Dynamic model of the duration of gaseous environment pumping from a limited volume

Abstract

An analytical equation for the duration of air pumping from a limited volume has been developed. The equation of the mechanical energy of air movement takes into account the law of mass conservation for a gas in a controlled volume, the work of the energy of air movement and the work to overcome air friction. Gaseous medium is Newtonian. The duration of pumping (filling) the limited volume of the pneumatic chamber with air was calculated by comparing the mass flow per second and the increase in mass, as a differential of the change in air density. The mathematical model enables the simulation of air pumping time depending on pressure, as a density parameter and at different Mach numbers in the subsonic range. The 𝑲𝑲𝟏𝟏∗ proportionality coefficient, which characterizes the ratio of the dynamic force of gas mass displacement to the static pressure relative to the diameter of the air pipeline, is proposed as a criterion for evaluating the dynamics of the flow. It should be noted that the analytical dependence works for Newtonian media and Mach numbers of M < 1, the gas flow is caused by the pressure difference, the gas itself is limited by a chamber space characterized by a volume as design parameter of structure.