Name: fluid stress and flow equations
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 28 s
Channel: JoVE

No movimento do fluido sob condições viscosas, a tensão de cisalhamento é diretamente proporcional à deformação do fluido. Em fluidos newtonianos incompressíveis, esse estresse varia linearmente com a taxa de deformação.
As tensões normais dependem das taxas de pressão e deformação em direções específicas, definindo o comportamento do fluxo de fluido sob diferentes pressões.
As tensões de cisalhamento agem tangencialmente, descrevendo como diferentes camadas de fluido deslizam umas sobre as outras, conectando a tensão com as mudanças de velocidade entre as camadas.
Substituir essas relações de tensão em equações diferenciais de movimentos forma as equações de Navier-Stokes, que equilibram forças como inércia, pressão e gravidade em um fluido viscoso.
O termo inércia captura a aceleração do fluido, mostrando como um fluido em movimento resiste a mudanças repentinas em sua velocidade ou direção.
Os gradientes de pressão impulsionam o movimento do fluido de áreas de alta pressão para áreas de baixa pressão, enquanto os termos viscosos representam o atrito interno dentro do fluido.
Cada equação direcional captura forças internas, como viscosidade, e forças externas, como gravidade, prevendo a resposta do fluido em várias condições.
As equações de Navier-Stokes podem ser simplificadas para cenários de fluxo constante ou laminar, permitindo uma análise mais simples em cenários controlados, como camada limite e fluxos de Couette.

equações de navier-stokes

Navier&#8211;Stokes Equations

Para fluidos newtonianos incompressíveis, onde a densidade permanece constante, as tensões mostram uma relação linear com a taxa de deformação, definida por tensões normais e de cisalhamento. As tensões normais dependem da pressão exercida sobre o fluido e da taxa de deformação em direções específicas, determinando como o fluido flui sob pressões variáveis. As tensões de cisalhamento, por outro lado, agem tangencialmente por camadas de fluido. Elas explicam como camadas de fluido adjacentes deslizam em relação umas às outras, conectando a tensão tangencial às diferenças de velocidade entre as camadas. As tensões normais e de cisalhamento definem as forças internas em um fluido que influenciam seu movimento.

As equações de Navier-Stokes são derivadas pela incorporação dessas relações de tensão em equações diferenciais de movimento.

<img alt="Equation 1" src="/files/ftp_upload/18062/18062_Equation_1.svg" style="text-align: center; height: 106px;">

Essas equações equilibram as forças inerciais, de pressão e gravitacionais em um fluido viscoso fundamentais para prever o comportamento do fluido sob várias condições. O termo de inércia nas equações de Navier-Stokes é responsável pela aceleração do fluido, representando a resistência do fluido a mudanças na velocidade. Este termo é crítico para capturar a conservação do momento de um fluido em movimento por demonstrar como os fluidos resistem a mudanças repentinas de velocidade ou direção.

O termo gradiente de pressão nas equações de Navier-Stokes impulsiona o movimento do fluido criando uma força líquida de áreas de alta pressão para baixa pressão. Enquanto isso, os termos viscosos representam o atrito interno decorrente de interações moleculares no fluido. Dependendo dos gradientes de velocidade presentes, essas forças viscosas agem para desacelerar o movimento do fluido.

Cada equação direcional de Navier-Stokes captura forças internas como estresse viscoso e forças externas como gravidade. Essas equações permitem prever o movimento do fluido em várias condições, de fluxos simples a complexos. Para cenários de fluxo estável ou laminar, onde o fluxo é suave e ordenado, as equações se tornam mais gerenciáveis, permitindo uma análise mais direta. Essa simplificação é útil em cenários controlados, como fluxo de camada limite, onde o fluxo próximo a uma superfície tem uma camada estruturada, e no fluxo de Couette, descrevendo o fluido entre duas superfícies paralelas se movendo em velocidades diferentes.

Equações de Navier-Stokes

No movimento do fluido sob condições viscosas, a tensão de cisalhamento é diretamente proporcional à deformação do fluido. Em fluidos newtonianos incompressíveis, esse estresse ...

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Civil Engineering

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Differential Analysis of Fluid Flow

Análise Diferencial do Escoamento de Fluidos

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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 differences between layers matter.

These normal and shear stresses create the internal forces that control fluid motion. The Navier-Stokes equations are formed by putting these stress relations into differential equations of motion. They balance inertial, pressure, and gravitational forces in a viscous fluid and help predict how the fluid will behave.

The inertia term describes fluid acceleration and its resistance to changes in velocity. It is important for momentum conservation in moving fluids. The pressure gradient term pushes fluid from regions of high pressure to regions of low pressure, while viscous terms come from internal friction between molecules and slow the flow when velocity changes across the fluid.

Each directional Navier-Stokes equation includes both internal forces, such as viscous stress, and external forces, such as gravity. This makes the equations useful for many flow conditions, from simple to complex. For steady or laminar flow, where motion is smooth and orderly, the equations are easier to work with.

That simplification is helpful in boundary layer flow near a surface, where the fluid forms a structured layer. It is also useful for Couette flow, which describes fluid between two parallel surfaces moving at different velocities. These cases show how the same equations can describe controlled fluid motion in practical settings.

Fluid Stress and Flow Equations

euler&#39;s equations of motion

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navier&#8211;stokes 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...

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steady-laminar-flow-between-parallel-plates

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couette flow

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key terms and concepts

Learn how normal stress, shear stress, and the Navier-Stokes equations explain fluid motion, pressure forces, viscosity, boundary layers, and Couette flow.

Fluid Stress and Flow Equations | JoVE K12

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civil engineering

Fluid Stress and Flow Equations

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