Name: turbine work from energy changes
Uploaded: 2025-02-13T15:43:22.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

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South Carolina College and Career Ready Science Standards

High School

Chemistry

Energy

C-PS3-4

Conservation of Energy in Control Volume

La primera ley de la termodinámica establece que la tasa de cambio de la energía total almacenada en un sistema es igual a la tasa neta de calor y trabajo transferidos a un sistema.
Para un volumen de control que coincide con el sistema en un momento dado, el calor neto y el trabajo que entran en el sistema son iguales al calor neto y al trabajo que entra en el volumen de control.
Para este sistema y volumen de control coincidente, se aplica el Teorema de Transporte de Reynolds.
La tasa total de cambio de energía dentro del volumen de control está determinada tanto por la tasa de cambio de tiempo en la energía almacenada como por el flujo neto de energía a través del límite.
La energía que fluye a través del límite incluye las contribuciones del calor y el trabajo, como el trabajo del eje y el trabajo a presión.
El trabajo en el eje es el resultado de la rotación de componentes como las turbinas, mientras que las tensiones de los fluidos producen trabajo a presión.
La ecuación general de energía combina todos los elementos: energía almacenada, calor, trabajo en el eje y trabajo en presión debido a tensiones normales.
Esta ecuación representa la conservación de energía en los sistemas de fluidos, incorporando la transferencia de calor, el trabajo del eje y las fuerzas de presión en la superficie de control.

conservación de la energía en el volumen de control

Considere una turbina que funciona en condiciones de flujo constante. El volumen de control se dibuja alrededor de la turbina, con fluido entrando en un punto y saliendo en otro. La turbina extrae energía del fluido, que realiza trabajo mecánico (trabajo del eje). Para sistemas de flujo constante, la derivada temporal de la energía almacenada se vuelve cero ya que no hay acumulación de energía dentro del volumen de control. Esto simplifica la ecuación de energía a: <img alt="Equation 1" src="/files/ftp_upload/18054/18054_Equation_1.svg" style="text-align: center; height: 27px;"> Dado que nos centramos en el trabajo realizado por el eje de la turbina y asumimos una transferencia de calor insignificante, <img src="data:image/png;base64,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" style="height: 12px;" />. Por lo tanto, la ecuación de energía se simplifica aún más a: <img alt="Equation 2" src="/files/ftp_upload/18054/18054_Equation_2.svg" style="text-align: center; height: 27px;"> El flujo se divide en dos componentes: el fluido que entra en la turbina (entrada) y que sale de la turbina (salida). El caudal másico en ambos puntos es constante, y el flujo de energía en la entrada y la salida está dado por: <img alt="Equation 3" src="/files/ftp_upload/18054/18054_Equation_3.svg" style="text-align: center; height: 27px;"> Donde: 

 - <img src="data:image/png;base64,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" style="height: 12px;" /> es el caudal másico,

- ũ1, V1, y z1 se refieren a la energía interna, la velocidad y la altura en la entrada,
- ũ2, V2, y z2 se refieren a la energía interna, la velocidad y la altura en la salida,

 En una turbina típica, la energía cinética e interna del fluido disminuye a medida que pasa a través de la turbina, lo que da como resultado un trabajo útil en el eje. Suponga que una turbina opera con una velocidad de entrada de V1=50 m/s, una velocidad de salida de V2= 20 m/s, una altura de entrada z1=100 m y una altura de salida z_2 = 90 m. Suponga que el cambio de energía interna es pequeño en comparación con los cambios de energía cinética y potencial, y que el caudal másico es 10 kg/s.

 <img alt="Equation 4" src="/files/ftp_upload/18054/18054_Equation_4.svg" style="text-align: center; height: 27px;"> Como resultado, la turbina produce aproximadamente 11,48 kW de potencia mecánica extrayendo energía del fluido que fluye.

Conservación de la energía en el volumen de control

La primera ley de la termodinámica establece que la tasa de cambio de la energía total almacenada en un sistema es igual a la tasa neta de calor y trabajo transferidos a un ...

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

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 is then described by the mass flow rate and by the fluid’s internal energy, velocity, and height at each location.

For the inlet and outlet, the mass flow rate is constant. The energy flux depends on ṁ, u1, V1, and z1 at the inlet, and on ṁ, u2, V2, and z2 at the outlet. Here, u is internal energy, V is velocity, and z is height.

In a typical turbine, the fluid loses internal energy and kinetic energy as it moves through the device. That energy loss becomes useful shaft work. For example, if V1 = 50 m/s, V2 = 20 m/s, z1 = 100 m, z2 = 90 m, and the mass flow rate is 10 kg/s, with a small internal energy change, the turbine produces about 11.48 kW of mechanical power.

Turbine Work from Energy Changes

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-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...

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

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 a steady-flow turbine uses changes in velocity, height, and internal energy to produce shaft work, with a worked 11.48 kW example.

Turbine Work from Energy 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

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Turbine Work from Energy Changes

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