Daniel Bernoulli - Revision history

Bmcfarland7 at 21:26, 30 November 2015

2015-11-30T21:26:00Z

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	"Euler-Bernoulli Beam Equation." EFunda, 2015. Web. 30 Nov. 2015. <http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm>.		"Euler-Bernoulli Beam Equation." EFunda, 2015. Web. 30 Nov. 2015. <http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm>.

			''This page was created by Brynn McFarland''

Bmcfarland7 at 21:24, 30 November 2015

2015-11-30T21:24:17Z

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	~~Claimed by Brynn McFarland, this is a work in progress!~~

	==Personal Life==		==Personal Life==
	Daniel Bernoulli was born on February 9, 1700 in Groningen, the Netherlands. He came from a family of distinguished mathematicians, but reportedly was the brightest of three children of the family. While growing up in Switzerland, his relationship with his father gradually deteriorated due to competition in academia.		Daniel Bernoulli was born on February 9, 1700 in Groningen, the Netherlands. He came from a family of distinguished mathematicians, but reportedly was the brightest of three children of the family. While growing up in Switzerland, his relationship with his father gradually deteriorated due to competition in academia.

Bmcfarland7: /* References */

2015-11-30T21:23:31Z

References

← Older revision		Revision as of 17:23, 30 November 2015
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	==References==		==References==

			Wilkins, D.R. "The Bernoullis." Web. 30 Nov. 2015. <http://www.maths.tcd.ie/pub/HistMath/People/Bernoullis/RouseBall/RB_Bernoullis.html#DanielBernoulli>.

			Rothbard, Murray. "Daniel Bernoulli and the Founding of Mathematical Economics." Mises Institute. Mises Institute, 10 Feb. 2011. Web. 30 Nov. 2015. <https://mises.org/library/daniel-bernoulli-and-founding-mathematical-economics>.

			Guinness, I. "Daniel Bernoulli, Hydrodynamica (1738)." Landmark Writings in Western Mathematics 1640-1940. Amsterdam: Elsevier, 2005. Print.

			Dahr, S. "3.1 Theory of Elasticity." Web. 30 Nov. 2015. <http://www.iue.tuwien.ac.at/phd/dhar/node17.html>.

			"Euler-Bernoulli Beam Equation." EFunda, 2015. Web. 30 Nov. 2015. <http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm>.

Bmcfarland7: /* Euler-Bernoulli Beam Equation */

2015-11-30T21:13:19Z

Euler-Bernoulli Beam Equation

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	===Euler-Bernoulli Beam Equation===		===Euler-Bernoulli Beam Equation===
			The Euler-Bernoulli Beam Equation is based on the theory of elasticity, which states that elasticity is the property of solid materials to deform under the application of an external force and to regain their original shape after the force is removed.

			The equation is:

			<math>{d^2 \over dx^2}[{EI}{d^2w \over dx^2}]=p</math>

			where:
			:<math>w\,</math> is the displacement of the beam
			:<math>p\,</math> is the force per unit length acting in the direction of w
			:<math>E\,</math> is the Young's Modulus for the beam
			:<math>I\,</math> is the moment of inertia of the beam's cross section
			:<math>x\,</math> is the position along the beam

			The Euler-Bernoulli Beam Equation relates the displacement, or deflection of the beam (w) to its pressure loading (p). The equation is widely used in engineering applications, such as civil or mechanical to determine the strength of beams when stress is applied.

	==References==		==References==

Bmcfarland7: /* Elasticity */

2015-11-30T20:51:36Z

Elasticity

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	The main idea of the Bernoulli Principle is that for a steady flow, the sum of all the energies involved will be the same at any point in the tube, therefore, the velocity of the fluid through the tube will increase coinciding with a decrease in pressure or a decrease in the potential energy.		The main idea of the Bernoulli Principle is that for a steady flow, the sum of all the energies involved will be the same at any point in the tube, therefore, the velocity of the fluid through the tube will increase coinciding with a decrease in pressure or a decrease in the potential energy.

	~~===Elasticity===~~

	===Euler-Bernoulli Beam Equation===		===Euler-Bernoulli Beam Equation===

	==References==		==References==

Bmcfarland7 at 20:11, 30 November 2015

2015-11-30T20:11:28Z

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	===Euler-Bernoulli Beam Equation===		===Euler-Bernoulli Beam Equation===

			==References==

Bmcfarland7: /* The Bernoulli Principle */

2015-11-30T20:10:51Z

The Bernoulli Principle

← Older revision		Revision as of 16:10, 30 November 2015
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	:<math>p\,</math> is the pressure		:<math>p\,</math> is the pressure
	:<math>\rho\,</math> is the density of the fluid		:<math>\rho\,</math> is the density of the fluid

			The main idea of the Bernoulli Principle is that for a steady flow, the sum of all the energies involved will be the same at any point in the tube, therefore, the velocity of the fluid through the tube will increase coinciding with a decrease in pressure or a decrease in the potential energy.

	===Elasticity===		===Elasticity===

	===Euler-Bernoulli Beam Equation===		===Euler-Bernoulli Beam Equation===

Bmcfarland7 at 16:59, 30 November 2015

2015-11-30T16:59:35Z

@@ Line 14: / Line 14: @@
 ===The Bernoulli Principle===
 ===Elasticity===
 ===Euler-Bernoulli Beam Equation===

Bmcfarland7 at 05:38, 30 November 2015

2015-11-30T05:38:56Z

← Older revision		Revision as of 01:38, 30 November 2015
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	Claimed by Brynn McFarland, this is a work in progress!		Claimed by Brynn McFarland, this is a work in progress!

			==Personal Life==
			Daniel Bernoulli was born on February 9, 1700 in Groningen, the Netherlands. He came from a family of distinguished mathematicians, but reportedly was the brightest of three children of the family. While growing up in Switzerland, his relationship with his father gradually deteriorated due to competition in academia.

			First studying at the University in Basel, he was later invited to study at the Saint Petersburg Academy of Sciences. He studied mathematics, business, medicine, anatomy, and botany, eventually earning his Ph.D. in the latter two. Eventually he returned to Basel as a professor of anatomy, botany, and physics.

			He made significant contributions to Physics, most notably '''the Bernoulli Principle''', which is used extensively in aerodynamics and fluid dynamics. His contributions were not limited to only Physics though, he has also been called the founder of mathematical economics and was one of the first people to begin work on a kinetic theory of gases.

			==Contributions to Physics==

			===''Hydrodynamica''===
			Bernoulli published ''Hydrodynamica'' in 1738, and the title eventually gave rise to the name "hydrodynamics" for the field of fluid dynamics. The full title of the text was "Hydrodynamics, or commentaries on the forces and motions of fluids". In the book, Bernoulli characterizes fluid mechanics according to conservation of energy by examining several examples such as fluid coming out of an opening or fluid flowing through a tube. These examples gave the first adequate theory of the motion of incompressible fluids and also hydrodynamic pressure. In the text he also describes work and efficiency of hydraulic machines, the kinetic theory of gases, and several ideas that would eventually be formulated into the Bernoulli Principle.

			===The Bernoulli Principle===

			===Elasticity===

			===Euler-Bernoulli Beam Equation===

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2015-11-30T05:04:43Z

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