Name: fluid flow in narrowing pipes
Uploaded: 2023-04-30T11:05:06.000Z
Duration: 1 min 12 s
Channel: JoVE

Le volume de fluide circulant en un point dans une zone en unité de temps donne le débit volumique.
En remplaçant le volume par l’aire multipliée par la distance, et en utilisant la relation entre la vitesse et la distance, le débit volumique est égal à l’aire multipliée par la vitesse du fluide.
Considérons un fluide incompressible de même densité en tous points s’écoulant régulièrement dans un tuyau de section irrégulière. Pour un écoulement régulier, la vitesse et la densité du fluide en un point restent constantes avec le temps.
La masse du fluide passant par un point par unité de temps est appelée débit massique, et elle est égale à la densité multipliée par le débit volumique.
Étant donné que le tuyau n’a pas d’autre source ou d’évier, la masse qui s’écoule dans le tuyau doit être égale à la masse sortant du tuyau. Cela donne l’équation générale de continuité pour les fluides.
Pour les fluides incompressibles, la densité s’annule. Par conséquent, le débit volumique dans le tuyau est égal au débit volumique sortant du tuyau.

Équation de la continuité

Le mouvement d'un fluide est représenté soit par des vecteurs de vélocité, soit par des lignes de courant. Le volume d'un fluide qui s'écoule au-delà d'un emplacement donné à travers une zone pendant une période de temps est appelé débit Q, ou plus précisément le débit volumique. Le débit et la vélocité sont liés ; par exemple, une rivière a un débit plus élevé si la vélocité de l'eau qui la traverse est plus grande. Cependant, le débit dépend également de la taille et de la forme de la rivière. La relation entre le débit (Q) et la vitesse moyenne (v) suggère que le débit est directement proportionnel à la fois à la vitesse moyenne du fluide et à la section transversale d'une rivière, d'un tuyau ou d'un autre conduit. Plus le conduit est grand, plus sa section transversale est grande.

Considérons un fluide incompressible qui s'écoule à travers un tuyau de rayon décroissant. Ici, puisque le fluide est incompressible, la même quantité de fluide doit passer devant n'importe quel point dans le tube en un temps donné pour assurer la continuité de l'écoulement. L'écoulement est continu car il n'y a pas de sources ou de puits qui ajoutent ou enlèvent de la masse, de sorte que la masse qui entre dans le tuyau doit être égale à la masse qui en sort. Dans ce cas, étant donné que la section transversale du tuyau diminue, il est nécessaire que la vélocité augmente. Cette logique peut être étendue pour dire que le débit doit être le même à tous les points le long du tuyau. Cela s'appelle l'équation de la continuité, et elle est valable pour tout fluide incompressible (avec une densité constante). Comme les liquides sont essentiellement incompressibles, l'équation de la continuité est valable pour tous les liquides. Cependant, les gaz sont compressibles, donc l'équation doit être appliquée avec prudence aux gaz s'ils sont soumis à une compression ou à une expansion.

Ce texte est adapté de <a href="https://openstax.org/books/university-physics-volume-1/pages/14-5-fluid-dynamics">Openstax, University Physics Volume 1, Section 14.5: Fluid Dynamics. </a>

Équation de la Continuité

Le mouvement des fluides est représenté par des vecteurs de vitesse ou des lignes de courant. Le volume d’un fluide s’écoulant au-delà d’un endroit donné à travers une zone au cours d’une période ...

Education

Enseignement

JoVE Core

Physics

Physique

Unit 1

Unité 1

Fluid Mechanics

Mécanique des fluides

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

Equation of Continuity

fluid flow in narrowing pipes

Fluid flow in a pipe is described by flow rate and average speed. Flow rate, or volume flow rate, is the amount of fluid that passes a point through an area in a given time. It depends on both how fast the fluid moves and the size and shape of the conduit.

For a river or pipe, a greater speed usually means a greater flow rate. A larger cross-sectional area also increases flow rate. That is why the same fluid can move differently through conduits of different sizes.

The relationship becomes clear for an incompressible fluid moving through a pipe with a decreasing radius. Because the fluid is incompressible, the same amount of fluid must pass each point in the tube during the same time. This keeps the flow continuous, since no sources or sinks add or remove mass.

As the pipe gets narrower, the cross-sectional area decreases. To keep the flow rate the same, the fluid must move faster. This idea leads to the equation of continuity, which says the flow rate is the same at all points along the pipe.

The equation of continuity applies to any incompressible fluid with constant density. Since liquids are essentially incompressible, the rule works for liquids. Gases can be compressible, so this equation must be used with caution when gases are compressed or expanded.

Fluid Flow in Narrowing Pipes

characteristics of fluids

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Fluid behavior under force differs from the behavior of solids. When a force acts parallel to the top surface of a solid, the solid resists it because of internal friction between its layers. This is called shearing resistance. If the force is removed, the shearing forces help the solid return to its original shape. Other deformation forces can also change the shape of a solid for a short time, as long as the force stays below a threshold magnitude. Solids usually keep their shape, which makes...

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density

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pascal's law

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application of pascal's law

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archimedes' principle

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buoyancy

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equation of continuity

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bernoulli's equation

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bernoulli's principle

Fluid Pressure and Speed Changes

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energy conservation and bernoulli's equation

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viscosity

Viscosity and How Fluids Flow

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stokes' law

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key terms and concepts

Learn how flow rate, area, and speed stay linked in pipes. See why fluid speeds up in narrow sections and how continuity applies to liquids and gases.

Fluid Flow in Narrowing Pipes | 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.

Fluid Flow in Narrowing Pipes

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