Name: pressure and speed in bernoulli's equation
Uploaded: 2025-02-13T15:43:14.000Z
Duration: 1 min 30 s
Channel: JoVE

La ecuación de Bernoulli describe el comportamiento de los fluidos en movimiento relacionando la presión, la velocidad y la elevación a lo largo de una línea de corriente.
Se basa en el principio de conservación de energía, asumiendo un flujo constante, fluidos incompresibles y sin viscosidad, lo que significa que no hay fuerzas de fricción.
El término de presión representa la fuerza que ejerce el fluido en un punto específico.
El término de velocidad representa la energía cinética del fluido, lo que indica que la presión disminuye a medida que aumenta la velocidad del fluido.
El término de elevación refleja la energía potencial del fluido en función de su posición vertical en relación con un punto de referencia.
Este principio se aplica a situaciones del mundo real, como los sistemas de distribución de agua, los aliviaderos de presas y los medidores Venturi.
En los sistemas de distribución de agua, la ecuación de Bernoulli predice cómo cae la presión a medida que el agua fluye a través de tuberías de diferentes diámetros, lo que garantiza un suministro eficiente a través de las redes urbanas.
La ecuación de Bernoulli explica cómo la velocidad del agua aumenta y la presión disminuye a medida que fluye hacia abajo en los aliviaderos de las presas, lo que ayuda a los ingenieros a diseñar estructuras que puedan manejar de manera segura los caudales variables.
Los medidores Venturi, comúnmente utilizados en los sistemas de alcantarillado, miden los caudales mediante la detección de diferencias de presión entre las secciones de la tubería, lo que garantiza una gestión eficaz de las aguas residuales.

ecuación de bernoulli para el flujo a lo largo de una línea de corriente

Bernoulli's Equation for Flow Along a Streamline

La ecuación de Bernoulli relaciona la conservación de la energía en un fluido que se mueve a lo largo de una línea de corriente. La ecuación se aplica a fluidos incompresibles y no viscosos bajo flujo constante. Para un flujo de este tipo, se aplica la segunda ley de Newton a un pequeño elemento de fluido, que experimenta fuerzas debido a las diferencias de presión, la gravedad y las variaciones de velocidad. El equilibrio de fuerzas conduce a la siguiente forma de la ecuación de Bernoulli: <img alt="Equation 1" src="/files/ftp_upload/18033/18033_Equation_1.svg" style="text-align: center; height: 26px;"> Aquí, P es la presión, ρ es la densidad del fluido, v es la velocidad, g denota la aceleración debido a la gravedad y la elevación se denota por h. Cada término en esta ecuación representa la energía por unidad de volumen del fluido. Considere el agua que fluye a través de una tubería horizontal con dos secciones de diferentes diámetros. En el punto 1, la tubería tiene un diámetro grande, mientras que en el punto 2, la tubería se estrecha. La ecuación de Bernoulli nos dice que si la velocidad del agua aumenta en la sección más estrecha (punto 2), la presión debe disminuir para conservar energía a lo largo de la línea de corriente. Al aplicar la ecuación de Bernoulli a las secciones de las tuberías, obtenemos: <img alt="Equation 2" src="/files/ftp_upload/18033/18033_Equation_2.svg" style="text-align: center; height: 26px;"> El principio de Bernoulli es crucial para comprender y diseñar sistemas de flujo de fluidos. Por ejemplo, en las redes de distribución de agua, las variaciones en los diámetros de las tuberías provocan cambios de presión que afectan la eficiencia del flujo. Como dicta la ecuación, una tubería más estrecha aumenta la velocidad al tiempo que reduce la presión, lo que garantiza un suministro constante en los sistemas urbanos. En los aliviaderos de las presas, la energía potencial del fluido debido a la elevación se convierte en energía cinética a medida que el agua desciende. Esto da como resultado un aumento de la velocidad y una caída correspondiente de la presión, un fenómeno que se utiliza para diseñar aliviaderos capaces de gestionar de forma segura las distintas tasas de descarga.

Ecuación de Bernoulli para el flujo a lo largo de una línea de corriente

La ecuación de Bernoulli describe el comportamiento de los fluidos en movimiento relacionando la presión, la velocidad y la elevación a lo largo de una línea de corriente.
Se basa en el ...

bernoulli-s-equation-for-flow-along-a-streamline

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pressure and speed in bernoulli's equation

Bernoulli's equation links pressure, speed, and height in a moving fluid along a streamline. It is used for incompressible, inviscid fluids under steady flow. The idea comes from applying Newton's second law to a small fluid element. That element feels forces from pressure differences, gravity, and changes in velocity.

The resulting equation shows how fluid energy is shared. In the equation, P is pressure, ρ is fluid density, v is velocity, g is the acceleration due to gravity, and h is elevation. Each term represents energy per unit volume of the fluid. This makes Bernoulli's equation a useful way to track how energy changes as fluid moves.

A simple pipe example shows the main effect. Water flows through a horizontal pipe with two sections. Point 1 has a large diameter, and point 2 has a narrower diameter. When the water speeds up at the narrow section, the pressure must drop to keep energy conserved along the streamline.

Bernoulli's principle also helps explain real flow systems. In water distribution networks, changes in pipe diameter create pressure changes that affect flow efficiency. A narrower pipe raises velocity and lowers pressure, which helps support a steady supply across urban systems. In dam spillways, water loses potential energy as it falls. That energy turns into kinetic energy, so velocity increases and pressure decreases. Engineers use this effect to design spillways that can handle changing discharge rates safely.

Pressure and Speed in Bernoulli's Equation

pressure-and-speed-in-bernoullis-equation

bernoulli's equation for flow along a streamline

Bernoulli's equation links pressure, speed, and height in a moving fluid along a streamline. It is used for incompressible, inviscid fluids under steady flow. The idea comes from applying Newton's second law to a small fluid element. That element feels forces from pressure differences, gravity, and changes in velocity. The resulting equation shows how fluid energy is shared. In the equation, P is pressure, ρ is fluid density, v is velocity, g is the acceleration due to gravity, and h is...

bernoulli's equation for flow normal to a streamline

bernoulli-s-equation-for-flow-normal-to-a-streamline

Pressure Changes Across Curved Streamlines

Bernoulli's equation for flow normal to a streamline describes how pressure changes across curved streamlines. When a fluid follows a curved path, the outer side of the curve experiences centrifugal force, which pushes the fluid outward. The pressure is therefore higher on the inner side, near the center of curvature, and lower farther out. The size of this pressure difference depends on the fluid's velocity and the radius of curvature. In flows with nearly straight streamlines, the pressure...

bernoulli's equation: problem solving

Venturi Meter Flow Rate from Pressure

A Venturi meter measures fluid flow rate in a pipeline by using pressure changes and Bernoulli's equation. In a sewage system, it can be used to determine wastewater flow rate by reading the pressure difference across the meter. The narrowed throat makes the fluid speed up, and that change in speed is linked to pressure drop. The first step is to find the cross-sectional areas of the pipe and the Venturi throat. These areas are needed to interpret the pressure difference shown on the pressure...

static, stagnation, dynamic and total pressure

static-stagnation-dynamic-and-total-pressure

Pitot-Static Measurement in Bernoulli Flow

Static pressure, dynamic pressure, stagnation pressure, and total pressure are key ideas in fluid dynamics. They are often explained with Bernoulli's equation. In that equation, p is static pressure, 1/2ρV^2 is dynamic pressure, γz is hydrostatic pressure or potential energy pressure, and pT is total pressure. For incompressible flow, the total pressure stays constant along a streamline. Static pressure is the pressure a fluid exerts when it is at rest, or when flowing fluid is brought to rest...

free jet

Liquid Speed from Reservoir Outlets

Free jets show how liquid moves after leaving a reservoir through an opening and flowing into the air without resistance. The jet speed is found with Bernoulli’s principle, and it depends on the height of liquid above the opening. This relationship assumes atmospheric pressure at both the reservoir surface and the jet exit. The liquid column’s height controls the speed at the nozzle because the fluid’s potential energy changes into kinetic energy during flow. As the liquid leaves the...

continuity equation

Fluid Flow and Area Changes

Fluid flow and area changes are linked by the continuity equation. For a steady flow of an incompressible fluid in a confined system, the mass flow rate stays constant. This idea is useful in nozzles, syringes, and pipes where the cross-sectional area changes. The mass flow rate is written as an equation that connects density, area, and velocity. For incompressible flow, the density stays the same, so the equation becomes simpler. When the area gets smaller, the fluid speed must increase. When...

energy line and hydraulic gradient line

Fluid Head Profiles in Pipes and Channels

Fluid head profiles in pipes and channels show how pressure, speed, and height change in a flowing fluid. These profiles come from Bernoulli's equation for steady, incompressible, inviscid flow. In that equation, total head includes pressure head, velocity head, and elevation head. The energy line (EL) shows the total head available in the flow. It sits above the datum and includes all three energy parts. Under ideal conditions, the EL stays horizontal because the total energy does not change...

design example: designing water slide

Water Slide Speed and Bernoulli's Principle

Water slide speed is controlled by Bernoulli's principle and the height of the slide. Engineers use these ideas to keep the ride exciting while making sure the water stays safe for riders. As water moves downhill, gravity makes it speed up. The water at the bottom depends on the height it starts from. A taller slide gives the water more potential energy at the top. That energy changes into kinetic energy as the water descends, so the flow becomes faster. Bernoulli's principle helps describe...

key terms and concepts

Learn how Bernoulli's equation links pressure, speed, and height in flowing fluids, with pipe and dam spillway examples for high school science.

Pressure and Speed in Bernoulli's Equation | 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

Pressure and Speed in Bernoulli's Equation

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