Analytical Model of Fluid Flow through Closed Structures for Vacuum Tube Systems

Abstract

An analytical model is developed to evaluate airtightness, which is one of the most important requirements of vacuum tube transportation systems. The main objective of the model is to anticipate the pressure inside a closed structure, which initially decreases and then rises with time owing to the inflow of the air outside. The model is formulated by using Darcy’s law and by solving the differential equations that consider the air permeability of the material and physical configuration of the tube. Equations are derived for a tube section in two cases: one with constant thickness and another with variable thickness. Although the developed model must be verified experimentally, results simulated by using the model with several assumed sections were consistent with the findings of a previous study. The mathematical model developed here to predict the behavior of the pressure inside a vacuum tube structure could be effectively used to evaluate the airtightness of vacuum tube transportation systems. Such data could provide background technical information for the practical design of the system.