Name: irrotational flow near boundaries
Uploaded: 2025-02-13T15:43:25.000Z
Duration: 1 min 28 s
Channel: JoVE

O fluxo irrotacional refere-se ao movimento de partículas de fluido que não giram ao longo do caminho do fluxo, caracterizado por um campo de velocidade com ondulação zero e sem vorticidade.
Um fluxo uniforme com apenas um componente de velocidade diferente de zero, uma constante u = U, é um exemplo de fluxo irrotacional porque não possui gradientes de velocidade.
Quando um objeto sólido é introduzido em um fluxo uniforme, o fluxo permanece irrotacional, exceto perto dos limites. Perto de sua superfície, a velocidade aumenta drasticamente a partir de zero, criando gradientes acentuados e tensão de cisalhamento significativa.
No caso de um fluxo verdadeiramente invíscido, o fluxo deslizaria além do limite, preservando o movimento irrotacional. No entanto, em fluidos reais, a viscosidade forma uma camada limite perto de superfícies fixas, produzindo efeitos rotacionais e às vezes causando separação a jusante.
No fluxo do tubo, a região de entrada inicialmente exibe um núcleo irrotacional com fluxo uniforme, mas à medida que uma camada limite se forma ao longo da parede do tubo e engrossa, ela faz a transição para uma região totalmente desenvolvida dominada por forças viscosas.
Assumindo que o fluxo é irrotacional, incompressível, estável e invíscido, a equação de Bernoulli pode ser aplicada no campo de fluxo.

fluxo irrotacional

Irrotational Flow

O fluxo irrotacional é caracterizado pelo movimento do fluido onde as partículas não giram em torno de seus eixos, resultando em vorticidade zero. Para um fluxo ser irrotacional, a curvatura do campo de velocidade deve ser zero. Isso impõe condições específicas aos gradientes de velocidade. Por exemplo, para manter rotação zero em torno do eixo z, a condição de gradiente:

<img alt="Equation 1" src="/files/ftp_upload/18059/18059_Equation_1.svg" style="text-align: center; height: 27px;">

Deve ser satisfeita, juntamente com condições semelhantes para outros eixos:

<img alt="Equation 2" src="/files/ftp_upload/18059/18059_Equation_2.svg" style="text-align: center; height: 27px;">

Um fluxo uniforme, onde u é constante e v e w são ambos zero, satisfaz essas condições e serve como um exemplo simples de fluxo irrotacional. No entanto, quando um objeto sólido é introduzido, a irrotacionalidade persiste apenas longe do objeto. Perto do limite, a velocidade aumenta acentuadamente de zero (devido à condição de não deslizamento) para o valor de fluxo livre, criando tensão de cisalhamento significativa e uma camada limite em fluidos viscosos.

Quando o fluido entra em um tubo de um grande reservatório, o fluxo inicial é quase uniforme, resultando em um núcleo irrotacional onde a distribuição de velocidade é plana. À medida que o fluido se move a jusante, uma camada limite se forma ao longo das paredes do tubo devido à viscosidade, fazendo com que o perfil de velocidade desenvolva gradientes que, em última análise, levam a um perfil parabólico totalmente desenvolvido. Nesta região totalmente desenvolvida, os efeitos rotacionais dominam perto das paredes, enquanto um núcleo central pode permanecer aproximadamente irrotacional.

Na região irrotacional inicial do fluxo do tubo, a equação de Bernoulli

<img alt="Equation 3" src="/files/ftp_upload/18059/18059_Equation_3.svg" style="text-align: center; height: 27px;">

Pode ser aplicada entre pontos ao longo de uma linha de corrente, pois as condições de incompressibilidade, fluxo invíscido e irrotacionalidade se mantêm. No entanto, à medida que a camada limite cresce e os efeitos rotacionais se tornam significativos perto das paredes, as suposições da equação de Bernoulli se quebram. Isso significa que a equação de Bernoulli é aplicável apenas na região de entrada e no núcleo irrotacional, mas não na região rotacional totalmente desenvolvida, onde os efeitos de viscosidade dominam.

Fluxo irrotacional

O fluxo irrotacional refere-se ao movimento de partículas de fluido que não giram ao longo do caminho do fluxo, caracterizado por um campo de velocidade com ondulação zero e ...

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Differential Analysis of Fluid Flow

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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 far from the object. Near the surface, the fluid speed rises sharply from zero because of the no-slip condition. This creates strong shear stress and a boundary layer in viscous fluids.

A similar change happens when fluid enters a pipe from a large reservoir. At first, the flow is nearly uniform, so the center region forms an irrotational core with a flat velocity profile. Farther downstream, viscosity causes boundary layers to grow along the pipe walls.

As the flow continues, the velocity profile develops more gradient and becomes fully developed and parabolic. In that region, rotational effects are strongest near the walls, while the center may still be approximately irrotational. Bernoulli's equation can apply in the entrance region and in the irrotational core, where the flow is incompressible, inviscid, and irrotational. It no longer applies well in the fully developed region, where viscosity and rotation dominate.

Irrotational Flow Near Boundaries

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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...

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Irrotational Flow Near Boundaries

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