# Error Characteristic Analysis of Fluid Momentum Law Test Apparatus
## 5 Conclusions  
This paper takes the jet impingement type momentum law experimental device as the research object, combined with the actual operation of the experiment, adopts the SPH-FEM numerical analysis method to analyze the displacement response characteristics and deformation characteristics of the characteristic point C of the sensor structure under different momentum jet loads. Based on these, the error cause, error classification, changing law, error scope and influence are analyzed and calculated, comparing with the experimental results, and the validity of the analysis and calculation method is verified. The conclusions obtained from the above analysis are as follows:  
1. Under the action of jet impact, the sensor structure vibrates and produces displacement and deformation. The jet direction (X direction) vibrates first and stabilizes after oscillation adjustment. After the vibration of the jet direction is stable, the non-jet Y direction starts periodic vibration;
2. Among the vibrations in the non-jet direction, the vibration in the Y direction is the main source of error, and the vibration in the Z direction is mainly caused by the deformation caused by the vibration in the X and Y directions;
3. The linear error of the system is mainly caused by the deformation of the base in the jet direction (X direction), and its size is positively related to the jet load. The linear error can be reduced by improving the stiffness of the base;
4. The periodic error of the system is mainly caused by the periodic vibration in the Y direction and the lateral effect of the sensor. Its magnitude is negatively related to the jet load. The periodic error can be reduced by the method of sensor correction.  
The analytical methods used and the conclusions obtained in this article, which have been partially applied to the experimental teaching of undergraduates to provide help for students to understand the causes of experimental errors.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Jet Flow Rate** & **Theoretical Impact** & **Measured Impact** & **Relative Error** \\ **(m\({}^{3}\)/h)** & **Force \(N\)** & **Force \(N\)** & **\%** \\ \hline  & & & 7.51 & 1.08\% \\  & & & 7.36 & \(-\)0.94\% \\
2.2 & 7.43 & 7.59 & 2.15\% \\  & & & 7.45 & 0.27\% \\  & & & 7.49 & 0.81\% \\ \hline  & & & 8.95 & 1.24\% \\  & & & 9.10 & 2.94\% \\
2.4 & 8.84 & 8.93 & 1.02\% \\  & & & 8.85 & 0.11\% \\  & & & 8.82 & \(-\)0.23\% \\ \hline  & & & 10.40 & 0.19\% \\  & & & 10.45 & 0.67\% \\
2.6 & 10.38 & 10.35 & \(-\)0.29\% \\  & & & 10.27 & \(-\)1.06\% \\  & & & 10.30 & \(-\)0.77\% \\ \hline  & & & 12.15 & 0.91\% \\
2.8 & 12.04 & 12.20 & 1.33\% \\  & & & 11.95 & \(-\)0.75\% \\  & & & 12.10 & 0.50\% \\  & & & 12.23 & 1.58\% \\ \hline  & & & 13.95 & 0.94\% \\  & & & 13.75 & \(-\)0.51\% \\
3.0 & 13.82 & 13.80 & \(-\)0.14\% \\  & & & 13.90 & 0.58\% \\  & & & 14.00 & 1.30\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Experiment Error.  
**Author Contributions:** S.Y., X.Z. and H.W. conceived the conceptualization; S.Y. and H.W. designed the experiments; S.Y., X.Z. and H.W. performed the experiments, S.Y. and X.Z. analyzed the data; S.Y. wrote the paper. All authors have read and agreed to the published version of the manuscript.  
**Funding:** Higher Education Research Project of Jilin Province (No. JGJX2020D18).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data is contained within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.