Theoretical reconstruction of Galileo's two-bucket experiment

TL;DR

This paper theoretically reconstructs Galileo's two-bucket experiment using fluid mechanics equations, revealing that Galileo's original method for calculating jet percussion force was incorrect and that the net force is nearly zero.

Contribution

It provides a novel theoretical analysis of Galileo's experiment, clarifying the forces involved and correcting historical assumptions about the percussion force calculation.

Findings

Galileo's method for calculating jet percussion force is incorrect.

The net force during the experiment is practically zero.

Galileo's account of balance movements is credible despite force miscalculations.

Abstract

In the present work, we address the solution of a problem extracted from a historical context, in which Galileo supposedly conducted an experiment to measure the percussion force of a water jet. To this end, the conservation equations of fluid mechanics in unsteady state are employed in the theoretical reconstruction of the experiment. The experimental apparatus consists of a balance, in which a counterweight hangs on to one of its extremities, and two buckets, in the same vertical, hang on to the other extremity. The water jet issuing from an orifice in the bottom of the upper bucket strikes the lower bucket. The objective is to find the jet percussion force on the lower bucket. The result of the analysis revealed that the method proposed by Galileo for the calculation of the jet percussion force is incorrect. The analysis also revealed that the resultant force during the process is practically null, which would make Galileo's account of the major movements of the balance credible, despite his having not identified all the forces acting on the system.