## 5 Conclusions  
1. The presence of blockage results in significant pressure and velocity gradients near the blockage point. As the blockage increases, so does the pressure gradient, particularly beyond 50%, where a strong correlation with blockage characteristics is observed. Similarly, the velocity gradient increases with the blockage degree, and the relationship between the velocity gradient and the blockage characteristics is also positively correlated. Therefore, by detecting the pressure drop at the pipeline's starting point, initial velocity, and the sharp changes in the pressure and velocity distribution curves, it is possible to detect and locate the blockage.
2. The effects of the three blockage shapes on the internal pressure of the pipeline are ranked as follows: B-blockage has the greatest impact, followed by C-blockage, and A-blockage has the least impact. When the blockage degree is less than 50%, the changes in the pressure drop along the pipeline caused by the three blockage types are not significantly different. However, as the blockage degree increases, the pressure variations, particularly in B- and C-blockages, become more pronounced, with a larger fluctuation in the pressure along the pipeline. Among these, the B-blockage results in the most dramatic pressure changes. The formation of such blockages was analyzed in detail, and corresponding suggestions were proposed to address them.
3. In all three blockage types, the flow of slurry in the pipeline is characterized by distinct laminar flow, with the maximum flow velocity occurring at the center of the pipeline, forming a \"flow core\". The velocity at the top and bottom is lower due to friction with the pipeline surface. Moreover, the blockage shape significantly affects the flow velocity and pipeline safety. The stagnant flow region (dead zone) area for B- and C-blockages is larger than that for A-blockage, underscoring the importance of timely blockage removal. To prevent blockages, it is recommended to use pipeline materials with smooth inner surfaces and low roughness.  
Figure 19: Variation in pipeline velocity under different degrees of blockage.  
**Author Contributions:** Conceptualization, L.Z. and Z.L.; methodology, L.Z. and C.L.; software, L.G.; validation, D.Z., J.C. and W.G.; data curation, C.M. and F.Q.; writing--original draft preparation, L.G. and D.Z.; writing--review and editing, L.Z. and D.Z.; visualization, D.Z. and Z.D.; supervision, Y.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The work was supported by the financial supports from the National Natural Science Foundation of China (NSFC) (Grant number: 52474147), Shanxi Province Qin Chuangyuan \"Scientists+Engineers\" Team (Grant number: 2023 KJ-144) and Xi'an Qin Chuangyuan \"Scientists+Engineers\" Team (Grant number: 23 KGDW0027-2022).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed toward the corresponding author.  
**Conflicts of Interest:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.