On super free fall

Abstract

Villermaux & Pomeau (J. Fluid Mech., vol. 642, 2010, p. 147) analysed 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, which provides 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. Interestingly, the error does not affect any of the conclusions given in the 2010 paper. Further new results are reported here such as the equation governing the centre of mass and proof that the end point acceleration is exactly that of gravity.

Super free fall of an inviscid liquid through interconnected vertical pipes

“…This means that when the upper pipe is filled up to a small height, the acceleration of the upper free surface increases. This result is in apparent contradiction to that occurring in the conical pipes [1,2], because if such a pipe is brimful the super acceleration is stronger. However, in this latter case the value of α is a function of β and decreases as β increases.…”

“…Our experimental studies allow to show that the inertial instability (nipple) growing in the upper free surface in conical pipes [1,2] does not appear in the case of super free fall in interconnected pipes. Details of this point will be given later.…”

“…Introduction. -Super free fall, i.e., motion with acceleration higher than the gravity acceleration, g, has been recently reported as typical of gravity-induced fluid flows in geometries where the cross-section of vertical pipes increases smoothly and continuously along the flow direction [1,2]. The condition of liquid with very low viscosity also is critical in order to minimize the viscous effects such as the viscous dissipation and the viscous boundary layer.…”