Enunciado

Pressure in a water container can be measured by an open vertical tube—see Fig. P2.11 for a sketch. If the expected water

rise is about 20 cm, what tube diameter is needed to ensure that

the error due to capillarity will be less than 3 percent?

Passo 1

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

Considerando a equação para o aumento da capilaridade

h = 4 σ cos ⁡ θ ρ g d

Resolvendo para d

d = 4 σ cos ⁡ θ ρ g h

Aqui, d é o diâmetro do tubo, σ é a tensão de superfície, ρ é a densidade da água e h é o nível da água

Passo 2

Considerando um erro de 3 % devido à capilaridade

É esperado um aumento de 20   c m da água

Calculando o aumento atual da água incluindo o aumento da capilaridade

h a = 20 + 20 ⋅ 3 100 = 20,6   c m

→ h a = 20,6 ⋅ 10 2   m

Calculando o peso extra devido a capilaridade

h = h a - 20,6 ⋅ 10 - 2   m = 20,6 ⋅ 10 - 2 - 20 ⋅ 10 - 2

→ h = 0,6 ⋅ 10 - 2   m

Passo 3

Substituindo na equação para o Passo 1

d = 4 0,07199 cos ⁡ 0 ° C 1000 ⋅ 9,81 ⋅ 0,6 ⋅ 10 - 2

∴ d = 4,8   m m

Resposta

d = 4,8   m m

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