Pneumatic systemThere are many methods for calculating pressure loss in pipelines, and some models treat it as a variable temperature and variable flow gas. The calculation requires a large number of parameters, which is very cumbersome and difficult to calculate; Some models simplify it too much, although the calculation is very simple, the calculation results deviate greatly from reality and have no practical value. The calculation model of this article is: the transported gas flows in the pipeline, and its pressure and velocity are constantly changing. The temperature variation range of the transported gas is small and can be ignored as a constant temperature treatment. Due to the fact that the gas state in the case of pressure conveying under lower pressure or suction conveying under vacuum is close to the ideal state, this article studies it as an ideal state, and its gas equation is:

ρ=PM/RT （1）

     Among them, ρ is the density of the mixed gas, P is the static pressure of the system, M is the molecular weight of the gas, R is the gas constant, and T is the absolute temperature. For the convenience of research, this article assumes that the pneumatic conveying inside the pipeline is carried out at a constant temperature, and the gas density at different positions of the pipeline is only related to the static pressure, thus obtaining the formula:

ρ1/ρ2=P1/P2 （2）

Because the fluid is constantly flowing, the continuity equation can be obtained:

υ1A1ρ1=υ2A2ρ2 （3）

Among them, A1 and A2 are the cross-sectional areas of the pipeline, and υ 1 and υ 2 are the flow velocities of the fluid. In the process of pneumatic conveying, the diameter of the pipe is generally constant, so the continuity equation of the fluid can be simplified as:

υ1ρ1=υ2ρ2 （4）

    Through factual verification, it has been found that there is a significant difference between the initial and final velocities of the airflow during pipeline transportation, resulting in significant pressure loss. However, for fluids with the same properties within the same section of the pipeline, the velocity of the airflow changes very little. This article assumes that it is basically constant. Below, the specific formula for calculating pressure loss will be derived. （1） Calculation and analysis of pressure loss in horizontal pipelines in pneumatic conveying systems. The pressure loss caused by the conveyed gas in horizontal pipelines is mainly due to the friction along the pipe wall during transportation, the mutual friction and collision between gas molecules, and the pressure loss consumed when the conveyed gas is in a suspended state. There are three types of pressure loss. The first type is before adding the transported gas, which is thin air or residual transported gas from before, close to a vacuum state. The calculation formula for its pressure loss is:

△P1=λaL1/Dρυ12/2 （5）

Among them, υ 1 is the gas velocity entering the section, L1 is the length of the section, ρ is the density of air, and λ a is the friction coefficient, which can be obtained by referring to a table based on specific production practices. The second type is the pressure loss when introducing the transported gas, which is:

△P2=Cmρυ22/2 （6）

Among them, C is the production experience parameter for accelerating the transportation of gas (the value parameter is known from actual production experience to be between 1 and 10, with the minimum value for uniform transportation of gas and the maximum value for discontinuous transportation of gas), m is the mixing ratio (suction type: low vacuum state takes 1 to 8, high vacuum state takes 8 to 20; compression type: low pressure state takes 1 to 10, high pressure state takes 10 to 20), and υ 2 is the speed entering this section.

The third type is the pressure loss when the transported gas enters a stable state after being introduced, and its calculation formula is:

    P3=α1 to Pα (7)

△Pα=λa L3/Dρυ32/2 （8）

In the formula, α 1 is the pressure loss ratio (α=30/υ 3+0.2m). 

(II)Pneumatic conveying systemCalculation and analysis of pressure loss in vertical pipelines, including resistance loss along the transported gas and lifting loss of the transported gas, including gravity loss, calculated according to the following formula:

   P4=α2 Pα (9)

△Pα2=λa2 L3/Dρυ32/2 （10）

Among them, α 2 is the pressure loss factor in the vertical state (α 2=(250/υ 3) 1.5+0.15m), △ P4 is the pressure loss in the vertical state, and △ P α 2 is the frictional pressure loss of gas in the vertical state.