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

Un ingeniero necesita diseñar un oleoducto para transportar petróleo desde un tanque de almacenamiento hasta una instalación de procesamiento.
Dada la viscosidad del petróleo, la densidad y el radio de la tubería, el objetivo es mantener un caudal de aceite constante a través de una tubería circular y, al mismo tiempo, garantizar el flujo laminar para minimizar la fricción y la pérdida de presión.
Utilizando la ley de Hagen-Poiseuille, la caída de presión requerida a través de la tubería se calcula teniendo en cuenta factores como la longitud de la tubería, el radio, la viscosidad del aceite y el caudal deseado.
Este cálculo muestra la caída de presión necesaria para lograr el caudal especificado a lo largo de la longitud de la tubería.
Para garantizar que el flujo permanezca laminar, se verifica el número de Reynolds, que depende de la velocidad, densidad y viscosidad del aceite.
Un número de Reynolds por debajo de 2100 confirma el flujo laminar, lo que hace aplicable la ley de Hagen-Poiseuille.
Además, se estima la velocidad máxima en el centro de la tubería verificando que el diseño cumpla con los requisitos operativos.
Este ejemplo destaca la importancia del radio de la tubería para determinar el caudal, ya que incluso los ajustes menores pueden afectar significativamente los requisitos de presión y la eficiencia del flujo en el diseño de la tubería.

ejemplo de diseño: flujo de petróleo a través de tuberías circulares

Design Example: Flow of Oil Through Circular Pipes

Entender el comportamiento del flujo de fluidos a través de tuberías es fundamental en la mecánica de fluidos, especialmente en aplicaciones como el transporte de petróleo a través de tuberías. La ley de Hagen-Poiseuille proporciona una solución exacta derivada de las ecuaciones de Navier-Stokes para el flujo constante, incompresible y laminar dentro de una tubería circular. La ley de Hagen-Poiseuille ayuda a determinar la caída de presión necesaria a lo largo de una sección de tubería al determinar parámetros como la longitud de la tubería, el radio, la viscosidad del petróleo y el caudal volumétrico deseado. La ley de Hagen-Poiseuille describe la caída de presión (ΔP) necesaria para mantener un caudal específico en una tubería circular en condiciones laminares. La ley se expresa como: <img alt="Equation 1" src="/files/ftp_upload/18066/18066_Equation_1.svg" style="text-align: center; height: 30px;"> Donde: <ol style="list-style-type: circle;"> <li>μ es la viscosidad dinámica del petróleo,</li> <li>L es la longitud de la tubería</li> <li>Q es el caudal volumétrico deseado y</li> <li>r es el radio interior de la tubería.</li> </ol> Esta relación resalta el papel del radio de la tubería en la determinación de la caída de presión. Debido a que el radio se eleva a la cuarta potencia, cambios menores en el diámetro de la tubería pueden afectar profundamente la presión requerida para mantener un caudal determinado. Para garantizar un flujo laminar es necesario calcular el número de Reynolds (Re), que evalúa si el movimiento del fluido será suave (laminar) o caótico (turbulento). El número de Reynolds se obtiene mediante: <img alt="Equation 2" src="/files/ftp_upload/18066/18066_Equation_2.svg" style="text-align: center; height: 30px;"> Donde: <ol style="list-style-type: circle;"> <li>⍴ es la densidad del petróleo,</li> <li>v es la velocidad media del petróleo,</li> <li>D es el diámetro de la tubería (el doble del radio) y</li> <li>μ es la viscosidad dinámica.</li> </ol> El flujo se considera laminar para números de Reynolds inferiores a 2100, lo que hace que sea aplicable la ley de Hagen-Poiseuille. Si el número de Reynolds supera este umbral, pueden ser necesarios ajustes, como reducir el caudal o aumentar el diámetro de la tubería para mantener las condiciones laminares. La ley de Hagen-Poiseuille puede determinar las dimensiones óptimas de las tuberías para satisfacer requisitos específicos de caudal y restricciones de presión, ya sea en la distribución de agua, la gestión de aguas residuales o el transporte de petróleo. La selección del radio de tubería correcto garantiza un movimiento eficiente del fluido, minimiza la pérdida de energía y reduce los costos operativos, mejorando el rendimiento general de los sistemas de infraestructura.

Ejemplo de diseño: flujo de petróleo a través de tuberías circulares

Un ingeniero necesita diseñar un oleoducto para transportar petróleo desde un tanque de almacenamiento hasta una instalación de procesamiento.
Dada la viscosidad, la densidad y la ...

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

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Civil Engineering

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Differential Analysis of Fluid Flow

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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

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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.

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Pressure Drop in Oil Pipe Design

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