When side-walls of a rectangular tank, which is filled up with water, is vibrating, the inside water will also make a vibratory motion. Accordingly, the value of natural frequency of vibration of side-wall will be considerably lowered, due to the presence of water. This effect is represented by "virtual mass" of water.
The author have reported, in previous papers of the same title, some results of theoretical study about the "virtual mass" of water. In these studies, two conditions at the top surface of water were considered, namely; (a) the top of water is directly in contact with a rigid plane wall. (b) the top of water is left free, forming a state of "free surface".
As to the case (b) , an approximate formula for the "virtual mass" of water was obtained, by assuming that value of the factor K =ω²H/g (wherein ω=angular frequency of vibration, H=depth of the tank, g=acceleration due to gravitation of the earth) is very large in comparison with unity. It is thought that this assumption is appropriate, at least in the case of vibration of side-walls constituting the water-or oil-tank of a ship.
But, there may arise the questions as to, (a) what degree of approximation it will give? (b) what will take place, if the factor K was not so large in comparison with unity? In the present report, these questions are studied theoretically. As before, the water is assumed to be an incompressble ideal fluid, and the vibration to be of infinitesimally small amplitude. It is shown, by taking up the numerical example for the case of a rectungular water tank having the proportion of H :B :L = 3 : 3: 5, that, if the value of cofficient K is as large as 1000, the author's approximate formula (given in Report I), is suffiiciently accurate for a practical use, but that if the value of K is as low as 10 it requires considerable modifiication.