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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. ~~ |