# Improved Calculation Method for Siphon Drainage with Extended Horizontal Sections
## 5 Discussions  
According to the improved flow rate calculation method, the values of siphon flow rates for different lengths of 4 mm and 5 mm diameter siphons obtained by iterative calculation based on MATLAB programming are shown in Figure 10. In the legend, \"H-No.\" is the numerical simulation lift condition; \"TH\" refers to the test lift. \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **D/mm** & **L\({}_{hori}\)/m** & **H\({}_{lipq}\)/m** \\ \hline
1\(\sim\)4 & 4 & 0 & 3, 4, 5, 6 \\
5\(\sim\)6 & 4 & 0 & 7, 8 \\
7\(\sim\)12 & 4 & 80, 160 & 3, 4, 5 \\
13\(\sim\)18 & 4 & 80, 160 & 6, 7, 8 \\
19\(\sim\)22 & 5 & 0 & 3, 4, 5, 6 \\
23\(\sim\)24 & 5 & 0 & 7, 8 \\
25\(\sim\)32 & 5 & 100, 160 & 3, 4, 5, 6 \\
33\(\sim\)36 & 5 & 100, 160 & 7, 8 \\ \hline \end{tabular}
\end{table} 
Table 1: Experimental schemes of siphon drainage (T = 25 \({}^{\circ}\)C, \(P_{ls}\) = 100.53 kPa). Figure 10: Comparison of MATLAB iterative calculation results with experimental data of siphon flow rate: (a) D-4; (b) D-5. The results in Figure 10a show that (1) for Experiment Schemes 1-4, the calculated values from Equation (50) and [PERSON]'s theory are close to the experimental measurements; (2) for Schemes 5-12, the calculated values from the two formulae have significant errors, yet the values from the improved method in this paper are still closed to the experimental measurements; (3) for Schemes 13-18, the errors between the calculated values from the improved method in this paper and the experimental measurements are less than 5%. The traditional siphon calculation theory can predict the short pipe-siphon flow velocity relatively well for smaller lifts. However, for higher lifts, its flow velocity calculation differs from the actual value by about 26%, which is improved in the calculation of [PERSON]'s theoretical equation. However, [PERSON]'s formula is also limited to improving the accuracy of flow velocity calculations for short pipe siphons at high-lift conditions. In the case of long siphons, especially with extended horizontal sections of discharge conditions, if the formula continues to be used, the error between the calculated and the experimental results is about 12%, and the error value exceeds the safety limit used for production calculations. Figure 10b shows that the calculated results obtained by the improved method still agree well with the experimental measurements. For the siphon with the long horizontal section, the fitting formula in this study solved this problem relatively well. When the calculation program initially set the calculation conditions according to the actual horizontal section length of the test, the error rate between the program calculation results and the test results appeared to increase exponentially, which was caused by the over-selection of the calculated pipe length of the horizontal section. This is because in the siphon system the highest horizontal position has a certain degree of \"negative pressure\". That is, the air pressure at this position is much smaller than the local atmospheric pressure. For this reason, the reduction in air solubility caused by the reduction in air pressure is significantly magnified in the horizontal section of a siphon with a long horizontal section. In other words, the length of the air bubbles in the long horizontal section is much larger than the length of the air bubbles in the horizontal section of the short tube, which also demonstrates the problem described above regarding the value of the horizontal tube length in the flow rate calculation method. It should be noted that in the process of calculating the siphon flow velocity in the long horizontal section, although the process of air pressure change in the rising section is similar to that in the short tube, the interaction between the fluid and the tube wall in the horizontal section has a considerable effect on the change of flow velocity.