Hydrodynamics of the Flow of an Ideal Liquid When It Flows Out of the Bottom Hole of a Parabolic Tank

Abstract

AbstractIn order to clarify the relationship between the geometry of the tank and the physical content of its emptying process, experimental studies were carried out to determine the expiration time through the bottom holes of vessels pre-filled with water of various geometric shapes with equal overall dimensions (cylinder, cone, paraboloid). The dependence of the time of complete emptying on the shape of the vessel was found. A feature was observed when the liquid flows out of the paraboloid: the uniformity of the level decrease and the deformation of the free surface. To explain such an anomaly of the process of outflow from a vessel of a parabolic shape, a hydrodynamic model is proposed based on the idea of the movement of particles of an ideal liquid through current tubes of various curvature that completely fill the volume of the paraboloid. Analytical expressions of the main kinematic parameters of the outflow (emptying time, acceleration of liquid particles), as well as the equation of the deformed free surface and its rate of decrease are obtained. The proposed work provides for a series of experiments on emptying vessels of various geometric shapes of the same overall dimensions, as well as a description of the results obtained using a hydrodynamic model based on the flow of liquid through curved current tubes.KeywordsCurrent tubeAxisymmetric emptyingParaboloidHydrodynamic modelBottom hole