Daniel Bernoulli
Daniel Bernoulli FRS (/bɜːrˈnuːli/ bur-NOO-lee, Swiss Standard German: [ˈdaːni̯eːl bɛrˈnʊli];[1] 8 February [O.S. 29 January] 1700 – 27 March 1782[2]) was a Swiss mathematician and physicist[2] and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics.[3] His name is commemorated in the Bernoulli's principle, a particular example of the conservation of energy, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the aeroplane wing.[4][5]
Daniel Bernoulli
8 February 1700
27 March 1782 (aged 82)
Swiss
A 1738 copy of Bernoulli's Hydrodynamica
First page of the first section of a 1738 copy of Hydrodynamica
His earliest mathematical work was the Exercitationes (Mathematical Exercises), published in 1724 with the help of Goldbach. Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motion of rotation. His chief work is Hydrodynamica, published in 1738. It resembles Joseph Louis Lagrange's Mécanique Analytique in being arranged so that all the results are consequences of a single principle, namely, conservation of energy. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and Colin Maclaurin, a prize was awarded by the French Academy: these three memoirs contain all that was done on this subject between the publication of Isaac Newton's Philosophiae Naturalis Principia Mathematica and the investigations of Pierre-Simon Laplace. Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with vibrating strings, and the solutions given by Brook Taylor and by Jean le Rond d'Alembert.[7]
Together Bernoulli and Euler tried to discover more about the flow of fluids. In particular, they wanted to know about the relationship between the speed at which blood flows and its pressure. To investigate this, Daniel experimented by puncturing the wall of a pipe with a small open ended straw and noted that the height to which the fluid rose up the straw was related to fluid's pressure in the pipe.[15]
Soon physicians all over Europe were measuring patients' blood pressure by sticking point-ended glass tubes directly into their arteries. It was not until about 170 years later, in 1896 that an Italian doctor discovered a less painful method which is still in use today. However, Bernoulli's method of measuring pressure is still used today in modern aircraft to measure the speed of the air passing the plane; that is its air speed.
Taking his discoveries further, Daniel Bernoulli now returned to his earlier work on Conservation of Energy. It was known that a moving body exchanges its kinetic energy for potential energy when it gains height. Daniel realised that in a similar way, a moving fluid exchanges its specific kinetic energy for pressure, the former being the kinetic energy per unit volume. Mathematically this law is now written:
where P is pressure, ρ is the density of the fluid and u is its velocity.
Economics and statistics[edit]
In his 1738 book Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk),[16] Bernoulli offered a solution to the St. Petersburg paradox as the basis of the economic theory of risk aversion, risk premium, and utility.[17] Bernoulli often noticed that when making decisions that involved some uncertainty, people did not always try to maximize their possible monetary gain, but rather tried to maximize "utility", an economic term encompassing their personal satisfaction and benefit. Bernoulli realized that for humans, there is a direct relationship between money gained and utility, but that it diminishes as the money gained increases. For example, to a person whose income is $10,000 per year, an additional $100 in income will provide more utility than it would to a person whose income is $50,000 per year.[18]
One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of inoculation.[19]
Physics[edit]
In Hydrodynamica (1738) he laid the basis for the kinetic theory of gases, and applied the idea to explain Boyle's law.[7]
He worked with Euler on elasticity and the development of the Euler–Bernoulli beam equation.[20] Bernoulli's principle is of critical use in aerodynamics.[13]
According to Léon Brillouin, the principle of superposition was first stated by Daniel Bernoulli in 1753: "The general motion of a vibrating system is given by a superposition of its proper vibrations."[21]
Legacy[edit]
In 2002, Bernoulli was inducted into the International Air & Space Hall of Fame at the San Diego Air & Space Museum.[22]