Name: continuity and velocity in pipe flow
Uploaded: 2025-02-13T15:43:21.000Z
Duration: 1 min 7 s
Channel: JoVE

El principio de conservación de la masa establece que, dentro de un volumen de control fijo, cualquier cambio en la masa a lo largo del tiempo debe equilibrarse mediante el flujo de masa a través de las superficies de control.
Considere una tubería de alcantarillado como ejemplo de un volumen de control fijo y no deformante, donde la masa que entra es igual a la masa que sale.
En este caso, el volumen de control representa la sección de la tubería de alcantarillado entre su entrada y salida, con superficies de control en cada extremo.
Dado que el flujo es constante e incompresible, no hay cambios en la masa con el tiempo, lo que significa que el caudal másico del fluido es constante a través de las superficies de control.
A medida que el agua fluye a través de la tubería, la velocidad puede cambiar dependiendo del área de la sección transversal de la tubería en la entrada y salida.
Cuando el área de la sección transversal en la salida disminuye, la velocidad del agua aumenta para garantizar el mismo caudal másico
Los ingenieros utilizan este principio para analizar los caudales y las velocidades, lo que garantiza un diseño adecuado del sistema sin violar la conservación de la masa.

conservación de la masa en un volumen de control fijo y no deformable

El principio de conservación de la masa es fundamental en la dinámica de fluidos y resulta crucial para analizar el flujo dentro de volúmenes de control fijos, como tuberías o conductos. Este principio establece que la masa total dentro de un volumen de control permanece constante a menos que se altere por la entrada o salida de masa a través de las superficies de control. Esto da como resultado una relación vital para el flujo constante e incompresible, en el que la masa que ingresa a un sistema es igual a la masa que lo abandona. En el caso de una tubería de alcantarillado, que se puede modelar como un volumen de control fijo y no deformable, la conservación de la masa dicta que el caudal másico de la entrada debe ser igual al caudal másico de la salida. Las superficies de control en este escenario se encuentran en la entrada y la salida de la tubería, y encierran la región de flujo. Dado que el flujo es incompresible, la densidad del fluido permanece constante. Esto significa que la relación entre la velocidad y el área de la sección transversal se vuelve crítica. Caudal másico y área de la sección transversal 

 El caudal másico (ṁ) se expresa en términos de densidad del fluido (P) y caudal (Q). Aquí, el caudal se determina multiplicando la velocidad (V) por el área de la sección transversal (A).


 <img alt="Equation 1" src="/files/ftp_upload/18049/18049_Equation_1.svg" style="text-align: center; height: 12px;">

 En el caso de un flujo constante, en el que la densidad permanece constante, esta ecuación se simplifica para indicar que cualquier cambio en la velocidad debe corresponder a un cambio en el área de la sección transversal de la tubería. Cuando el área de la sección transversal de la tubería disminuye, como podría suceder en la salida de una tubería de alcantarillado, la velocidad del fluido debe aumentar para conservar el caudal másico. La ecuación de continuidad describe este fenómeno:

 <img alt="Equation 2" src="/files/ftp_upload/18049/18049_Equation_2.svg" style="text-align: center; height: 12px;">

 Donde V1 y A1 denotan la velocidad y el área de la sección transversal en la entrada y V2 y A2 en la salida. Esta relación predice el comportamiento del flujo y diseña sistemas que mantienen tasas de flujo apropiadas mientras se adhieren al principio de conservación de la masa.

Conservación de la masa en un volumen de control fijo y no deformable

El principio de conservación de la masa establece que, dentro de un volumen de control fijo, cualquier cambio en la masa a lo largo del tiempo debe equilibrarse mediante el flujo de masa a través de ...

conservation-of-mass-in-fixed-nondeforming-control-volume

Education

Educación

JoVE Core

Civil Engineering

Ingeniería Civil

Unit 1

Unidad 1

Finite Control Volume Analysis

Análisis de Volumen de Control Finito

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Conservation of Mass in Fixed, Nondeforming Control Volume

continuity and velocity in pipe flow

Conservation of mass explains how fluid moves through a fixed control volume such as a pipe or duct. In a fixed, nondeforming control volume, the total mass stays constant unless mass enters or leaves through the control surfaces. For steady, incompressible flow, the mass entering the system equals the mass leaving it.

A sewer pipe is a useful example of this idea. It can be treated as a fixed control volume with inlet and outlet control surfaces around the flow region. Because the fluid is incompressible, its density stays constant as it moves through the pipe.

This makes cross-sectional area an important part of the analysis. Mass flow rate, written as m-dot, depends on fluid density and flow rate. The flow rate is found by multiplying velocity by cross-sectional area, so a change in area must be matched by a change in velocity when density stays the same.

The continuity equation describes this relationship. At the inlet and outlet, V1 and A1 at one end must balance V2 and A2 at the other end for steady flow. If the pipe becomes narrower, the fluid speed increases to keep the mass flow rate constant. This relationship helps predict flow behavior and supports the design of systems that maintain the right flow rate while following mass conservation.

Continuity and Velocity in Pipe Flow

conservation of mass in finite cotrol volume

conservation-of-mass-in-finite-cotrol-volume

Continuity Equation for a Fixed Control Volume

The continuity equation describes conservation of mass for a fixed control volume. In fluid mechanics, a system is a collection of the same contents over time, and its mass stays constant. That idea is the starting point for deriving the equation. To analyze flow, a fixed, non-deforming control volume is chosen so it matches the system at one instant. The Reynolds transport theorem then links the system to the control volume. It shows that the rate of change of system mass has two parts: mass...

conservation of mass in fixed, nondeforming control volume

Conservation of mass explains how fluid moves through a fixed control volume such as a pipe or duct. In a fixed, nondeforming control volume, the total mass stays constant unless mass enters or leaves through the control surfaces. For steady, incompressible flow, the mass entering the system equals the mass leaving it. A sewer pipe is a useful example of this idea. It can be treated as a fixed control volume with inlet and outlet control surfaces around the flow region. Because the fluid is...

conservation of mass in moving, nondeforming control volume

conservation-of-mass-in-moving-nondeforming-control-volume

Stormwater Detention Basin Mass Balance

Stormwater detention basins use mass balance to manage runoff during heavy rainfall. These basins are especially important in urban areas, where impervious surfaces can increase flooding risk. Engineers use the conservation of mass to track how water enters, is stored in, and leaves the basin. In a detention basin, the control volume is the water inside the basin. Its boundaries are the basin walls, the inflow pipes, and the outflow structures. During a rain event, water comes in through the...

linear momentum in control volume

Momentum Balance for Fluid Control Volumes

Linear momentum balance for a fluid control volume links Newton’s second law to moving fluid. The law says that the rate of change of linear momentum equals the sum of the external forces acting on the system. In a fluid system, this idea helps explain how motion and force are related. A control volume can match the fluid system at a specific moment. When that happens, the forces on the control volume and the system are the same. Reynolds transport theorem explains this connection by splitting...

application of the linear momentum equation

application-of-the-linear-momentum-equation

Forces in a 180° Pipe Bend

Forces in a 180-degree pipe bend can be found by applying the linear momentum equation to flowing water. The pipe has a constant cross-sectional area of 0.01 square meters, and the water moves at 15 meters per second. The pressure at the inlet is 0.2 megapascals, and the pressure at the outlet is 0.16 megapascals. The goal is to find the force components in the x and y directions that hold the bend in place. In this case, the flow is only in the y direction at both the entrance and the exit.

moment-of-momentum equation

Wind Turbine Torque and Angular Momentum

The moment-of-momentum equation helps explain how wind turbine blades create torque. Torque is the turning effect of a force around an axis. In rotating systems, this equation links the motion of the wind with the force acting on it. The equation begins with Newton's second law for a fluid particle. That law says the rate of change of linear momentum equals the external force on the particle. To find torque, the position of the particle relative to the rotation axis is combined with that force.

conservation of energy in control volume

Turbine Work from Energy Changes

A turbine can turn fluid energy into shaft work when flow passes through a control volume. The fluid enters the turbine at one point and leaves at another. Under steady-flow conditions, there is no energy buildup inside the control volume, so the stored energy does not change with time. This steady-flow setup makes the energy equation simpler. The turbine is treated as doing mechanical work, and heat transfer is taken as negligible, so Q̇ is approximately zero. The flow at the inlet and outlet...

application of the energy equation

Centrifugal Pump Flow Rate Calculation

Centrifugal pump flow rate can be calculated with the energy equation. In this problem, water moves between two reservoirs at different elevations, and the pump provides the energy needed for the transfer. The pump input is 7500 joules per second, the elevation difference is 10 meters, and the head loss from friction and other resistances is 5 meters. Both reservoirs are open to the atmosphere, so the pressure at the inlet and outlet is the same. That means the pressure terms in the energy...

design example: forces in sluice gate

Sluice Gate Water Pressure and Reaction Force

Sluice gates control water flow in channels, reservoirs, and irrigation systems. They work as vertical barriers with an opening that can be raised or lowered. Changing the opening height changes the water velocity and pressure below the gate. The forces on a sluice gate depend on the water depths upstream and downstream, written as z1 and z2. When the gate is closed, the upstream water depth is greater. That creates a strong pressure difference across the gate and a net force toward the...

key terms and concepts

Learn how mass conservation links pipe area and fluid speed. See why steady, incompressible flow follows the continuity equation in a fixed control volume.

Continuity and Velocity in Pipe Flow | 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

Continuity and Velocity in Pipe Flow

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