The commonly used calculation formulas for headloss in inclined pipes are mostly based on gravity hypothesis, which cannot fully reflect the influence of solid particles. This paper studies and establishes a unified formula for headloss calculation in horizontal pipes, vertical pipes and inclined pipes, on the basis of energy hypothesis, referred to as DRC model. Then, it is verified by laboratory test data of coarse and fine sand, and compared with Wilson Formula. The results show that: for total headloss calculation, both formulas are with high accuracy, as error less than ±4%; while for solid/particle effect (additional headloss caused by presence of solids/particles) calculation, average deviation of DRC model is within ± 5%, obviously lower than that of Wilson formula, indicating that DRC model can better reflect the influence of particles on the headloss in inclined pipes.


Pipeline is one of the most competitive mode for solid materials transportation, due to its advantages of continuity, high efficiency, safety, low cost, etc. It is widely used in dredging, construction, energy, mining, bulk materials and other industrial and engineering fields. Normally, pipeline transport system is composed of horizontal section, vertical section, curved section and inclined section as connection and transition. Behavior of transported fluid in pipeline, for instance, flow structure, energy consumption, and other flow information, will change due to different pipe sections, especially for settling slurry, which will further affect design and operation of the transport system. However, researches is mainly carried out for horizontal pipes, due to various factors. A variety of calculation formulas are put forward for different scenarios (Wang, 1998). There are relatively little researches on transport characteristics of settling slurry in inclined pipes (Vlasák et al., 2018; Kesely et al., 2019), and calculation formulas established are mainly based on gravity hypothesis. Lack of information concerning slurry flow in inclined pipe sections has caused additional safety factors designed to avoid possible problems, which might occur during operation, startup, and shutdown of the transport system (Vlasák et al., 2020). This means increase in construction and operating costs of the transport system, as well as limitation on its performance.

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