Problem 3.119 - Problem*3.119[Difficulty 2 R Given...

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Problem *3.119 [Difficulty: 2] R c ω d Given: Centrifugal manometer consists of pair of parallel disks that rotate to develop a radial pressure difference. There is no flow between the disks. Find: (a) an expression for the pressure difference, p, as a function of ω , R, and ρ . (b) find ω if p = 8 μm H2O and R = 50 mm 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) Standard air between disks (3) Rigid body motion (4) Radial direction is horizontal For rigid body motion: a r V 2 r = r ω ( ) 2 r = r ω 2 = In addition, since r is horizontal:
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