Daniel Bernoulli

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Daniel Bernoulli bigraphy, stories - Swiss mathematician and physicist

Daniel Bernoulli : biography

8 February 1700 – 8 March 1782

Daniel Bernoulli FRS ( Swiss ;Mangold, Max (1990) Duden — Das Aussprachewörterbuch. 3. Auflage. Mannheim/Wien/Zürich, Dudenverlag. 8 February 1700 – 17 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. His name is commemorated in the Bernoulli principle, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the airplane wing. Bernoulli’s work is still studied at length by many schools of science throughout the world.

Mathematical work

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 his Hydrodynamique (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.

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.The Turner Collection, Keele University, includes Bernoulli’s diagram to illustrate how pressure is measured. See also part of Bernoulli’s original Latin explanation.

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 kinetic energy for pressure. Mathematically this law is now written:

tfrac12 rho u^2 + P = text

where P is pressure, ρ is the density of the fluid and u is its velocity. A consequence of this law is that if the velocity increases then the pressure falls. This is exploited by the wing of an aeroplane which is designed to create an area above its surface where the air velocity increases. The pressure of this area is lower and so the wing is sucked upwards.

Early life

Daniel Bernoulli was born in Groningen, in the Netherlands, into a family of distinguished mathematicians.Rothbard, Murray. , Mises Institute (excerpted from An Austrian Perspective on the History of Economic Thought) The Bernoulli family came originally from Antwerp, at that time in the Spanish Netherlands, but emigrated to escape the Spanish persecution of the Huguenots. After a brief period in Frankfurt the family moved to Basel, in Switzerland.