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Daniel Bernoulli FRS


Daniel BernoulliFRS (/bərˈnuːli/; Swiss [bɛʁˈnʊli];[1] 8 February 1700– 17 March 1782) was a Swiss mathematician and physicist and was one of themany prominent mathematicians in the Bernoulli family. He is particularlyremembered for his applications of mathematics to mechanics, especially fluidmechanics, and for his pioneering work in probability and statistics. His nameis commemorated in the Bernoulli principle, a particular example of theconservation of energy, which describes the mathematics of the mechanismunderlying the operation of two important technologies of the 20th century: thecarburetor and the airplane wing.

Early life[edit]

Frontpage ofHydrodynamica (1738)Daniel Bernoulli was born inGroningen,in theNetherlands, into afamily of distinguished mathematicians.[2] The Bernoulli family came originallyfromAntwerp,at that time in the Spanish Netherlands, but emigrated to escape the Spanishpersecution of the Huguenots. After a brief period in Frankfurt the familymoved toBasel, inSwitzerland.


Daniel was theson of Johann Bernoulli (one of the "early developers" ofcalculus),[2] nephew of Jakob Bernoulli (who "was the first to discoverthe theory of probability"),[2] and older brother of Johann II.  Daniel Bernoulli was described by W. W. RouseBall as "by far the ablest of the younger Bernoullis".[3] He is saidto have had a bad relationship with his father, Johann. Upon both of thementering and tying for first place in a scientific contest at the University ofParis, Johann, unable to bear the "shame" of being compared asDaniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarizedsome key ideas from Daniel's book Hydrodynamica in his own book Hydraulicawhich he backdated to before Hydrodynamica. Despite Daniel's attempts atreconciliation, his father carried the grudge until his death.[4]


When Daniel wasseven, his younger brother Johann II Bernoulli was born. Around schooling age,his father, Johann Bernoulli, encouraged him to study business, there being poorrewards awaiting a mathematician. However, Daniel refused, because he wanted tostudy mathematics. He later gave in to his father's wish and studied business.His father then asked him to study in medicine, and Daniel agreed under thecondition that his father would teach him mathematics privately, which theycontinued for some time.[4] Daniel studied medicine inBasel,Heidelberg, andStrasbourg, and earned a PhD in anatomy andbotany in 1721.[5]


He was acontemporary and close friend of Leonhard Euler. He went toSt. Petersburgin 1724 as professor of mathematics, but was unhappythere, and a temporary illness in 1733 gave him an excuse for leaving.[4] Hereturned to theUniversityofBasel, where hesuccessively held the chairs of medicine, metaphysics, and natural philosophyuntil his death.[6]


In May, 1750 hewas elected a Fellow of the Royal Society.[7]


Mathematicalwork[edit]His earliest mathematical work was the Exercitationes (MathematicalExercises), published in 1724 with the help of Goldbach. Two years later hepointed out for the first time the frequent desirability of resolving acompound motion into motions of translation and motion of rotation. His chiefwork is Hydrodynamica, published in 1738; it resembles Joseph Louis Lagrange'sMécanique Analytique in being arranged so that all the results are consequencesof a single principle, namely, conservation of energy. This was followed by amemoir on the theory of the tides, to which, conjointly with the memoirs byEuler and Colin Maclaurin, a prize was awarded by theFrenchAcademy:these three memoirs contain all that was done on this subject between thepublication of Isaac Newton's Philosophiae Naturalis Principia Mathematica andthe investigations of Pierre-Simon Laplace. Bernoulli also wrote a large numberof papers on various mechanical questions, especially on problems connectedwith vibrating strings, and the solutions given by Brook Taylor and by Jean leRond d'Alembert.[3]


TogetherBernoulli and Euler tried to discover more about the flow of fluids. Inparticular, they wanted to know about the relationship between the speed atwhich blood flows and its pressure. To investigate this, Daniel experimented bypuncturing the wall of a pipe with a small open ended straw and noted that theheight to which the fluid rose up the straw was related to fluid's pressure inthe pipe.[8]


Soon physiciansall overEuropewere measuring patients' bloodpressure by sticking point-ended glass tubes directly into their arteries. Itwas not until about 170 years later, in 1896 that an Italian doctor discovereda less painful method which is still in use today. However, Bernoulli's methodof measuring pressure is still used today in modern aircraft to measure thespeed of the air passing the plane; that is its air speed.


Taking hisdiscoveries further, Daniel Bernoulli now returned to his earlier work onConservation of Energy. It was known that a moving body exchanges its kineticenergy for potential energy when it gains height. Daniel realised that in a similarway, a moving fluid exchanges its kinetic energy for pressure. Mathematicallythis law is now written:



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


Statistics[edit]DanielBernoulli was also the author in 1738 of Specimen theoriae novae de mensurasortis (Exposition of a New Theory on the Measurement of Risk),[9] in which theSt. Petersburg paradox was the base of the economic theory of risk aversion,risk premium and utility.[10]


One of theearliest attempts to analyze a statistical problem involving censored data wasBernoulli's 1766 analysis of smallpox morbidity and mortality data todemonstrate the efficacy of vaccination.[11]


Physics[edit]InHydrodynamica (1738) he laid the basis for the kinetic theory of gases, andapplied the idea to explain Boyle's law.[3]


He worked withEuler on elasticity and the development of the Euler-Bernoulli beamequation.[12] Bernoulli's principle is of critical use in aerodynamics.


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