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# Class29_HW2 - 6 IOIS A viscous fluid is contained between...

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Unformatted text preview: 6. IOIS A viscous fluid is contained between two inﬁnitely long vertical concentric cylinders. The outer cylinder has a radius 1:, and rotates with an angular velocity to. The inner cylinder is ﬁxed and has a radius 5. Make use of the Navier—Stokes equations to obtain an exact solution for the ve- locity distribution in the gap. Assume that the flow in the gap is axisyrnmetric (neither velocity nor preSSure are functions of angular position 6' within gap) and that there are no velocity com- ponents other than the tangential component. The only body fame is the weight. The Velociiy distributes?» lid The annular- .rpare Ls given by 1716: agitation C +- r: 1);: ‘J'E' 1. Ti: H) (see was“ +n Poem ass to, dfrlée‘étoir.) WIW The. boundary condiivéas #4333, urea} and f": JG J 15 =' ’3 (13 (See injure Er haieﬂenh if kilows ﬁwm 53.13!) “the-E: C! V; 6‘; 0: F_. + —- 2.. 1‘1 66:.) = 6,5: + i a is Time re e5 , .. Em C. II- J i- PE}. 1.52. ﬁnal 1 c -.~ "41' m a. l— ’1',“ 7-3:. .50 734113 FLU 3- % : r“:- _ r; m a. it“ .i ._ 1": i3”- l-‘(f E») or 1 Pa.) Y; ...
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