Problem 2.78 - = θ 0 deg ⋅ = and for water ρ 1000 kg m...

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Problem 2.78 [Difficulty: 2] Given: Data on size of various needles Find: Which needles, if any, will float Solution: For a steel needle of length L , diameter D , density ρ s , to float in water with surface tension σ and contact angle θ , the vertical force due to surface tension must equal or exceed the weight 2L σ cos θ () W mg = π D 2 4 ρ s L g = or D 8 σ cos θ () πρ s g From Table A.4 σ 72.8 10 3 × N m
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Unformatted text preview: = θ 0 deg ⋅ = and for water ρ 1000 kg m 3 ⋅ = From Table A.1, for steel SG 7.83 = Hence 8 σ ⋅ cos θ ( ) ⋅ π SG ⋅ ρ ⋅ g ⋅ 8 π 7.83 ⋅ 72.8 × 10 3 − × N m ⋅ m 3 999 kg ⋅ × s 2 9.81 m ⋅ × kg m ⋅ N s 2 ⋅ × = 1.55 10 3 − × m ⋅ = 1.55 mm ⋅ = Hence D < 1.55 mm. Only the 1 mm needles float (needle length is irrelevant)...
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