On Several Problems Ralated to Columns Running across the Water Surface

Abstract

1. The height of wave that rises ahead of a column, such as periscope of submarine, running across the water surface is nearly equal to the velocity head (V^2)/(2g) of the column, when the speed is comparatively low. However, when the speed becomes higher, the height of wave crest, followed by splash resulting from its crumbling, is less than the velocity head. The relation between the wave height H, or velocity head (V^2)/(2g) (V is the speed of column and g acceleration of gravity), and Froude's number 〓 is shown by the authors as follows : For 0 < 〓 < 3.4 [numerical formula] and for 3.4 < 〓 < about 9 [numerical formula], and the ratio of the wave height H to the diameter D is [numerical formula] 2. The number of Karman vortices generated behind the column in expressed, as is commonly known, by the following formula :(ND) / V �� 0.2 where N is the number of vortices generated in a unit time, D the diameter of the column, and V its speed. Our experiments carried out at Reynolds' numbers over 10^5 reveal, however, that (ND) / V is not always about 0.2.