Analytical solution of filling and exhausting process in a pneumatic system

The filling and exhausting processes in a pneumatic system are involved with many factors, and numerical solutions of many partial differential equations are always adapted in the study of those processes, which have been proved to be troublesome and less intuitive. Analytical solutions based on loss-less tube model and average friction model are found respectively by using fluid net theory, and they fit the experimental results well. The research work shows that: 1) Fluid net theory can be used to solve the analytical solution of filling and exhausting processes of pneumatic system, and 2) the result of loss-less tube model is close to that of average friction model, so loss-less tube model is recommended since it is simpler, and 3) the difference between filling time and exhausting time is determined by initial and final pressures, the volume of container and the section area of tube, and had nothing to do with the length of the tube.