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

Um engenheiro precisa projetar um oleoduto para transportar petróleo de um tanque de armazenamento para uma instalação de processamento.
Dada a viscosidade, densidade e raio do oleoduto, o objetivo é manter uma taxa de fluxo de óleo constante através de um tubo circular, garantindo o fluxo laminar para minimizar o atrito e a perda de pressão.
Usando a lei de Hagen-Poiseuille, a queda de pressão necessária na tubulação é calculada considerando fatores como comprimento do tubo, raio, viscosidade do óleo e a vazão desejada.
Este cálculo mostra a queda de pressão necessária para atingir a vazão especificada ao longo do comprimento do tubo.
Para garantir que o fluxo permaneça laminar, o número de Reynolds, que depende da velocidade, densidade e viscosidade do óleo, é verificado.
Um número de Reynolds abaixo de 2100 confirma o fluxo laminar, tornando a lei de Hagen-Poiseuille aplicável.
Além disso, a velocidade máxima no centro do tubo é estimada verificando se o projeto atende aos requisitos operacionais.
Este exemplo destaca a importância do raio do tubo na determinação da vazão, pois mesmo pequenos ajustes podem afetar significativamente os requisitos de pressão e a eficiência do fluxo no projeto da tubulação.

exemplo de projeto: fluxo de óleo por meio de tubos circulares

Design Example: Flow of Oil Through Circular Pipes

Entender o comportamento do fluxo de fluidos por meio de tubos é essencial na mecânica dos fluidos, especialmente em aplicações como transporte de óleo por meio de oleodutos. A lei de Hagen-Poiseuille fornece uma solução exata derivada das equações de Navier-Stokes para fluxo estável, incompressível e laminar em um tubo circular. A lei de Hagen-Poiseuille ajuda a determinar a queda de pressão necessária em uma seção de oleoduto, determinando parâmetros como comprimento do tubo, raio, viscosidade do óleo e a vazão volumétrica desejada.

A lei de Hagen-Poiseuille descreve a queda de pressão (ΔP) necessária para sustentar uma vazão específica em um tubo circular sob condições laminares. A lei é expressa como:

<img alt="Equation 1" src="/files/ftp_upload/18066/18066_Equation_1.svg" style="text-align: center; height: 30px;" />

Onde:

<ol style="list-style-type: circle;">
	<li>μ é a viscosidade dinâmica do óleo,</li>
	<li>L é o comprimento do oleoduto</li>
	<li>Q é a vazão volumétrica desejada e</li>
	<li>r é o raio interno do tubo.</li>
</ol>

Essa relação destaca o papel do raio do tubo na determinação da queda de pressão. Como o raio é elevado à quarta potência, pequenas alterações no diâmetro do tubo podem afetar profundamente a pressão necessária para manter uma determinada taxa de fluxo.

Garantir o fluxo laminar requer o cálculo do número de Reynolds (Re), que avalia se o movimento do fluido será suave (laminar) ou caótico (turbulento). O número de Reynolds é dado por:

<img alt="Equation 2" src="/files/ftp_upload/18066/18066_Equation_2.svg" style="text-align: center; height: 30px;" />

Onde:

<ol style="list-style-type: circle;">
	<li>⍴ é a densidade do óleo,</li>
	<li>v é a velocidade média do óleo,</li>
	<li>D é o diâmetro do tubo (duas vezes o raio) e</li>
	<li>μ é a viscosidade dinâmica.</li>
</ol>

O fluxo é considerado laminar para números de Reynolds abaixo de 2100, tornando a lei de Hagen-Poiseuille aplicável. Se o número de Reynolds exceder esse limite, ajustes podem ser necessários, como reduzir a taxa de fluxo ou aumentar o diâmetro do tubo para manter as condições laminares.

A lei de Hagen-Poiseuille pode determinar as dimensões ideais do tubo para atender a requisitos de fluxo específicos e restrições de pressão, seja na distribuição de água, gerenciamento de águas residuais ou transporte de petróleo. Selecionar o raio correto do tubo garante movimento eficiente do fluido, minimiza a perda de energia e reduz os custos operacionais, melhorando o desempenho geral dos sistemas de infraestrutura.

Exemplo de projeto: Fluxo de óleo por meio de tubos circulares

Um engenheiro precisa projetar um oleoduto para transportar petróleo de um tanque de armazenamento para uma instalação de processamento.
Dada a viscosidade, densidade e ...

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 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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