# Experimental Study on Horizontal Pipeline Transportation Characteristics of Coarse Particle
## 4 Results and Discussion
### Analysis of Coarse Particle Flow Characteristics  
In order to better analyze and compare the followability of coarse particles with water flow, a followability coefficient kk is introduced to characterize the followability characteristics of coarse particles in relation to water flow. The followability coefficient of particles is defined as the ratio of particle flow velocity to clean water flow velocity, as shown in Equation (7). \[k=\frac{V_{s}}{V_{l}} \tag{8}\]  
where \(k\) represents the particle followability coefficient, \(V_{s}\) represents the particle flow rate, and \(V_{l}\) represents the clear water flow rate. By using Equation (7) and the previous data, the following relationships of three different particle sizes of coarse particles with water flow can be obtained, as shown in Figure 13. Among them, the horizontal axis of the coordinate axis represents the particle's followability coefficient \(k\), and the vertical axis of the coordinate axis represents the ratio of the actual height in the vertical direction inside the pipe to the pipe diameter \(y\cdot D^{-1}\). As shown in Figure 13, for coarse particles with a diameter of 0.9 mm, the increase in water flow velocity causes the maximum velocity of the particles to shift vertically, indicat  
Figure 13: Follow-up relationship of coarse particles with different particle sizes with water flow. (**a**) Particle diameter d = 0.9 mm; (**b**) particle diameter d = 1.5 mm; (**c**) particle diameter d = 2.5 mm. ing that as the water flow velocity increases, the particles are gradually lifted by the water flow. For coarse particles with diameters of 1.5 mm and 2.5 mm, the maximum velocity of the particles consistently occurs near the centerline of the pipeline. The smaller the particle size, the larger both the maximum and overall values of the particle's followability coefficient kk. Additionally, the overall span of the followability coefficient kk for coarse particles with a diameter of 0.9 mm is much larger than that for coarse particles with a diameter of 2.5 mm. This suggests that the followability of particles varies significantly across different areas of the pipeline, with particles near the centerline being more easily accelerated by the water flow. The Influence of Particle Bed Types on the Flow Pattern of Coarse Particle Clusters in Various Motion States  
The following text summarizes the percentage distribution of each moving particle layer within the pipeline cross-sectional area for three distinct particle sizes, analyzed under varying material volume concentrations and mixed average velocities, as depicted in Figures 14-16. In these figures, the particle bed layers corresponding to different coarse particle motion states are illustrated using differently colored bar graphs. The horizontal axis denotes the mixed average velocity of the coarse particle group, while the vertical axis represents the percentage of the particle bed layer relative to the pipeline cross-sectional area. Figure 14: Proportion of particle layer to pipeline cross-sectional area in different motion states (particle diameter d = 0.9 mm). (**a**) Material volume concentration \(\text{Cv}=10\%\); (**b**) material volume concentration \(\text{Cv}=15\%\); (**c**) material volume concentration \(\text{Cv}=20\%\). As shown in Figure 14, for particles with a diameter of 0.9 mm, a stationary deposition layer is present at low mixed average velocities. As the material volume concentration increases, the proportion of the stationary deposition layer also rises, with no suspending movement layer observed. When the velocity reaches 1.5 m/s, the suspending movement layer begins to emerge. As the velocity continues to increase, the proportion of the suspending movement layer also grows. As shown in Figure 15, for particles with a diameter of 1.5 mm, the stationary deposition layer occupies a substantial proportion at low mixed average velocities.