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

El flujo irrotacional se refiere al movimiento de las partículas de fluido que no giran a lo largo de la trayectoria del flujo, caracterizado por un campo de velocidad con rizo cero y sin vorticidad.
Un flujo uniforme con un solo componente de velocidad distinto de cero, una constante u = U, es un ejemplo de flujo irrotacional porque carece de gradientes de velocidad.
Cuando un objeto sólido se introduce en un flujo uniforme, el flujo permanece irrotacional excepto cerca de los límites. Cerca de su superficie, la velocidad aumenta bruscamente desde cero, creando pendientes pronunciadas y un esfuerzo cortante significativo.
En el caso de un flujo verdaderamente invisible, el flujo se deslizaría más allá del límite, preservando el movimiento de rotación. Sin embargo, en los fluidos reales, la viscosidad forma una capa límite cerca de las superficies fijas, produciendo efectos de rotación y, a veces, causando una separación aguas abajo.
En el flujo de la tubería, la región de entrada inicialmente exhibe un núcleo irrotacional con flujo uniforme, pero a medida que se forma una capa límite a lo largo de la pared de la tubería y se engrosa, pasa a una región completamente desarrollada dominada por fuerzas viscosas.
Suponiendo que el flujo es irrotacional, incompresible, constante e invisible, la ecuación de Bernoulli se puede aplicar en el campo de flujo.

flujo irrotacional

Irrotational Flow

El flujo irrotacional se caracteriza por el movimiento del fluido en el que las partículas no rotan alrededor de sus ejes, lo que da como resultado una vorticidad cero. Para que un flujo sea irrotacional, el rizo del campo de velocidad debe ser cero. Esto impone condiciones específicas a los gradientes de velocidad. Por ejemplo, para mantener una rotación cero sobre el eje z, la condición del gradiente: <img alt="Equation 1" src="/files/ftp_upload/18059/18059_Equation_1.svg" style="text-align: center; height: 27px;"> Deben cumplirse, junto con condiciones similares para los demás ejes: <img alt="Equation 2" src="/files/ftp_upload/18059/18059_Equation_2.svg" style="text-align: center; height: 27px;"> Un flujo uniforme, donde u es constante y v y w son ambos cero, satisface estas condiciones y sirve como un ejemplo simple de flujo irrotacional. Sin embargo, cuando se introduce un objeto sólido, la irrotacionalidad solo persiste lejos del objeto. Cerca del límite, la velocidad aumenta bruscamente desde cero (debido a la condición de no deslizamiento) hasta el valor de flujo libre, lo que crea una tensión de corte significativa y una capa límite en fluidos viscosos. Cuando un fluido ingresa en una tubería desde un gran depósito, el flujo inicial es casi uniforme, lo que da lugar a un núcleo irrotacional con una distribución de velocidad plana. A medida que el fluido avanza aguas abajo, se forma una capa límite a lo largo de las paredes de la tubería debido a la viscosidad, lo que provoca que el perfil de velocidad desarrolle gradientes que finalmente derivan en un perfil parabólico completamente desarrollado. En esta región completamente desarrollada, los efectos rotacionales predominan cerca de las paredes, mientras que en el núcleo central puede mantenerse un comportamiento aproximadamente irrotacional. En la región irrotacional inicial del flujo de la tubería, la ecuación de Bernoulli <img alt="Equation 3" src="/files/ftp_upload/18059/18059_Equation_3.svg" style="text-align: center; height: 27px;"> Se puede aplicar entre puntos a lo largo de una línea de corriente cuando se cumplen las condiciones de incompresibilidad, flujo no viscoso e irrotacionalidad. Sin embargo, a medida que la capa límite crece y los efectos rotacionales se vuelven significativos cerca de las paredes, las suposiciones de la ecuación de Bernoulli se rompen. Esto significa que la ecuación de Bernoulli solo es aplicable en la región de entrada y el núcleo irrotacional, pero no en la región rotacional completamente desarrollada donde dominan los efectos de la viscosidad.

Flujo irrotacional

El flujo irrotacional se refiere al movimiento de partículas de fluido que no giran a lo largo de la trayectoria del flujo, caracterizado por un campo de velocidad con rizo cero y ...

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Civil Engineering

Ingeniería Civil

Unit 1

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Differential Analysis of Fluid Flow

Análisis Diferencial del Flujo de Fluidos

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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

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...

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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...

irrotational flow

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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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...

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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...

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Learn how irrotational flow behaves near solids and in pipe entrance flow, including boundary layers, rotational effects, and when Bernoulli's equation applies.

Irrotational Flow Near Boundaries | 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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Irrotational Flow Near Boundaries

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