ME 367 HW 4 Solution - Problem 3.71[3 Part 1/2 Problem...

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Problem 3.71 [3] Part 1/2
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Problem 3.71 [3] Part 2/2
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Problem 3.73 [2]
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Problem *3.90 [2]
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Problem *3.90 [2]
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Problem *3.104 [4] F B W F L F U Given: Data on sphere and tank bottom Find: Expression for SG of sphere at which it will float to surface; minimum SG to remain in position Solution: Basic equations F B ρ g V = and Σ F y 0 = Σ F y 0 = F L F U F B + W = where F L p atm π a 2 = F U p atm ρ g H 2 R ( ) + π a 2 = F B ρ g V net = V net 4 3 π R 3 π a 2 2 R = W SG ρ g V = with V 4 3 π R 3 = Note that we treat the sphere as a sphere with SG, and for fluid effects a sphere minus a cylinder (buoyancy) and cylinder with hydrostatic pressures Hence p atm π a 2 p atm ρ g H 2 R ( ) + π a 2 ρ g 4 3 π R 3 2 π R a 2 + SG ρ g 4 3 π R 3 0 = Solving for SG SG 3 4 π ρ g R 3 π ρ g H 2 R
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