Modelling the general corrosion of a steel tube under its own weight

A vertically standing or hanging long initially cylindrical tube is considered subjected to mechanochemical corrosion under its own weight. The corrosion rate is supposed to be a linear function of mechanical stress. The problem is reduced to a system of differential and integral equations that are solved numerically. It is clear that the own weight of the tube gives a rather small increase in the corrosion rate for relatively short tubes. The following questions arise. At what length of the tube do we need to take into account its own weight for the life assessment? Is there any simple approach to this consideration? These questions are investigated in the present paper.