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Problem 3.124

# Problem 3.124 - Problem*3.124[Difficulty 3 Given Gas...

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Problem *3.124 [Difficulty: 3] r 2 V max = ω r 2 Given: Gas centrifuge, with maximum peripheral speed Vmax = 950 ft/s contains uranium hexafluoride gas (M = 352 lb/lbmol) at 620 deg F. Find: (a) Ratio of maximum pressure to pressure at the centrifuge axis (b) Evaluate pressure ratio at 620 deg F. 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 radial component) Assumptions: (1) Incompressible fluid (2) Rigid body motion (3) Ideal gas behavior, constant temperature 2 ω ρ r T R p a r p g r = = For rigid body motion: a r V 2 r = r ω ( ) 2 r = r ω 2 = Thus: Separating variables and integrating: p 1 p 2 p 1 p d ω 2 R g
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