## 1 Introduction  
Centrifugal pumps are widely applicable in fields ranging from the energy industry to wastewater treatment. Pumps are used to generate a flow rate, which needs to be adapted to the requirements of the specific application using one of various possible control methods. In particular, the flow rate is considered the main control variable in many applications, e.g., in the process industry [1, 2] and is a significant factor in optimising pump operation. The operating point of the pump can be determined based on corresponding information. A large number of publications have already addressed the issue of determining the flow rate of centrifugal pumps using soft sensors. [PERSON] gave an overview of the most common approaches of flow rate estimation [1]. These approaches can be divided into static and dynamic methods [1]. Depending on the kind of estimation approach, the measured values either of the head or the power consumption of the pump are required as input parameters of the empirical equations for deriving the flow rate. The dynamic method according to [PERSON] and [PERSON] also uses the standard pump characteristics under prewhirl-free inlet conditions, but needs to calculate a family of characteristics for deriving the dynamic flow rate [3]. Even more recent publications such as [PERSON] et al. or [PERSON]. [PERSON] et al. require the manufacturer's pump curve as starting point of their flow rate estimation [4, 5]. A discrepancy between the characteristic curve and the manufacturer's specifications or initial measurements may result in an increase in the margin of error when determining the flow rate using soft sensors. However, intentional or unintentional design modifications of the suction pipe, i.e., deviations from the standard, can alter the pump curve significantly. [PERSON] showed that, depending on the installation situation of flange flap valves and elbows, losses in the head up to 2.8% and at shaft power up to 1.7% can be expected at best-efficiency-point (BEP) of the pump [6]. In addition to an unfavourable design of the suction pipe, prewhirl can also occur in pumps that are used to extract liquid from buildings. [PERSON] et al. demonstrated that the presence of minor obstructions within the suction chamber can result in non-uniform flow profiles, which subsequently give rise to whirl formations in front of the pump [7]. This has a significant impact on the characteristic curves of the pumps. The impact of prewhirl on the pump's characteristic curve can be determined through the utilisation of the Euler equation for turbomachines. Prior research, as exemplified by the work of [PERSON] [8], has indicated that the influence of prewhirl on the characteristic curves is especially pronounced in pumps with a medium or high specific speed (\(n_{\text{q}}\)). The pump investigated by [PERSON] had a specific speed of \(n_{\text{q}}=100\) min\({}^{-1}\)[8]. In addition to the characteristic curves of pumps with high specific speeds, those of pumps with low and medium specific speeds are also influenced. [PERSON] employed prewhirl bodies to generate a uniform whirl across the pipe cross-section of the suction line upstream of two pumps with specific speeds of \(n_{\text{q}}=33\) min\({}^{-1}\) and \(n_{\text{q}}=62\) min\({}^{-1}\)[9]. It was demonstrated that even at these specific speeds, a discernible impact was observed on the characteristic curves of the pumps. In addition to the unintentional alteration of the characteristic curves, prewhirl is also employed for the purpose of regulating pumps. The focus of [PERSON] et al. (2010) was performance optimisation of a pump with a specific speed of \(n_{\text{q}}=35\) min\({}^{-1}\) at partial load operation [10]. Those authors suggested an appropriate design of the inlet guide valve (IGV) for adjusting the flow at the impeller inlet. The blades of the IGV were determined through the application of an inverse design methodology. They even showed that the prewhirl may have a positive effect on the flow at partial-load operation of the pump.