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Problem 3.120

# Problem 3.120 - Problem*3.120[Difficulty 2 = 1000 s-1 r1 r1...

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Problem *3.120 [Difficulty: 2] ω = 1000 s -1 r 2 r 1 = 50 mm r 1 r 2 = 130 mm ρ Given: Test tube with water Find: (a) Radial acceleration (b) Radial pressure gradient (c) Rotational speed needed to generate 250 MPa pressure at the bottom of the tube Solution: We will apply the hydrostatics equations to this system. a g p G G ρ ρ = + Governing Equations: (Hydrostatic equation) r r a g r p ρ ρ = + (Hydrostatic equation in radial direction) Assumptions: (1) Incompressible fluid (2) Rigid body motion (3) Radial direction is horizontal For rigid body motion: a r V 2 r = r ω ( ) 2 r = r ω 2 = a r r ω 2 = 2 ω ρ r r p = In addition, since r is horizontal: g r 0 = Thus, the hydrostatic equation becomes:
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