유동화물의 유효자유표면에 관한 연구

A Study on the Effective Free Surface of Fluid Cargo

It is well known that the height of tank metacenter above the centroid of fluid in a tank is given by i/v where I is the inertia moment of free surface and v is the fluid volume. It is supposed in this formula that the inclination of ship is small and that the free surface of fluid do not touch the top and the bottom of tank. It the inclination of ship is large, the height of tank metacenter may be possibly greater than that given by i/v. The height of tank metacenter is smaller than i/v when the free surface of fluid touch the top or the bottom of tank. The reasonable method to calculate the height of tank metacenter is presented in this paper and prepared in FORTRAN program by FUNCTION EFFRES. The approximate formula was also developed and given by $g_m=(1+\frac{2}{1}tan^2\theta)[1-EXP\{-12(\frac{\alpha(1-\alpha)k}{tan\theta})^{1.25}\}]\frac{i}{v}$ where $g_m$ is the distance from the centroid of fluid to the tank metacenter, $\theta$ is inclined angle of ship, $\alpha$ is the ratio of filled volume to tank capacity and k is the ratio of the depth to the width of tank. The values calculated by the approximate formula given in this paper were compared with the exact values from the computer program and proved out to be sufficiently precise for practical use.