*3.1. Turbine Operation Mode*

Because it was not possible to measure water discharge through the tested machine using both methods (volumetric gauging and pressure-time methods) simultaneously, the comparison of the results measured for the turbine operation mode was performed using the Winter–Kennedy method. According to this method, the measurement of discharge is based on the relationship between the discharge, *Q*, and the difference of pressures, Δ*pwk*, between the outer and the inner side of a spiral case of the machine under test:

$$Q = k \Delta p\_{\text{nok}}^n \tag{8}$$

where *k* and *n* are constant coefficients experimentally determined during the calibration process. A value of the exponent, *n*, was assumed from the theory as equal to 0.5. Such assumption insignificantly

influenced the measuring results as was proven in [17] and it is negligible for purposes of comparison presented in this paper. For the tested machine, the values of *k* coefficient were determined independently on the basis of discharge measurement conducted using the volumetric gauging and the pressure-time methods—in Figure 10. The difference between *k* coefficient values obtained using these two different methods is very small, only about 0.2%. It should be emphasized that for the penstock geometric factor, *F*, used in the pressure-time method without the Δ*f* correction, the difference in the value of the *k* coefficient is slightly larger and amounts to approximately 0.33%. Although in the case under consideration the difference is not large, taking into account the various pipeline geometries that encounter in practice, it is recommended to support the pressure-time method by means of CFD analysis in the case of measuring sections of pipelines with irregular elements causing disturbances in the flow.

**Figure 10.** Turbine operation mode of the tested hydrounit: Comparison of the volumetric measurement method and the pressure-time method based on the results of calibration of the technical installation of the Winter–Kennedy method, with which the tested pump-turbine was equipped.
