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Topic: Bernoullis equation

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Euler equations

Relativistic Euler equations

Potential flow

Fluid Dynamics

Incompressible flow

Inviscid

Pressure

Compressible flow

Fluid power

Boussinesq approximation

Partial differential equation

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	Bernoulli's Equation
		The equation states that the static pressure ps in the flow plus the dynamic pressure, one half of the density r times the velocity V squared, is equal to a constant throughout the flow.
		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 (1049 words)

	Bernoulli's Equation
		Although these restrictions sound severe, the Bernoulli equation is very useful, partly because it is very simple to use and partly because it can give great insight into the balance between pressure, velocity and elevation.
		Bernoulli's equation leads to some interesting conclusions regarding the variation of pressure along a streamline.
		Bernoulli's equation along the streamline that begins far upstream of the tube and comes to rest in the mouth of the Pitot tube shows the Pitot tube measures the stagnation pressure in the flow.
	www.princeton.edu /~asmits/Bicycle_web/Bernoulli.html (1268 words)

	CYCLOID - LoveToKnow Article on CYCLOID (Site not responding. Last check: 2007-10-31)
		The intrinsic Q P equation is s=4a sin ~, and the equation to the evolute is s4a cos ~, which proves the evolute to be a similar cycloid placed as in fig.
		The cartesian equation in terms similar to those used above is x=aO+b sin 0; y=ab cos 0, where a is the radius of the generating circle and b the distance of the carried point from the centre of the circle.
		The cartesian equation, referred to the fixed diameter and the tangent at B as axes may be expressed in the forms x = a0, y = a(I cos 0) and,y a = a sin (xfa 3/4~r); the latter form shows that the locus is the harmonic curve.
	51.1911encyclopedia.org /C/CY/CYCLOID.htm (1317 words)

	Ordinary differential equation - Wikipedia, the free encyclopedia
		In mathematics, and particularly in analysis, an ordinary differential equation (or ODE) is an equation that involves the derivatives of an unknown function of one variable.
		In the case where the equations are linear, the original equation can be solved by breaking it down into smaller equations, solving those, and then adding the results back together.
		This is a first-order, second-degree equation, thus any point can have at most two solutions passing through it, corresponding to the two roots of y' in the quadratic equation that would result after fixing x and y.
	en.wikipedia.org /wiki/Ordinary_differential_equation (2849 words)

	Differential equation (Site not responding. Last check: 2007-10-31)
		In mathematics, a differential equation is an equation that describes the relationship between an unknown function and its derivatives.
		Ordinary differential equations are to be distinguished from partial differential equations where is a function of several variables, and the differential equation involves partial derivatives.
		Monge (1809) treated ordinary and partial differential equations of the first and second order, uniting the theory to geometry, and introducing the notion of the "characteristic", the curve represented by, which has recently been investigated by Darboux, Levy, and Lie.
	www.brainyencyclopedia.com /encyclopedia/d/di/differential_equation.html (1279 words)

	Bernoulli Equation: History of Daniel Bernoulli and his Equation (Site not responding. Last check: 2007-10-31)
		The Bernoulli family is renowned for having produced several generations of mathematicians of historical importance as well as being partly responsible for the rapid spread and development of Leibniz's calculus in the eighteenth century.
		In Hydrodynamica, Bernoulli was the first to give the correct analysis of the tank draining problem; the latter was derived using his ideas of energy conservation.
		His equation for steady flow is essentially the same as my (C2), perhaps with a more general potential for the body force.
	www.fluidmech.net /tutorials/bernoulli/bernoulli-history.htm (1254 words)

	The Bernoullis
		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)

	HYDRAULICS - LoveToKnow Article on HYDRAULICS
		But equations (I) and (2) may both be expressed in one equation if K and e are replaced by a constant varying inversely as the thickness of the layer.
		The general equation of the steady motion of a fluid given under Hydrodynamics furnishes immediately three results as to the distribution of pressure in a stream which may here be assumed.
		The equation of Bernoulli gives the variation of pressure and velocity from point to point along a stream line, and shows that the total energy of the flow across any two sections is the same.
	www.1911encyclopedia.org /H/HY/HYDRAULICS.htm (20985 words)

	Bernoulli's principle: Encyclopedia topic (Site not responding. Last check: 2007-10-31)
		Bernoulli's principle is also important in carburetor (carburetor: Mixes air with gasoline vapor prior to explosion) s.
		In a carburetor, air is passed through a Venturi tube (Venturi tube: A measuring instrument used to measure the rate of flow of a liquid) to increase its speed and therefore decrease its pressure.
		The latter may be detected by means of sonar (sonar: A measuring instrument that sends out an acoustic pulse in water and measures distances in terms of the time for the echo of the pulse to return; sonar is an acronym for sound navigation ranging; asdic is an acronym for anti-submarine detection investigat).
	www.absoluteastronomy.com /reference/bernoullis_principle (514 words)

	Bernoullis Inviscid Flow - (Site not responding. Last check: 2007-10-31)
		Born as the son of Johann Bernoulli, and nephew of Jakob Bernoulli, Daniel Bernoulli was by far the ablest of the younger Bernoullis.
		Euler equations for the motion of an inviscid incompressible fluid...
		equations for the motion of an inviscid incompressible fluid...
	equation.fabca.com /index.php?k=bernoullis-inviscid-flow (771 words)

	FUNCTION - Online Information article about FUNCTION
		The equation of the curve is approximately satisfied.
		In any rational equation containing x and y the expressions x+xo and y+90 are to be substituted for x and y, the resulting equation is to be divided by o, and afterwards o is to be omitted.
		Bernoulli were able by 1690 to begin to make substantial contributions to the development of the new calculus, and Leibnitz adopted their word " integral " in 1695, they at the same time adopting his symbol " f." In 1696 the See also:
	encyclopedia.jrank.org /FRA_GAE/FUNCTION.html (8016 words)

	Dept. of Physics - Course Description
		Thermal properties, heat capacities, latent heats, transport and the heat equation.
		Schroedinge's equation, applications to particle in a box, particle, harmonic oscillator and hydrogen atom.
		The Maxwell Equations, applications for infinite and finite media.
	www.emu.edu.tr /english/academics/facultiesdepartments/artsscience/physics/coursedescription.htm (606 words)

	History of Algebra - René Descartes (1596-1650).
		As in geography we refer every place on the earth's surface to the equator, and to a determine meridian, so he refereed every point of curve to some line given by position.
		This might serve as its definition ; and from the equation by the processes of algebra, all the properties of the curve could be investigated.
		Descartes availed himself of some of Harriot's view, particularly the manner of generating an equation, without acknowledgement; and on this account Dr Wallis, in his algebra, has reflected with considerable severity on the French algebraist.
	www.1902-encyclopedia.com /A/ALG/algebra-12.html (596 words)

	Archive on Irrotational Motions of Viscous and Viscoelastic Fluids (Site not responding. Last check: 2007-10-31)
		Bernoulli equation and the competition of elastic and inertial pressures in the potential flow of a second-order fluid
		A Bernoullis equation for potential flow of a second order fluid is derived.
		This equation is used to form an expression for normal extensional stresses at points of stagnation, in which elastic and inertial pressures complete.
	www.aem.umn.edu /people/faculty/joseph/ViscousPotentialFlow/198.html (117 words)

	Solutions Mock June (a)
		The final displacement of the shot putt is 13 m in the horizontal direction and –2 m in the vertical direction from the origin (at the level of the release point).
		In this equation, the angle has already been assumed to be small and therefore the sine of the angle is just equal to the angle (in radians).
		Use Bernoullis equation, remembering that at the top of the fluid within the tank the pressure is 3 atmospheres and the velocity of the water is effectively zero [v = 40 m/s]
	www.aspect.uct.ac.za /courses/phy111w/tests&rev/sol_juna.htm (1345 words)

	Archive on Irrotational Motions of Viscous & Viscoelastic Fluids
		Joseph, D.D. Bernoulli equation and the competition of elastic and inertial pressures in the potential flow of a second-order fluid,
		Potential flows of incompressible fluids admit a pressure (Bernoulli) equation when the divergence of the stress is a gradient as in inviscid fluids, viscous fluids, linear viscoelastic fluids and second-order fluids.
		We show that the equation balancing drag and acceleration is the same for all these fluids independent of the viscosity or any viscoelastic parameter and that the drag is zero in steady flow.
	www.aem.umn.edu /people/faculty/joseph/ViscousPotentialFlow (4970 words)

	phys101/spring03 lecture preflight responses (Site not responding. Last check: 2007-10-31)
		The equation of continuity states that the water will also leave the faucet in the same rate it came in so thats why water in the middle travels faster and becomes thinner as it beats the surrouding radius of slower flowing water.
		5: According to Bernoulli's equation, with larger height the pressure of the water pushing down on the hole is higher and thus causes the water to flow with a higher velocity.
		Using Bernoullis equation, it can be seen that when the pressure on one side goes up, the velocity on the other side of the equation must go up, too.
	wug.physics.uiuc.edu /courses/phys101/spring03/Lectures/Lect20_pf.htm (13437 words)

	Lift (force): Encyclopedia topic (Site not responding. Last check: 2007-10-31)
		The differences between the Bernoulli (Bernoulli: Swiss mathematician (1654-1705)) -predicted pressure values and the true values are small and related to viscosity (viscosity: Resistance of a liquid to sheer forces (and hence to flow)), which is neglected in the Bernoulli equation.
		A third way of calculating lift is a mathematical construction called circulation (circulation: Movement through a circuit; especially the movement of blood through the heart and blood vessels).
		L is the lift force (force: (physics) the influence that produces a change in a physical quantity) produced.
	www.absoluteastronomy.com /reference/lift_force (1124 words)

	Bernoulli - Wikipedia, the free encyclopedia
		Johann Bernoulli (1667–1748), father of Daniel and Nicolaus II Jakob Bernoulli (also James or Jacques) (1654–1705), brother of Johann
		Nicolaus I Bernoulli (1687–1759), nephew of Jakob and Johann.
		This is a disambiguation page: a list of articles associated with the same title.
	en.wikipedia.org /wiki/Bernoulli (118 words)

	Main Heading Goes Here Subheading Goes Here
		Grundlæggende fysiske størrelser, statisk tryk, Bernoullis ligning, kontinuitetssætningen, udstrømning af beholdere, strømning i rør, strømning rundt om objekter, hastighedsfelt, strømningsforårsagede kræfter, grænselag, separation, opdriftsprofiler, trykbølger, dyser og diffusorer, målinger.
		Fundamental physical parametres, statical pressure, Bernoullis equation, law og continuity, outflow from vessels, flow through pipes, flow around objects, flow velocity fields, flow impulse forces, boundary layers, flow separation, lifting profiles, pressure waves, nozzles and diffusors, measurements.
		Bernoullis sætning, udstrømning af åbning, strømningslinier og –baner, stationær og ikke-stationær bevægelse, konstant og variabel densitet,
	old.iot.dk /ceb/cebw52.htm (514 words)

	ipedia.com: Differential equation Article (Site not responding. Last check: 2007-10-31)
		In mathematics, a differential equation is an equation that describes a prescribed relationship between a set of unknowns which are to be regarded as an unknown function and its derivatives.
		A differential equation not depending on x is called autonomous or homogenous.
		Monge (1809) treated ordinary and partial differential equations of the first and second order, uniting the theory to geometry, and introducing the notion of the "characteristic", the curve represented by, which was investigated by Darboux, Levy, and Lie.
	www.ipedia.com /differential_equation.html (1324 words)

	Five Equations That Changed The World - Michael Guillen
		Guillen decides to present five equations which allow him to cover scientific history, by which he usually means physics, from the C17th to the present day, as well providing an opportunity to profile some of the more colourful personalities behind the science.
		Evidently it's not that easy for Guillen to get the equations typeset in their familiar form either, each is expressed in a clumsy, 'longhand' version instead of the compact forms familiar to me from my Physics days.
		I found that decision odd as one of his themes is the poetry implicit in mathematical descriptions of the world, that an equation can be appreciated properly only in its proper notation.
	dialspace.dial.pipex.com /town/pipexdsl/p/apuo30/C2025243227/E1581116549 (609 words)

	Bernoulli Equation
		Equation (3) is often referred to the head because all elements has the unit of length.
		The Bernoulli equation can be adapted to a streamline from the surface (1) to the orifice (2) as (e1):
		equation of continuity can be expressed as (e3), it's possible to transform (e1) to (e4).
	www.engineeringtoolbox.com /bernouilli-equation-d_183.html (845 words)

	FULL MODULE DESCRIPTION (Site not responding. Last check: 2007-10-31)
		Learning outcomes: The students will develop the quantitative skills associated with transforming physical problems into mathematical problems and will emerge with a good working knowledge of the most important concepts in open channel flows such as the hydraulic jump and the importance of the Froude number.
		use of conservation of mass and Bernoullis equation to model simple flows in pipes and channels.
		A good working knowledge of multivariable calculus (partial derivatives, multiple integrals and simple ordinary and partial differential equations) is required.
	www.open.mis.surrey.ac.uk /misweb/modules/8272.htm (174 words)

	Velocity Distributions
		Velocity and pressure are dependent on each other - Bernoulli's equation says that increasing the velocity decreases the local pressure and vice versa.
		The total force corresponds to the area enclosed between the curves for the upper and the lower surface.
		It is easy to transform Bernoullis equation, written once for a point in space far away from the airfoil (where the velocity is
	www.cartage.org.lb /en/themes/Sciences/Physics/FluidDynamics/FlyingDynamics/Aerodynamics/SelectedTopics/Velocity/Velocity/Velocity.htm (1118 words)

	Why is watercooling done this way? (And a FREE BONUS question!) - Topic Ars OpenForum
		Also, Bernoulli's Equation describes the changes in pressure that occur during these changes in cross-sectional area.
		This is a well-documented and proven scientific fact, explained by the Equation of Continuity.
		I think you may be confused slightly by what the continuity equations are telling you.
	episteme.arstechnica.com /eve/ubb.x/a/tpc/f/77909585/m/6780964185/p/2 (6465 words)

	Uttar Pradesh Combined Pre - Medical Test -Education in India (Site not responding. Last check: 2007-10-31)
		Deviation from the ideal gas equation at high pressure and low temperature.
		Numerical problems on chemical equations and volumetric analysis and qualitative analysis.
		Detailed study of Mandeleef's periodic table (leaving historical background), position of elements in the periodic table on the basis of atomic structure; Modern periodic table.
	www.webindia123.com /career/entrance/medicine/uttar.html (2858 words)

	Bernoulli Equations in Fluid Mechanics
		A non-turbulent, perfect, compressible, and barotropic fluid undergoing steady motion is governed by the Bernoulli Equation:
		If the flow is irrotational, then C has the same value for all streamlines.
		is the "pressure per density" in the fluid, and follows from the barotropic equation of state, p = p(
	www.efunda.com /formulae/fluids/bernoulli.cfm (176 words)

	School Work on Advantages and Disadvantages of TV
		Advantages and Disadvantages of TV Among the wide range of Mathematics pertaining to the Bernoullis are Bernoulli Numbers, Bernoulli Differential Equation, Bernoulli's Principle of Fluid Dynamics, Bernoulli Trial, Bernoulli Inequality, etc. Jacob (1654-1705) is the first of the Bernoullis to make Mathematics a career, despite pressure to seek a career elsewhere.
		He also solved what is now called Bernoulli Differential Equation: y' = p(x)y + q(x)yn Among his other works are: A general method to determine evolutes of a curve as the envelope of its circles of curvature.
		Caustic curves of parabola, logarithmic spiral and epicycloids (1692-93) Lemniscate of Bernoulli (1694).
	www.123schoolwork.com /show_essay/261276.html (350 words)

	[No title]
		Setting the equations in a linear fashion, with the values of the variables determined through experimentation, we can determine exactly what youll need to resist glare, or to polarize light in a correct manner.
		If that were to occur, modern physics would be thrown into turmoil, silicon would stop carrying signals and bernoullis equation would evaporate leaving aircraft to fall to the earth like stones.
		Lasers would cease to be anything but red flashlights, and the magnetic theory driving modern trains would no longer hold true freezing them to the tracks.
	www.xanga.com /InxHerxPrime/399603122/item.html (789 words)

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