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Problem 5.63 - Problem 5.63[Difficulty 3 Flow between...

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Problem 5.63 [Difficulty: 3] We will apply the continuity equation to the control volume shown: Given: Flow between parallel disks through porous surface Find: a pz V r r V z V z z V z v 0 r 2 h 0 v 0 1 z h v 0 h Solution: a pz v 0 2 h z h 1 CS CV A d V V d t 0 Governing Equations: (Continuity) t V V V Dt V D a p (Particle Accleration) Assumptions: (1) Steady flow (2) Incompressible flow (3) Uniform flow at every section (4) Velocity in θ -direction is zero Based on the above assumptions the continuity equation reduces to: 0 ρ v 0 π r 2 ρ V r 2 π r h Solving for Vr: V r v 0 r 2 h We apply the differential form of continuity to find V z 1 r r r V r z V z 0 1 r r r V r v 0 h z V z Therefore: V z z v 0 h d f r ( ) v 0 z h f r ( ) Now at z = 0: V z v 0 Therefore we can solve for f(r): v 0 v 0 0 h
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