Name: pressure and velocity in inviscid flow
Uploaded: 2025-02-13T15:43:25.000Z
Duration: 1 min 28 s
Channel: JoVE

En un fluido en movimiento, se desarrollan tensiones de cizallamiento debido a la viscosidad. Para el agua, que tiene baja viscosidad, estos efectos son insignificantes, lo que simplifica el análisis del movimiento del fluido.
Cuando los esfuerzos cortantes son insignificantes, el fluido se considera invisible o sin fricción. En los fluidos invisibles, la tensión normal es la misma en todas las direcciones, lo que significa que la presión es independiente de la dirección de la tensión.
La presión es el negativo de la tensión normal, lo que garantiza que las tensiones de compresión den como resultado un valor de presión positiva.
Las ecuaciones generales de movimiento para el flujo invisible, conocidas como ecuaciones de Euler, describen la conservación del momento. Estas ecuaciones representan la segunda ley de Newton aplicada a un elemento fluido, relacionando los cambios de velocidad con las fuerzas que actúan sobre el fluido.
Las ecuaciones de Euler tienen en cuenta los gradientes de presión, las fuerzas corporales como la gravedad y las aceleraciones, tanto locales como convectivas, que impulsan los cambios en la velocidad del fluido.
Descuidan las fuerzas viscosas, simplificando el análisis, pero siguen siendo difíciles de resolver debido a los términos de velocidad no lineal en las ecuaciones diferenciales parciales.
La integración de las ecuaciones de Euler a lo largo de una línea de corriente deriva la ecuación de Bernoulli, que proporciona información sobre las variaciones de presión, velocidad y elevación en flujos invisibles, lo que la convierte en una herramienta clave en mecánica de fluidos.

ecuaciones de movimiento de euler

Euler&#39;s Equations of Motion

En mecánica de fluidos, las tensiones de corte surgen de la viscosidad, que representa la resistencia interna de un fluido a la deformación. Para fluidos de baja viscosidad, como el agua, estas tensiones son mínimas, lo que simplifica el análisis del flujo al permitir que el fluido se trate como no viscoso o sin fricción. En un fluido no viscoso, las tensiones de corte están ausentes, dejando solo tensiones normales, que actúan perpendicularmente a los elementos del fluido. Cabe destacar que la presión, definida como el negativo de la tensión normal, permanece uniforme en diferentes direcciones y no se ve afectada por la orientación de la tensión. El movimiento de fluidos no viscosos está regido por las ecuaciones de Euler, derivadas de la segunda ley de Newton aplicada a la dinámica de fluidos. Estas ecuaciones describen la conservación del momento relacionando la tasa de cambio de velocidad con las fuerzas que actúan sobre un elemento de fluido. Para un fluido no viscoso, las fuerzas relevantes incluyen gradientes de presión y fuerzas del cuerpo, como la gravedad. Las ecuaciones de Euler expresan el equilibrio de estas fuerzas, excluyendo los términos viscosos, como: <img alt="Equation 1" src="/files/ftp_upload/18057/18057_Equation_1.svg" style="text-align: center; height: 30px;"> donde ρ es la densidad del fluido, v es el vector de velocidad, p es la presión y g​ representa la aceleración gravitacional. Si bien las ecuaciones de Euler ignoran la viscosidad, siguen siendo complejas debido a sus términos no lineales, que dan cuenta de la aceleración convectiva de las partículas del fluido. Cuando se integran a lo largo de una línea de corriente, estas ecuaciones dan como resultado la ecuación de Bernoulli, que describe una relación fundamental en la mecánica de fluidos, que vincula la presión, la velocidad y la elevación para flujos no viscosos. La ecuación de Bernoulli es una herramienta poderosa para analizar la distribución de energía dentro de los flujos de fluidos, lo que respalda las aplicaciones en el transporte de fluidos, la aerodinámica y la hidrodinámica.

Ecuaciones de movimiento de Euler

En un fluido en movimiento, se desarrollan tensiones de cizallamiento debido a la viscosidad. Para el agua, que tiene baja viscosidad, estos efectos son insignificantes, simplificando el movimiento del fluido ...

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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

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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 same in different directions and does not depend on how the stress is oriented.

Euler's equations come from Newton's second law applied to fluid motion. They describe momentum conservation by linking the change in velocity to the forces on a fluid element. For inviscid flow, those forces are pressure gradients and body forces such as gravity. The equations include density, velocity, pressure, and gravitational acceleration, but they leave out viscous terms.

Even without viscosity, Euler's equations are still nonlinear. That means they are complex because they include convective acceleration, which follows the motion of fluid particles. When the equations are integrated along a streamline, they lead to Bernoulli's equation. Bernoulli's equation connects pressure, velocity, and elevation in inviscid flows and is useful for fluid transport, aerodynamics, and hydrodynamics.

Pressure and Velocity in Inviscid Flow

euler&#39;s equations of motion

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

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irrotational flow

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velocity potential

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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

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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

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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

Learn how pressure, velocity, and gravity shape inviscid fluid motion through Euler's equations, and how they lead to Bernoulli's equation along a streamline.

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civil engineering

Pressure and Velocity in Inviscid Flow

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