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	Bernoulli - Wikipedia, the free encyclopedia
		The Bernoullis are a family of traders and scholars from Basel, Switzerland.
		The founder of the family, Leon Bernoulli, immigrated to Basel from Antwerp, Belgium in the 16th century.
		Nicolaus I Bernoulli (1687–1759), nephew of Jakob and Johann.
	en.wikipedia.org /wiki/Bernoulli (180 words)

	Daniel Bernoulli - Wikipedia, the free encyclopedia
		Bernoulli's principle is of critical use in aerodynamics.
		Born as the son of Johann Bernoulli, nephew of Jakob Bernoulli, younger brother of Nicolaus Bernoulli II, and older brother of Johann II, Daniel Bernoulli was by far the ablest of the younger Bernoullis.
		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 d'Alembert.
	en.wikipedia.org /wiki/Daniel_Bernoulli (568 words)

	BERNOULLI - LoveToKnow Article on BERNOULLI (Site not responding. Last check: 2007-10-08)
		JACQUES BERNOULLI (1654I 705), mathematician, was born at Basel on the 27th of December 1654.
		Jacques Bernoulli cannot be strictly called an independent discoverer; but, from his extensive and successful application of the calculus and other mathematical methods, he is deserving of a place by the side of Newton and Leibnitz.
		NIcoLAs BERNOULLI (1695-1726), the eldest of the three sons of Jean Bernoulli, was born on the 27th of January 1695.
	30.1911encyclopedia.org /B/BE/BERNOULLI.htm (2286 words)

	Bernoulli
		Jacob Bernoulli was the brother of Johann Bernoulli and the uncle of Daniel Bernoulli.
		Jacob Bernoulli was appointed professor of mathematics in Basel in 1687 and the two brothers began to study the calculus as presented by Leibniz in his 1684 paper on the differential calculus in Nova Methodus pro Maximis et Minimis, itemque Tangentibus...
		Bernoulli greatly advanced algebra, the infinitesimal calculus, the calculus of variations, mechanics, the theory of series, and the theory of probability.
	www.thocp.net /biographies/bernoulli.html (1914 words)

	James Bernoulli (1654-1705) (Site not responding. Last check: 2007-10-08)
		The Swiss Bernoulli brothers, James and John, were the first to achieve a full understanding of Leibniz’s presentation of the calculus.
		The Bernoulli brothers used the techniques of Leibniz’s calculus as a means for handling a wide range of astronomical and physical problems, sometimes working independently to solve the same problem.
		In 1690, James Bernoulli challenged the mathematicians of Europe to determine the shape (that is, to find the equation) of a hanging flexible cable suspended in equilibrium at two points.
	www.mhhe.com /math/calc/smithminton2e/cd/tools/timeline/bernoulli.html (342 words)

	Bernoulli's Equation
		Since density is a constant for a low speed problem, the equation at the bottom of the slide relates the pressure and velocity at station two to the conditions at station one.
		The surface of the airfoil is a streamline.
		Bernoulli's equation is also used on aircraft to provide a speedometer called a pitot tube.
	www.grc.nasa.gov /WWW/K-12/airplane/bern.html (1045 words)

	Physics at Minnesota: Bernoulli Effects
		Bernoulli’s Principle, when the speed of a fluid is increased the pressure in the fluid decreases, can be illustrated using the air from a leaf blower or a vacuum cleaner.
		Bernoulli's (ber-nool'-ee) principle, states that as the velocity of fluid flow increases the pressure produced by the fluid decreases.
		This is another demonstration of Bernoulli’s Principle where an area of higher speed fluid is used to lower the pressure and the visible movement of two plastic pop bottles is used to show the results.
	www.physics.umn.edu /outreach/pforce/Bernoulli.html (2840 words)

	Biographies
		Bernoulli's parents became promiment members of Basel society and compelled their eldest son Jakob to study theology and philosophy.
		Bernoulli's younger brother Johann was initially forced to study medicine but followed in Jakob's footsteps and studied mathematics and physics instead.
		Jakob Bernoulli held the chair in mathematics at Basel University until his death in 1705 when he was succeeded by his brother Johann who had long coveted the position.
	tulsagrad.ou.edu /statistics/biographies/Bernoulli.htm (417 words)

	Daniel Bernoulli (Site not responding. Last check: 2007-10-08)
		His older brother was Nicolaus(II) Bernoulli and his uncle was Jacob Bernoulli so he was born into a family of leading mathematicians but also into a family where there was unfortunate rivalry, jealousy and bitterness.
		Bernoulli determined the shape that a perfectly flexible thread assumes when acted upon by forces of which one component is vertical to the curve and the other is parallel to a given direction.
		Another important aspect of Daniel Bernoulli's work that proved important in the development of mathematical physics was his acceptance of many of Newton's theories and his use of these together with the tolls coming from the more powerful calculus of Leibniz.
	www.mathematik.ch /mathematiker/daniel_bernoulli.php (2115 words)

	Bernoulli's Principle
		Bernoulli's principle thus says that a rise (fall) in pressure in a flowing fluid must always be accompanied by a decrease (increase) in the speed, and conversely, if an increase (decrease) in, the speed of the fluid results in a decrease (increase) in the pressure.
		Another example of Bernoulli's principle at work is in the lift of aircraft wings and the motion of ``curve balls'' in baseball.
		In both cases the design is such as to create a speed differential of the flowing air past the object on the top and the bottom - for aircraft wings this comes from the movement of the flaps, and for the baseball it is the presence of ridges.
	theory.uwinnipeg.ca /mod_tech/node68.html (420 words)

	Johann Bernoulli
		Bernoulli received generous payment from de l'Hôpital for these lessons, and indeed they were worth a lot for few other people would have been able to have given them.
		Bernoulli's course is virtually identical with de l'Hôpital's book but it is worth pointing out that de l'Hôpital had corrected a number of errors such as Bernoulli's mistaken belief that the integral of 1/x is infinite.
		Bernoulli also made important contributions to mechanics with his work on kinetic energy, which, not surprisingly, was another topic on which mathematicians argued over for many years.
	www.mathematik.ch /mathematiker/johann_bernoulli.php (2449 words)

	Jakob Bernoulli Encyclopedia Article @ EveryAvenue.com (Site not responding. Last check: 2007-10-08)
		Jakob Bernoulli (Basel, December 27, 1654 - August 16, 1705), also known as Jacob, Jacques or James Bernoulli was a Swiss mathematician and scientist and the older brother of Johann Bernoulli.
		Jakob Bernoulli met Robert Boyle and Robert Hooke on a trip to England in 1676, after which he devoted his life to science and mathematics.
		Bernoulli crater, on the Moon, is also named after him jointly with his brother Johann.
	www.everyavenue.com /encyclopedia/Jakob_Bernoulli (325 words)

	Bernoulli. The Columbia Encyclopedia, Sixth Edition. 2001-05
		One of the chief developers both of the ordinary calculus and of the calculus of variations, he was the first to use the word integral in solving Leibniz’s problem of the isochronous curve.
		He was succeeded at Basel by his brother, Johann, Jean, or John Bernoulli, 1667–1748, who earlier had been professor at Gröningen and who was famous for his work in the field of integral and exponential calculus and was also a founder of the calculus of variations.
		His greatest work was his Hydrodynamica (1738), which included the principle now known as Bernoulli’s principle, and anticipated the law of conservation of energy and the kinetic-molecular theory of gases developed more than 100 years later.
	www.bartleby.com /65/be/BernoulFam.html (343 words)

	Bernoulli's principle on Encyclopedia.com (Site not responding. Last check: 2007-10-08)
		BERNOULLI'S PRINCIPLE [Bernoulli's principle] physical principle formulated by Daniel Bernoulli that states that as the speed of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases.
		The phenomenon described by Bernoulli's principle has many practical applications; it is employed in the carburetor and the atomizer, in which air is the moving fluid, and in the aspirator, in which water is the moving fluid.
		Bernoulli's principle can be explained in terms of the law of conservation of energy (see conservation laws, in physics).
	www.encyclopedia.com /html/B/Bernoull.asp (514 words)

	The Bernoullis (Site not responding. Last check: 2007-10-08)
		The Bernoullis (or as they are sometimes, and perhaps more correctly, called, the Bernouillis) were a family of Dutch origin, who were driven from Holland by the Spanish persecutions, and finally settled at Bâle in Switzerland.
		Jacob or James Bernoulli was born at Bâle on December 27, 1654; in 1687 he was appointed to a chair in mathematics in the university there; and occupied it until his death on August 16, 1705.
		Nicholas Bernoulli, the eldest of the three sons of John, was born on Jan. 27, 1695, and was drowned at St. Petersburg, where he was professor, on July 26, 1726.
	www.maths.tcd.ie /pub/HistMath/People/Bernoullis/RouseBall/RB_Bernoullis.html (1078 words)

	Bernoulli and Newton
		The proponents of the arguments usually fall into two camps: (1) those who support the "Bernoulli" position that lift is generated by a pressure difference across the wing, and (2) those who support the "Newton" position that lift is the reaction force on a body caused by deflecting a flow of gas.
		Bernoulli also worked in many areas of mathematics and physics and had a degree in medicine.
		Bernoulli's equation, which was named for Daniel Bernoulli, relates the pressure in a gas to the local velocity; so as the velocity changes around the object, the pressure changes as well.
	www.lerc.nasa.gov /WWW/K-12/airplane/bernnew.html (1026 words)

	Xah: Special Plane Curves: Lemniscate of Bernoulli
		Jacob Bernoulli was not aware that the curve he was describing was a special case of a Cassinian Oval which had been described by Cassini in 1680.
		The locus of the vector is one loop of the lemniscate of Bernoulli.
		Lemniscate of Bernoulli is the intersection of a plane tangent to the inner ring of a torus whose inner radius equals to its radius of generating circle.
	www.xahlee.org /SpecialPlaneCurves_dir/LemniscateOfBernoulli_dir/lemniscateOfBernoulli.html (450 words)

	Daniel Bernoulli and the making of the fluid equation
		At the age of five, the Bernoulli family returned home to Basel in Switzerland, so that Johann's wife could be with her ailing father.
		The young Bernoulli found a kindred spirit in the English physician William Harvey who wrote in his book On the Movement of Heat and Blood in Animals that the heart was like a pump which forced blood to flow like a fluid through our arteries.
		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.
	plus.maths.org /issue1/bern (1266 words)

	Bernoulli and Leibniz test Newton (Site not responding. Last check: 2007-10-08)
		Bernoulli allowed six months for the solutions but no solutions were received during this period.
		Following Bernoulli's suggestion the curve which solves the problem is called the `brachistochrone', which is the Greek for `the shortest time'.
		Bernoulli's problem was an early example of a class of problems called Calculus of Variations now.
	www.math.purdue.edu /~eremenko/bernoulli.html (522 words)

	Bernoulli Equation Calculator with Applications
		The Bernoulli equation is used to analyze fluid flow along a streamline from a location 1 to a location 2.
		The Bernoulli equation does not account for viscous effects of the holes in tanks or friction due to flow along pipes, thus the flowrate predicted by our Bernoulli equation calculator will be larger than the actual flow.
		The venturi flowmeter analysis is based on the Bernoulli equation except for an empirical coefficient of discharge, C. in the equation at the top of this page is known as the theoretical throat velocity.
	www.lmnoeng.com /Flow/bernoulli.htm (1426 words)

	Jacob Bernoulli (Site not responding. Last check: 2007-10-08)
		During the time that Jacob Bernoulli was taking his university degree in theology he was studying mathematics and astronomy against the wishes of his parents.
		Jacob Bernoulli was appointed professor of mathematics in Basel in 1687 and the two brothers began to study the calculus as presented by Leibniz in his 1684 paper on the differential calculus.
		In 1690 in a paper published in Acta Eruditorum, Jacob Bernoulli showed that the problem of determining the isochrone is equivalent to solving a first-order nonlinear differential equation.
	www.stetson.edu /~efriedma/periodictable/html/Br.html (785 words)

	Bernoulli Equation: Derivation for Compressible Flow (Site not responding. Last check: 2007-10-08)
		In nearly all elementary treatments of the Bernoulli equation, the flow is taken to be incompressible, i.e., the fluid density is taken to be a constant.
		With respect to the Bernoulli equation, the main difference between a compressible and incompressible flow is that the variations in the pressure in a compressible flow will result in compressions and expansions of the fluid blob as it moves along its own path.
		An alternate approach to the derivation of the Bernoulli equation for compressible flow is to ignore the mechanical energy principle used for incompressible flow and to rederive the full energy equation from first principles.
	www.fluidmech.net /tutorials/bernoulli/compressible-bernoulli.htm (1666 words)

	Introduction on Bernoulli's numbers
		Bernoulli's numbers play an important and quite mysterious role in mathematics and in various places like analysis, number theory and differential topology.
		Perhaps one of the most important result is Euler-Maclaurin summation formula, where Bernoulli's numbers are contained and which allows to accelerate the computation of slow converging series (see the essay on Euler's constant at [9]).
		According to Louis Saalschültz [17], the term Bernoulli's numbers was used for the first time by Abraham De Moivre (1667-1754) and also by Leonhard Euler (1707-1783) in 1755.
	numbers.computation.free.fr /Constants/Miscellaneous/bernoulli.html (1028 words)

	Bernoulli's Equation (Site not responding. Last check: 2007-10-08)
		This form of Bernoulli's Equation applies to steady irrotational flow, and the constant is really a constant throughout the volume of irrotational flow.
		The second form of Bernoulli's Equation arises from the fact that in steady flow the particles of fluid move along fixed streamlines, as on rails, and are accelerated and decelerated by the forces acting tangent to the sreamlines.
		Bernoulli himself took an equivalent approach, although the concept of energy was not well-developed in his time.
	www.du.edu /~jcalvert/tech/fluids/bernoul.htm (1496 words)

	Bernoulli's Principle - Advanced Discussion
		In the demo graph under the Bernoulli's Principle Animation, the red shading corresponds to the static pressure, and the blue shading corresponds to the dynamic pressure.
		If Bernoulli's Equation is applied to a small volume of fluid, then each term in that equation can be multiplied by the volume V. This transforms Bernoulli's Equation into an "energy equation", where each term corresponds to some type of energy (potential, kinetic or pressure).
		Bernoulli's Equation may also be derived using the conservation of energy.
	home.earthlink.net /~mmc1919/venturi_discuss_math.html (1460 words)

	Bernoulli's Principle
		Bernoulli's Principle is a physical phenomenon that was named after the Swiss scientist Daniel Bernoulli who lived during the eighteenth century.
		Bernoulli studied the relationship of the speed of a fluid and pressure.
		The principle states that "the pressure of a fluid [liquid or gas] decreases as the speed of the fluid increases." Within the same fluid (air in the example of aircraft moving through air), high-speed flow is associated with low pressure, and low-speed flow is associated with high pressure.
	www.centennialofflight.gov /essay/Dictionary/bernoulli/DI9.htm (217 words)

	Aeronautics - Principles of Flight (BERNOULLI'S PRINCIPLE)
		Daniel Bernoulli, an eighteenth-century Swiss scientist, discovered that as the velocity of a fluid increases, its pressure decreases.
		Bernoulli's principle applies to any fluid, and since air is a fluid, it applies to air.
		Many believe that this use of Bernoulli's principle to explain lift is incorrect because flat wings (such as seen on balsa wood airplanes, paper planes and others) also have managed to create lift.
	www.allstar.fiu.edu /aerojava/pic3-2.htm (420 words)

	Bernoulli
		Bernoulli's equation is only valid if one assumes the following: incompressible fluid (fluid velocity less than one third the speed of sound) and inviscid flow (this just means that the point in question along the flow is going to be away from where the flow and the object come into contact).
		It is best to look at an actual example in order to obtain a better understanding of the Bernoulli's equation as well as the continuity or momentum equation.
		Many believe that this explanation about the correlation of Bernoulli's principle and lift is incorrect because flat wings (such as seen on balsa wood airplanes, paper planes and others) also have managed to create lift.
	www.allstar.fiu.edu /aerojava/bernoulli.htm (1116 words)

	Pressure
		The qualitative behavior that is usually labeled with the term "Bernoulli effect" is the lowering of fluid pressure in regions where the flow velocity is increased.
		This is commonly interpreted as an application of the Bernoulli principle and involves the viscosity of the air and the boundary layer of air at the surface of the ball.
		The Bernoulli equation cannot really be used to predict the amount of curve of the ball; the flow of the air is compressible, and you can't track the density changes to quantify the change in effective pressure.
	hyperphysics.phy-astr.gsu.edu /hbase/pber.html (1131 words)

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