Name: pressure and velocity in inviscid flow
Uploaded: 2025-02-13T15:43:25.000Z
Duration: 1 min 28 s
Channel: JoVE

Em um fluido em movimento, as tensões de cisalhamento se desenvolvem devido à viscosidade. Para a água, que tem baixa viscosidade, esses efeitos são insignificantes, simplificando a análise do movimento do fluido.
Quando as tensões de cisalhamento são insignificantes, o fluido é considerado invíscido ou sem atrito. Em fluidos invíscidos, a tensão normal é a mesma em todas as direções, o que significa que a pressão é independente da direção da tensão.
A pressão é o negativo da tensão normal, garantindo que as tensões de compressão resultem em um valor de pressão positivo.
As equações gerais de movimento para fluxo invíscido, conhecidas como equações de Euler, descrevem a conservação do momento. Essas equações representam a segunda lei de Newton aplicada a um elemento fluido, relacionando as mudanças de velocidade com as forças que atuam sobre o fluido.
As equações de Euler levam em conta gradientes de pressão, forças corporais como a gravidade e acelerações - locais e convectivas - que impulsionam mudanças na velocidade do fluido.
Eles negligenciam as forças viscosas, simplificando a análise, mas permanecem difíceis de resolver devido aos termos de velocidade não lineares nas equações diferenciais parciais.
A integração das equações de Euler ao longo de uma linha de fluxo deriva a equação de Bernoulli, fornecendo informações sobre variações de pressão, velocidade e elevação em fluxos invíscidos, tornando-a uma ferramenta fundamental na mecânica dos fluidos.

equações de movimento de euler

Euler&#39;s Equations of Motion

Na mecânica dos fluidos, as tensões de cisalhamento surgem da viscosidade, que representa a resistência interna de um fluido à deformação. Para fluidos de baixa viscosidade, como a água, essas tensões são mínimas, simplificando a análise de fluxo ao permitir que o fluido seja tratado como invíscido ou sem atrito. Em um fluido invíscido, as tensões de cisalhamento estão ausentes, deixando apenas tensões normais, que agem perpendicularmente aos elementos do fluido. Notavelmente, a pressão — definida como o negativo da tensão normal — permanece uniforme em diferentes direções e não é afetada pela orientação da tensão.

O movimento de fluidos invíscidos é governado pelas equações de Euler, derivadas da segunda lei de Newton aplicada à dinâmica de fluidos. Essas equações descrevem a conservação do momento ao relacionar a taxa de mudança na velocidade às forças que atuam em um elemento fluido. Para um fluido invíscido, as forças relevantes incluem gradientes de pressão e forças corporais, como a gravidade. As equações de Euler expressam o equilíbrio dessas forças, excluindo termos viscosos, da seguinte forma:

<img alt="Equation 1" src="/files/ftp_upload/18057/18057_Equation_1.svg" style="text-align: center; height: 30px;">

onde ρ é a densidade do fluido, v é o vetor velocidade, p é a pressão e g​ representa a aceleração gravitacional.

Embora as equações de Euler ignorem a viscosidade, elas continuam complexas devido aos seus termos não lineares, que consideram a aceleração convectiva das partículas do fluido. Quando integradas ao longo de uma linha de corrente, essas equações produzem a equação de Bernoulli, que descreve uma relação fundamental na mecânica dos fluidos, ligando pressão, velocidade e elevação para fluxos invíscidos. A equação de Bernoulli é uma ferramenta poderosa para analisar a distribuição de energia dentro dos fluxos de fluido, apoiando aplicações em transporte de fluidos, aerodinâmica e hidrodinâmica.

Equações de movimento de Euler

Em um fluido em movimento, as tensões de cisalhamento se desenvolvem devido à viscosidade. Para a água, que tem baixa viscosidade, esses efeitos são insignificantes, simplificando o movimento do fluido ...

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Differential Analysis of Fluid Flow

Análise Diferencial do Escoamento de Fluidos

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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 same in different directions and does not depend on how the stress is oriented.

Euler's equations come from Newton's second law applied to fluid motion. They describe momentum conservation by linking the change in velocity to the forces on a fluid element. For inviscid flow, those forces are pressure gradients and body forces such as gravity. The equations include density, velocity, pressure, and gravitational acceleration, but they leave out viscous terms.

Even without viscosity, Euler's equations are still nonlinear. That means they are complex because they include convective acceleration, which follows the motion of fluid particles. When the equations are integrated along a streamline, they lead to Bernoulli's equation. Bernoulli's equation connects pressure, velocity, and elevation in inviscid flows and is useful for fluid transport, aerodynamics, and hydrodynamics.

Pressure and Velocity in Inviscid Flow

euler&#39;s equations of motion

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...

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Pressure and Velocity in Inviscid Flow

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