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Problem 3.13 - Problem 3.13[Difficulty 3 Given Model...

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Problem 3.13 [Difficulty: 3] Given: Model behavior of seawater by assuming constant bulk modulus Find: The percent deviations in (a) density and (b) pressure at depth h = 6.5 mi, as compared to values assuming constant density. Plot results over the range of 0 mi - 7 mi. Solution: From Table A.2, App. A: SG o 1.025 = E v 2.42 GPa 3.51 10 5 × psi = = h 6.5 mi = Governing Equations: dp dh ρ g = (Hydrostatic Pressure - h is positive downwards) (Definition of Bulk Modulus) E v dp d ρ ρ = Then dp ρ g dh = E v d ρ ρ = or d ρ ρ 2 g E v dh = Now if we integrate: ρ o ρ ρ 1 ρ 2 d 0 h h g E v d = After integrating: ρ ρ o ρ ρ o g h E v = Therefore: ρ E v ρ o E v ρ o g h = and ρ ρ o 1 1 ρ o g h E v = Δρ ρ o ρ ρ o ρ o = ρ ρ o 1 = 1 1 ρ o g h E v 1 = 1 1 ρ o g h E v 1 ρ o g h E v = ρ o g h E v 1 ρ o g h E v = Δρ ρ o ρ o g h E v 1 ρ o g
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