On super free fall
Patrick Weidman
Department of Mechanical Engineering, University of Colorado Boulder
Date and time:
Tuesday, October 6, 2015 - 4:00pm
Location:
ECOT 226
Abstract:
Villermaux & Pomeau (J. Fluid Mech. 2010) analyzed the motion of the interface of an inviscid liquid column released from rest in a vertical tube whose area expands gradually downwards, with application to an inverted conical container for which experimental measurements were carried out. An error in the analysis is found and corrected in the present investigation. We thus obtain the new governing equation for the super-accelerated interface motion down gradually varying tubes in general, and integrated results for interface trajectories, velocities and accelerations down a conical tube in particular. Further new results are reported here such as the equation governing the center of mass and proof that the terminal acceleration of the interface is exactly that of gravity. The theory is corroborated by experiment.
This work was done in collaboration with Francisco Higuera (Spain), Abraham Medina (Mexico), and Ayax Torres (Mexico).