Problem 3.89 - ρ w V w ⋅ ρ n V n ⋅ = When the...

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Problem *3.89 [Difficulty: 2] Given: Hydrometer as shown, submerged in nitric acid. When submerged in water, h = 0 and the immersed volume is 15 cubic cm. SG 1.5 = d6 m m = Find: The distance h when immersed in nitric acid. 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) Assumptions: (1) Static fluid (2) Incompressible fluid Taking a free body diagram of the hydrometer: Σ F z 0 = M g F buoy + 0 = Solving for the mass of the hydrometer: M F buoy g = ρ V d = When immersed in water: M ρ w V w = When immersed in nitric acid: M ρ n V n =
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Unformatted text preview: ρ w V w ⋅ ρ n V n ⋅ = When the hydrometer is in the nitric acid: V n V w π 4 d 2 ⋅ h ⋅ − = ρ n SG ρ w ⋅ = Therefore: ρ w V w ⋅ SG ρ w ⋅ V w π 4 d 2 ⋅ h ⋅ − ⎛ ⎝ ⎞ ⎠ ⋅ = Solving for the height h: V w SG V w π 4 d 2 ⋅ h ⋅ − ⎛ ⎝ ⎞ ⎠ ⋅ = V w 1 SG − ( ) ⋅ SG − π 4 ⋅ d 2 ⋅ h ⋅ = h V w SG 1 − SG ⎛ ⎝ ⎞ ⎠ ⋅ 4 π d 2 ⋅ ⋅ = h 15 cm 3 ⋅ 1.5 1 − 1.5 ⎛ ⎝ ⎞ ⎠ × 4 π 6 mm ⋅ ( ) 2 × × 10 mm ⋅ cm ⎛ ⎝ ⎞ ⎠ 3 × = h 177 mm ⋅ =...
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