Name: laminar flow profile between parallel plates
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 17 s
Channel: JoVE

El flujo laminar constante entre dos placas paralelas describe el movimiento del fluido en un canal estrecho y confinado, a menudo utilizado para modelar sistemas de fluidos simples.
Para el flujo entre dos placas fijas, las ecuaciones de Navier-Stokes se simplifican ya que la velocidad varía solo perpendicular a las placas, sin aceleración a lo largo de la dirección del flujo.
Esto conduce a un perfil de velocidad parabólica, donde el fluido se mueve más rápido en el centro y se ralentiza a cero en las placas debido a la fricción, conocida como condición de no deslizamiento.
El caudal entre las placas depende del gradiente de presión, la viscosidad del fluido y la separación de las placas; ensanchar el espacio o aumentar el gradiente de presión mejora el flujo.
La velocidad media del flujo también está relacionada con la caída de presión, siendo la velocidad máxima en el centro del canal 1,5 veces la velocidad media.
Este análisis sigue siendo válido solo para números de Reynolds bajos, lo que indica condiciones laminares, y falla para flujos turbulentos con números de Reynolds altos.
Las aplicaciones de este análisis incluyen canales de riego, flujo de agua subterránea y cuencas de sedimentación en plantas de tratamiento de agua, donde existen condiciones laminares.

flujo laminar constante entre placas paralelas

Steady, Laminar Flow Between Parallel Plates

Comprender el flujo laminar constante entre placas paralelas es esencial para analizar y diseñar el flujo en canales rectangulares estrechos, que se encuentran comúnmente en varios sistemas de conducción y drenaje de agua. Las ecuaciones de Navier-Stokes gobiernan el movimiento de fluidos y, por lo general, son difíciles de resolver debido a su no linealidad. Sin embargo, es posible realizar simplificaciones en ciertos casos, como el flujo laminar constante entre placas paralelas. Para este escenario, suponemos un flujo laminar constante e incompresible. Considerando dos placas horizontales alineadas a lo largo del eje x y separadas por una distancia '2h', con el eje y perpendicular a las placas, se supone que el movimiento del fluido es paralelo. Aquí, la ecuación de continuidad indica que no hay cambios en la velocidad a lo largo del eje x, y las ecuaciones de Navier-Stokes se reducen de la siguiente manera: <img alt="Equation 1" src="/files/ftp_upload/18063/18063_Equation_1.svg" style="text-align: center; height: 30px;"> Las ecuaciones en las direcciones y y z no muestran gradientes de presión a lo largo de estos ejes, lo que indica que la presión varía hidrostáticamente en la dirección y, lo que permite que la integración produzca: <img alt="Equation 2" src="/files/ftp_upload/18063/18063_Equation_2.svg" style="text-align: center; height: 12px;"> Para placas paralelas con un gradiente de presión a lo largo del eje x, la ecuación se simplifica: <img alt="Equation 3" src="/files/ftp_upload/18063/18063_Equation_3.svg" style="text-align: center; height: 30px;"> Al integrar dos veces y aplicar condiciones de contorno (u = 0 en y = +h e y = -h), obtenemos: <img alt="Equation 4" src="/files/ftp_upload/18063/18063_Equation_4.svg" style="text-align: center; height: 30px;"> Esta expresión revela que el perfil de velocidad a través del espacio entre las placas es parabólico, con una velocidad máxima en y = 0, a mitad de camino entre las placas. El caudal volumétrico a través de una unidad de ancho de las placas se obtiene integrando el perfil de velocidad a lo largo del espacio. Comprender el flujo laminar entre placas paralelas tiene aplicaciones prácticas en el flujo de aguas subterráneas, el tratamiento de aguas residuales y la lubricación. Por ejemplo, este modelo puede aproximar el flujo en capas de suelo, donde el agua se mueve entre partículas de suelo como el flujo entre placas. Conocer el caudal y la distribución de la velocidad ayuda a los ingenieros a diseñar sistemas de drenaje eficientes y predecir el movimiento de las aguas subterráneas.

Flujo laminar constante entre placas paralelas

El flujo laminar constante entre dos placas paralelas describe el movimiento del fluido en un canal estrecho y confinado, a menudo utilizado para modelar sistemas de fluidos simples.
Para...

steady-laminar-flow-between-parallel-plates

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JoVE Core

Civil Engineering

Ingeniería Civil

Unit 1

Unidad 1

Differential Analysis of Fluid Flow

Análisis Diferencial del Flujo de Fluidos

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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 becomes simpler because the flow is steady, incompressible, and laminar. Two horizontal plates are placed along the x-axis, and the gap between them is 2h. The y-axis is perpendicular to the plates, and the fluid moves parallel to the plates.

With these assumptions, the continuity equation shows that the velocity does not change along the x-axis. The Navier-Stokes equations also simplify in the y and z directions. They show no pressure gradient along those axes, so pressure changes hydrostatically in the y-direction. After integration, the x-direction equation includes the pressure gradient along the plates.

Solving that equation requires integrating twice and applying the no-slip boundary conditions, where u = 0 at y = +h and y = -h. The result is a parabolic velocity profile across the gap. The fluid moves fastest at y = 0, the midpoint between the plates. The volumetric flow rate for a unit width of the plates is then found by integrating the velocity profile across the space.

This flow model has practical uses in groundwater flow, wastewater treatment, and lubrication. It can also represent water moving through soil layers, where the flow resembles movement between plates. Engineers use the velocity distribution and flow rate to help design drainage systems and predict groundwater movement.

Laminar Flow Profile Between Parallel Plates

laminar-flow-profile-between-parallel-plates

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Learn how steady laminar flow between parallel plates leads to a parabolic velocity profile, pressure-gradient behavior, and flow-rate calculations.

Laminar Flow Profile Between Parallel Plates | JoVE K12

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Laminar Flow Profile Between Parallel Plates

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