Name: bernoulli’s equation in streamlined flow
Uploaded: 2025-05-22T09:06:09.000Z
Duration: 1 min 16 s
Channel: JoVE

Supposons qu’un fluide laminaire incompressible à l’état stationnaire passe à travers un tube de section transversale non uniforme.
Comme le fluide est incompressible, le volume de l’élément fluide et sa masse restent constants.
La vitesse à laquelle l’élément fluide entre et sort du tube est différente, ce qui entraîne une variation nette de l’énergie cinétique.
La force agissant sur l'élément fluide est due à la pression environnante du fluide.
Ainsi, le travail net effectué sur l’élément fluide par le fluide environnant pendant le déplacement est la différence entre le travail effectué à l’entrée et à la sortie du tube.
Lorsque l’élément fluide traverse la région élevée, il gagne de l’énergie potentielle gravitationnelle et la variation de l’énergie potentielle gravitationnelle est déterminée.
Selon le théorème de l’énergie cinétique du travail, le travail net effectué sur l’élément fluide est égal à la variation de l’énergie cinétique.
En divisant tout le tout par une valeur commune, on obtient une équation.
Le long d'une ligne de courant, l'énergie totale par unité de volume d'un fluide qui s'écoule est une constante, appelée équation de Bernoulli.

<ol>
	<li>Young, H.D et Freedman, R.A. (2012). La physique universitaire avec la physique moderne. San Francisco, Californie : Pearson : article 12.5 ; Pages 385 et 386.</li>
	<li>OpenStax. (2019). Physique universitaire Vol. 1. [Version Web]. Extrait de <a href="https://openstax.org/books/university-physics-volume-1/pages/1-introduction">https://openstax.org/books/university-physics-volume-1/pages/1-introduction</a> : section 14.6 ; Pages 716 à 718.</li>
</ol>

la conservation de l'énergie et l'équation de bernoulli

L'application du principe de conservation de l'énergie ou du théorème travail-énergie à un fluide incompressible, non visqueux en écoulement laminaire, continu et irrotationnel conduit à l'équation de Bernoulli. Elle affirme que la somme de la pression du fluide, de l'énergie potentielle et de l'énergie cinétique par unité de volume est constante le long d'une ligne de courant.

Tous les termes dans l'équation ont la dimension d'énergie par unité de volume. L'énergie cinétique par unité de volume est appelée densité d'énergie cinétique, et l'énergie potentielle par unité de volume est appelée densité d'énergie potentielle.

Il est important de noter que la densité du liquide ne doit pas changer au cours de l'écoulement ; c'est-à-dire, il doit être incompressible. L'écoulement doit également être laminaire et non turbulent. L'équation de Bernoulli s'applique aux gaz qui ont des effets de compressibilité négligeables. Pour de tels gaz, la densité est supposée constante et est traitée comme un fluide incompressible. Étant donné que les gaz sont généralement compressibles, l'équation ne s'applique pas à eux.

Bien qu'étant une simple reformulation du principe de conservation de l'énergie avec quelques hypothèses critiques, l'équation permet de calculer facilement la pression à différents points si les vitesses sont connues.

La conservation de l'énergie et l'équation de Bernoulli

En appliquant le principe de conservation de l’énergie ou le théorème de l’énergie de travail à un fluide incompressible et invisce dans un écoulement laminaire, stable et irrotationnel conduit ...

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energy-conservation-and-bernoulli-s-equation

Education

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Physics

Physique

Unit 1

Unité 1

Fluid Mechanics

Mécanique des fluides

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

Energy Conservation and Bernoulli's Equation

bernoulli’s equation in streamlined flow

Bernoulli’s equation describes energy in a moving fluid. It comes from the conservation of energy principle, or the work-energy theorem, applied to an incompressible, inviscid fluid in laminar, steady, irrotational flow.

The equation says that pressure energy, potential energy, and kinetic energy per unit volume stay constant along a streamline. Each term has the units of energy per unit volume. The kinetic energy per unit volume is called kinetic energy density, and the potential energy per unit volume is called potential energy density.

The fluid must keep the same density as it flows, so it must be incompressible. The flow also needs to be laminar, not turbulent. Bernoulli’s equation can also apply to gases when compressibility effects are negligible. In that case, the gas density is treated as constant and the gas is handled like an incompressible fluid.

Because gases are usually compressible, the equation does not apply to them in many situations. Even with these limits, Bernoulli’s equation is useful for finding pressure at different points when the speed is known. It gives a simple way to connect pressure and motion in fluid flow.

Bernoulli’s Equation in Streamlined Flow

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energy conservation and bernoulli's equation

Bernoulli’s equation describes energy in a moving fluid. It comes from the conservation of energy principle, or the work-energy theorem, applied to an incompressible, inviscid fluid in laminar, steady, irrotational flow. The equation says that pressure energy, potential energy, and kinetic energy per unit volume stay constant along a streamline. Each term has the units of energy per unit volume. The kinetic energy per unit volume is called kinetic energy density, and the potential energy per...

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key terms and concepts

Learn how Bernoulli’s equation links pressure, speed, and energy in laminar fluid flow, and why incompressible conditions matter.

Bernoulli’s Equation in Streamlined Flow | JoVE K12

physics

JoVE Core Physique présente plusieurs branches de la physique fondamentale grâce à des vidéos animées concises et faciles à comprendre ; cela inclut: la cinématique, la dynamique, la mécanique des fluides, la mécanique statique, les ondes et l'acoustique. En parallèle, les vidéos de scientifiques à l'action démontrent l'application de concepts associés à ces domaines dans des expériences de recherche classiques et originales réalisées dans des laboratoires modernes du monde entier.

Bernoulli’s Equation in Streamlined Flow

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