Effect of fill pipe on transient decay of surface potential in a cylindrical vessel containing charged liquid

Transient decay of the surface potential in an upright cylindrical vessel with a central fill pipe is investigated. The transient problem is solved analytically for the ideal case of the fill pipe extending fully to the vessel bottom. For the practical case in which the fill pipe does not reach the vessel bottom, this problem is studied by numerical calculation. In both solutions, constant ohmic resistivity is assumed and a surface conduction mechanism is introduced for the dissipation of surface charge. It is found that the existence of a fill pipe extending below the liquid surface modestly increases the relaxation rate of surface potential. However, when the fill pipe is located just above the liquid surface, the decay of surface potential is greatly slowed.<>