PROBLEM TO BE SOLVED: To theoretically calculate a damping ratio of sloshing to be produced in a tank disposed in a low-gravity field.SOLUTION: The mode equation of non-viscous sloshing in a surface tension-effected state is set up on the basis of a variation principle of a non-viscous fluid by assuming that a liquid 2 in a spherical tank 1 is a non-viscous fluid. Next, in the viscous term of a Navier-Stokes equation, the virtual work in a viscous boundary layer to be formed on the wall surface of the tank is expressed in mode coordinates. The virtual work in the viscous boundary layer expressed in the mode coordinates is added to the set-up mode-equation of the non-viscous sloshing and other mode equation including a first-order differential term which corresponds to a speed term and is expressed by the time of the mode coordinates, is set up. The damping ratio is calculated on the basis of a coefficient of the first-order differential term by the time of the mode coordinates.
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