## 3 Results and Discussion  
As a result of the numerical experiments performed, using Mesh1.2, various relationships are obtained regarding the energy indicators (parameters) of the pump stage studied and the pump flow rate. Most of the results are presented in dimensionless (relative) form, where the dimensionless parameters are calculated using the following equations:  
\[\rm Q_{rel} =\frac{Q_{i}}{Q_{n}} \tag{13}\] \[\rm H_{rel} =\frac{H_{i}}{H_{n}}\] (14) \[\rm h_{v,rel} =\frac{h_{v,i}}{h_{v,n}}\] (15) \[\rm\eta_{H,rel} =\frac{\eta_{v,i}}{h_{v,n}} \tag{16}\]  
where \(\rm H_{n}\), \(\rm h_{v,n}\) and \(\rm\eta_{i,n}\) are the values of the relevant parameters obtained while operating with the original RGV and flow rate \(\rm Q_{n}=11.39\)\(\rm dm^{3}/s\). Figure 6 represents the results obtained concerning the main operating parameters of the studied pump stage: relative head \(\rm H_{rel}\), relative theoretical head \(\rm H_{tr,rel}\), relative total energy loss \(\rm h_{v,rel}\) and relative hydraulic coefficient of efficiency \(\rm\eta_{H,rel}\), given as a function of the relative flow rate \(\rm Q_{rel}\). The theoretical head can be estimated using the following equation:  
\[\rm H_{t}=H+h_{v} \tag{17}\]  
where the total energy loss in the pump stage is determined as follows:  
\[\rm h_{v}=h_{v,impP}+h_{v,diff} \tag{18}\]  
The losses \(\rm h_{v,impP}\) in the studied impeller and those obtained in Radial diffuser \(\rm 1\ h_{v,diff}\) are determined by applying Equation (9) after determining entropy production in the impeller and diffuser \(\rm 1\) according to the methods described in Section 2.4. The analysis of the results presented in Figure 6 clearly indicates that when operating with RGV2, the head and theoretical head of the pump stage increase by nearly 20% compared to the original RGV. The values for RGV1 are between those obtained for RGV2 and the original RGV. The total energy losses and hydraulic coefficient of efficiency when operating with RGV2 and the original RGV differ slightly and are practically the same. In Figure 7, relationships regarding different types of losses are presented. These losses are caused by entropy production in Impeller 2 and Radial diffuser 2. The symbols hv,T, hv,V and hv,W are used to represent losses due to the velocity fluctuation, viscous diffusion and wall effect, respectively. By examining the graphs, it is evident that energy losses in the diffuser are predominant in all cases, with turbulent velocity fluctuation accounting for the largest share. The losses from viscous diffusion are minimal, and those came as a result while losses from friction on the walls correspond to the losses hv,T. Figure 6: The results obtained after conducting numerical experiment include **(a)** the relationship between the relative head and the relative flow rate of the studied pump stage when operating with the three types of RGV; **(b)** the relationship between the relative theoretical head and the relative flow rate of the studied pump stage when operating with the three types of RGV; **(c)** the relationship between the relative total energy loss and the relative flow rate of the studied pump stage when operating with the three types of RGV; **(d)** the relationship between the relative hydraulic coefficient of efficiency and the relative flow rate of the studied pump stage when operating with the three types of RGV. In order to illustrate the impact of RGV on the losses in the pump stage, the relationships between the relative losses, described by Equation (15), and the relative flow rate when operating with the three types of RGV are presented in Figure 8.  
Figure 7: Losses incurred in the Impeller and Radial diffuser 1 due to entropy production.