Problem 5.97 - 2 1 2 1 2 2 2 2 C h C E h u C h C E h u...

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Problem 5.97 [Difficulty: 3] Given: N-S equations Find: Fluid velocity Solution: Governing Equations: 0 u (Continuity equation) u u u 2 p - ρ (Momentum equation) Assumptions: (1) Two-dimensional fully developed flow (2) Zero pressure gradient (1) Write the continuity and momentum equations in Cartesian form: (3) ) ( ) ( (2) ) ( ) ( (1) 0 2 2 2 2 2 2 2 2 y v x v y p y v v x v u y u x u x p y u v x u u y v x u
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Simplify the above equations: ) ( 0 0 y u u x u v Using the assumption of zero pressure gradient, equation (3) vanishes, and equation (2) can be simplified as 2 2 0 dy u d (4) General solution for equation (4) is given as 2 1 C y C u (5) Apply the boundary condition into equation (5), we get
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Unformatted text preview: 2 1 2 1 2 ) 2 ( 2 ) 2 ( C h C E h u C h C E h u Therefore, C 1 =0 and E C 2 The fluid velocity is given as E y u ) ( (6) (2) Pressure-driven flow has a parabolic flow velocity profile; while EOF has a plug velocity profile and it is independent of the channel size. (3) Substituting =7.08 10-10 CV-1 m-1 , = 0.1V, Pa.s, and E=1000 V/m into equation (6), one obtains s m m s Pa N m s Pa V C V m V y u / 10 70.8 10 70.8 10 70.8 V/m 1000 s Pa 10 1 . C 10 7.08 ) ( 6-6-2 6-3 1 1-10...
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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Problem 5.97 - 2 1 2 1 2 2 2 2 C h C E h u C h C E h u...

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