# Research on Key Parameters and Engineering Experiments of Coal Gangue Slurry Filling Technology
## 4 Industrial-Grade Circular Pipe Conveying Test of Gangue Slurry
### Experimental Analysis of Long-Distance Pipeline Transportation  
#### 4.3.1 The Relationship Between the Pumping Flow Rate and Conveying Resistance  
According to the long-distance pipeline transportation monitoring system, the pressure of each monitoring point along the pipeline at different pumping flow rate was obtained, as shown in Figure 6. According to the data, as it was far from the outlet of the grouting pump, the pressure along the pipeline showed a decreasing trend; as the pumping flow rate increased, the pressure at the exact location along the pipeline also showed an increasing trend, and the larger the pumping flow rate, the faster the pressure decreased along the pipeline. To further explore the relationship between the pipeline length and the pressure along the pipeline, the fitting curve of the pipeline length and the pressure along the pipeline under three pumping flow rates were obtained through data analysis. Still, the appropriate angle and the origin line graph could only be partially coincident. In this pipeline transportation test, the number of elbow sections in each section along the pipeline led to different local frictional losses in each section, which led to further transportation resistance in each section along the pipeline. Based on the statistical analysis, the relationship between the spacing and pressure difference between the monitoring points of long-distance pipelines was obtained, as shown in Table 4. According to fluid mechanics and Table 1, the following relationship was established:  
\[i_{ij}=\frac{\Delta P_{ij}}{\Delta L_{ij}+x_{ij}l_{e0}+y_{ij}l_{e1}} \tag{2}\]  
namely  
\[\frac{P_{2}-P_{1}}{(L_{2}-L_{1})+x_{12}l_{e0}+y_{12}l_{e1}}=\frac{P_{3}-P_{2}} {(L_{3}-L_{2})+x_{23}l_{e0}+y_{23}l_{e1}}=\frac{P_{4}-P_{3}}{(L_{4}-L_{3})+x_{ 34}l_{e0}+y_{34}l_{e1}}=\frac{P_{5}-P_{4}}{(L_{5}-L_{4})+x_{45}l_{e0}+y_{45}l_{ e1}} \tag{3}\]  
In the formula, \(i_{ij}\) is the conveying resistance between two adjacent monitoring points on the conveying pipeline, MPa/km. \(\Delta P_{ij}\) is the pressure difference between two adjoining monitoring points on the conveying pipeline, MPa. \(\Delta L_{ij}\) is the distance between two adjoining monitoring points on the transmission pipeline, km. \(x_{ij}\) is the number of \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Spacing/km**} & **Number of** & **Number of** & **Pressure** & **Pressure** & **Pressure** \\  & **90-Degree** & **135-Degree** & **Difference at a** & **Difference at a** & **Difference at a** & **Flow Rate of** & **Difference at a** \\  & **Angles Included** & **Angles Included** & **Flow Rate of** & **Flow Rate of** & **Flow Rate of** \\  & & & **80 m\({}^{3}\)/MPa** & **100 m\({}^{3}\)/MPa** & **120 m\({}^{3}\)/MPa** \\ \hline
1.19 & 10 & 2 & 0.90 & 1.48 & 2.21 \\
0.45 & 4 & 0 & 0.33 & 0.55 & 0.82 \\
0.76 & 3 & 0 & 0.47 & 0.75 & 1.10 \\
1.64 & 13 & 0 & 1.18 & 1.94 & 2.87 \\ \hline \end{tabular}
\end{table} 
Table 4: Relationship between spacing and pressure difference between monitoring points of long-distance pipelines. Figure 6: Relationship between pipeline length and pressure along the pipeline. 90-degree angles between two adjacent monitoring points on the conveying pipeline. \(y_{ij}\) is the number of 135-degree angles between two adjacent monitoring points on the conveying pipeline. \(l_{e0}\) is the equivalent pipe length at a 90-degree angle, km. \(l_{e1}\) is the equivalent pipe length at a 135-degree angle, km.