Name: buckingham pi terms for wing lift
Uploaded: 2025-02-13T15:43:30.000Z
Duration: 1 min 15 s
Channel: JoVE

Para determinar os termos de Pi usando o teorema de Buckingham Pi, considere o exemplo de análise da força de sustentação em uma asa de avião.
As variáveis relevantes aqui incluem a força de sustentação gerada pela asa, densidade do ar, área da asa, velocidade da aeronave e viscosidade do ar.
Cada variável é expressa em dimensões fundamentais, como massa, comprimento e tempo, para fornecer uma base consistente para a construção de termos adimensionais.
O número de termos Pi é determinado subtraindo as dimensões fundamentais do total de variáveis.
 Nesse caso, cinco variáveis e três dimensões produzem dois termos Pi. Três variáveis, densidade do ar, velocidade e área da asa, são então escolhidas como variáveis repetidas para cobrir todas as dimensões, garantindo que sejam independentes.
As variáveis restantes - força de sustentação e viscosidade - são combinadas com as variáveis repetidas para formar termos Pi adimensionais.
Cada termo Pi é verificado para garantir que seja adimensional, confirmando que todas as unidades são canceladas. Os termos finais do Pi simplificam as variáveis originais em expressões que capturam as características essenciais do sistema de elevação.

determinação de termos π

Determination of Pi Terms

O teorema π de Buckingham é um método valioso em análise dimensional, reduzindo relacionamentos complexos entre variáveis ​​em termos adimensionais. Variáveis ​​relevantes na análise da força de sustentação em uma asa de avião incluem força de sustentação, densidade do ar, área da asa, velocidade da aeronave e viscosidade do ar. Expressar cada variável em termos de dimensões fundamentais — massa, comprimento e tempo — fornece uma base consistente para construir esses termos adimensionais.

O teorema indica que o número de termos π é igual ao total de variáveis ​​menos o número de dimensões fundamentais. Neste exemplo, cinco variáveis ​​e três dimensões resultam em dois termos Pi. Densidade do ar, velocidade e a área da asa são selecionadas como variáveis ​​repetidas, ao cobrirem todas as dimensões de forma independentes. Essas variáveis ​​repetidas combinam-se com força de sustentação e viscosidade para formar termos π adimensionais.

<img alt="Equation 1" src="/files/ftp_upload/18069/18069_Equation_1.svg" style="text-align: center; height: 100px;">

O primeiro termo π expressa a eficiência da geração de sustentação, representando como a sustentação depende da densidade, velocidade e área. O segundo termo π é responsável pelo impacto relativo da viscosidade, revelando como as forças viscosas interagem com a asa em relação à inércia.

Cada termo Pi é verificado como adimensional, permitindo que o comportamento aerodinâmico complexo seja representado em expressões simplificadas. Essa abordagem permite a previsão e a otimização da sustentação sob várias condições, capturando a dinâmica essencial sem precisar examinar cada fator individualmente.

Determinação de Termos π

Para determinar os termos de Pi usando o teorema de Buckingham Pi, considere o exemplo de análise da força de sustentação em uma asa de avião.
As variáveis relevantes aqui incluem ...

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buckingham pi terms for wing lift

Buckingham Pi terms help simplify the study of lift force on an airplane wing. Dimensional analysis is used to turn several related variables into dimensionless terms, which makes the problem easier to work with.

The wing-lift example uses five variables: lift force, air density, wing area, aircraft velocity, and air viscosity. Each variable is written in fundamental dimensions of mass, length, and time. The Buckingham Pi theorem then shows that the number of Pi terms equals the total number of variables minus the number of fundamental dimensions, so this case gives two Pi terms.

Air density, velocity, and wing area are chosen as repeating variables. They are selected because they independently cover all the needed dimensions. These repeating variables are then combined with lift force and viscosity to build the dimensionless Pi terms.

The first Pi term shows how lift depends on density, velocity, and area. It represents the efficiency of lift generation. The second Pi term shows the effect of viscosity. It compares viscous forces with inertia and helps describe how the wing interacts with the air.

Each Pi term is checked to make sure it has no units. That step confirms that the terms are truly dimensionless. With this method, complex aerodynamic behavior can be written in a simpler form, which helps predict and optimize lift under different conditions.

Buckingham Pi Terms for Wing Lift

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Learn how Buckingham Pi terms simplify airplane wing lift by using density, velocity, area, lift force, and viscosity to build dimensionless terms.

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Buckingham Pi Terms for Wing Lift

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