Name: terminal velocity in a viscous fluid
Uploaded: 2025-05-22T09:06:09.000Z
Duration: 1 min 20 s
Channel: JoVE

Considérons un objet se déplaçant à travers un fluide. Les couches de fluide près de l’objet sont entraînées avec lui et subissent une vitesse relative, ce qui entraîne une force visqueuse sur l’objet. La force visqueuse dépend de la forme, de la taille, de la vitesse et des propriétés du fluide de l'objet. 
Pour un corps sphérique se déplaçant à l'intérieur d'un fluide, la force visqueuse est proportionnelle au rayon, à la vitesse et à la viscosité du fluide de la sphère.
En résolvant l’équation de manière dimensionnelle, on obtient la dépendance de la force visqueuse sur ces paramètres. L'expression obtenue est la loi de Stokes, indiquant que la force visqueuse est directement proportionnelle à la vitesse de l'objet.
Si une sphère est lâchée à travers un fluide, le poids de l'objet la tire vers le bas, tandis que les forces visqueuses et flottantes agissent vers le haut.
Lorsque la vitesse augmente en raison de l’accélération, la force visqueuse augmente. Lorsque la force visqueuse équilibre le poids et la flottabilité, la sphère tombe à vitesse constante, appelée vitesse terminale.
Pour un liquide très visqueux, la vitesse terminale peut être mesurée expérimentalement. Ensuite, en utilisant la loi de Stokes, la viscosité peut être obtenue.

<ol>
	<li>Verma, H.C. (2008). Concepts de physique. Volume 1, Bharati Bhawan Pub. & Dis. : articles 14.17, 14.18 ; Pages 291 et 292.</li>
</ol>

la loi de stokes

Stokes' Law

Les forces visqueuses, telles que la friction, sont des forces intermoléculaires qui résistent au mouvement relatif des molécules les unes par rapport aux autres. Lorsqu'un corps solide se déplace à travers un liquide, les forces visqueuses l'entraînent dans la direction opposée. L'intensité de la force dépend de la forme et de la taille du solide, ainsi que de sa vitesse, du coefficient de viscosité du liquide, de sa densité et de sa température.

L'expression de la force exercée sur un objet sphérique solide dans un fluide est appelée loi de Stokes. La loi de Stokes n'est valable que pour les fluides de faible nombre de Reynolds, ce qui signifie qu'elle s'applique uniquement lorsque l'écoulement du fluide est laminaire et non turbulent. La force exercée sur l'objet solide est expérimentalement trouvée proportionnelle au rayon et à la vitesse de l'objet, ainsi qu'au coefficient de viscosité du liquide. L'ordre de dépendance de chaque variable peut être obtenu par l'analyse dimensionnelle. La constante de proportionnalité est obtenue expérimentalement.

Le mouvement d'un solide sphérique à travers un liquide peut être analysé en utilisant la deuxième loi de Newton. Au début, il n'y a pas de traînée visqueuse car le solide est au repos. La force nette vers le bas, qui est donnée par la différence entre son poids et la force de flottaison du liquide, accélère sa vitesse vers le bas. Cependant, une augmentation de la vitesse accroît la traînée visqueuse. Une fois qu'il y a une traînée visqueuse significative vers le haut, il n'y a pas de force nette car les trois forces s'équilibrent entre elles : le poids vers le bas, la flottabilité vers le haut et la traînée visqueuse vers le haut. Le solide atteint alors une vitesse constante appelée vitesse limite.

La loi de Stokes

Les forces visqueuses, comme le frottement, sont des forces intermoléculaires qui résistent au mouvement relatif des molécules les unes sur les autres. Lorsqu’un corps solide se déplace à travers un ...

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Education

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Physics

Physique

Unit 1

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Fluid Mechanics

Mécanique des fluides

KEY TERMS AND CONCEPTS

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terminal velocity in a viscous fluid

Viscous forces act like friction in a liquid. They resist the relative motion of molecules and pull back on a solid body moving through the fluid. The size of this force depends on the body’s shape and size, its speed, and the liquid’s viscosity, density, and temperature.

For a spherical solid object, the force in a fluid is described by Stokes’ law. This law applies only at low Reynolds number, when the flow is laminar and not turbulent. Experiments show that the force is proportional to the sphere’s radius, its speed, and the liquid’s viscosity coefficient. Dimensional analysis helps determine how these variables depend on one another, while the proportionality constant is found experimentally.

A sphere moving through a liquid can also be studied with Newton’s second law. At first, the sphere has no viscous drag because it is at rest. The downward net force, which comes from the difference between its weight and the liquid’s buoyant force, makes it speed up.

As the speed increases, the viscous drag also increases. Eventually, the upward viscous drag becomes large enough to balance the downward weight and the upward buoyant force. When these three forces balance, there is no net force, and the sphere continues at a steady speed called terminal velocity.

Terminal Velocity in a Viscous Fluid

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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 viscous drag, buoyancy, and weight act on a sphere in a liquid, and how Stokes’ law leads to terminal velocity in low Reynolds number flow.

Terminal Velocity in a Viscous Fluid | JoVE K12

physics

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Terminal Velocity in a Viscous Fluid

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