# Bernoulli, Daniel

### From Enlightenment Revolution

**Bernoulli, Daniel** (1700-82): Swiss Mathematician.

Daniel Bernoulli, born on January 29, 1700, was a mathematician and the founder of hydraulic engineering. He stemmed from a family of Swiss mathematicians. Jakob Bernoulli, Daniel’s grandfather, left Antwerp in 1583 because he was being persecuted as a devout Huguenot. The family eventually settled in Basel, Switzerland. Jakob Bernoulli’s sons were bitter rivals in their common pursuit of recognition from the scholarly community. Johann (or Jean) Bernoulli, the older son and Daniel’s father, was a fervid supporter of Leibnitz, while his son became the prodigy and advocate for Leibnitz’s rival Isaac Newton.

Nicholas Bernoulli served as his younger brother Daniel’s tutor until Daniel began his formal education in Italy. As a medical student, Daniel Bernoulli became acquainted with British physician William Harvey, in whom he found a kindred spirit. Daniel had already become interested in applying principles of mathematics to the study of fluids. Inspired by Harvey’s research on the circulation system, Bernoulli examined blood pressure within the framework of fluid properties. Applying his interests in another field, he won first prize in the annual competition sponsored by the French Academy of Sciences, at the age of 24, by designing an hourglass that would maintain a steady trickle of sand or water despite turbulence in the seas. In all, Bernoulli shared with Euler, Leonhard the distinction of having gained the French Academy prize ten times.

In 1723 Bernoulli accepted the invitation from Catharine I to become professor of mathematics at the Imperial Academy of Sciences in St. Petersburg. While there, Bernoulli further pursued his study of fluids. His most notable contribution, known as “Bernoulli’s equation” defines the basic rules by which fluids move. In his experiments, Bernoulli observed that an inverse relationship exists between the speed with which fluid flowed and its pressure. One hundred years earlier, Leonardo da Vinci had discovered that water flowing from a narrow pipe to a wider one slowed down. Bernoulli’s experiments confirmed this Law of Continuity and led Bernoulli to further discover that the pressure of water increased as it slowed down. To express the principles he discovered, Bernoulli adapted Isaac Newton’s Law of *Vis Viva* Conservation by substituting the mass of a solid object (m) with a reference to the density of the fluid (P), and substituting the measurement of pressure (ρ) in the place of altitude. Bernoulli’s formula thus came to be: P + ρ² x ν = CONSTANT. A century later, Gustave Gaspard, a German physicist, added a factor of one-half to the original formula. Thereafter, Daniel Bernoulli’s principle has been known as: P + ρ x ½ ρ² = CONSTANT.

Bernoulli’s experiments with the kinetics of fluids were published in 1738 in his *Hydrodynamics*. This treatise is widely attributed for laying the groundwork for much of modern technology, most notably for aerodynamics. The book furthermore contains Bernoulli’s method of expressing gas pressure, which anticipates the method used one hundred years later. Bernoulli died in Basel on March 17, 1782.

Further Reading:

Michael Guillen, *Five Equations that Changed the World: The Power and Poetry of Mathematics*, 1995.

**Sarah Tusa**

Lamar University