How do I derive this voltage equalization process? Urgently need help!
Thread Content
There are two containers with the same volume V and the same temperature; one container is at 0.65 MPa while the other is at atmospheric pressure. They are connected by a pipe, and the high-pressure container uses this pipe to fill the low-pressure container with pressure. The flow is stopped when the pressure difference between the two containers reaches 30 KPa. What is the relationship between this equalization time and the diameter of the pipe? I really don’t know how to derive this; I’m urgently asking for help from fellow users! Thank you so much!
Personally, I think the larger the pipe diameter, the shorter the equalization time.
Well, I’m looking for someone to help derive the formula
I think, first of all, it is necessary to calculate the average gas volume, as it is essentially isothermal pressure equalization. By determining the relationship between gas volume and pressure, as well as between gas volume and pipe flow velocity, it is possible to determine the relationship between pressure, pipe flow velocity, and time. Since the pressure is known, the pipe diameter and time can be determined. Time is inversely proportional to the square of the diameter.