Problem 3.10 - D 2 D 1 p 1 p 2 1 3 = D 1 p atm sea g h 1 +...

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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 sea g h 1 + ( ) p atm 1 3 = D 1 1 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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