Name: parabolic flow in circular tubes
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 23 s
Channel: JoVE

Considere el flujo constante e incompresible a través de un tubo cilíndrico recto de radio constante R, conocido como flujo de Hagen-Poiseuille.
La geometría cilíndrica permite el uso de las coordenadas r, θ y z para mediciones radiales, angulares y axiales.
El fluido que fluye paralelo al eje del tubo tiene un componente de velocidad puramente axial y varía solo con la distancia radial.
Estas condiciones simplifican las ecuaciones de Navier-Stokes, revelando un perfil de velocidad parabólica que muestra que la velocidad es más alta en el centro y disminuye hacia las paredes, llegando a cero en el límite.
Esto demuestra el flujo laminar, donde las partículas de fluido se mueven suavemente en capas organizadas.
La integración de este perfil sobre la sección transversal del tubo da la ley de Poiseuille, que expresa el caudal Q como dependiente de la cuarta potencia del radio del tubo, la viscosidad del fluido y el gradiente de presión.
La velocidad media V, calculada a partir de Q, es la mitad de la velocidad máxima observada en el centro del tubo.
Esta distribución de velocidad confirma que el flujo es más alto en el centro y disminuye parabólicamente a cero en la pared.

flujo laminar constante en tubos circulares

Steady, Laminar Flow in Circular Tubes

El flujo de Hagen-Poiseuille describe el flujo constante e incompresible de un fluido viscoso a través de un tubo cilíndrico con un radio constante R. Este perfil de flujo se aplica a menudo para comprender el transporte de fluidos en canales estrechos, como los capilares. Sirve como un ejemplo básico de flujo laminar. En este modelo, las coordenadas cilíndricas (r,θ,z) se utilizan para describir las dimensiones radial (r), angular (θ) y axial (z) dentro del tubo. Para el flujo de Hagen-Poiseuille, el perfil de velocidad es puramente axial, lo que significa que el vector de velocidad apunta solo a lo largo del eje z y varía únicamente con la distancia radial r desde el centro del tubo. Las ecuaciones que rigen el movimiento de fluidos, las ecuaciones de Navier-Stokes, se simplifican en estas condiciones. Sin componentes de velocidad angular o radial, la velocidad axial vz(r) surge como una función de r únicamente. La solución de las ecuaciones reducidas de Navier-Stokes produce un perfil de velocidad parabólico: <img alt="Equation 1" src="/files/ftp_upload/18065/18065_Equation 1.svg" style="text-align: center; height: 27px;"> Este perfil demuestra que la fricción viscosa disminuye la velocidad del fluido desde el máximo en el centro hasta cero en la pared del tubo. Esta velocidad cero en el límite, conocida como condición de no deslizamiento, resulta de la fricción entre el fluido y la pared del tubo. En consecuencia, el flujo es laminar, con partículas de fluido que se mueven en capas paralelas sin mezcla lateral. La integración del perfil de velocidad sobre el área de la sección transversal del tubo produce el caudal volumétrico Q, conocido como ley de Poiseuille: <img alt="Equation 2" src="/files/ftp_upload/18065/18065_Equation 2.svg" style="text-align: center; height: 27px;"> Donde ΔP es la diferencia de presión a lo largo de la longitud L del tubo y μ es la viscosidad dinámica del fluido. Esta relación muestra que Q es muy sensible al radio del tubo, aumentando con la cuarta potencia de R. De ello se deduce que incluso un ligero aumento del radio aumenta significativamente el caudal, un principio fundamental en las aplicaciones de transporte de fluidos. Según la ley de Poiseuille, la velocidad media V del fluido se puede expresar como: <img alt="Equation 3" src="/files/ftp_upload/18065/18065_Equation 3.svg" style="text-align: center; height: 27px;"> Esta velocidad media es exactamente la mitad de la velocidad máxima en el centro del tubo, lo que confirma la distribución parabólica de la velocidad y demuestra la naturaleza predecible y estratificada del flujo laminar en un tubo cilíndrico.

Flujo laminar constante en tubos circulares

Considere el flujo constante e incompresible a través de un tubo cilíndrico recto de radio constante R, conocido como flujo de Hagen-Poiseuille.
El cilindro ...

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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

parabolic flow in circular tubes

Parabolic flow in circular tubes describes the steady, incompressible motion of a viscous fluid through a tube with a constant radius. This Hagen-Poiseuille flow is a classic example of laminar flow. It is often used to study fluid transport in narrow channels, including capillaries.

Cylindrical coordinates are used to describe the tube. The radial direction is r, the angular direction is θ, and the axial direction is z. In this flow, the velocity is purely axial. That means the fluid moves only along the z-axis and changes with distance r from the center of the tube.

Under these conditions, the Navier-Stokes equations become simpler. With no angular or radial velocity components, the axial velocity vz(r) depends only on r. Solving the reduced equations gives a parabolic velocity profile. The fluid moves fastest at the center and slows toward the wall because viscous drag reduces the speed.

At the tube wall, the velocity is zero. This is the no-slip condition, which comes from friction between the fluid and the wall. The result is laminar flow, where fluid particles travel in parallel layers with no lateral mixing.

Integrating the velocity profile over the tube cross section gives the volumetric flow rate Q. This is Poiseuille’s law. In this relation, ΔP is the pressure difference across tube length L, and μ is the fluid’s dynamic viscosity. The flow rate depends strongly on the tube radius and increases with the fourth power of R, so even a small increase in radius can greatly raise Q.

Poiseuille’s law also gives the mean velocity V of the fluid. The average velocity is exactly half of the maximum velocity at the tube center. This matches the parabolic profile and shows the predictable, layered nature of flow in a circular tube.

Parabolic Flow in Circular Tubes

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steady, laminar flow in circular tubes

Parabolic flow in circular tubes describes the steady, incompressible motion of a viscous fluid through a tube with a constant radius. This Hagen-Poiseuille flow is a classic example of laminar flow. It is often used to study fluid transport in narrow channels, including capillaries. Cylindrical coordinates are used to describe the tube. The radial direction is r, the angular direction is θ, and the axial direction is z. In this flow, the velocity is purely axial. That means the fluid moves...

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key terms and concepts

Explore how Hagen-Poiseuille flow creates a parabolic velocity profile in circular tubes, with no-slip at the wall and Poiseuille’s law for flow rate.

Parabolic Flow in Circular Tubes | 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.

civil engineering

Parabolic Flow in Circular Tubes

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