## 3 Results and Discussion
In Figure 9, a velocity field of the absolute velocity c is presented in a cross-section located just before the inlet of Impeller 2. The impeller rotates counterclockwise. In the presented figure, it can be observed that when operating with RGV2 (b), the vector field is mainly oriented in a direction opposite to the rotation of the impeller. This affects the value of circumferential velocity c\({}_{\text{u1}}\). To assess this impact, the value of \(\overline{\text{c}_{\text{u1}}}\) is to be calculated--the mass flow averaged circumferential velocity in the studied cross-section. Figure 10 presents a relationship of the type \(\overline{\text{c}_{\text{u1}}}=\text{f}(\text{Q}_{\text{rel}})\), which is obtained based on the results of CFD modeling. \[\rm H_{rel} =\frac{H_{i}}{H_{n}}\]1 A velocity field of the absolute velocity c concerning a cross-section located just at the inlet of Impeller 2 being analyzed under the following conditions (**a**) when operating with the original RGV and flow rate Q = 11.39 dm\({}^{3}\)/s; (**b**) when operating with RGV1 and flow rate Q = 11.39 dm\({}^{3}\)/s; (**c**) when operating with RGV2 and flow rate Q = 11.39 dm\({}^{3}\)/s. The analysis of the relationships, presented graphically in Figure 10, clearly indicates that in all pump modes, when operating with the original RGV, \(\overline{\mathrm{c_{u1}}}>0\). In the case of using RGV1 and RGV2 \(\overline{\mathrm{c_{u1}}}<0\) in all cases studied, as, in addition \(\overline{\mathrm{c_{u1}}}\), it is observed that operating with RGV2 has a lower value (larger absolute value) than \(\overline{\mathrm{c_{u1}}}\), operating with RGV1. Based on the previous statement, in the authors' opinion, the impact of the RGV angle \(\alpha_{\mathrm{c}}\) on the velocity distribution in front of the inlet of the next impeller can be seen, and thus also on the theoretical head of the studied impeller. When RGV has the largest angle (128 deg), \(\overline{\mathrm{c_{u1}}}\) has the lowest value, which, according to Equation (17), leads to an increase in head H\({}_{\mathrm{t}}\). Since the shape (design) of the vane does not result in a significant increase in losses, this leads to obtaining a greater head H of the pump stage. The impact of the RGV shape on the flow kinematics in front of the Impeller 2 inlet can also be observed in the results presented in \[\rm H_{rel} =\frac{H_{i}}{H_{n}}\]2  
Figure 11a shows velocity triangles in front of the impeller inlet when the angle \(\alpha_{1}\) between the absolute velocity \(\mathrm{c_{1}}\) and the transition velocity \(\mathrm{u_{1}}\) has positive and negative values. It is well known that in the case of \(\alpha_{1}>0\), the theoretical head of the pump stage is less than at \(\alpha_{1}<0\). At the same time, negative values of \(\alpha_{1}\) lead to an increase in shock (kick) losses at the inlet of the impeller blades. In Figure 11b, the results obtained after performing numerical simulations for averaged angle (\(\alpha_{1}\)) values in the section just in front  
\[\rm H_{rel} =\frac{H_{i}}{H_{n}}\]3 Impact of RGV on (**a**) velocity triangle in front of Impeller 2 inlet; (**b**) angle \(\alpha_{1}\) in the studied range of flow rates. \[\rm H_{rel} =\frac{H_{i}}{H_{n}}\]4 Relationships of mass flow averaged circumferential velocity are presented as a function of \(\mathrm{Q_{rel}}\), regarding the cross-section situated just before the inlet of Impeller 2, when operating with the three RGV. of the impeller inlet are presented when the studied pump stage operates with the three RGVs. It is clear that when operating with the original RGV, \(\alpha_{1}>0\) for the entire range of studied flow rates. When operating with RGV1, \(\alpha_{1}>0\), but takes lower values than when operating with the original RGV. Using RGV2 leads to \(\alpha_{1}<0\) concerning the entire range of flow rates studied, resulting in the generation of the greatest head when this type of RGV is used.