## 3 Results and Discussion  
### Influence Analysis of Connected Piping on Weighting Results  
Figure 5a is the correlation diagram of the beam stiffness coefficient \(a\), the measurement induction coefficient \(b\), and the mass of the materials inside the unit equipment \(m\), in the case of the mass change coefficient \(m^{*}\leq 1\%\). The diagram can provide a reference for the preliminary selection of parameters. In Figure 5b, for a certain mass \(m\), the maximum beam stiffness coefficient of the piping decreases rapidly at first, and then basically remains unchanged with the increase of characteristic parameters of the load cell. So, the range of the beam stiffness coefficient can be defined quantitatively when the material mass or the load cell is determined. This analysis method can be applied to the engineering design of the material weighing system inside process equipment with connected piping to meet the requirements of weighing linearization. From Equations (15) and (16), it can be seen that the characteristic parameters of the connected piping are inter-related under certain weighing accuracy. The analysis of this section can provide a basis for parameter optimization. The weighing coefficient \(m^{c}\) is defined as the ratio of the material mass to the measurement induction coefficient, \(m^{c}=\mathrm{m/b}\). In the project, the coefficient can be used to evaluate the mass measurement characteristics of the system synthetically. This section focuses on the relationship between connected piping parameters and the weighing coefficient \(m^{c}\) under specific accuracy conditions, as shown in Figure 6. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Pressure/Pa & 76/81/85/91/93 \\ Steam flow rate/L-h-1 & 0/0.3 \\ Water flow rate/g-min-1 & 10/20/30/40/50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental conditions. Figure 5: Parameter ranges under linearization condition (\(m^{*}\leq 1\%\)): (**a**) characteristic parameter relationship; (**b**) certain mass of the unit equipment \(m\). It can be seen from Figure 6 that the influence of the characteristic parameters of the connected piping decreases rapidly with the increase of the material mass initially, then slows down and eventually stabilizes. This indicates that, as the mass increases, the sensitivity of the load cell to the change of material weight is greater than the change of beam structure displacement. In the stable stage, the relative change caused by the connected piping is a constant value, and the measuring value has a linear relationship with the true value. Figure 6a shows the correlation diagram of the elastic modulus of the materials, the moment of inertia, and the length of connected pipe in the case of the weighing coefficient \(m^{\text{c}}\) = 4.0 \(\times\) 10\({}^{10}\) kg\({}^{2}\)/m\({}^{2}\). The diagram can provide a basis for quantitative matching design among the characteristic parameters of the connected piping. The influence on the weighing results is small or even negligible, where the larger the elastic modulus, the longer the length or the smaller the moment of inertia of the pipe. Figure 6b shows that the influence of the elastic modulus on the mass change coefficient \(m^{\text{*}}\) is almost proportional. As shown in Figure 6c, when the moment of inertia of the pipe is greater than 4.5 \(\times\) 10\({}^{3}\) mm\({}^{4}\), the influence on \(m^{\text{*}}\) increases gradually. When the moment of inertia is less than 1.5 \(\times\) 10\({}^{3}\) mm\({}^{4}\), the value of the mass change coefficient \(m^{\text{*}}\)\(\leq\) 2%, it has little influence on the measurement results. However, Figure 6d indicates that the change of the pipe length has a significant effect on the weighing results. When the length is greater than 560 mm, the pipe has little influence on the weighing result, and the measurement accuracy is still within the accuracy requirement range. However, when the length of the pipe is less than 360 mm, the influence cannot be ignored.