Name: fluid flow and area changes
Uploaded: 2026-01-30T03:08:26.000Z
Duration: 1 min 28 s
Channel: JoVE

La ecuación de continuidad se deriva del principio de conservación de la masa, que establece que la masa del fluido que entra y sale de un sistema permanece constante.
Para fluidos incompresibles, el producto del área de flujo y la velocidad permanece constante a lo largo de la trayectoria del flujo, ajustándose a los cambios en las secciones transversales.
A medida que disminuye el área de la sección transversal, la velocidad del fluido aumenta para mantener un caudal constante.
Esta relación es crucial para analizar sistemas como tuberías de agua, gestión de aguas pluviales y canales abiertos, lo que garantiza la estabilidad y la eficiencia en diversas aplicaciones de flujo de fluidos.
En los sistemas de suministro de agua, la ecuación de continuidad ayuda a mantener una distribución constante al predecir los cambios de velocidad cuando las tuberías se estrechan, lo cual es esencial para evitar caídas de presión.
Ayuda a diseñar cuencas de retención para la gestión de aguas pluviales. Cuando la escorrentía ingresa a la cuenca durante una tormenta, la tasa de salida debe coincidir con la tasa de entrada, ajustada para evitar inundaciones aguas abajo.
En el caso de los canales abiertos, como ríos o canales, la ecuación de continuidad ayuda a comprender cómo las variaciones de anchura o profundidad afectan a los niveles de agua y a la velocidad del flujo. Esta comprensión es vital para diseñar sistemas efectivos de control de inundaciones y navegación.

ecuación de continuidad

La ecuación de continuidad establece que el caudal másico debe permanecer constante en un flujo constante de un fluido incompresible dentro de un sistema confinado. Este principio se aplica a sistemas donde el fluido fluye a través de áreas transversales variables, como boquillas, jeringas y tuberías. El caudal másico se expresa como: <img alt="Equation 1" src="/files/ftp_upload/18038/18038_Equation_1.svg" style="text-align: center; height: 12px;"> Para un flujo incompresible, donde la densidad permanece constante, la ecuación de continuidad se simplifica a: <img alt="Equation 2" src="/files/ftp_upload/18038/18038_Equation_2.svg" style="text-align: center; height: 12px;"> Esta ecuación ilustra que la velocidad aumenta cuando el área transversal disminuye y viceversa, lo que garantiza la conservación de la masa. Un ejemplo es el flujo a través de una jeringa. Cuando el émbolo comprime el fluido a través de una boquilla, la ecuación de continuidad muestra que si el área de salida es la mitad del área de entrada, la velocidad de salida debe ser el doble de la velocidad de entrada. Otro ejemplo es el flujo en un tanque impulsado por gravedad. La aplicación de la ecuación de Bernoulli y la ecuación de continuidad a puntos a lo largo del flujo ayuda a determinar la velocidad de salida y el caudal volumétrico: <img alt="Equation 3" src="/files/ftp_upload/18038/18038_Equation_3a.svg" style="text-align: center; height: 75px;"> <img alt="Equation 3" src="/files/ftp_upload/18038/18038_Equation_3b.svg" style="text-align: center; height: 20px;"> donde h es la altura del fluido, D es el diámetro del tanque y d es el diámetro de salida. Esta relación muestra que el caudal converge a un valor estable a medida que el diámetro de salida se vuelve pequeño en relación con el diámetro del tanque. Estas derivaciones ejemplifican la utilidad de la ecuación de continuidad para predecir el comportamiento del fluido bajo diversas restricciones, lo que garantiza la conservación de la masa en sistemas dinámicos.

Ecuación de continuidad

La ecuación de continuidad se deriva del principio de conservación de la masa, que establece que la masa del fluido que entra y sale de un sistema permanece constante.
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Education

Educación

JoVE Core

Civil Engineering

Ingeniería Civil

Unit 1

Unidad 1

Fluid Dynamics

Dinámica de fluidos

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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 the area gets larger, the speed must decrease. This keeps mass conserved as the fluid moves.

A syringe shows this relationship clearly. When the plunger pushes fluid through a nozzle, the outlet speed rises if the outlet area is smaller than the inlet area. If the outlet area is half the inlet area, the outlet velocity is twice the inlet velocity.

A gravity-driven tank gives another example. Here, Bernoulli's equation and the continuity equation can be used together at points along the flow. They help find the outlet velocity and the volumetric flow rate. In this setup, h is the fluid height, D is the tank diameter, and d is the outlet diameter. The flow rate approaches a stable value as the outlet diameter becomes small compared with the tank diameter.

Fluid Flow and Area Changes

bernoulli's equation for flow along a streamline

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

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...

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 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 the continuity equation links area, velocity, and mass conservation in steady fluid flow, with examples from syringes and gravity-driven tanks.

Fluid Flow and Area Changes | 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

Fluid Flow and Area Changes

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