# Error Characteristic Analysis of Fluid Momentum Law Test Apparatus
## 3 Analysis of Sensor Displacement Response Characteristics  
The preliminary research foundation shows that the displacement response characteristics of the sensor structure can be used as the basis for error characteristic analysis [14]. In the momentum law experimental device, the sensor is arranged in a cantilever beam structure. With reference to the existing research results, the midpoint C on the side wall of the sensor is selected as the characteristic point of the displacement response characteristic of the sensor, referred to as the characteristic point C of the sensor, as shown in Figure 3[14]. The displacement response of the sensor characteristic point C in the X, Y and Z directions under the action of the jet impact is shown in Figures 4-7, respectively. It can be seen from Figures 4-7, under the impact of different momentum jets, the sensor is displaced in the X direction (jet impact direction), Y direction and Z direction, for further analysis, a frequency spectrum analysis is performed on the displacement in the y direction, as \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No** & **Name** & **Material** & **Element Type** & **Element Size (mm)** \\ \hline
1 & Base & PMMA & SOLID & 2 \\
2 & Sensor & STEEL & SOLID & 1 \\
3 & Flat plate & PMMA & SOLID & 5 \\
4 & Jet & Water & Particle & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The categories of material and element of parts. Figure 3: The distribution graph of observation points on sensor. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material Name** & \begin{tabular}{c} **Density** \\ **T/mm3** \\ \end{tabular} & \
\begin{tabular}{c} **Elasticity Modulus** \\ **MPa** \\ \end{tabular} & **Poisson Ratio** \\ \hline PMMA & \(1.18\times 10^{-9}\) & 5000 & 0.25 \\ STEEL & \(7.89\times 10^{-9}\) & \(2.1\times 10^{5}\) & 0.3 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c} \hline \hline
**Water** & \begin{tabular}{c} Density \\ **T/mm3** \\ \end{tabular} & \
\begin{tabular}{c} Sound velocity \\ **C\({}_{0}\) mm/s** \\ \end{tabular} &
\begin{tabular}{c} Viscosity \\ MPa-s \\ \end{tabular} \\ \cline{2-3}  & \(1\times 10^{-9}\) & \(1.45\times 10^{6}\) & \(1\times 10^{-9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The properties of material PMMA, STEEL and WATER. Figure 2: The numerical simulation graph of jet impact model. As Figure 4 shows, the impact force generated by the change of the jet flow momentum acts on the sensor in the X direction, which causes the characteristic point C to be displaced. The displacement curve of characteristic point C in the X direction becomes stable after oscillation adjustment. Under the action of different momentum jets, the oscillation law of characteristic point C is similar, but the amplitude and adjustment time are different. The basic rules are as follows: the greater the initial momentum of the jet, the greater displacement amplitude of the characteristic point C. The greater the jet flow increment, the greater the displacement increment of the characteristic point C, the longer the oscillation stability adjustment time, and all the oscillation adjustment time is less than 5 ms, which indicates that the force \(F_{sx}\) of the sensor in the X direction become stable after a period of adjustment. As Figure 5 shows, the characteristic point C is subjected to external force in the Y direction, resulting in displacement. The displacement curve of the characteristic point C in the Y direction has a small change in the time range of [0 ms, 5 ms]. After 5 ms, the vibration amplitude gradually increases, and the oscillation continues without a stable trend. This indicates that under the impact of the jet, the sensor first moves in X direction, after the adjustment in the X direction is stable, the sensor in Y direction starts to perform a large oscillation adjustment.