Bernoulli's theorem

Bernoulli's theorem
1. Statistics. See law of averages (def. 1).
2. Hydrodynamics. an expression of the conservation of energy in streamline flow, stating that the sum of the ratio of the pressure to the mass density, the product of the gravitational constant and the vertical height, and the square of the velocity divided by 2 are constant.
[1920-25; (in def. 1) named after Jakob BERNOULLI; (in def. 2) named after Daniel BERNOULLI]

* * *

      in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar. First derived (1738) by the Swiss mathematician Daniel Bernoulli (Bernoulli, Daniel), the theorem states, in effect, that the total mechanical energy of the flowing fluid, comprising the energy associated with fluid pressure, the gravitational potential energy of elevation, and the kinetic energy of fluid motion, remains constant. Bernoulli's theorem is the principle of energy conservation for ideal fluids in steady, or streamline, flow.

      Bernoulli's theorem implies, therefore, that if the fluid flows horizontally so that no change in gravitational potential energy occurs, then a decrease in fluid pressure is associated with an increase in fluid velocity. If the fluid is flowing through a horizontal pipe of varying cross-sectional area, for example, the fluid speeds up in constricted areas so that the pressure the fluid exerts is least where the cross section is smallest. This phenomenon is sometimes called the Venturi effect, after the Italian scientist G.B. Venturi (1746–1822), who first noted the effects of constricted channels on fluid flow.

      Bernoulli's theorem is the basis for many engineering applications, such as aircraft-wing design. The air flowing over the upper curved surface of an aircraft wing moves faster than the air beneath the wing, so that the pressure underneath is greater than that on the top of the wing, causing lift.

* * *

Universalium. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Bernoulli's theorem — Title used for the ‘law of large numbers’ in probability theory, proved by Jakob Bernoulli (1654–1705). The theorem provides the best known link between probability and the frequency of occurrence of events in a sequence of trials. It is thus… …   Philosophy dictionary

  • bernoulli's theorem — noun Usage: usually capitalized B 1. [after Jacques Bernoulli] : a basic principle of statistics: as the number of independent trials of an event of theoretical probability p is indefinitely increased, the observed ratio of actual occurrences of… …   Useful english dictionary

  • Bernoulli’s theorem — In a steady streamline flow of an ideal liquid, the sum of all energies present remains constant, provided no work is done by the airflow or on it. In other words, in a horizontal flow the sum of kinetic energy and pressure energy is constant or… …   Aviation dictionary

  • Bernoulli's theorem — Bernoul′li s the′orem n. sta • Etymology: 1920–25; after Jakob Bernoulli …   From formal English to slang

  • Bernoulli distribution theorem trial — Ber·noul·li distribution, theorem, trial (bər nooґle) (bār noo eґ) [Jakob Bernoulli, Swiss mathematician, 1654–1705] see under distribution, theorem, and trial …   Medical dictionary

  • bernoulli's Theorem — in stream of liquid, the sum of elevation head, pressure head, and velocity remains constant along any line of flow provided no work is done by or upon liquid on course of its flow; decreases in proportion to energy lost in flow …   Dictionary of automotive terms

  • Bernoulli's principle — n. 〚after BERNOULLI Daniel〛 the statement that an increase in the speed of a fluid produces a decrease in pressure and a decrease in the speed produces an increase in pressure * * * or Bernoulli s theorem Principle that relates pressure, velocity …   Universalium

  • Bernoulli's principle — This article is about Bernoulli s principle and Bernoulli s equation in fluid dynamics. For Bernoulli s Theorem (probability), see Law of large numbers. For an unrelated topic in ordinary differential equations, see Bernoulli differential… …   Wikipedia

  • theorem — theorematic /thee euhr euh mat ik, thear euh /, adj. theorematically, adv. /thee euhr euhm, thear euhm/, n. 1. Math. a theoretical proposition, statement, or formula embodying something to be proved from other propositions or formulas. 2. a rule… …   Universalium

  • Bernoulli, Daniel — ▪ Swiss mathematician born Feb. 8 [Jan. 29, Old Style], 1700, Groningen, Neth. died March 17, 1782, Basel, Switz.       the most distinguished of the second generation of the Bernoulli family of Swiss mathematicians. He investigated not only… …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”