Problem 3.92 - ice V tot g sw g V d = V d V tot ice sw = V...

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Problem *3.92 [Difficulty: 2] Given: Iceberg floating in seawater Find: Quantify the statement, "Only the tip of an iceberg shows (in seawater)." Solution: We will apply the hydrostatics equations to this system. Governing Equations: F buoy ρ g V d = (Buoyant force is equal to weight of displaced fluid) F buoy Mg Assumptions: (1) Static fluid (2) Incompressible fluid Taking a free body diagram of the iceberg: Σ F z 0 = M g F buoy + 0 = Mg F buoy = ρ sw g V d = But the mass of the iceberg is also: M ρ ice V tot = Combining these expressions:
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Unformatted text preview: ice V tot g sw g V d = V d V tot ice sw = V tot SG ice SG sw = The volume of the iceberg above the water is: V show V tot V d = V tot 1 SG ice SG sw = Therefore we may define a volume fraction: VF V show V tot = 1 SG ice SG sw = Substituting in data from Tables A.1 and A.2 we get: VF 1 0.917 1.025 = VF 0.1054 = Only 10% of the iceberg is above wate...
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