# Experimental Study on Horizontal Pipeline Transportation Characteristics of Coarse Particle
## 4 Results and Discussion
### Statistical Analysis of Coarse Particle Flow Transitions  
By summarizing and analyzing the motion characteristics of particle layers in different motion states and observing and recording phenomena in experiments, the various velocities at which coarse particles undergo motion state transitions under different particle sizes (0.9 mm, 1.5 mm, and 2.5 mm) and material volume concentrations (10%, 15%, and 20%) were summarized, as shown in Figure 17. The horizontal coordinate of the graph indicates the average speed of mixing, and the vertical coordinate indicates the material volume concentration. The red line is the velocity profile of each kinematic state transition for a particle size of 0.9 mm, the blue line is the velocity profile of each kinematic state transition for a particle size of 1.5 mm, and the green line is the velocity profile of each kinematic state transition for a particle size of 2.5 mm.  
The starting speed \(V_{cd}\), sedimentation critical speed \(V_{d}\), and floating critical speed \(V_{B}\), respectively, indicate the speed at which particles in the pipeline begin to move, the speed at which all particles in the pipeline begin to move without stationary sedimentation particles, and the speed at which coarse particles exceeding 50% of the pipeline section begin to suspend, corresponding to the transition of the coarse particle group flow pattern from a sedimentation bed type to a sedimentation bed type with jumping and rolling particles, and then to translational and heterogeneous flow suspension flow patterns. Due to the limitation of the velocity range during the experiment, particles with diameters of 1.5 mm and 2.5 mm did not reach the critical velocity for floating, and therefore are not shown in Figure 17.  
Figure 17: Transition speed of coarse particles in various motion states.  
It can be observed that the range of particle starting velocity variation is relatively narrow, consistently below 0.5 m/s, while the range of sedimentation critical velocity variation is considerably wider. The sedimentation critical velocity is highly sensitive to changes in particle diameter and material volume concentration. Specifically, larger particle diameters and higher concentrations result in greater sedimentation critical velocities for the coarse particle group, necessitating higher speeds for the transition of the coarse particle group flow pattern to translational motion. For a 0.9 mm coarse particle group, the critical velocity of planktonic particles is significantly higher, exceeding 2.5 m/s, and it increases linearly with rising material volume concentration, demonstrating a strong linear correlation.  
The above phenomenon indicates that the initial conditions of particle motion are not significantly influenced by the particle diameter and material volume concentration, whereas the mixed average flow rate has a more pronounced effect on particle initiation. The critical sedimentation velocity exhibits a linear correlation with both the material volume concentration and particle diameter. Specifically, larger particle diameters and higher material volume concentrations make it more challenging for the coarse particle group to transition from a sedimentation bed with jumping and rolling particles to translational motion. Within the experimental scope of this study, only the 0.9 mm coarse particle group achieved the transition to a non-homogeneous flow suspension motion flow pattern, with its critical floating velocity demonstrating a clear linear relationship with the material volume concentration.