Name: laminar flow profile between parallel plates
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 17 s
Channel: JoVE

O fluxo laminar constante entre duas placas paralelas descreve o movimento do fluido em um canal estreito e confinado, frequentemente usado para modelar sistemas de fluidos simples.
Para o fluxo entre duas placas fixas, as equações de Navier-Stokes simplificam, pois a velocidade varia apenas perpendicularmente às placas, sem aceleração ao longo da direção do fluxo.
Isso leva a um perfil de velocidade parabólica, onde o fluido se move mais rápido no centro e desacelera para zero nas placas devido ao atrito, conhecido como condição antiderrapante.
A vazão entre as placas depende do gradiente de pressão, da viscosidade do fluido e da separação da placa; alargar a lacuna ou aumentar o gradiente de pressão aumenta o fluxo.
A velocidade média do fluxo também está relacionada à queda de pressão, com a velocidade de pico no centro do canal sendo 1,5 vezes a velocidade média.
Esta análise permanece válida apenas para baixos números de Reynolds, indicando condições laminares, e falha para fluxos turbulentos e de alto número de Reynolds.
As aplicações desta análise incluem canais de irrigação, fluxo de água subterrânea e bacias de sedimentação em estações de tratamento de água, onde existem condições laminares.

fluxo laminar estacionário entre placas paralelas

Steady, Laminar Flow Between Parallel Plates

Compreender o fluxo laminar estável entre placas paralelas é essencial para analisar e projetar o fluxo em canais retangulares estreitos, comumente encontrados em vários sistemas de transporte e drenagem de água. As equações de Navier-Stokes governam o movimento do fluido e geralmente são desafiadoras de resolver devido à sua não linearidade. No entanto, simplificações são possíveis em certos casos, como o fluxo laminar estável entre placas paralelas. Para este cenário, assumimos um fluxo laminar estável e incompressível.

Considerando duas placas horizontais alinhadas ao longo do eixo x e espaçadas a uma distância '2h' de distância, com o eixo y perpendicular às placas, o movimento do fluido é assumido como paralelo. Aqui, a equação de continuidade indica não haver alteração na velocidade ao longo do eixo x, e as equações de Navier-Stokes são reduzidas da seguinte forma:

<img alt="Equation 1" src="/files/ftp_upload/18063/18063_Equation_1.svg" style="text-align: center; height: 30px;">


As equações nas direções y e z não mostram gradiente de pressão ao longo desses eixos, indicando que a pressão varia hidrostaticamente na direção y, permitindo que a integração produza:

<img alt="Equation 2" src="/files/ftp_upload/18063/18063_Equation_2.svg" style="text-align: center; height: 12px;">


Para placas paralelas com um gradiente de pressão ao longo do eixo x, a equação simplifica:

<img alt="Equation 3" src="/files/ftp_upload/18063/18063_Equation_3.svg" style="text-align: center; height: 30px;">


Integrando duas vezes e aplicando condições de contorno (u = 0 em y = +h e y = -h), obtemos:

<img alt="Equation 4" src="/files/ftp_upload/18063/18063_Equation_4.svg" style="text-align: center; height: 30px;">

Esta expressão revela que o perfil de velocidade através do vão entre as placas é parabólica, com velocidade máxima em y = 0, no meio do caminho entre as placas. A vazão volumétrica por meio de uma unidade de largura das placas é obtida integrando o perfil de velocidade através da lacuna.

Entender o fluxo laminar entre placas paralelas tem aplicações práticas no fluxo de águas subterrâneas, tratamento de águas residuais e lubrificação. Por exemplo, este modelo pode aproximar o fluxo em camadas de solo, onde a água se move entre partículas de solo como o fluxo entre placas. Conhecer a vazão e a distribuição de velocidade ajuda os engenheiros a projetar sistemas de drenagem eficientes e prever o movimento das águas subterrâneas.

Fluxo Laminar Estacionário Entre Placas Paralelas

O fluxo laminar constante entre duas placas paralelas descreve o movimento do fluido em um canal estreito e confinado, frequentemente usado para modelar sistemas de fluidos simples.
Durante...

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JoVE Core

Civil Engineering

Engenharia Civil

Unit 1

Unidade 1

Differential Analysis of Fluid Flow

Análise Diferencial do Escoamento de Fluidos

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

laminar flow profile between parallel plates

Laminar flow between parallel plates shows how fluid moves through a narrow, flat channel. This model helps describe flow in water conveyance and drainage systems, where the space is limited and the motion stays orderly. It is also useful for analyzing flow in rectangular channels used in many engineering settings.

The flow is studied with the Navier-Stokes equations, which govern fluid motion. These equations are often difficult to solve because they are nonlinear. In this case, the problem becomes simpler because the flow is steady, incompressible, and laminar. Two horizontal plates are placed along the x-axis, and the gap between them is 2h. The y-axis is perpendicular to the plates, and the fluid moves parallel to the plates.

With these assumptions, the continuity equation shows that the velocity does not change along the x-axis. The Navier-Stokes equations also simplify in the y and z directions. They show no pressure gradient along those axes, so pressure changes hydrostatically in the y-direction. After integration, the x-direction equation includes the pressure gradient along the plates.

Solving that equation requires integrating twice and applying the no-slip boundary conditions, where u = 0 at y = +h and y = -h. The result is a parabolic velocity profile across the gap. The fluid moves fastest at y = 0, the midpoint between the plates. The volumetric flow rate for a unit width of the plates is then found by integrating the velocity profile across the space.

This flow model has practical uses in groundwater flow, wastewater treatment, and lubrication. It can also represent water moving through soil layers, where the flow resembles movement between plates. Engineers use the velocity distribution and flow rate to help design drainage systems and predict groundwater movement.

Laminar Flow Profile Between Parallel Plates

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steady, laminar flow between parallel plates

Laminar flow between parallel plates shows how fluid moves through a narrow, flat channel. This model helps describe flow in water conveyance and drainage systems, where the space is limited and the motion stays orderly. It is also useful for analyzing flow in rectangular channels used in many engineering settings. The flow is studied with the Navier-Stokes equations, which govern fluid motion. These equations are often difficult to solve because they are nonlinear. In this case, the problem...

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key terms and concepts

Learn how steady laminar flow between parallel plates leads to a parabolic velocity profile, pressure-gradient behavior, and flow-rate calculations.

Laminar Flow Profile Between Parallel Plates | 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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Laminar Flow Profile Between Parallel Plates

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