Name: plane potential flow patterns and models
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 23 s
Channel: JoVE

Los flujos de potencial plano simplifican el movimiento del fluido al asumir un flujo irrotacional e incompresible, gobernado por una función de potencial de velocidad y una función de corriente para describir el campo de flujo.
En flujo uniforme, el fluido se mueve a una velocidad constante en una dirección, creando líneas de corriente paralelas y espaciadas uniformemente que son útiles para estimar caudales en canales rectos.
Los flujos de fuente y sumidero implican que el fluido se mueva radialmente hacia afuera desde un punto o converja hacia adentro, creando patrones de flujo simétricos. El agua subterránea que se filtra o drena hacia un pozo ejemplifica estos flujos.
El flujo de vórtice implica un movimiento circular alrededor de un punto central, donde el fluido gira a diferentes velocidades según la distancia desde el centro. Este tipo es relevante en el diseño de aliviaderos para gestionar el agua que cae en espiral por los desagües.
Las redes de flujo combinan líneas de corriente y líneas equipotenciales, lo que ayuda a visualizar patrones de flujo complejos, como las trayectorias de filtración debajo de las presas. Esto ayuda a prevenir el debilitamiento estructural debido a la infiltración de agua.
Estos flujos potenciales son esenciales para diseñar estructuras que interactúan con fluidos, como presas, diques y sistemas de aguas subterráneas, mediante la predicción de patrones de flujo y la gestión eficaz de los recursos hídricos.

flujos potenciales planos

Plane Potential Flows

Los flujos potenciales planos simplifican el movimiento de fluidos al suponer que el fluido es irrotacional e incompresible. Estas características permiten que estos flujos se describan mediante una función de potencial de velocidad, ϕ, que representa la velocidad del flujo en una dirección determinada, y una función de corriente, ψ, que visualiza la trayectoria del flujo, ambas regidas por la ecuación de Laplace. Estos parámetros ayudan a estimar patrones de flujo, distribuciones de velocidad y campos de presión alrededor de varias estructuras hidráulicas. Flujo uniforme El flujo uniforme representa la forma más sencilla de flujo potencial, caracterizado por un fluido que se desplaza en línea recta a una velocidad constante. Las líneas de corriente son rectas, paralelas y equidistantes, lo que permite visualizar claramente el flujo a través de canales o tuberías con velocidad constante. Este tipo de flujo es fundamental en el diseño de canales, tuberías y sistemas de drenaje, ya que el supuesto de velocidad constante facilita la estimación del caudal y el diseño hidráulico. Flujos de fuente y sumidero Los flujos de fuente y sumidero describen flujos radialmente simétricos que se originan en un punto o convergen hacia él. En un flujo de fuente, el fluido se mueve radialmente hacia afuera desde un punto central, mientras que en un flujo de sumidero, converge hacia adentro. Estos flujos se modelan utilizando un parámetro de caudal para representar la fuerza de la fuente o sumidero. Este modelo se utiliza ampliamente en hidrología de aguas subterráneas, donde los flujos de fuente representan la recarga de agua subterránea, como la de un pozo de inyección, y los flujos de sumidero representan la extracción de agua subterránea en un pozo de bombeo. Flujo de vórtice El flujo de vórtice implica que el fluido circula por un punto central y aparece en dos formas: libre y forzado. En un vórtice libre, las partículas se mueven en trayectorias circulares alrededor de un punto central sin fuerza externa, creando un efecto de remolino que se observa a menudo en cuerpos de agua naturales. Este modelo se utiliza para diseñar aliviaderos y sistemas de drenaje que controlan el flujo de agua en espiral para evitar obstrucciones o turbulencias. En un vórtice forzado, una fuerza externa impulsa la rotación del fluido, creando un escenario donde el fluido gira como un cuerpo rígido. Los vórtices forzados se utilizan en tanques de sedimentación y ciertos dispositivos hidráulicos donde la rotación uniforme ayuda a la separación de sedimentos y la mezcla de fluidos. Redes de flujo En las redes de flujo, las líneas de corriente representan la trayectoria del flujo del fluido, mientras que las líneas equipotenciales marcan los puntos de igual potencial hidráulico. Estas líneas se intersecan perpendicularmente, creando un patrón de cuadrícula que ayuda a identificar distribuciones de presión y posibles trayectorias de filtración alrededor de las estructuras. Las redes de flujo se construyen para evaluar la filtración en el suelo o en medios porosos. Las tasas de filtración se calculan analizando cuidadosamente el espaciamiento y la orientación de estas líneas e identificando áreas potenciales de erosión o debilidad estructural.

Flujos potenciales planos

Los flujos de potencial plano simplifican el movimiento del fluido al asumir un flujo irrotacional e incompresible, gobernado por una función de potencial de velocidad y una corriente ...

Education

Educación

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

plane potential flow patterns and models

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 simplest potential flow. The fluid moves in a straight line at a constant velocity. Its streamlines are straight, parallel, and evenly spaced. This model helps in canal, pipeline, and drainage system design because a constant-velocity assumption can support flow rate estimation and hydraulic design.

Source and sink flows show radial motion around a point. In a source flow, fluid moves outward from the center. In a sink flow, fluid moves inward toward the center. A flow rate parameter gives the strength of the source or sink. These flows are used in groundwater hydrology, where a source can represent groundwater recharge, such as from an injection well, and a sink can represent groundwater extraction from a pumping well.

Vortex flow describes fluid that circulates around a center point. It appears as a free vortex or a forced vortex. In a free vortex, particles move in circular paths without an external force, like a whirlpool in natural water. This model helps in spillway and drainage system design to reduce clogging or turbulence. In a forced vortex, an external force causes the fluid to rotate as a rigid body. Forced vortices are used in sedimentation tanks and some hydraulic devices, where steady rotation helps with sediment separation and fluid mixing.

Flow nets combine streamlines and equipotential lines. Streamlines show the path of the fluid, while equipotential lines mark points with equal hydraulic potential. These lines cross at right angles and form a grid pattern. Flow nets are used to study seepage in soil or porous media and to estimate seepage rates. They also help identify pressure distributions, possible seepage paths, and areas where erosion or structural weakness may occur.

Plane Potential Flow Patterns and Models

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...

stream function

Stream Function for Incompressible Flow

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 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...

velocity potential

Velocity Potential in Pipe Flow

Velocity potential in pipe flow describes the motion of fluid in the central region of a long, straight pipe with a uniform cross-section. In this region, the flow is steady, incompressible, and irrotational. Irrotational means the fluid particles do not spin around their own axes. A scalar function called the velocity potential, written as φ, is used to describe this motion. The velocity field V is defined as the gradient of φ. Because the curl of a gradient is always zero, this form of V...

plane potential flows

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...

navier&#8211;stokes equations

Fluid Stress and Flow Equations

Fluid stress and flow equations describe how incompressible Newtonian fluids move under pressure, shear, and gravity. In these fluids, density stays constant, and stress changes linearly with the rate of deformation. The main stress types are normal stress and shear stress. Normal stress depends on pressure acting on the fluid and on deformation rate in specific directions. Shear stress acts along the surface of a fluid layer. It shows how neighboring layers slide past one another, so velocity...

steady, laminar flow between parallel plates

steady-laminar-flow-between-parallel-plates

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...

couette flow

Linear Shear Between Moving Plates

Linear shear between moving plates describes fluid motion in a simple channel with two parallel plates. One plate stays fixed, and the other moves at a constant speed. This setup helps show how viscosity and incompressible flow shape fluid motion under the Navier-Stokes equations. The model uses a steady, laminar, incompressible flow with no pressure gradient in the flow direction. The x-axis points along the moving direction of the upper plate, and the y-axis is perpendicular to both plates.

steady, laminar flow in circular tubes

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...

design example: flow of oil through circular pipes

design-example-flow-of-oil-through-circular-pipes

Pressure Drop in Oil Pipe Design

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...

key terms and concepts

Explore plane potential flow patterns, including uniform, source, sink, and vortex flows, plus flow nets used to study seepage and pressure fields.

Plane Potential Flow Patterns and Models | 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

Plane Potential Flow Patterns and Models

Description

Transcript

Tags