Name: wind turbine torque and angular momentum
Uploaded: 2025-02-13T15:43:22.000Z
Duration: 1 min 9 s
Channel: JoVE

A equação do momento de momento analisa o torque produzido pelas pás rotativas de uma turbina eólica.
A equação do momento de momento é encontrada aplicando a segunda lei de Newton a uma pequena partícula de fluido. Esta lei afirma que a taxa de variação do momento linear é igual à força externa que atua sobre ele.
O momento de força é calculado considerando a posição da partícula de fluido para determinar o torque.
O vetor de posição é combinado com a força externa para encontrar o torque que atua na partícula.
A derivada do tempo é então expandida em duas partes. Uma parte representa a taxa de variação do momento angular devido à velocidade do fluido, enquanto a outra explica como o fluido se move pelo espaço.
A mudança de posição ao longo do tempo é igual à velocidade da partícula, simplificando a expansão.
A equação do momento de momento é obtida integrando esses termos sobre o volume de controle.
Esta equação relaciona o torque no sistema com o momento angular que entra e sai do volume de controle e as forças externas que atuam sobre ele.

equação do momento do momento

A equação do momento de momento é uma ferramenta essencial para analisar o torque produzido pelas pás rotativas de uma turbina eólica. Esta equação é derivada aplicando a segunda lei de Newton a uma partícula fluida, que afirma que a taxa de mudança do momento linear é igual à força externa que atua sobre a partícula.

<img alt="Equation 1" src="/files/ftp_upload/18053/18053_Equation_1.svg" style="text-align: center; height: 48px;">


No caso de sistemas rotativos como turbinas eólicas, o momento desta força, ou torque, é determinado considerando a posição da partícula fluida em relação ao eixo de rotação.

Para calcular o torque, o vetor de posição da partícula fluida é combinado com a força externa que atua sobre ela. Esta combinação produz o torque experimentado pela partícula.

<img alt="Equation 2" src="/files/ftp_upload/18053/18053_Equation_2.svg" style="text-align: center; height: 52px;">


A próxima etapa envolve expandir a derivada temporal do momento de momento. Esta expansão é dividida em duas partes: uma representando a taxa de mudança do momento angular devido à velocidade da partícula, e a outra representando o movimento do fluido através do espaço.

<img alt="Equation 3" src="/files/ftp_upload/18053/18053_Equation_3.svg" style="text-align: center; height: 96px;">


Como a mudança na posição ao longo do tempo é igual à velocidade da partícula, a expansão matemática simplifica, levando a uma compreensão mais clara de como as forças agem dentro do sistema rotativo.

A forma final da equação do momento de momento é obtida pela integração dos termos relevantes sobre o volume de controle, que abrange a região do fluido interagindo com a turbina.

<img alt="Equation 4" src="/files/ftp_upload/18053/18053_Equation_4.svg" style="text-align: center; height: 62px;">

Esta equação fornece uma relação entre o torque exercido no sistema e o momento angular entrando e saindo do volume de controle, bem como as forças externas atuando no sistema. No contexto de turbinas eólicas, isso permite uma análise detalhada de como as pás geram energia rotacional do vento, melhorando a eficiência e o desempenho da turbina.

Equação do momento do momento

A equação do momento de momento analisa o torque produzido pelas pás rotativas de uma turbina eólica.
A equação do momento de momento é encontrada por ...

Education

JoVE Core

Civil Engineering

Engenharia Civil

Unit 1

Unidade 1

Finite Control Volume Analysis

Análise de Volume de Controle Finito

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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.

The next step is to expand the time derivative of the moment of momentum. One part describes the change in angular momentum caused by the particle's own velocity. The other part accounts for the fluid moving through space.

Because the change in position over time equals the particle's velocity, the expression simplifies. The final form is found by integrating over the control volume, which is the region of fluid that interacts with the turbine. This relationship connects torque with the angular momentum entering and leaving the control volume and with the external forces acting on the system.

For wind turbines, this equation helps show how the blades turn wind energy into rotational energy. It also supports more detailed analysis of turbine performance. That makes it useful for improving efficiency and understanding how the blades work.

Wind Turbine Torque and Angular Momentum

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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.

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Wind Turbine Torque and Angular Momentum

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