## 5 Evaluation of Hydraulic Losses  
The proposed multistage centrifugal pump was tested for its operability with multiple fluids of lower viscosities, and it was proven to be feasible. However, the design feasibility test of the pump could not be concluded without the loss analysis at each stage. To determine the head loss and efficiency loss, the normalized efficiency and head coefficient curves are plotted against the flow coefficient at each stage of the pump for water in Figure 9.  
A significant decline was observed in the second stage for both the efficiency and head at higher flow rates. The efficiency obtained at 0.5 \(\varphi\)/\(\varphi_{d}\) was almost similar at all stages. As the flow rate increased, the efficiency followed a similar trend for Stages 1, 3, 4 and 5, while the efficiency at Stage 2 dropped significantly. The head also decreased at Stage 2, indicating huge pressure loss at this stage. The reason for the losses at the second stage needed to be investigated in-depth and design modifications must be advocated before manufacturing the pump. The pump operating at the design point with water as the fluid was selected for the in-depth loss analysis. A trend graph is plotted at the impeller mid-span at each stage along the streamwise direction to identify the amount of losses in head and efficiency in Figure 10. The head and efficiency were divided by their maximum values for normalization. Stage 1 had two spikes due to the dual suction impeller design. It can be seen that the head dropped at the beginning of the second stage by 67% before rising again at the end of the stage. There was no drop in head observed in the rest of the stages. The maximum head was obtained at the end of the fifth stage impeller, which also corresponded to the  
Figure 8: Axial velocity comparison along the impeller mid-span for Stages 2-5.  
cumulative head of the entire pump. A similar drop in the efficiency curve was witnessed at the second stage. The dive in the efficiency curve at the beginning of each stage was due to the sudden change in the pressure gradient as the fluid moved from one stage to another. Although the efficiency dove at the leading edge of each impeller, it climbed back up immediately and rose sharply at the trailing edge. This was not the case with the second stage, where the efficiency remained the lowest throughout the blade streamwise. The elimination of losses at the second stage can improve the overall performance of the pump. The blade loading curves for the impellers at Stages 2, 3, 4 and 5 are plotted in Figure 11. The normalized pressure was plotted along the streamwise direction at the design point for water. A pressure drop was observed at the leading edge of the second stage impeller, which recovered toward the trailing edge. The huge dive in the absolute pressure at the leading edge may succumb to cavitation in the long run. It is necessary to identify the source of the loss at the second stage. A drop in pressure at the pressure side of the impeller was observed at the 20% streamwise location, as marked in Figure 11. A severe pressure drop at this location indicates an obstruction to the flow at the pressure side. The pressure and velocity contours at the meridional plane of the blade are shown in Figure 12. A low-pressure region could be found at approximately the 20% streamwise location, and the corresponding low-velocity region confirmed the formation of a stagnation zone, causing blockage to the flow. Figure 10: (**a**) Head and (**b**) efficiency trend graphs, plotted at the mid-span of the impellers for water at \(Q_{d}\). Figure 9: (**a**) Efficiency and (**b**) head coefficient curve of the individual stages for water. The velocity streamlines at the mid-span from a blade-to-blade view of the impellers at each stage is shown in Figure 13. The fluid flowed along the blade angle for all stages except for Stage 2. The fluid incidence angle was found to be larger than 90\({}^{\circ}\) to the second stage impeller blade angle.