Analytical dynamic model of coefficient of friction of air pipeline under pressure

To transport of the air in the pipeline, an analytical model is developed that takes into account the gas velocity, its kinematic and dynamic characteristics - density, viscosity depending on the pressure in a given space of the pipeline. The analytical model makes it possible to calculate the coefficient of friction of gas transportation in the pipeline at intervals of the absolute pressure from 220 to 2 kPa and M < 1 Mach numbers, depending on the diameter and length of the pipeline and physical and technological characteristics of the gas. The K₁* aspect ratio is proposed, which characterizes in time the ratio of the dynamic force of movement of gas to the static pressure related to the diameter of the pipeline. The coefficient of air friction was modeled according to the vacuum pressure as a parameter of density and air flow. Air flow was taken from 1.917·10-3 m 3/s to 44.5·10-3 m 3/s respectively, diameters from 0.030 to 0.070 m and Mach number was M = 0.005-0.13. At the vacuum and excess pressures with increasing of Reynolds number and decreasing of Mach number the gas friction coefficient increased linearly. According to the simulation results as the pressure loss and the diameter of the pipeline are increased the friction coefficient increased as well. Analogically, at the vacuum metric pressure when the pressure loss and the diameter of the pipeline are increased the friction coefficient increased. At the pipeline internal diameters of 22, 30, 36 mm accordingly for pressure losses from 2 to 14 kPa the coefficient of air friction varies from 0.006 to 54.527 respectively.