Name: fluid resistance, viscosity, and flow regime
Uploaded: 2025-05-22T09:05:41.000Z
Duration: 1 min 10 s
Channel: JoVE

Dans un écoulement laminaire, à travers un tube horizontal, le débit est défini comme le rapport entre la différence de pression en deux points et la résistance à l’écoulement.
Ici, la résistance est directement proportionnelle au coefficient de viscosité et à la longueur du tube, et inversement proportionnelle à la quatrième puissance du rayon du tube. Lorsqu'elle est combinée avec l'équation du débit, cette relation donne la loi de Poiseuille pour l'écoulement laminaire.
Si l’on considère que la viscosité est constante, une légère diminution du rayon du tube entraîne une réduction significative du débit. Pour maintenir le même débit, la différence de pression doit augmenter en conséquence.
De même, il est difficile pour un fluide plus visqueux de s’écouler dans le tube qu’un fluide moins visqueux à température constante.
Le nombre de Reynolds est une valeur qui indique si l’écoulement d’un fluide est laminaire ou turbulent.
Si le nombre de Reynolds est inférieur à deux mille, l’écoulement est laminaire, et turbulent s’il est supérieur à trois mille. Entre deux et trois mille, le flux est instable et peut présenter un comportement chaotique.

la loi de poiseuille et le nombre de reynolds

Poiseuille's Law and Reynolds Number

Tout fluide dans un tube horizontal peut s'écouler en raison de différences de pression - le fluide s'écoule d'une pression élevée à une pression faible. Le débit (Q) est le rapport entre la différence de pression et la résistance à travers un tube horizontal. Plus la différence de pression est grande, plus le débit est élevé. La résistance d'écoulement est exprimée comme suit :

<img alt="Equation1" src="/files/ftp_upload/12743/12743_Equation_1.png" style="text-align: center; height: 32px;" />

Lorsqu'elle est combinée avec le débit (Q), cette relation donne la loi de Poiseuille pour l'écoulement laminaire d'un fluide incompressible dans un tube.

<img alt="Equation2" src="/files/ftp_upload/12743/12743_Equation_2.png" style="text-align: center; height: 32px;" />

Tous les facteurs qui affectent le débit, à l'exception de la pression, sont inclus dans la résistance. La résistance dépend des dimensions du tube et de la viscosité du fluide. La résistance est directement proportionnelle à la longueur du tube et inversement proportionnelle à la quatrième puissance du rayon du tube.

Dans le cas d'un fluide non visqueux, l'écoulement du fluide est sans frottement et la résistance à l'écoulement est nulle. Cela entraîne le déplacement de toutes les couches à la même vélocité. En revanche, la résistance à l'écoulement des fluides visqueux est non nulle. Dans de tels cas, la vélocité est maximale pour la partie centrale et diminue vers le bord du tube. Nous pouvons observer cet effet dans une flamme de brûleur Bunsen.

Le débit peut être considéré comme laminaire ou turbulent, classifié par le nombre de Reynolds. Si le nombre de Reynolds est inférieur à 2 000, l'écoulement est laminaire ; s'il est supérieur à 3 000, l'écoulement est turbulent. L'écoulement est considéré comme instable et peut présenter un comportement chaotique si le nombre de Reynolds se situe entre 2 000 et 3 000. Un écoulement instable indique qu'il est initialement laminaire, mais en raison d'obstructions ou de rugosités de surface, l'écoulement peut devenir turbulent et osciller de manière aléatoire entre le laminaire et le turbulent. Ici, une petite variation dans un facteur peut avoir un effet exagéré (ou non linéaire) sur un système, ce qui montre un comportement chaotique.

Ce texte est adapté de <a href="https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence">Openstax, University Physics Volume 1, Section 14.7: Viscosity and Turbulence.</a>

La loi de Poiseuille et le nombre de Reynolds

Tout fluide dans un tube horizontal peut s’écouler en raison des différences de pression - le fluide s’écoule de la haute à la basse pression. Le débit (Q) est le rapport de ...

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fluid resistance, viscosity, and flow regime

Fluid resistance, viscosity, and flow regime shape how liquid moves through a horizontal tube. Fluid flows from high pressure to low pressure. The flow rate, Q, is the ratio of the pressure difference to the resistance in the tube. A larger pressure difference gives a higher flow rate.

Poiseuille's law describes laminar flow of an incompressible fluid in a tube. In this relation, the factors that affect flow rate except pressure are grouped into resistance. Resistance depends on the tube size and the fluid's viscosity. It is directly proportional to tube length and inversely proportional to the fourth power of the tube radius.

A non-viscous fluid has frictionless flow, so its resistance is zero. In that case, all layers move at the same speed. Viscous fluids behave differently. Their flow resistance is not zero, and the speed is highest in the middle of the tube and lower near the edges. A Bunsen burner flame can show this effect.

Flow can also be classified by the Reynolds number. When the Reynolds number is below 2,000, the flow is laminar. When it is above 3,000, the flow is turbulent. If the Reynolds number is between 2,000 and 3,000, the flow is unstable and may switch between laminar and turbulent behavior. Small obstructions or surface roughness can trigger this change and lead to chaotic motion.

Fluid Resistance, Viscosity, and Flow Regime

fluid-resistance-viscosity-and-flow-regime

characteristics of fluids

Fluid Behavior Under Force

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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archimedes' principle

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buoyancy

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bernoulli's equation

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bernoulli's principle

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energy conservation and bernoulli's equation

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Bernoulli’s Equation in Streamlined Flow

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viscosity

Viscosity and How Fluids Flow

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poiseuille's law and reynolds number

Fluid resistance, viscosity, and flow regime shape how liquid moves through a horizontal tube. Fluid flows from high pressure to low pressure. The flow rate, Q, is the ratio of the pressure difference to the resistance in the tube. A larger pressure difference gives a higher flow rate. Poiseuille's law describes laminar flow of an incompressible fluid in a tube. In this relation, the factors that affect flow rate except pressure are grouped into resistance. Resistance depends on the tube size...

stokes' law

Terminal Velocity in a Viscous Fluid

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key terms and concepts

Explore how pressure, viscosity, and tube size affect fluid flow. Learn Poiseuille's law, laminar flow, and Reynolds number thresholds in tubes.

Fluid Resistance, Viscosity, and Flow Regime | 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 Resistance, Viscosity, and Flow Regime

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