Problem 5.54 - T t Az T t A T t rA z V V r V V a r z r r...

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Problem 5.54 [Difficulty: 4] Given: Z component of an axisymmetric transient flow. Find: Radial component of flow and total acceleration. Solution: Governing Equations:  0 1 1 z V V r r rV r z r (Continuity Equation for an Incompressible Fluid) t V z V V V r V r V V a t V z V V r V V r V r V V a z z z z z r p z r r z r r r p r , 2 , (Particle acceleration) Assumptions: Incompressible fluid No motion along the wall (z = 0) limited to two dimensions (V θ = 0 and all partials with respect to θ are zero). The given or available data is: T t Az V Z 2 sin 0 V   0 Simplify the continuity equation to find V r :     T t A r r rV z V r rV r r z r 2 sin 1 Solve using separation of variables: C T t A r rV r 2 sin 2 2 Use the boundary condition of no flow at the origin to solve for the constant of integration Find the convective terms of acceleration. 0 2 sin 2 sin 2 2 sin 2 ,
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Unformatted text preview: T t Az T t A T t rA z V V r V V a r z r r conv r T t A T t Az T t rA z V V r V V a z z z r conv z 2 sin 2 sin 2 sin 2 , T t rA V r 2 sin 2 T t rA a conv r 2 sin 4 2 2 , T t zA a conv z 2 sin 2 2 , Find the local terms: T t rA T t V a r local r 2 cos 2 2 , T t Az T t V a z local z 2 cos 2 , T t T rA a local r 2 cos , T t T zA a local z 2 cos 2 ,...
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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 5.54 - T t Az T t A T t rA z V V r V V a r z r r...

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