July 2026 

Volume 94, Issue No. 7

The physics behind Heron's fountain

Daniele Battesimo Provenzano Am. J. Phys. 94, 530–539 (2026) https://doi.org/10.1119/5.0303689

Heron's fountain looks like a simple trick: water spurts upward as if the device could run forever. In reality, it is a showcase of several physical phenomena at work—gravity, air compression, viscosity, turbulence, and energy dissipation all intertwined. Surprisingly, this classic demonstration has rarely been treated beyond a qualitative level. In this work, we build a consistent theoretical framework, extending Bernoulli's equation to include viscous effects and clarifying the limits of its applicability within the system. We complement the model with experiments that allow a direct comparison between predictions and data. The result is a new perspective on a two-thousand-year-old invention, in which a familiar classroom curiosity becomes a precise tool to explore fundamental fluid mechanics. From an educational standpoint, the system also provides a flexible platform for laboratory or classroom activities, suitable for advanced undergraduate and early graduate students, and well-suited to illustrate hydrostatics, viscous flow, and the interplay between theory and experiment.

EDITORIAL

In this issue: July 2026 by John Essick; Jesse Kinder; Claire A. Marrache-Kikuchi; Beth Parks; Donald Salisbury; Keith Zengel. DOI: 10.1119/5.0345002.

LETTERS TO THE EDITOR

Physics as a branch of poetry by Níckolas de Aguiar Alves. DOI: 10.1119/5.0335472.

Benford's law in superconducting critical temperatures by Hiroki Wadati. DOI: 10.1119/5.0332762.

Solving quadratic equations as a fixed-point problem by Ramandeep S. Johal. DOI: 10.1119/5.0333320.

Early use of dimensional analysis in quantum theory by Kirk T. McDonald. DOI: 10.1119/5.0337153.

Jackson's formalism of gauge transformation by V. Hnizdo. DOI: 10.1119/5.0308912.

AWARDS

Lighting the way by Meghan DiBacco. DOI: 10.1119/5.0345333.
Editor's Note: This paper is the text of a plenary talk given by the author at the AAPT Winter 2026 meeting when she accepted the Doc Brown Futures Award.

PAPERS

How bright is a firefly? Resolving a century of overestimation by David H. Silver. DOI: 10.1119/5.0325834.
Editor's Note: This paper starts with a fun question and shows how to examine it from many angles to reach a reliable answer. While the paper may not succeed in correcting all the errors on the internet, their inexpensive apparatus, combined with a useful tutorial on units, will allow readers to try this experiment whenever the fireflies come out in their region. Share your results in a Letter!

Viscosity, liquid flow, and energy conservation in continuum mechanics by M. Gil-Fraca; A. Fernandez-Nieves. DOI: 10.1119/5.0295017.
Editor's Note: This article shares an insightful way to understand fluid flow and viscosity as a short-term storage of energy via the elastic modulus followed by a relaxation time in which particles rearrange. This model can inform the teaching of fluid mechanics even at the introductory level.

The physics behind Heron's fountain by Daniele Battesimo Provenzano. DOI: 10.1119/5.0303689.
Editor's Note: Heron's fountain is a classic hydraulic device that spits out water thanks to the interplay between hydrostatic pressure and compressed air in a system of interconnected vessels. This paper goes beyond the usual qualitative description of the phenomenon and develops a model that includes viscosity to quantitatively track how the liquid level in each vessel evolves in time and predict when the fountain eventually stops. Appropriate for introductory fluid mechanics class to derive the stopping time, but

A new (old?) coupled pendulum experiment by Neil G. R. Broderick; Benjamin Pollard; Karthik Sivasubramanian; Marc Lescano; Chengjie Chen. DOI: 10.1119/5.0271406.
Editor's Note: Coupled pendula are a staple of undergraduate laboratory experiments. In a typical setup, pendulum bobs hung from a common horizontal mount are connected by springs. However, this can be awkward if it is desired to change the coupling between the bobs, a constraint that limits the range over which the dynamical theory that can easily be tested. This paper describes an experiment where the bobs are connected by strings to a node that lies below the common mount. The node is a twisted wire or paperclip whose vertical position can be easily varied, thus changing the coupling between the bobs. The paper summarizes the rather complicated Lagrangian of the coupled motion, and compares experimentally measured oscillatory frequencies for various modes to the theory, finding excellent agreement. The complexity of the analysis is such that students also gain experience with using computer algebra systems. Appropriate for students in advanced laboratory/classical dynamics courses.

Scientific modeling and the nature of science: The case of Thomson's atom by Luisa Lovisetti; Marco Giliberti. DOI: 10.1119/5.0318972.
Editor's Note: Have you given the Thomson model a fair hearing? Too often, students are taught a caricature of the real thing: that Thomson thought the atom was a positive “pudding” filled with negative “plums.” In reality, Thomson's model was a work of genius. It explained contemporary experimental observations and solved the electrodynamic riddle of stability. Read this article if you're looking for a new case study to teach students about scientific modeling.

What if active and passive gravitational masses were not equal? by Domenico Giulini. DOI: 10.1119/5.0280019.
Editor's Note: The distinction between what is identified as an active mass that creates a Newtonian gravitational force on a responding so-called passive mass is seldom, if ever, brought to the attention of physics students. They and instructors will be surprised to learn that we do not possess a definitive proof of their equivalence.

Educational approach to general relativity through its approximate vectorial form by Kjell Prytz. DOI: 10.1119/5.0304356.
Editor's Note: This article extends several known behaviors in classical electrodynamics to gravitational effects, thus requiring only special relativity with no knowledge of general relativity. A wide audience can benefit from this analysis of moving particle gravitational interactions and the creation of gravitational waves.

INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS

Macroscopic Brownian motion on a chaotic fluid interface by Jack-William Barotta; Caroline M. Barotta; Eli Silver; Daniel M. Harris. DOI: 10.1119/5.0317318.
Editor's Note: Normally when students observe Brownian motion in the lab, they have to accept that the crossover from ballistic to diffusive motion happened on a timescale too short to observe. While this rapid crossover simplifies the analysis of the motion, it poses a challenge to student understanding. This paper introduces a Brownian motion experiment in which a plastic disc is randomly driven by Faraday waves on a liquid surface. Video capture of the motion enables students to observe and analyze both the ballistic and the diffusive regimes. As a bonus, they will also be introduced to the fascinating phenomenon of Faraday waves.

Rubidium isotope shift measurement made simple by A. Anderson; T. Ayers; B. E. Bish; S. Cart; V. Tobar Correa; A. O'Brien; R. Stipanovich; M. Crescimanno. DOI: 10.1119/5.0313772.
Editor's Note: This paper offers a two-photon experiment by which advanced undergraduates can measure the isotope shift of rubidium, an important atomic physics effect. The authors provide a detailed description of the experimental setup, which is based on free-running diode lasers, as well as the necessary theoretical background to analyze the acquired data.

NOTES AND DISCUSSIONS

A shortcut to the eigenvalues of the harmonic oscillator and the hydrogen atom by J. M. Zhang; R. K. Lin. DOI: 10.1119/5.0332743.
Editor's Note: This Note will delight quantum mechanics instructors, as it points out a simple way to derive the eigenstates and energies of the harmonic oscillator and hydrogen atom potentials. Do not miss it!

Additional Resources