With centrifugal pumps, it is counted as belonging to the state of the art, to detect the pressure, the differential pressure and for example the temperature within the pump by way of sensors.  Moreover, the electrical variables of the drive motor such as power and rotational speed are available in any case, since modern centrifugal pumps are typically controlled by way of a frequency converter, wherein the rotational speed can also be detected by sensor without any problem.  In contrast, the flow measurement requires more effort, since mechanical flow meters are expensive and prone to malfunctioning, and electronic detection systems in contrast are quite expensive and therefore are less suitable in particular for pumps of a small and medium construction. 
Basically, the flow rate of a centrifugal pump can be determined in a speed-dependent manner and specifically selectively with a hydraulic pump model which in dependence on the rotational speed and the delivery head, specifies the flow rate, or with the help of an electrical-hydraulic model, with which the flow rate is determined in a manner depending on the speed and the drive power.  The former model however has the disadvantage that it provides inaccurate or ambiguous flow rate results in the region of low delivery rates.  The latter in contrast is unsuitable for determining large flow rates, since with a high electrical power it provides inaccurate or ambiguous results. 
For this reason, it is counted as belonging to the state of the art, to combine these methods, wherein the electrical-hydraulic model is applied for the region of smaller delivery rates and the hydraulic pump model for the region of large delivery rates.  This, however, results to jumps being able to arise in the region, in which one changes from the one method to the other method and vice versa, and these jumps are not desirable.  Moreover, it is also possible that the regions can overlap or have a gap.  This can lead to oscillation problems and as a whole this is not favorable. 
It is counted as belonging to the state of the art from U.S. Pat.  No.  7,454,986 B2, to determine the throughput by way of electrical variables of the motor, wherein the flow rate is determined by way of values stored in tabular form, by way of the phase shift between the supply voltage and the back-EMF. 
It is counted as belong to the state of the art from EP 1 721 131 B1, to determine the throughput by way of both above-mentioned methods, wherein the evaluation is effected by way of values stored in tabular form. 
From GB 2 313 197 A, it is counted as belonging to the state of the art, to determine the flow rate by way of the pump pressure, thus the delivery head, from the power or from the efficiency.  For the regions, in which one of these types of evaluation leads to inaccurate or ambiguous results, then one of the other modules is to be used or the flow rate is to be determined by way of forming averages of two methods.