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**Daniel Bernoulli** (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****, 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 was born in Groningen, in the Netherlands, into a family of distinguished mathematicians. Daniel was the **son of ****Johann Bernoulli**** (one of the "early developers" of ****calculus****), nephew of ****Jakob Bernoulli**** (who "was the first to discover the****theory of probability****")**, and older brother of Johann II. Daniel Bernoulli was described by W. W. Rouse Ball as "by far the ablest of the younger Bernoullis". He is **said to have had a bad relationship with his father.** **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 as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book ****Hydrodynamica**** in his own book ****Hydraulica**** which he backdated to before ****Hydrodynamica****. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.**

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When Daniel was seven, his younger brother Johann II Bernoulli was born. Around schooling age, **his father encouraged him to study business, there being poor rewards awaiting a mathematician**. However, Daniel refused, because he wanted to study 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 the condition that his father would teach him mathematics privately, which they continued for some time.**** Daniel studied medicine in Basel, ****Heidelberg****, and ****Strasbourg****, and earned a PhD in anatomy and botany in 1721. **

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His **earliest mathematical work was the ****Exercitationes**** (****Mathematical Exercises****)**, published in 1724. 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. 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. ****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. **

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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. **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:

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.

**Daniel Bernoulli was also the author in 1738 of ****Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk)****, in which the ****St. Petersburg paradox**** was the base of the economic theory of ****risk aversion****, ****risk premium**** and ****utility****.**

**In ****Hydrodynamica (1738)**** he laid the basis for the ****kinetic theory of gases****, and applied the idea to explain ****Boyle's law****. ****He worked with Euler on ****elasticity**** and the development of the ****Euler-Bernoulli beam equation****.**** ****Bernoulli's principle**** is of critical use in ****aerodynamics****.**

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