# Software for Monitoring the In-Service Efficiency of Hydraulic Pumps
## 4 The Laboratory Validation of the Software Module for the Pump's Full Operating Range
Figure 5: The validation of the software module for the pump’s full operating range. \begin{table}
\begin{tabular}{c c c c c} \hline \(\mathbf{n}\) [**rpm**] & \(\mathbf{p_{0}}\) & \(\mathbf{p_{1}}\) & \(\mathbf{p_{2}}\) & \(\mathbf{p_{3}}\) & \(\mathbf{R^{2}}\) \\ \hline
2900 & 3.554 & 881.109 & \(-13\),978.015 & 40,315.701 & 0.96804 \\ \hline \end{tabular}
\end{table} 
Table 3: The coefficients of the 3 rd-degree approximation polynomial function for the pump mechanical power \(P_{m}=f(Q)\) at speed of 2900 rpm. The input parameters corresponding to the configuration of the test rig available at the \"Politehnica\" University Timisoara are as follows: the diameter of the suction line \(D_{s}=0.11\) m, the diameter of the discharge line \(D_{d}=0.08\) m, the position of the instrument on the suction line compared to the pump flange \(l_{s}=1.0\) m, the position of the instrument on the discharge line compared to the pump flange \(l_{d}=0.5\) m, the distributed hydraulic loss coefficient for the suction line \(\lambda_{s}=0.0158835\), the distributed hydraulic loss coefficient for the discharge line \(\lambda_{d}=0.0166889\), the local hydraulic loss coefficients for the suction and discharge lines \(\zeta_{s}=\zeta_{d}=0\) because no elbow was installed in the pump suction or discharge, the level difference between the position of the instrument on the discharge line and on the suction line \(\Delta_{z}=0.85\) m.  
The last two columns in Table 5 \(\varepsilon_{Q}\) and \(\varepsilon_{\eta_{P}}\) are defined as \(\varepsilon_{\otimes}\) in Equation (20):  
\[\varepsilon_{\otimes}=\frac{\otimes_{ms}-\otimes}{\otimes_{ms}}100[\%] \tag{20}\]  
(corresponding to \(y_{i}-f(x_{i})\) in Equation (17)). \(\eta_{P_{ms}}\) is the experimental data from Table 1, and \(\eta_{P}\) is the value calculated with curve fitting in Equation (11) with coefficients from Table 4. \(Q_{ms}\) is experimental read data in Table 1 and \(Q\) is calculated based on Equation (9). The \(\eta_{P_{ms}}\) experimental data in Table 1 are shown in Figures 5 and 7 with a black dot (\(\bullet\)) and the calculated \(\eta_{P}\) values are shown with a white circle (\(\circ\)). The input variables of each operating point are the static pressure measured at suction \(p_{s}\) [Pa], static pressure measured at discharge \(p_{d}\) [Pa] and optionally, the value of the measured volumetric flow rate \(Q_{ms}\) [m\({}^{3}\)/s]. The following data are obtained for the pump speed of \(n=2900\) rpm: \(H(\eta_{P_{BEP}})=37.33\) m, \(P_{m}(\eta_{P_{BEP}})=17.19\) kW, \(Q(\eta_{P_{BEP}})=35.7\times 10^{-3}\) m\({}^{3}\)/s. See Figure 7a for operating point number 7 (OP7) set on partial flow rate during abnormal regime (AO). Our input values were: static pressure measured at suction \(p_{s}=-9933.191\) Pa, static pressure measured at discharge \(p_{d}=47.0631.463\) Pa and the value of the volumetric flow rate measured by the flowmeter \(Q_{ms}=6.727\times 10^{-3}\) m\({}^{3}\)/s. The results provided by the software module for OP7 are: \(Q=6.35\times 10^{-3}\) m\({}^{3}\)/s, with a percentage error of \(-5.6\%\) compared to \(Q_{ms}=6.727\times 10^{-3}\) m\({}^{3}\)/s, \(\eta_{P}=24.10\) %, \(H=50.01\) m, \(P_{m}=8.6\) kW. The abnormal operation diagnostic RED supplied is correctly determined. Operating point number 9 (OP9) set on partial flow rate during abnormal regime (AO) (see Figure 7b) was checked with the following input values: static pressure measured at suction \(p_{s}=-17\),270.447 Pa, static pressure measured at discharge \(p_{d}=435\),108.521 Pa and  
Figure 6: The experimental data for pumping head \(H=f(Q)\) (\(\blacksquare\)), mechanical power at the pump shaft \(P_{m}=f(Q)\) (\(\blacktriangle\)) and pump efficiency \(\eta_{P}=f(Q)\) (\(\bullet\)) at speed of 2900 rpm, together with polynomial curve fittings (solid lines). the value of the volumetric flow rate measured by the flowmeter \(Q_{ms}=18.64\times 10^{-3}\) m\({}^{3}\)/s.