Problem 2.78 - = 0 deg = and for water 1000 kg m 3 = From...

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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: = 0 deg = and for water 1000 kg m 3 = From Table A.1, for steel SG 7.83 = Hence 8 cos ( ) SG g 8 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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