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Sylvio R. Bistafa

Publications and source records attributed to Sylvio R. Bistafa.

15 recordsLinked to original sources
arXiv2025

An Annotated Translation of D. Bernoulli's "A New Theory on the Motion of Waters Through Channels of Any Kind"

This paper presents an annotated English translation of Daniel Bernoulli's 1727 work A New Theory on the Motion of Waters through Channels of Any Kind, originally published in the Commentarii Academiae Scientiarum Imperialis Petropolitanae. Written over a decade before his renowned Hydrodynamica (1738), this early treatise reveals D. Bernoulli's foundational approach to fluid motion based on the conservation of vis viva-the kinetic energy of moving bodies-at a time when the principle was still under active debate. In this work, D. Bernoulli applies mechanical reasoning to fluids flowing through channels of arbitrary shape, deriving relationships between velocity, cross-sectional area, and efflux under ideal conditions. He anticipates core results of Hydrodynamica, including the inverse relationship between flow velocity and cross-sectional area, and emphasizes the role of energy balance in analyzing steady flow. The text also includes reflections on experimental limitations, the influence of friction, and the boundaries of theoretical applicability. This translation highlights the historical and conceptual significance of the 1727 paper as a precursor to D. Bernoulli's mature hydrodynamic theory.

physics.hist-ph↗
arXiv2024

A translation of L. Euler's " Examination of an artifice for propelling a ship by the principle of internal motion"

The following translation of Leonhard Euler's "Examination of an Artifice for Propelling a Ship by the Principle of Internal Motion," originally published in 1750, offers a glimpse into a fascinating historical debate in the field of mechanics. This work critically examines a proposal by Jacob Bernoulli, one of the foremost mathematicians of the 17th century, who suggested that a ship could be propelled by forces entirely confined within the vessel itself-a concept that contradicts the principles of classical mechanics. This translation is intended to make Euler's insights accessible to a modern audience, highlighting the enduring relevance of these foundational principles. The commentary provided offers context and clarification, drawing parallels between Euler's work and contemporary understandings of mechanics. By examining the arguments of two of the greatest minds in the history of science, readers are invited to appreciate the depth and precision of classical mechanics as it was developed during the Enlightenment.

physics.hist-ph↗
arXiv2024

Evaluating Jacob Bernoulli's Ship Propulsion Artifice: Euler's Analysis and Critique

The present work examines and compares the approaches of Jacob Bernoulli and Leonhard Euler to the problem of ship propulsion generated by internal forces. Jacob Bernoulli's analysis, developed in the late 17th century, relies on geometric interpretations and algebraic relationships to estimate the impulse exerted by a pendulum within a ship. His results, however, are shown to overestimate the force by scaling it with the height of fall rather than the velocity at the end of the fall and by amplifying it with a time dependence factor that proves to be erroneous. Euler's subsequent analysis, conducted nearly 50 years later, provides a more rigorous and mechanically sound treatment of the problem. Utilizing differential equations and a deeper understanding of the principles of motion, Euler demonstrates that no net motion can be generated by internal forces alone, thus refuting the concept of perpetual motion as proposed by Jacob Bernoulli. By comparing the two methodologies, this work highlights the evolution of mathematical and physical analysis from the intuitive but flawed approaches of the early calculus pioneers to the more precise and reliable methods established by later mathematicians. Euler's work not only corrects the errors in Jacob Bernoulli's analysis but also solidifies the understanding that propulsion requires external forces, a conclusion consistent with the laws of Newtonian mechanics.

physics.hist-ph↗
arXiv2024

Early theories on fluid resistance and translation of Euler's "Dilucidationes de resistentia fluidorum"

In 1763, Euler published "Dilucidationes de resistentia fluidorum" (Explanations on the resistance of fluids), a memoir that challenges the fluid resistance theories proposed by Isaac Newton and d'Alembert. Euler's work explores the resistance experienced by solid bodies moving through fluids, critiquing both Newton's "common rule" and d'Alembert's paradox, which predicted zero resistance for non-viscous fluids. Euler's treatise is divided into two parts: the first focuses on the mathematical modeling of fluid flow patterns, while the second addresses the calculation of fluid resistance on surfaces. Despite significant advancements, Euler's work remains constrained by the limitations of non-viscous fluid assumptions, ultimately grappling with the same paradoxes he sought to overcome. This paper reviews the key contributions and limitations of "Dilucidationes", emphasizing the ongoing relevance of Euler's insights in the context of classical fluid dynamics. Additionally, it highlights the translation capabilities of AI-powered tools, specifically ChatGPT, in translating complex mathematical texts, marking a noticeable improvement in handling notation-heavy content.

physics.hist-ph↗
arXiv2024

Translating scientific Latin texts with artificial intelligence: the works of Euler and contemporaries

The major hindrance in the study of earlier scientific literature is the availability of Latin translations into modern languages. This is particular true for the works of Euler who authored about 850 manuscripts and wrote a thousand letters and received back almost two thousand more. The translation of many of these manuscripts, books and letters have been published in various sources over the last two centuries, but many more have not yet appeared. Fortunately, nowadays, artificial intelligence (AI) translation can be used to circumvent the challenges of translating such substantial number of texts. To validate this tool, benchmark tests have been performed to compare the performance of two popular AI translating algorithms, namely Google Translate and ChatGPT. Additional tests were accomplished in translating an excerpt of a 1739 letter from Johann Bernoulli to Euler, where he announces that he was sending Euler the first part of his manuscript Hydraulica. Overall, the comparative results show that ChatGPT performed better that Google Translate not only in the benchmark tests but also in the translation of this letter, highlighting the superiority of ChatGPT as a translation tool, catering not only to general Latin practitioners but also proving beneficial for specialized Latin translators.

math.HO↗
arXiv2023

200 Years of the Navier-Stokes Equation

The year 2022 marked the 200th anniversary of the first appearance of the Navier-Stokes equation, a landmark in Fluid Dynamics introduced by Claude-Louis Navier in 1822. This equation revolutionized the understanding of fluid motion by incorporating viscosity and friction into the equations, expanding their applicability beyond idealized fluids. In this manuscript, we explore the historical development of the Navier-Stokes equation and its profound impact on Fluid Dynamics over the past two centuries. From Navier's initial insights to George Stokes' experimental validations and subsequent contributions by other scientists, we trace the evolution of this equation. We also delve into its practical applications, including its role in the development of Computational Fluid Dynamics. The Navier-Stokes equation has played a pivotal role in advancing our understanding of fluid behavior, making it a cornerstone of modern science and engineering.

physics.hist-ph↗
arXiv2023

Lagrangians for variational formulations of the Navier-Stokes equation

Variational formulations for viscous flows which lead to the Navier-Stokes equation are examined. Since viscosity leads to dissipation and, therefore, to the irreversible transfer of mechanical energy to heat, thermal degrees of freedom have been included in the construction of viscous dissipative Lagrangians, by embedding of thermodynamics aspects of the flow, such as thermasy and flow exergy. Another approach is based on the presumption that the pressure gradient force is a constrained force, whose sole role is to maintain the continuity constraint, with a magnitude that is minimum at every instant. From these considerations, Lagrangians based on the minimal energy dissipation principal have been constructed from which the application of the Euler-Lagrange equation leads to the standard form of the Navier-Stokes equation directly, or at least they are capable of generating the same equations of motion for simple steady and unsteady 1 D viscous flows. These efforts show that there is equivalence between Lagrangian, Hamiltonian, and Newtonian mechanics as far as the derivation of the Navier-Stokes equation is concerned. However, one of the conclusions is that the attractiveness of the variational approach in more complex situations is still an open question for the applied fluid mechanician.

physics.flu-dyn↗
arXiv2023

Euler's variational approach to the elastica

The history of the elastica is examined through the works of various contributors, including those of Jacob and Daniel Bernoulli, since its first appearance in a 1690 contest on finding the profile of a hanging flexible cord. Emphasis will be given to Leonhard Euler's variational approach to the elastica, laid out in his landmark 1744 book on variational techniques. Euler's variational approach based on the concept of differential value is highlighted, including the derivation of the general equation for the elastica from the differential value of the first kind, from which nine shapes adopted by a flexed lamina under different end conditions are obtained. To show the potential of Euler's variational method, the development of the unequal curvature of elastic bands based on the differential value of the second kind is also examined. We also revisited some of Euler's examples of application, including the derivation of the Euler-Bernoulli equation for the bending of a beam from the Euler-Poisson equation, the pillar critical load before buckling, and the vibration of elastic laminas, including the derivation of the equations for the mode shapes and the corresponding natural frequencies. Finally, the pervasiveness of Euler's elastica solution found in various studies over the years as given on recent reviews by third parties is highlighted, which also includes its major role in the development of the theory of elliptic functions.

physics.hist-ph↗
arXiv2022

An annotated translation from Latin of L. Euler's 'On the motion of boats propelled by oars in rivers'

Euler considers the following problem: A boat with a perfect rudder moves at constant speed across a stream flowing in straight fillets at assigned speeds. Assuming that the downstream velocity of the boat equals that of the river, how should the rudder be set so that the boat traverses a given path? He works out various instances, one of which gives rise to a variational problem, in detail. (From Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances.)

physics.hist-ph↗
arXiv2021

Euler Analysis of a Machine for Raising Waters Proposed by Mr. de Mour

We revisited an analysis made by Euler in a memoir of 1753 'Sur une nouvelle maniere d'elever de l'eau propose par M. de Mour' (On a new method to raise water proposed by Mr. de Mour), addressing a type of water sprinkler, consisting of an inclined tube with its lower end immersed into water, and discharging water at its top by turning a vertical axis to which the inclined tube is attached.

physics.hist-ph↗
arXiv2019

Experiments made before the instituted society in confirmation of the theory of the pressures which the walls of the channel sustain due to the flowing water

This is an annotated translation from Latin of "Experimenta coram societate instituta in confirmationem theoriae pressionum quas latera canalis ab aqua tranfluente sustinet" in which Daniel Bernoulli describes six experiments conducted before the St. Petersburg Academy in 1729, in confirmation of his theory dedicated to the motion of water through ducts, which contains the developments that led to the relation between pressure and velocity in fluid flows, known as Bernoulli's principle.

physics.hist-ph↗
arXiv2018

Theoretical reconstruction of Galileo's two-bucket experiment

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.

physics.hist-ph↗
arXiv2018

Defining the principles for the motion of blood through arteries

This is an annotated translation from Latin of 'Principia pro motu sanguinis per arterias determinando' in which Euler develops the first known work on the mechanics of flows in elastic tubes, intended to the first contest of the Dijon Academy of 1742. In this work, Euler applied the principles of mass conservation and momentum conservation to the one dimensional flow of an incompressible fluid through an elastic tube driven by a piston pump. These would allow the analytical treatment of circulatory physiology and hemodynamics, which still undergird the most advanced numerical methods in use today for blood flow analysis in arterial networks.

physics.hist-ph↗
arXiv2017

Attempt at a theory of the friction of fluids

This is a translation from Latin to Portuguese of Euler's 'Attempt at a theory of the friction of fluids'. According to the records, a treatise by Euler with the title 'Tentamen theoriae de frictione fluidorum' was presented to the St. Petersburg Academy on June 17, 1754, and perhaps was read to the Berlin Academy on December 2, 1751. In this treatise, Euler assumes that as for the solid friction, the fluid friction is proportional to the applied normal force. A detailed development of five different problems of discharge are presented in his treatise, taking into account the loss of head in the conduits. In the appendix, an example is given for the calculation of the jet heights of a particular fountain, fed with conduits of different amplitudes.

physics.hist-ph↗