## 4 Conclusions  
In this study, a mathematical model between the material weighing value inside unit equipment and the true value was established for a continuous gas-liquid contact weighing system with multiple pipe connections. In order to meet the specific requirements of measurement accuracy, the corresponding criteria were obtained through linearization analysis of the model, and the effects of connected piping and dynamic load on the weighing results were further studied. Finally, the theoretical analysis results were verified by static/dynamic experiments of continuous gas-liquid contact weighing. The main conclusions are summarized as follows:  
(1) According to the mathematical model under static conditions, which includes the material mass, the maximum deflection of the cantilever beam, strain gauge deformation, and bridge output voltage, the linear power function relationship between the measured mass value and the truth value can be modified and simplified within a certain range. It provides a theoretical basis for improving the weighing accuracy in practical engineering application.  
(2) In the required range of weighing accuracy, the quantitative relation of the beam stiffness coefficient, measurement induction coefficient, and mass of the materials inside unit equipment was obtained and provided a reference for the preliminary selection of parameters.  
(3) The analysis results showed that the length of the piping has a significant effect on the weighing result, followed by the moment of inertia and the elastic modulus. Under the condition of setting the measurement accuracy, the influence of the elastic modulus on the mass change coefficient is almost proportional. Meanwhile, the moment of inertia and length can be confirmed with additional consideration of the mass measurement coefficient.  
(4) Excellent linear fits were observed in the regression equations of the static experiment between the measured value and the true value, which was consistent with the linear simplification results of the theoretical model. The dynamic experimental results showed that the change of weighing value caused by operating pressure can be ignored within the operating range of this experiment. The influence of liquid velocity on weighing results was mainly reflected in the fluctuation of mass, which may be caused by the harmonic load generated by the liquid feeding device. The maximum linearity of the weighing results is 0.311%, the maximum repeatability is 0.501%, the maximum hysteresis is 0.401%, and the overall measurement accuracy meets the set requirements.  
From the results of this work, theoretical analysis and experimental research are carried out on the weighing measurement of a chemical continuous system with multiple connected piping systems. Considering some problems neglected in the past, a universal mathematical model is obtained, and it provides some basis for engineering application.  
[PERSON], [PERSON], [PERSON] and [PERSON] designed and performed the experiments. [PERSON] analyzed the data and wrote the article. [PERSON] and [PERSON] reviewed and edited the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Institutional Review Board Statement**: Not applicable.  
**Informed Consent Statement**: Not applicable.  
**Data Availability Statement**: Not applicable.  
**Acknowledgments:** The authors gratefully acknowledge the comments of the reviewers and the editor, which enormously improved the presentation of the manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.