Enunciado

Clift et al. [46] forneceram a fórmula F ≈ 6 π 5 ( 4 + a b ) μ U b para o arrasto de um esferoide prolato em um escoamento muito lento (creeping flow), como mostra a Figura P7.52. A semiespessura b é 4 mm. Se o fluido é óleo SAE 50W a 20°C, (a) verifique se R e b < 1 e (b) estime o comprimento do esferoide para um arrasto de 0,02 N.

Passo 1

Bora lá, resolver mais umazinha!

Para o óleo SAE 50W temos ρ = 902   k g / m 3 e μ = 0,86   k g / ( m ⋅ s ) , assim, Reynolds

R e b = ρ U b μ = 902 k g m 3 0,2 m s 0,004   m 0,86 k g m ⋅ s = 0,84 < 1

Logo, cumprimos (a)!

Passo 2

Bora utilizar a expressão dada para tentar estimar o tamanho desses esferoide, assim:

F = 0,02   N = 6 π 5 4 + a b μ U b = 6 π 5 ( 4 + a 0,004 m ) ( 0,86 k g m ⋅ s ) ( 0,20 m s ) ( 0,004   m )

a = 0,0148   m

Assim, o comprimento do esferoide é dada por:

2 a = 0,030   m

Resposta

  1. R e b = 0,84 < 1
  2. 0,030 m
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