pumping of non-Newtonian fluids remain to be clarified due to complexity of the matter and the scarcity of investigations. In addition to experimental tests, in recent years some CFD fluid dynamics simulations have been realized to analyze the performance of centrifugal pumps with non-Newtonian fluids. Knowledge of rheology is required to correctly simulate the fluid inside the pump and predict the performance. The aim of this work is to emphasize the criticalities in the simulation of centrifugal pumps with non-Newtonian fluids, since, starting from the same rheological data, can be deduced different rheological laws, however reliable, that produce different effects on the simulations. In this paper, the performances of a model pump were measured experimentally with pear juice and accompanied by the rheological characterization of the fluid. Subsequently, the pump was simulated using five different rheology laws, all fitted to the same experimental rheogram, that differ from each other in predicting viscosity out of shear rate range experimentally measured. The pump performances were affected by the different rheology implemented. The simulations showed that the shear rates developed inside the pump are much higher than those measured with the rheometer. Consequently is necessary to achieve higher shear rates in the experimental rheogram to make sure to correctly model the rheology for shear rates values typically present in the pump.