Name: pressure drop in oil pipe design
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 25 s
Channel: JoVE

Un ingénieur doit concevoir un pipeline pour transporter le pétrole d’un réservoir de stockage à une installation de traitement.
Compte tenu de la viscosité, de la densité et du rayon de l'huile du pipeline, l'objectif est de maintenir un débit d'huile constant à travers un tuyau circulaire tout en assurant un écoulement laminaire pour minimiser la friction et la perte de pression.
À l'aide de la loi de Hagen-Poiseuille, la perte de charge requise à travers le pipeline est calculée en tenant compte de facteurs tels que la longueur du tuyau, le rayon, la viscosité de l'huile et le débit souhaité.
Ce calcul indique la perte de charge nécessaire pour atteindre le débit spécifié sur la longueur du tuyau.
Pour s'assurer que l'écoulement reste laminaire, le nombre de Reynolds, qui dépend de la vitesse, de la densité et de la viscosité de l'huile, est vérifié.
Un nombre de Reynolds inférieur à 2100 confirme l'écoulement laminaire, ce qui rend la loi de Hagen-Poiseuille applicable.
De plus, la vitesse maximale au centre de la conduite est estimée pour vérifier que la conception répond aux exigences opérationnelles.
Cet exemple met en évidence l’importance du rayon de la conduite dans la détermination du débit, car même des ajustements mineurs peuvent avoir un impact significatif sur les exigences de pression et l’efficacité du débit dans la conception des pipelines.

exemple de conception: écoulement de pétrole dans des conduites circulaires

Design Example: Flow of Oil Through Circular Pipes

Il est essentiel de comprendre le comportement de l'écoulement des fluides dans les conduites en mécanique des fluides, en particulier dans des applications telles que le transport de pétrole par pipeline. La loi de Hagen-Poiseuille fournit une solution exacte dérivée des équations de Navier-Stokes pour un écoulement stable, incompressible et laminaire dans une conduite circulaire. La loi de Hagen-Poiseuille permet de déterminer la chute de pression nécessaire sur une section de conduite en déterminant des paramètres tels que la longueur de la conduite, le rayon, la viscosité de l'huile et le débit volumétrique souhaité.

La loi de Hagen-Poiseuille décrit la chute de pression (ΔP) requise pour maintenir un débit spécifique dans une conduite circulaire dans des conditions laminaires. La loi est exprimée comme suit:

<img alt="Equation 1" src="/files/ftp_upload/18066/18066_Equation_1.svg" style="text-align: center; height: 30px;">

Où:

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>μ est la viscosité dynamique de l'huile,</li>
 <li>L est la longueur de la conduite</li>
 <li>Q est le débit volumétrique souhaité et</li>
 <li>r est le rayon intérieur de la conduite.</li>
</ul>

Cette relation met en évidence le rôle du rayon du tuyau dans la détermination de la chute de pression. Étant donné que le rayon est élevé à la quatrième puissance, des modifications mineures du diamètre du tuyau peuvent profondément affecter la pression requise pour maintenir un débit donné.

Pour garantir un écoulement laminaire, il faut calculer le nombre de Reynolds (Re), qui évalue si le mouvement du fluide sera régulier (laminaire) ou chaotique (turbulent). Le nombre de Reynolds est donné par:

<img alt="Equation 2" src="/files/ftp_upload/18066/18066_Equation_2.svg" style="text-align: center; height: 30px;">

Où:

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
 <li>⍴ est la densité de l'huile,</li>
 <li>v est la vitesse moyenne de l'huile,</li>
 <li>D est le diamètre du tuyau (deux fois le rayon) et</li>
 <li>μ est la viscosité dynamique.</li>
</ul>

L'écoulement est considéré comme laminaire pour les nombres de Reynolds inférieurs à 2 100, ce qui rend la loi de Hagen-Poiseuille applicable. Si le nombre de Reynolds dépasse ce seuil, des ajustements peuvent être nécessaires, comme la réduction du débit ou l'augmentation du diamètre du tuyau pour maintenir des conditions laminaires.

La loi de Hagen-Poiseuille permet de déterminer les dimensions optimales des conduites pour répondre à des exigences de débit et à des contraintes de pression spécifiques, que ce soit dans la distribution d'eau, la gestion des eaux usées ou le transport de pétrole. Le choix du rayon de conduite approprié garantit un mouvement efficace des fluides, minimise les pertes d'énergie et réduit les coûts d'exploitation, améliorant ainsi les performances globales des systèmes d'infrastructure.

Exemple de conception: écoulement de pétrole dans des conduites circulaires

Un ingénieur doit concevoir un pipeline pour transporter le pétrole d’un réservoir de stockage à une installation de traitement.
Compte tenu de la viscosité, de la densité et de la ...

design-example-flow-of-oil-through-circular-pipes

Education

Enseignement

JoVE Core

Civil Engineering

Génie civil

Unit 1

Unité 1

Differential Analysis of Fluid Flow

Analyse différentielle de l'écoulement des fluides

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

pressure drop in oil pipe design

Pressure drop in oil pipe design depends on pipe size, oil properties, and the flow rate needed through a circular pipe. For steady, incompressible, laminar flow, Hagen-Poiseuille's law gives an exact solution from the Navier-Stokes equations. It is used to find the pressure difference needed to keep oil moving through a pipeline section.

The pressure drop equation uses the oil's dynamic viscosity, the pipeline length, the desired volumetric flow rate, and the pipe's inner radius. This relationship shows why pipe radius matters so much. Because radius is raised to the fourth power, even a small change in diameter can greatly change the pressure needed to maintain the same flow rate.

To know whether Hagen-Poiseuille's law applies, engineers calculate the Reynolds number. The Reynolds number uses the oil's density, mean velocity, pipe diameter, and dynamic viscosity. Flow is considered laminar when Reynolds number is below 2100, which means the motion stays smooth instead of becoming chaotic or turbulent.

If the Reynolds number is too high, the design may need changes. A lower flow rate or a larger pipe diameter can help keep the flow laminar. This method is useful in oil transport and also in systems such as water distribution and wastewater management, where the goal is efficient fluid movement, less energy loss, and lower operating cost.

Pressure Drop in Oil Pipe Design

euler&#39;s equations of motion

Pressure and Velocity in Inviscid Flow

Pressure and velocity in inviscid flow are linked by Euler's equations of motion. In fluid mechanics, viscosity creates shear stress, which is a force that acts along a surface. For low-viscosity fluids like water, these shear stresses are very small. That lets the fluid be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent. Only normal stresses remain, and these act perpendicular to a fluid element. Pressure is the negative of the normal stress. It stays the...

stream function

Stream Function for Incompressible Flow

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irrotational flow

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Irrotational flow is fluid motion in which particles do not spin around their own axes. It has zero vorticity, which means the curl of the velocity field is zero. That condition places limits on the velocity gradients in the flow. A simple example is uniform flow. In this case, the velocity u stays constant, while v and w are both zero. This satisfies the irrotational conditions and gives a basic model of non-rotating flow. When a solid object is added, irrotational flow usually remains only...

velocity potential

Velocity Potential in Pipe Flow

Velocity potential in pipe flow describes the motion of fluid in the central region of a long, straight pipe with a uniform cross-section. In this region, the flow is steady, incompressible, and irrotational. Irrotational means the fluid particles do not spin around their own axes. A scalar function called the velocity potential, written as φ, is used to describe this motion. The velocity field V is defined as the gradient of φ. Because the curl of a gradient is always zero, this form of V...

plane potential flows

Plane Potential Flow Patterns and Models

Plane potential flows describe fluid motion using simple flow patterns and models. They assume the fluid is irrotational and incompressible. These assumptions let the flow be written with a velocity potential function, φ, which gives the flow speed in a direction, and a stream function, ψ, which shows the flow path. Both are governed by Laplace's equation and are useful for estimating flow patterns, velocity distributions, and pressure fields around hydraulic structures. Uniform flow is the...

navier&#8211;stokes equations

Fluid Stress and Flow Equations

Fluid stress and flow equations describe how incompressible Newtonian fluids move under pressure, shear, and gravity. In these fluids, density stays constant, and stress changes linearly with the rate of deformation. The main stress types are normal stress and shear stress. Normal stress depends on pressure acting on the fluid and on deformation rate in specific directions. Shear stress acts along the surface of a fluid layer. It shows how neighboring layers slide past one another, so velocity...

steady, laminar flow between parallel plates

steady-laminar-flow-between-parallel-plates

Laminar Flow Profile Between Parallel Plates

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couette flow

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steady, laminar flow in circular tubes

Parabolic Flow in Circular Tubes

Parabolic flow in circular tubes describes the steady, incompressible motion of a viscous fluid through a tube with a constant radius. This Hagen-Poiseuille flow is a classic example of laminar flow. It is often used to study fluid transport in narrow channels, including capillaries. Cylindrical coordinates are used to describe the tube. The radial direction is r, the angular direction is θ, and the axial direction is z. In this flow, the velocity is purely axial. That means the fluid moves...

design example: flow of oil through circular pipes

Pressure drop in oil pipe design depends on pipe size, oil properties, and the flow rate needed through a circular pipe. For steady, incompressible, laminar flow, Hagen-Poiseuille's law gives an exact solution from the Navier-Stokes equations. It is used to find the pressure difference needed to keep oil moving through a pipeline section. The pressure drop equation uses the oil's dynamic viscosity, the pipeline length, the desired volumetric flow rate, and the pipe's inner radius. This...

key terms and concepts

Learn how Hagen-Poiseuille's law and Reynolds number help design oil flow in circular pipes by linking pipe radius, viscosity, pressure drop, and laminar flow.

Pressure Drop in Oil Pipe Design | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Pressure Drop in Oil Pipe Design

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