# 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
### Sensitivity Analysis of the Algorithm for Various Operating Points
The algorithm sensitivity analysis for determining the pump efficiency for the variation of the line inner diameter at discharge \(\epsilon_{D_{d}}\) for the five operating points across the operating range is shown in Figure 10. One can observe a significant variation of the pump efficiency (\(\epsilon_{pp}>\pm 3\%\)) when we consider a deviation of the line inner diameter at discharge greater with \(\epsilon_{D_{d}}>25\%\) compared to its real value. The assessments for the two operating points located in the green area are an exception; the variation of the pump efficiency is below 3% (\(\epsilon_{pp}<-3\%\)) even for a deviation of the line inner diameter at discharge greater up to \(\epsilon_{D_{d}}<50\%\) compared to its real value. For the situations where the exact value of the discharge line inner diameter \(D_{d}\) cannot be determined, it is preferable to consider a value higher than the real one. Figure 10: Algorithm sensitivity analysis regarding the determination of the pump efficiency \(\epsilon_{pp}\) or deviations in the input of the discharge line diameter \(\epsilon_{D_{d}}\) for five operating points: OP8, OP9, OP10, OP12 and OP14. Figure 9: The algorithm sensitivity analysis regarding the determination of the pump efficiency \(\epsilon_{pp}\) for deviations in the reading of the suction pressure \(\epsilon_{p_{s}}\) for five operating points: OP8, OP9, OP10, OP12 and OP14. Figure 11 shows the algorithm sensitivity analysis regarding the determination of pump efficiency for the variation of the suction line inner diameter \(\varepsilon_{D_{s}}\) for the five operating points across the full range. In Figure 11, one can notice a variation of the pump efficiency of up to 3% lower for the five operating points when the deviation of the suction pipe inner diameter is greater by up to \(\varepsilon_{D_{s}}<50\%\) compared to its real value. In exchange, one can notice a significant variation of the pump efficiency (\(\varepsilon_{\eta_{p}}>\pm 5\%\)) when it is considered a deviation of the suction line inner diameter below 33%, compared to its real value. An exception regarding the deviation of the suction line inner diameter is the situation where the assessment of the output is performed for the BEP. For the situations where the exact value of the suction line inner diameter \(D_{s}\) cannot be determined, it is preferable to consider a value higher than the real one. A reasonable approximation would be the outer diameter. In most cases, the approximation falls within the efficiency deviation \(\varepsilon_{\eta_{p}}<-3\%\). If the suction and discharge diameters can be correctly measured on the outside, the inner values can be found in tables showing the thicknesses of the pipe wall. When establishing the inner diameters, it is preferable to consider a value that is greater than the real one. Another input parameter with an important influence on the efficiency algorithm is the variation of discharge pressure, Figure 8. The greatest deviations in the efficiency values are obtained at off-design conditions far away from the BEP corresponding to the maximum efficiency \(\eta_{P_{BEP}}\). The algorithm sensitivity analysis regarding the determination of the pump efficiency for the level variation between the two instruments that measure the suction/discharge pressure for the five operating points across the full range is shown in Figure 12.  
One can notice a linear distribution of the pump efficiency variation with the deviation of the level \(\varepsilon_{\Delta z}\) defined in Equation (8) between the taps of the two instruments measuring the suction/discharge pressure compared to the reference value for the five operating points. As a result, a greater/smaller value of the pump efficiency is obtained when the deviation of the level \(\varepsilon_{\Delta z}\) is smaller or greater than the reference value.