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Enunciado

FenTrans, MecFlu, TransCal e TransMassa - Frank White - Mecânica dos Fluidos- Ed: 8º - Capítulo 1.Problemas - Ex. 81

Use Eq. (1.39) to fi nd and sketch the streamlines of the following flow fi eld:

u 5 Kx; v 5 2Ky; w 5 0, where K is a constant

Passo 1

Saaaalve, tranquilo? Vamos lá resolver mais uma questão juntos?! 😊

Escrevendo a equação diferencial para a linha de fluxo

d x u = d y v = d z w

Aqui, u é a velocidade na direção x , v é a velocidade na direção y e w é a velocidade na direção z

Passo 2

Substituindo k x para u , - k y para v e 0 para w temos

d x k x = - d y k y = 0

Integrando essa equação de ambos os lados

ln ⁡ x + ln ⁡ y = C

→ ln ⁡ x y = C

→ x y = e C

→ x y = c o n s t

Passo 3

Desenhando o modelo de gráfico para x y = c o n s t

Resposta

Resposta nos passos.

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