Daniel Bernoulli (1700-1782)

Daniel Bernoulli was born on January 20,1700 in Groningen, Netherlands. He was the son of Johann Bernoulli, brother of Nicolaus (II) Bernoulli and nephew of Jacob Bernoulli. So he was born into a family of leading mathematicians.

When Daniel was five years old, the family returned to their native city of Basel. His brother, Johann (II) Bernoulli, was born also when Daniel was five. Daniel was sent to Basel University at the age of 13 to study philosophy and logic. He obtained his master’s degree in 1716.

In 1718, he spent time studying medicine at Heidelberg and Strasbourg in 1719. He returned to Basel in 1720 to complete his doctorate in medicine. By this time, Johann Bernoulli was prepared to teach his son more mathematics while he studied medicine and he studied his father’s theories of kinetic energy. Daniel then went to Venice to study medicine.

In Venice Daniel was severely ill and was unable to carry out his intention of travelling to Padua to further his medicine studies. However, while in Venice he worked on mathematics and his first mathematical work were published in 1724 with the assistance of Goldbach. This mathematical work was entitled Mathematical exercises. It consists of four parts being four topics that had attracted his interest while in Venice. The first part described the game of faro and is of little importance other than showing that Daniel was learning about probability at this time. The second part was on the flow of water from a hole in a container and discussed Newton’s theories (which were incorrect). The third part of Mathematical exercises was on the Riccati differential equation while the final part was on a geometry question concerning figures bounded by two acres of a circle.

While in Venice, Daniel had also designed an hourglass to be used at sea so that the trickle of sand was constant even when the ship was rolling in heavy seas. He submitted his work on this to the Paris Academy and in 1725, the year returned from Italy from Basel, he learnt that he had won the prize of the Paris Academy. Daniel had also attained fame through his work Mathematics exercises and on the strength to take up the chair of mathematics at St. Petersburg. His brother, Nicolaus (II) Bernoulli was also offered a chair of mathematics at St. Petersburg, so in late 1725 the two brothers traveled to St. Petersburg.

After eight months of working together, Daniel’s brother died of fever. Daniel was left greatly saddened at the loss of his brother and also very unhappy with the harsh climate. He thought of returning to Basel and wrote to his father telling him how unhappy he was in St, Petersburg. Johann Bernoulli arranged for one of his best pupils, Leonard Euler, to go to St. Petersburg to work with Daniel. Euler arrived in 1727 and this period in St. Petersburg, which Daniel left in 1733, was his most productive time.

While in St. Petersburg, he made one of his most famous discoveries when he defined the simple nodes and the frequencies of oscillation of a system. He showed that the movements of strings of musical instruments are composed of an infinite number of harmonic vibrations all superimposed on the string.

Undoubtedly the most important work, which Daniel did while in St. Petersburg, was his work on hydrodynamics. Even the term itself is based on the title of the work which he produced called Hydrodynamica and, before he left St. Petersburg, Daniel left a draft copy of the book with a printer. However the work was not published until 1738 and although he revised it considerably between 1734 and 1738, it is more the presentation that he changed rather than the substance.

This work contains for the first time the correct analysis of water flowing from a hole in a container. This was based on the principle of conservation of energy, which he had studied with his father in 1720. This "theorem states that the total mechanical energy of the flowing fluid, comprising the energy associated with the fluid pressure, the gravitational potential energy of elevation, and the kinetic energy of fluid motion, remains constant. Bernoulli’s theorem is the principle of energy conservation for ideal fluids in steady, or streamline, flow." (Britanica.com)

"Bernoulli’s theorem implies that if the fluid flows horizontally so that no change in gravitational potential energy occurs, then a decrease in fluid pressure is associated with an increase in fluid velocity. If the water is flowing through a horizontal pipe of varying cross-sectional area, the fluid speeds up in constricted areas so that the pressure the fluid exerts is least where the cross section is smallest. This phenomenon is sometimes called the Venturi effect after the Italian scientist G.B.Vunturi (1746-1822), who first noted the effects of constricted channels on fluid flow." (Britanica.com)

Bernoulli’s theorem is the basis for many engineering applications, such as aircraft wing design. The air flowing over the upper curved surface of an aircraft wing moves faster than the air beneath the wing, so that the pressure underneath is greater than that on the top of the wing, causing lift.

Daniel submitted an entry for the Grand Prize of the Paris Academy for 1734 giving an application of his ideas to astronomy. This had unfortunate consequences since his father also entered for the prize and their entries were declared joint winners of the Grand Prize. This result had unhappy consequences for Daniel because his father was furious to think that his son had been rated as his equal and this resulted in a breakdown in relationships between the two.

Although Daniel had left St. Petersburg, he still remained in contact with Euler and the two exchanged many ideas. Daniel continued to work on polishing his masterpiece Hydrodynamica for publication and added a chapter on the force of reaction of a jet of fluid and the force of a jet of water on an inclined plane.

In 1737 Daniel again won the Paris Academy prize. Its theme was the best shape for a ship’s anchor. He was again a joint winner, this time with Poleni. Hydrodynamica was published in 1738 but in the following year Johann Bernoulli publishedHydraulica, which is based on his son’s work. Johann tried to make it look as if Daniel had based Hydrodynamica onHydraulica by predating the date of publication on his book to 1732 instead of its real date, which is probably 1739.

Daniel Bernoulli died on March 17, 1782 in Basel, Switzerland. He was much honored in his lifetime. "He was elected to most of the leading scientific societies of his day including those in Bologna, St. Petersburg, Berlin, Paris, London, Bern, Turin, Zurich and Mannheim."