Study on the velocity distribution around a bathtub vortex

Flow field around a bathtub vortex was investigated. A finite cylindrical vessel was used for experiments. The vessel had a tangential inlet open channel at the top, and a vertical outlet pipe at the bottom center, respectively. Flow field was visualized by ink and particle tracers, and velocity distributions were obtained. Vortex profile, a radius of stagnant region, and a radius of fast downward flow region were measured simultaneously. Two major flows were observed in the vessel; one was through the central region of the vessel, and another was along the wall of vessel, i.e., the side and bottom walls. Flow through the central region was found to increase its velocity in proportion to a distance from the free surface and to form a stagnant region along the vortex center under some experimental conditions. The flow field and the vortex profile seemed to be optimized by strength of circulation and flow rates of the major flows. However, these factors depended on both the total flow rate and the outlet pipe diameter complicatedly. A new flow field model was proposed, which based on an exact solution of the Navier-Stokes equations called an expanding vortex flow. The vortex profiles analytically calculated with the new flow model showed good agreement with experimental results. Validity of the model was verified and formation of the stagnant region was analytically discussed. (author)