Daniel Bernoulli

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  • Topic: Fluid dynamics, Bernoulli's principle, Aerodynamics
  • Pages : 10 (3176 words )
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  • Published : January 9, 2012
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Daniel Bernoulli (Groningen, 8 February 1700 – Basel, 8 March 1782) was aDutch-Swiss mathematician and was one of the many prominent mathematicians in theBernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability andstatistics. Bernoulli's work is still studied at length by many schools of science throughout the world. In Physics :-

He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law.[2] He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation.[9] Bernoulli's principle is of critical use inaerodynamics.[4]

Daniel Bernoulli, an eighteenth-century Swiss scientist, discovered that as the velocity of a fluid increases, its pressure decreases The relationship between the velocity and pressure exerted by a moving liquid is described by the Bernoulli's principle: as the velocity of a fluid increases, the pressure exerted by that fluid decreases.

Airplanes get a part of their lift by taking advantage of Bernoulli's principle. Race cars employ Bernoulli's principle to keep their rear wheels on the ground while traveling at high speeds.

The Continuity Equation relates the speed of a fluid moving through a pipe to the cross sectional area of the pipe. It says that as a radius of the pipe decreases the speed of fluid flow must increase and visa-versa. This interactive tool lets you explore this principle of fluids. You can change the diameter of the red section of the pipe by dragging the top red edge up or down.

In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.[1][2] Bernoulli's principle is named after the Dutch-Swiss mathematician Daniel Bernoulliwho published his principle in his book Hydrodynamica in 1738.[3] Bernoulli's principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli's equation. In fact, there are different forms of the Bernoulli equation for different types of flow. The simple form of Bernoulli's principle is valid for incompressible flows (e.g. most liquid flows) and also for compressible flows (e.g. gases) moving at low Mach numbers. More advanced forms may in some cases be applied to compressible flows at higher Mach numbers(see the derivations of the Bernoulli equation). Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy, and a decrease in its static pressure andpotential energy. If the fluid is flowing out of a reservoir the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit mass (the sum of pressure and gravitational potential ρ g h) is the same everywhere.[4] Bernoulli's principle can also be derived directly from Newton's 2nd law. If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline. [5][6] Fluid particles are subject only to pressure and their own weight. If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure; and if its speed decreases, it can only be because it has moved from a...
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