Name: linear shear between moving plates
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 22 s
Channel: JoVE

O fluxo de Couette descreve o movimento do fluido entre duas placas paralelas, onde uma está estacionária e a outra se move com velocidade constante, criando um fluxo constante e laminar acionado por cisalhamento.
Essa configuração simplifica as equações de Navier-Stokes, que podem ser expressas de forma adimensional.
Um parâmetro adimensional, relacionado ao gradiente de pressão, define variações nos perfis de fluxo de Couette.
Quando não há gradiente de pressão ao longo da direção do fluxo, esse parâmetro se torna zero, indicando uma variação linear da velocidade entre as duas placas.
O perfil de velocidade do fluido entre as placas é linear, aumentando de zero na placa estacionária até a velocidade da placa em movimento.
O fluxo de Couette é comumente usado para modelar o comportamento do fluido em mancais levemente carregados, como aqueles em bombas de água, onde uma fina camada de lubrificante separa um eixo rotativo dentro de um mancal fixo.
Nesses rolamentos levemente carregados, os efeitos de pressão são mínimos, de modo que as características de fluxo se assemelham muito às do fluxo Couette puro.
A tensão de cisalhamento e a vazão da camada de lubrificante dependem da velocidade de rotação do eixo e da largura da folga entre o eixo e o mancal.

fluxo couette

Couette Flow

O fluxo Couette representa o fluxo de fluido entre duas placas paralelas, uma com uma placa fixa e a outra se movendo com uma velocidade constante. Esta configuração permite uma análise simplificada usando as equações de Navier-Stokes, que governam o movimento do fluido sob condições de viscosidade e incompressibilidade. Para o fluxo Couette, as suposições incluem um fluxo estável, laminar e incompressível com um gradiente de pressão zero na direção do fluxo. Este tipo de fluxo é benéfico para entender fluxos acionados por cisalhamento e é relevante para aplicações em cenários de lubrificação e engenharia civil, como transporte de sedimentos e erosão.

Em uma configuração de fluxo Couette, deixe o eixo x se alinhar com a direção de movimento da placa superior enquanto o eixo y é perpendicular a ambas as placas. O fluxo é estável, laminar e totalmente desenvolvido, sem variação perpendicular ao movimento.

Para o fluxo de Couette, a equação de distribuição de velocidade é dada por:

<img alt="Equation 1" src="/files/ftp_upload/18064/18064_Equation_1.svg" style="text-align: center; height: 30px;" />

Onde:

<ol style="list-style-type: circle;">
	<li>U é a velocidade constante da placa superior,</li>
	<li>b é a distância entre as placas,</li>
	<li>μ é a viscosidade dinâmica do fluido.</li>
</ol>

Na forma adimensional, dividindo ambos os lados por U, obtemos:

<img alt="Equation 2" src="/files/ftp_upload/18064/18064_Equation_2.svg" style="text-align: center; height: 30px;" />

Onde u/U representa a velocidade adimensional e y/b representa a distância normalizada da placa estacionária. Para analisar condições específicas, definimos o parâmetro adimensional P como:

<img alt="Equation 3" src="/files/ftp_upload/18064/18064_Equation_3.svg" style="text-align: center; height: 30px;" />

Sob essas condições, P se torna zero quando não há gradiente de pressão (∂p/∂x=0) na direção x, reduzindo a equação de velocidade para:

<img alt="Equation 4" src="/files/ftp_upload/18064/18064_Equation_4.svg" style="text-align: center; height: 26px;" />

Este perfil linear indica que a velocidade do fluido aumenta linearmente de zero na placa estacionária para U na placa móvel, resultando em uma taxa de cisalhamento uniforme na camada de fluido.

Fluxo Couette

O fluxo de Couette descreve o movimento fluido entre duas placas paralelas, onde uma está estacionária e a outra se move com velocidade constante, criando um ...

Education

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

linear shear between moving plates

Linear shear between moving plates describes fluid motion in a simple channel with two parallel plates. One plate stays fixed, and the other moves at a constant speed. This setup helps show how viscosity and incompressible flow shape fluid motion under the Navier-Stokes equations.

The model uses a steady, laminar, incompressible flow with no pressure gradient in the flow direction. The x-axis points along the moving direction of the upper plate, and the y-axis is perpendicular to both plates. These assumptions make the flow fully developed and easier to analyze.

For this case, the velocity changes with distance from the stationary plate. The upper plate speed is U, the plate spacing is b, and the fluid’s dynamic viscosity is μ. In dimensionless form, the velocity is written as u/U, and the position is written as y/b.

A dimensionless parameter P is used to describe pressure effects. When there is no pressure gradient in the x-direction, P becomes zero because ∂p/∂x = 0. The velocity equation then reduces to a straight line, so the fluid speed rises from zero at the fixed plate to U at the moving plate.

This linear profile creates a uniform shear rate across the fluid layer. Shear-driven flow like this is useful for understanding lubrication and civil engineering problems. It also helps explain processes such as sediment transport and erosion.

Linear Shear Between Moving Plates

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

The stream function helps describe two-dimensional incompressible flow. In this type of flow, the continuity equation keeps mass conserved. That means fluid entering a region must be balanced by fluid leaving it. For incompressible flow, the density stays constant. The continuity requirement then becomes a zero-divergence condition for the velocity field. In two dimensions, the horizontal and vertical velocity components are usually written as u and v. A stream function, written as ψ, is used...

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Irrotational Flow Near Boundaries

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...

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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

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...

couette flow

Linear shear between moving plates describes fluid motion in a simple channel with two parallel plates. One plate stays fixed, and the other moves at a constant speed. This setup helps show how viscosity and incompressible flow shape fluid motion under the Navier-Stokes equations. The model uses a steady, laminar, incompressible flow with no pressure gradient in the flow direction. The x-axis points along the moving direction of the upper plate, and the y-axis is perpendicular to both plates.

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

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

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...

key terms and concepts

Learn how fluid moves between two parallel plates when one plate is fixed and the other moves. See the linear velocity profile, shear rate, and key assumptions.

Linear Shear Between Moving 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.

civil engineering

Linear Shear Between Moving Plates

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