Bottle Emptying: A Fluid Mechanics and Measurements Exercise for Engineering Undergraduate Students

Abstract

A comprehensive exercise, suitable for an undergraduate engineering audience studying fluid mechanics, is presented, in which participants were tasked with emptying a bottle. That simple request yielded data collected by students and the author for N = 454 commercially available bottles, spanning nearly four orders of magnitude for volume [ s c a l e = 1 ] D e f i n i t i o n s / V . p d f , and representing the largest experimental dataset available in the literature. Fundamental statistics are used to describe the emptying time, T ¯ e , for any single bottle. Dimensional analysis is used to transform the raw data to yield a predictive trend, and a method of least-squares regression analysis is performed to find an empirical correlation relating dimensionless time T ¯ e g / d and dimensionless volume [ s c a l e = 1 ] D e f i n i t i o n s / V . p d f / d 3 . We find that volume, [ s c a l e = 1 ] D e f i n i t i o n s / V . p d f , and neck diameter, d, can be used to estimate the emptying time for any bottle, although the data suggests that the shape of the neck plays a role. Furthermore, two basic analytical models found in the literature compare favorably to our data and empirical correlation when recast using our dimensionless groups. The documented exercise provides students with the opportunity to use basic engineering statistics and to see the utility of dimensional analysis.