Problem 3.10 - D 2 D 1 p 1 p 2 ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 1 3...

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Problem 3.10 [Difficulty: 2] Given: Data on air bubble Find: Bubble diameter as it reaches surface Solution: Basic equation dp dy ρ sea g = and the ideal gas equation p ρ R T = M V R T = We assume the temperature is constant, and the density of sea water is constant For constant sea water density pp atm SG sea ρ g h + = where p is the pressure at any depth h Then the pressure at the initial depth is p 1 p atm SG sea ρ g h 1 + = The pressure as it reaches the surface is p 2 p atm = For the bubble p MR T V = but M and T are constant MR T const = pV = Hence p 1 V 1 p 2 V 2 = or V 2 V 1 P 1 p 2 = or D 2 3 D 1 3 p 1 p 2 = Then the size of the bubble at the surface is D
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Unformatted text preview: D 2 D 1 p 1 p 2 ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 1 3 ⋅ = D 1 p atm ρ sea g ⋅ h 1 ⋅ + ( ) p atm ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ 1 3 ⋅ = D 1 1 ρ sea g ⋅ h 1 ⋅ p atm + ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 1 3 ⋅ = From Table A.2 SG sea 1.025 = (This is at 68 o F) D 2 0.3 in ⋅ 1 1.025 1.94 × slug ft 3 ⋅ 32.2 × ft s 2 × 100 × ft ⋅ in 2 14.7 lbf ⋅ × 1 ft ⋅ 12 in ⋅ ⎛ ⎝ ⎞ ⎠ 2 × lbf s 2 ⋅ slugft ⋅ × + ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ 1 3 × = D 2 0.477 in ⋅ =...
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