Improved Equations for the Profile of a Vertical Air-Core Vortex

Abstract

The available formulas for the profile of a vertical non-air-entraining vortex are not practical because they involve unknown parameters and need measurements of the local viscous-core radii across the height of the air-core vortex. Also, these formulas can not be used for the air-entraining vortices. In the present study, the available formulas involving unknown parameters were further improved. Findings are as follows. 1) the magnitudes of the unknown parameters vary across the height of the profile of the air-core vortex and they are the function of the ratio of the height of the air-core vortex to the submergence of the intake; 2) simple charts and formulas were obtained for the variations of the unknown parameters for the air-core vortices with and without an intake; 3) in lieu of the local viscous-core radius, the radius at the half-depth of the profile of the air-core vortex was used; 4) no laborious work of measurements are needed to determine the local viscous-core radii along the profile of the vortex; and 5) the improved formulas are in good agreement with available test data for the profiles of both the non-air-entraining and the air-entraining vortices with or without a vertically flowing downward intake.