## 1 Introduction
[PERSON] et al., confirmed that the affinity laws lead to an increasing error in the characteristic curve when the speed is greatly reduced [13]. They measured the pump characteristic curves at different speeds and subsequently created plots that relate power to discrete flow rates as a function of the pump speed. They interpolated between the discrete curves to estimate the flow rate. They contrasted the results of their flow rate estimation method using interpolation with those obtained from a back-propagation neural network (BPNN) and the application of affinity laws to the \(Q(P_{K})\)-curve. They achieved an average deviation of 2%. In addition to the previously mentioned polynomial flow rate calculation approaches, [PERSON] et al., presented a method that uses Gaussian Process Regression (GPR) [14]. This method stores the flow rate within kernels as a function of both the pump speed and the position of the discharge control valve. Linked to a mechanical model, other parameters such as pump efficiency and pump head can be determined. This approach achieves an average deviation in flow rate estimation of less than 2%, but again, additional measurements are required. As shown, the deviations of the affinity laws can be improved by modifying approximation functions, the boundary curve method, or the GPR approach, which requires additional measurements. Additionally, the pump performance curves might change when centrifugal pumps are used within pumping systems. Deliberate or unintended design modifications to the suction pipe, such as deviations from the standard, can profoundly impact the pump curve. [PERSON] shows that, depending on the installation situation of flange flap valves and elbows, losses in pumping head up to 2.8% and at shaft power values up to 1.7% can be expected at the best efficiency point (BEP) of the pump [15]. [PERSON] named prewhirl as the main reason for such changes [15]. She showed that prewhirl has different impacts depending on its direction. The effect of prewhirl on the performance curves of centrifugal pumps with medium to high specific speeds has already been investigated in several studies. These studies mainly focus on prewhirl control, which is a common control method for these types of pumps [10]. The review of [PERSON] et al., cites various studies dealing with prewhirl control with respect to centrifugal pumps, in which the influence of the prewhirl on pump curves was studied experimentally as well as numerically [16]. Here, it is shown that the characteristic curves of pumps can also be influenced by a prewhirl guide valve at medium specific speeds. [PERSON] et al., focused on the performance optimization of a pump with a specific speed of \(n_{q}=38\) min\({}^{-1}\) at partial load operation [17]. These authors suggested an appropriate design of the prewhirl guide valve for adjusting the flow at the impeller inlet. They even showed that the prewhirl may have a positive effect on the flow when the pump is working under partial load operating conditions. [PERSON] et al., numerically studied the influence of prewhirl on the inlet flow at an impeller of an axial pump operating at different flow rates [18]. [PERSON] et al., in their numerical investigations, demonstrated that the BEP of the pump shifts depend on the prewhirl direction [19]. [PERSON] analysed the behaviour of the characteristic curve under the influence of prewhirl [20]. He showed that the prewhirl direction affects the specific work. Several publications have shown that the impact of prewhirl on the specific work increases with the specific speed of the pump [10,21,22]. [PERSON] also examined a pump with a lower specific speed in terms of prewhirl impact on the pump curves and was able to show that a significant influence can also be expected for such pumps [21]. There are two aspects of the published studies presented here that require further investigation. The accuracy of flow rate determination for variable speed pumps can only be improved by additional measurements. This requires extra effort.