Free liquid oscillations in paraboloidal containers
Abstract
Approximate expressions are obtained for the natural frequencies of a liquid with a free surface in an arbitrary tank of paraboloidal geometry. The values yield especially good approximations for these tank shapes when the free liquid surfaces can be approximated by a coordinate surface. In this way the liquid behavior may be approximately determined for a large variety of paraboloidal container geometries. The mechanically important values, such as surface elevation, pressure and velocity distribution, liquid forces and moments can be determined by differentiations and integrations of the velocity potential
 Publication:

Zeitschrift fur Flugwissenschaften und Weltraumforschung
 Pub Date:
 August 1981
 Bibcode:
 1981ZFlWe...5..249B
 Keywords:

 Liquid Filled Shells;
 Liquid Sloshing;
 Oscillating Flow;
 Parabolic Bodies;
 Resonant Frequencies;
 Tank Geometry;
 Coordinates;
 Cylindrical Tanks;
 Free Boundaries;
 Incompressible Fluids;
 Pressure Distribution;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer