Universal Dependencies - English - GUM

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Daniel Bernoulli

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Daniel Bernoulli FRS (German pronunciation: [bɛʁˈnʊli]; 8 February 1700 – 17 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family.

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He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics.

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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 airplane wing.

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Daniel Bernoulli

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Early life

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Frontpage of Hydrodynamica (1738)

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Daniel Bernoulli was born in Groningen, in the Netherlands, into a family of distinguished mathematicians.

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The Bernoulli family came originally from Antwerp, at that time in the Spanish Netherlands, but emigrated to escape the Spanish persecution of the Huguenots.

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After a brief period in Frankfurt the family moved to Basel, in Switzerland.

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Daniel was a son of Johann Bernoulli (one of the 'early developers' of calculus) and a nephew of Jacob Bernoulli (who' was the first to discover the theory of probability').

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He had two brothers, Niklaus and Johann II.

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Daniel Bernoulli was described by W. W. Rouse Ball as 'by far the ablest of the younger Bernoullis'.

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He is said to have had a bad relationship with his father.

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Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the 'shame' of being compared Daniel's equal, banned Daniel from his house.

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Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica.

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Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.

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Around schooling age, his father, Johann, encouraged him to study business, there being poor rewards awaiting a mathematician.

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However, Daniel refused, because he wanted to study mathematics.

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He later gave in to his father's wish and studied business.

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His father then asked him to study in medicine, and Daniel agreed under the condition that his father would teach him mathematics privately, which they continued for some time.

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Daniel studied medicine at Basel, Heidelberg, and Strasbourg, and earned a PhD in anatomy and botany in 1721.

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He was a contemporary and close friend of Leonhard Euler.

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He went to St. Petersburg in 1724 as professor of mathematics, but was very unhappy there, and a temporary illness in 1733 gave him an excuse for leaving St. Petersburg.

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He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics, and natural philosophy until his death.

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In May, 1750 he was elected a Fellow of the Royal Society.

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Mathematical work

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His earliest mathematical work was the Exercitationes (Mathematical Exercises), published in 1724 with the help of Goldbach.

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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.

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His chief work is Hydrodynamica, published in 1738;

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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.

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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.

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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.

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Together Bernoulli and Euler tried to discover more about the flow of fluids.

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In particular, they wanted to know about the relationship between the speed at which blood flows and its pressure.

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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.

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Soon physicians all over Europe were measuring patients' blood pressure by sticking point-ended glass tubes directly into their arteries.

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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.

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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.

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Taking his discoveries further, Daniel Bernoulli now returned to his earlier work on Conservation of Energy.

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It was known that a moving body exchanges its kinetic energy for potential energy when it gains height.

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Daniel realised that in a similar way, a moving fluid exchanges its kinetic energy for pressure.

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Mathematically this law is now written: ½ ρ u 2 + P = constant where P is pressure, ρ is the density of the fluid and u is its velocity.

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A consequence of this law is that if the velocity increases then the pressure falls.

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This is exploited by the wing of an aeroplane which is designed to create an area above its surface where the air velocity increases.

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The pressure in this area is lower than that under the wing, so the wing is pushed upwards by the relatively higher pressure under the wing.