Voltage calculations for annular tanks partly-filled with charged liquid

A Bessel function expression is developed for the voltages produced when annular tanks (vertical axis cylindrical tanks with central conductors) are filled with liquids of uniform charge density. The expression is used to calculate the maximum surface voltage and this is compared with the maximum voltage predicted for tanks without a central conductor. Previous estimates of the percentage voltage reduction produced by a central conductor during tank filling have indicated a reduction of about 42% for practical tank dimensions. The new results, which are obtained with a more realistic model geometry, suggest a reduction of only about 29%.