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

Transient decay of 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 when the fill pipe does not reach to 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 revealed that the existence of a fill pipe beyond the liquid surface increases modestly the relaxation rate of surface potential. However, for the case when the fill pipe is located just above the liquid surface, decay of surface potential is dramatically slowed