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

K12 Standards

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

High School

Chemistry

Energy

C-PS3-4

Conservation of Energy in Control Volume

A primeira lei da termodinâmica afirma que a taxa de variação da energia total armazenada em um sistema é igual à taxa líquida de calor e trabalho transferido para um sistema.
Para um volume de controle que coincide com o sistema em um determinado momento, o calor líquido e o trabalho que entram no sistema são iguais ao calor líquido e o trabalho que entra no volume de controle.
Para este sistema e volume de controle coincidente, o Teorema de Transporte de Reynolds é aplicado.
A taxa total de mudança de energia dentro do volume de controle é determinada pela taxa de variação no tempo na energia armazenada e pelo fluxo líquido de energia através do limite.
A energia que flui através do limite inclui contribuições de calor e trabalho, como trabalho de eixo e trabalho de pressão.
O trabalho do eixo resulta de componentes rotativos, como turbinas, enquanto as tensões do fluido produzem trabalho de pressão.
A equação geral de energia combina todos os elementos: energia armazenada, calor, trabalho do eixo e trabalho de pressão devido a tensões normais.
Esta equação representa a conservação de energia em sistemas de fluidos, incorporando transferência de calor, trabalho do eixo e forças de pressão na superfície de controle.

conservação de energia no volume de controle

Considere uma turbina operando sob condições de fluxo constante. O volume de controle é desenhado ao redor da turbina, com fluido entrando em um ponto e saindo em outro. A turbina extrai energia do fluido, que realiza trabalho mecânico (trabalho de eixo).

Para sistemas de fluxo constante, a derivada temporal da energia armazenada se torna zero, pois não há acúmulo de energia dentro do volume de controle. Isso simplifica a equação de energia para:

<img alt="Equation 1" src="/files/ftp_upload/18054/18054_Equation_1.svg" style="text-align: center; height: 27px;">

Como focamos no trabalho feito pelo eixo da turbina e assumimos transferência de calor insignificante, . Portanto, a equação de energia simplifica ainda mais para:

<img alt="Equation 2" src="/files/ftp_upload/18054/18054_Equation_2.svg" style="text-align: center; height: 27px;">


O fluxo é dividido em dois componentes: o fluido entrando na turbina (entrada) e saindo da turbina (saída). A vazão da massa em ambos os pontos é constante, e o fluxo de energia na entrada e na saída é dado por:

<img alt="Equation 3" src="/files/ftp_upload/18054/18054_Equation_3.svg" style="text-align: center; height: 27px;">


Onde:

-ṁ é a vazão da massa,

-ũ1 , V_1 e z_1 referem-se à energia interna, velocidade e altura na entrada,

-ũ2 , V_2 e z_2 referem-se à energia interna, velocidade e altura na saída,

Em uma turbina típica, a vazão interna e a energia cinética diminui à medida que passa pela turbina, o que resulta em trabalho útil no eixo. Suponha que uma turbina opere com uma velocidade de entrada de V_1=50 m/s, uma velocidade de saída de V_2=20 m/s, uma altura de entrada z_1=100 m e uma altura de saída z_2=90 m. Suponha que a mudança de energia interna seja pequena em comparação com as mudanças de energia cinética e potencial, e a taxa de fluxo de massa é 10 kg/s.

<img alt="Equation 4" src="/files/ftp_upload/18054/18054_Equation_4.svg" style="text-align: center; height: 27px;">

Como resultado, a turbina produz aproximadamente 11,48 kW de potência mecânica extraindo energia do fluido que flui.

Conservação de Energia no Volume de Controle

A primeira lei da termodinâmica afirma que a taxa de variação da energia total armazenada em um sistema é igual à taxa líquida de calor e trabalho transferido para um ...

Education

JoVE Core

Civil Engineering

Engenharia Civil

Unit 1

Unidade 1

Finite Control Volume Analysis

Análise de Volume de Controle Finito

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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

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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...

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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.

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Turbine Work from Energy Changes

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