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Problem 3.128

# Problem 3.128 - Problem*3.128[Difficulty 4 A steel liner is...

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Problem *3.128 [Difficulty: 4] x r o θ r i y Given: A steel liner is to be formed in a spinning horizontal mold. To insure uniform thickness the minimum angular velocity should be at least 300 rpm. For steel, SG = 7.8 Find: (a) The resulting radial acceleration on the inside surface of the liner (b) the maximum and minimum pressures on the surface of the mold (gravity is downward in this diagram) Solution: We will apply the hydrostatics equations to this system. a g p G G ρ = + Governing Equations: (Hydrostatic equation) r r a g r p = + (Hydrostatic equation radial component) θ a g p r = + 1 (Hydrostatic equation transeverse component) z z a g z p = + (Hydrostatic equation z component) Assumptions: (1) Incompressible fluid (2) Rigid body motion a r V 2 r = r ω () 2 r = r ω 2 = a θ 0 = a z 0 = g r g cos θ = g θ g sin θ = g z 0 = Hence: a r 4in 300 rev min × 2 π rad rev × min 60 s × 2 × ft 12 in × = a r 329 ft s 2 = a r 10.23 g = ω cos 2 g r a g r p

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Problem 3.128 - Problem*3.128[Difficulty 4 A steel liner is...

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