Daniel Bernoulli and energy conservation
Daniel Bernoulli (1700–1782) was a significant mathematician and physicist known for his foundational work in hydrodynamics and the conservation of energy. Born into a family of mathematicians in the Netherlands, he demonstrated exceptional intellect from a young age, earning a baccalaureate by 1715 and later studying medicine. His most notable contribution, Bernoulli's principle, emerged from his research on fluid dynamics, stating that an increase in the velocity of a fluid or gas leads to a decrease in pressure. This principle not only explains various phenomena, such as the lift on airplane wings and the curve of a baseball but also plays a crucial role in the broader understanding of kinetic energy.
Bernoulli's work anticipated the law of conservation of energy, which was later empirically validated by J. P. Joule in the 1840s. Throughout his career, he explored the intersection of mathematics with other fields, including sound physics and virology, showcasing the extensive applicability of his mathematical understanding to natural phenomena. Despite facing controversy, particularly regarding his relationship with his father and contemporaries, Bernoulli's contributions laid the groundwork for future advancements in both physics and engineering. He spent his later years in Basel, where he continued his research until his retirement in 1776, passing away in 1782.
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Daniel Bernoulli and energy conservation
Dates: 1700–1782.
Summary: Daniel Bernoulli was a mathematician and physicist who helped discover the laws of hydrodynamic pressure and conservation of energy.
Daniel Bernoulli was born February 8, 1700, at Gröningen, the Netherlands, into a Swiss family of mathematicians. He was the second son of Johann Bernoulli, professor of mathematics at the University of Gröningen, and Dorothea Falkner. In 1705, the family moved to Basel, where Johann took the chair of mathematics at the University of Basel that had been vacated by his brother Jakob Bernoulli’s (1654–1705) untimely death. In their youth, the brothers mastered the calculus invented by Gottfried Wilhelm Leibniz (1646–1716). In their careers, both used calculus to make contributions to probability theory, analytic geometry, optics, and studies of the sails of ships, astronomy, and tides.
A precocious youth, Daniel studied logic, philosophy, and mathematics to earn a baccalaureate in 1715. He taught mathematics while earning his master’s degree by the age of 16. His father wanted him to pursue a nonscientific career, but he reluctantly permitted Daniel to study medicine. In 1721, Daniel completed his medical studies with a dissertation on the mechanics of breathing, De respiration.
He then went to Italy to further his medical studies, and there he continued his mathematical studies. In Italy, he wrote Exercitationes quaedam mathematicae (Venice, 1721). Exercitationes so impressed the scientific community that he was offered a teaching position at the St. Petersburg Academy. In 1725, he moved to St. Petersburg, having also won a prize (ultimately 10 prizes altogether) awarded by the French Académie Royale des Sciences.
Once in St. Petersburg, Bernoulli officially taught mathematics, but he also published papers on muscular contraction and the optic nerve. In addition, he published a physics paper on oscillation. However, mathematics continued to keep his attention. He also demonstrated applications of probability theory to economics in the area of choice under risk. An unusual idea that Bernoulli discussed was the relationship between prosperity and ethics. He asserted the hypothesis that if someone’s assets increased geometrically, their moral growth would only be an arithmetical progression. In 1726, Bernoulli issued a paper on mechanics that discussed a method for solving the results of parallelogram of forces when applied to the same object. He also began corresponding with Leonhard Euler (1707–83), with whom he shared an interest in mechanics.
The work in St. Petersburg was highly successful; however, Bernoulli was so eager to obtain a post in Basel that in 1732 he left St. Petersburg. Returning to Basel, he was appointed to a post in anatomy and botany. In 1743, he was appointed to a position in physiology, and in 1750 as professor of natural philosophy. Very much the polymath, Bernoulli continued his researches into mathematics, medicine, botany, anatomy, and philosophy. In 1737, he delivered a historic lecture detailing the calculations needed to measure the work done by the heart.
Hydrostatics had come into existence with Archimedes’s famous “Eureka.” Bernoulli’s most important contributions were in the area of hydrodynamic principles leading to the development of Bernoulli’s principle (or law). It describes the effect that occurs when a fluid (or gas) is moving, versus standing still. The principle states that as a fluid or gas increases in velocity, the pressure is reduced. This relationship was first expressed in Bernoulli’s book, Hydrodynamics (Traite d’Hydrodynamique), in 1738. It was an expression of kinetic energy. Unfortunately, his manner of expressing the principle was unclear. Meanwhile, his father, jealous of his son’s success, published in 1739 the book Hydraulica, which he pre-dated to 1732, and claimed credit for the discovery. Controversy erupted when Daniel discovered what the elder Johann Bernoulli had done. Even more controversy came when Euler, a student of Johann and a colleague of Daniel’s, generalized a rate-of-change relationship between pressure and density on speed of flow. This stated Bernoulli’s principle in its recognizable form.
Bernoulli’s principle explains the lift of an airplane’s wings. The wings are designed so that the speed of the air above the wing is less than the speed of the air below, which allows the airplane to fly because the air below the wing is pushing it upward. The curve ball in baseball also is an illustration of the Bernoulli principle because the velocity of the ball’s spin causes its curving.
The Bernoulli principle advanced knowledge about the “living force” (vis viva) used by Christiaan Huygens and Leibniz in the vis viva controversy with Isaac Newton. Instead of solids, however, Bernoulli dealt with “living” (kinetic) energy of fluids. The principle anticipated the law of the conservation of energy, which was empirically confirmed by J. P. Joule in the 1840s. During Bernoulli’s years at Basel, he applied his mathematical talents to many natural phenomena, including the physics of sound, thereby linking mathematics and music.
He also made contributions to medicine in the field of virology, with mathematical statements of the spread of diseases. Bernoulli retired in 1776 and died March 17, 1782, at Basel. He was buried in the Peterskirche, near the Kleine Engelhof, where he had lived.
Bibliography
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