Problem 3.17 - Problem 3.17 Given[Difficulty 4 Container of...

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Problem 3.17 [Difficulty: 4] Given: Container of mercury with vertical tubes of known diameter, brass cylinder of known dimensions introduced into larger tube, where it floats. d 1 39.5 mm = d 2 12.7 mm = D 37.5 mm = H 76.2 mm = SG Hg 13.55 = SG b 8.55 = Find: (a) Pressureon the bottom of the cylinder (b) New equlibrium level, h, of the mercury Solution: We will analyze a free body diagram of the cylinder, and apply the hydrostatics equation. Governing equations: Σ F z 0 = (Vertical Equilibrium) dp dz ρ g = (Hydrostatic Pressure - z is positive upwards) ρ SG ρ water = (Definition of Specific Gravity) pA mg z Assumptions: (1) Static liquid (2) Incompressible liquid If we take a free body diagram of the cylinder: Σ F z p π 4 D 2 ρ b g π 4 D 2 H = 0 = thus: p ρ b g H = SG b ρ water g H = p 8.55 1000 × kg m 3 9.81 × m s 2 76.2 × mm m 10 3 mm × = p 6.39 kPa = (gage) This pressure must be generated by a column of mercury h+x in height.
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